mm-1015 === Subject: Re: Parameter Estimamtion of a Exponential Dist. > However, I plan to use A=sqrt(Sample Variance). Does any one have > an idea about the robustness of the estimation ? Sample variance is a biased estimator of population variance: = A^2 (n-1) / n. I can prove that A is a biased estimator of A, but havent been able to derive a closed expression for /A in terms of n. Unfortunately, setting A = sqrt(Sample Variance * n / (n-1)) does not remove the bias. === Subject: Taylor Series Can anyone find Taylor series for 1/sqrt(x) centered at 9? Sorry to hear you lost it. Will 1/sqrt(x) = (1/3)*(1 + (x-9)/9)^(-1/2) help? that is not a taylor series... let f(x) = x^k f^(n)(x) = product(k - i, i = 0..n-1)*x^(k-n) but product(k - i, i = 0..n-1) = (-1)^n*Gamma(n-k)/Gamma(-k) if k < n and k a positive integer, else 0 so the nth derivative of f(x) is f^(n)(c) = (-1)^n*Gamma(n-k)/Gamma(-k)*c^n since Ive found the nth coefficient for you, I think you can find the rest. (now, there maybe easier ways using more indirect methods, but this is a direct application of the theorem. (and in its most general form for any power of x) and incase you dont know what gamma is, its basically factorial, except it can handle non integral arguments. Gamma(n) = (n-1)! for integer n, and Gamma(z) = z*Gamma(z-1)) === Subject: Re: Taylor Series > Can anyone find Taylor series for 1/sqrt(x) centered at 9? >> Sorry to hear you lost it. >> Will 1/sqrt(x) = (1/3)*(1 + (x-9)/9)^(-1/2) help? > that is not a taylor series... > let f(x) = x^k > f^(n)(x) = product(k - i, i = 0..n-1)*x^(k-n) > but > product(k - i, i = 0..n-1) = (-1)^n*Gamma(n-k)/Gamma(-k) if k < n and k a > positive integer, else 0 > so the nth derivative of f(x) is > f^(n)(c) = (-1)^n*Gamma(n-k)/Gamma(-k)*c^n oops that should be k-n on the c. > since Ive found the nth coefficient for you, I think you can find the > rest. > (now, there maybe easier ways using more indirect methods, but this is a > direct application of the theorem. (and in its most general form for any > power of x) and incase you dont know what gamma is, its basically > factorial, except it can handle non integral arguments. Gamma(n) = (n-1)! > for integer n, and Gamma(z) = z*Gamma(z-1)) === Subject: Re: Taylor Series <10s8c7fcg2pq370@corp.supernews.com> Can anyone find Taylor series for 1/sqrt(x) centered at 9? > Sorry to hear you lost it. > Will 1/sqrt(x) = (1/3)*(1 + (x-9)/9)^(-1/2) help? > that is not a taylor series... I did not claim it is. But it can help find one, and I thought, perhaps naively, that a hint is better than serving the final result on a silver plate. > let f(x) = x^k > f^(n)(x) = product(k - i, i = 0..n-1)*x^(k-n) > but > product(k - i, i = 0..n-1) = (-1)^n*Gamma(n-k)/Gamma(-k) if k < n and k a > positive integer, else 0 > so the nth derivative of f(x) is > f^(n)(c) = (-1)^n*Gamma(n-k)/Gamma(-k)*c^n > since Ive found the nth coefficient for you, I think you can find the rest. > (now, there maybe easier ways using more indirect methods, but this is a > direct application of the theorem. My question: is direct application of the theorem helpful in expanding, say, exp(-x^2/2) into Taylor Series around 0? The derivatives involve polynomials of ever increasing degrees (Hermite polynomials), and this complication is fully avoidable by an indirect method, that is, changing the variable and using Uniqueness Theorem. A simpler problem: the (formulas for) high derivatives of 1/(1+x^2) are also increasingly messy, and the indirect method goes smoothly, as most readers have experienced. Binomial Formula for (1+z)^k was on my mind; it is on the list of standard expansions, and all you need is to apply it to z = (x-9)/9 and divide the expansion by 3. Too sophisticated? > (and in its most general form for any > power of x) and incase you dont know what gamma is, its basically > factorial, except it can handle non integral arguments. Gamma(n) = (n-1)! > for integer n, and Gamma(z) = z*Gamma(z-1)) Using a cannon to kill a mosquito? === Subject: Re: Taylor Series > Can anyone find Taylor series for 1/sqrt(x) centered at 9? >> Sorry to hear you lost it. >> Will 1/sqrt(x) = (1/3)*(1 + (x-9)/9)^(-1/2) help? >> that is not a taylor series... > I did not claim it is. But it can help find one, and I thought, perhaps > naively, that a hint is better than serving the final result on a silver > plate. >> let f(x) = x^k >> f^(n)(x) = product(k - i, i = 0..n-1)*x^(k-n) >> but >> product(k - i, i = 0..n-1) = (-1)^n*Gamma(n-k)/Gamma(-k) if k < n and k a >> positive integer, else 0 >> so the nth derivative of f(x) is >> f^(n)(c) = (-1)^n*Gamma(n-k)/Gamma(-k)*c^n >> since Ive found the nth coefficient for you, I think you can find the >> rest. >> (now, there maybe easier ways using more indirect methods, but this is a >> direct application of the theorem. > My question: is direct application of the theorem helpful in expanding, > say, exp(-x^2/2) into Taylor Series around 0? The derivatives involve > polynomials of ever increasing degrees (Hermite polynomials), and this > complication is fully avoidable by an indirect method, that is, changing > the variable and using Uniqueness Theorem. > A simpler problem: the (formulas for) high derivatives of 1/(1+x^2) are > also increasingly messy, and the indirect method goes smoothly, as most > readers have experienced. > Binomial Formula for (1+z)^k was on my mind; it is on the list of standard > expansions, and all you need is to apply it to z = (x-9)/9 and divide the > expansion by 3. Too sophisticated? >> (and in its most general form for any >> power of x) and incase you dont know what gamma is, its basically >> factorial, except it can handle non integral arguments. Gamma(n) = >> (n-1)! >> for integer n, and Gamma(z) = z*Gamma(z-1)) > Using a cannon to kill a mosquito? Are you scared of the Gamma function? My method is much more intuitive than yours. While one without any ingenuity might be lost, if one can do x^k for integer k, there is no difficulty to extend this to non-integral k... but the same method applies... it is direct and intuitive and simple... what more could you ask for? Me thinks you are afraid of the gamma... just remember, it doesnt bite. === Subject: Re: Taylor Series Jon Slaughter a .8ecrit : >Can anyone find Taylor series for 1/sqrt(x) centered at 9? >>Sorry to hear you lost it. >>Will 1/sqrt(x) = (1/3)*(1 + (x-9)/9)^(-1/2) help? > that is not a taylor series... No, but it helps to find it > let f(x) = x^k > f^(n)(x) = product(k - i, i = 0..n-1)*x^(k-n) > but > product(k - i, i = 0..n-1) = (-1)^n*Gamma(n-k)/Gamma(-k) if k < n and k a > positive integer, else 0 > so the nth derivative of f(x) is > f^(n)(c) = (-1)^n*Gamma(n-k)/Gamma(-k)*c^n > since Ive found the nth coefficient for you, I think you can find the rest. > (now, there maybe easier ways using more indirect methods, but this is a > direct application of the theorem. (and in its most general form for any > power of x) and incase you dont know what gamma is, its basically > factorial, except it can handle non integral arguments. Gamma(n) = (n-1)! > for integer n, and Gamma(z) = z*Gamma(z-1)) === Subject: Complex Fittings by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iBI3LPp01529; Hello all, I am trying to do a fitting of many variables (~ 20 - 100) but I need the returned constants to only be positive. I am currently using a least squares fitting method written in python and I would like to stick with python if possible. I was hoping someone may be able to help me with some theory behind getting only positive values returned. Matthew === Subject: Re: Lebesgue measurable functions R such > that inverse image of a Lebesgue measurable set is not Lebesgue measurable. > Examples through cardinality argument will be accepted. Can you find a Lebesgue measurable f that maps [0,1] bijectively to the > Cantor set? Every subset of the Cantor set is Lebesgue measurable, but > not every subset of [0,1] is. > -- > G. A. Edgar http://www.math.ohio-state.edu/~edgar/ > There is also a continuous (strictly increasing) bijection of [0,1] onto > [0,2] which maps the Cator set (of Lebesgue measure 0) onto a Cantor-like > set of Lebesgue measure 1. It appeared recently: x+C(x) where C is the > Cantor function. Cator set is of course my private nickname for the Cantor set. (Sitting in my office on Saturday night, ready to answer questions from students writing a final exam...) === Subject: ethics and mathematics posting-account=JKe5pgwAAABshOT4LtiAVjJ9JJ_HZvuQ John Nash proved you have to think not only about yourself. Is possible to prove that people should be ethical with mathematics? If somebody proved that absolute truth exists and, for example, economists read another proof written in business language that they should choose to follow the path of peace and love instead of war and hate, would economists ignore both proofs? Since the intellectual elite and the rich elite study mathematics, can mathematics be a bridge between them? === Subject: Re: ethics and mathematics > John Nash proved you have to think not only about yourself. Why not say that John von Neumann and Oskar Morgenstern showed this? > Is possible to prove that people should be ethical with mathematics? I dont think this is the sort of thing that can be mathematically proven. > If somebody proved that absolute truth exists and, for example, > economists read another proof written in business language that they > should choose to follow the path of peace and love instead of war and > hate, would economists ignore both proofs? Sure. It was mathematically demonstrated about half a century ago that much of what mainstream economics teach and practice is mistaken. Mainstream economists just ignore the demonstration. For one of my expositions of some elements of this demonstration, see: By the way, the empirical evidence is that studying economics tends to make one nasty: -- Mostly economics: r c v s a Whether strength of body or of mind, or wisdom, or i m p virtue, are found in proportion to the power or wealth e a e of a man is a question fit perhaps to be discussed by n e . slaves in the hearing of their masters, but highly @ r c m unbecoming to reasonable and free men in search of d o the truth. -- Rousseau >Is possible to prove that people should be ethical with mathematics? No. Mathematics proves things from axioms; it cannot manufacture the axioms. >If somebody proved that absolute truth exists and, for example, >economists read another proof written in business language that they >should choose to follow the path of peace and love instead of war >and hate, would economists ignore both proofs? Youd have to ask the economists. But why do you believe that the politicians would pay attention to the economists in that scenario? >Since the intellectual elite and the rich elite study mathematics, >can mathematics be a bridge between them? Why do you believe that the rich elite study Mathematics? And if they do, what does it have to do with their ethics? Plenty of highly educated and intelligent people have supported evil, including some Mathematicians. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolicited bulk E-mail subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not === Subject: Re: ethics and mathematics > Since the intellectual elite and the rich elite study mathematics Do they? sirix. === Subject: Re: ethics and mathematics > If somebody proved that absolute truth exists and, for example, > economists read another proof written in business language that they > should choose to follow the path of peace and love instead of war and > hate, would economists ignore both proofs? This is nonsense. Mathematics has nothing to do with peace and love. As for absolute truth, that is easy. ~(p&~p) for any proposition p. That is as absolute as truth gets. Bob Kolker === Subject: Re: job advice - math student posting-account=2Lbxhg0AAACPgQos9yMpmxCwf0XKMqMJ You could check out FindAJob.com ( http://www.findajob.com ) for university math jobs or academic jobs in general. They have about 20,000 jobs up now. === Subject: Re: Polysigned Numbers posting-account=NRsM-wwAAAAi5GV8YXCgqBCSyfE5DQT7 Ive been toying with the square root of minus one in four-signed since you posted this. How do you prove that it does not exist? So Far I dont have an answer, but my method goes like this: (-a+b*c#d)(-a+b*c#d) = -1. As a result: | - 2ad - 2bc | = 1 | + aa + cc + 2bd | = 0 | * 2ab * 2cd | = 0 | # 2ac # bb # dd | = 0 . Or in real values: 2ad + 2bc = 1 aa + cc + 2bd = 0 2ab + 2cd = 0 2ac + bb + dd = 0 Now, we can arbitrarily choose a value for a,b,c,or d since the system is nonorthogonal. So I chose a = 1.0 . Then I boiled down to a large polynomial in c which I couldnt solve. So I graphed it in gnuplot and got some roots. But neither of them actually worked out so I must have made a mistake along the way, or the method is bogus. I think that this method is alright, except for the part where I zoom in on the zero solutions of a complicated polynomial in gnuplot. Ill try to spend a little more time with it. -Tim === Subject: Re: Polysigned Numbers posting-account=NRsM-wwAAAAi5GV8YXCgqBCSyfE5DQT7 > Ive been toying with the square root of minus one in four-signed since > you posted this. > How do you prove that it does not exist? Well I can claim to have verified that sqrt( - 1 ) in four signs does not exist now. That is, assuming I havent made any more errors on top of my old errors. Corrections to the method below... > So Far I dont have an answer, but my method goes like this: > (-a+b*c#d)(-a+b*c#d) = -1. > As a result: > | - 2ad - 2bc | = 1 > | + aa + cc + 2bd | = 0 > | * 2ab * 2cd | = 0 > | # 2ac # bb # dd | = 0 . This should be: | - 2ad - 2bc | = 1 + x | + aa + cc + 2bd | = x | * 2ab * 2cd | = x | # 2ac # bb # dd | = x . where x is a magnitude > Or in real values: > 2ad + 2bc = 1 > aa + cc + 2bd = 0 > 2ab + 2cd = 0 > 2ac + bb + dd = 0 Or in real values: 2ad + 2bc = 1 + x aa + cc + 2bd = x 2ab + 2cd = x 2ac + bb + dd = x Now choose a value for one of a,b,c,d, or x. So choosing x = 0 disallows a free choice of a = 1. Well its apparent that some of these must be zero. OK. it shows a = 0, b = 0, c = 0, d = 0. Therefore there is no sqrt( -1 ) since square(0) is zero. But these equations are the general square on the left. Just substitute in something that works to check them... sqrt( # 1 ) should make 2ac + bb + dd = 1 and the rest equate to zero. and so a = 0, c = 0, b = 1, d = 0 is a solution and a = 0, c = 0, b = 0, d = 1 is a solution Yes, that check is good. > Now, we can arbitrarily choose a value for a,b,c,or d since the system > is nonorthogonal. So I chose a = 1.0 . > Then I boiled down to a large polynomial in c which I couldnt solve. This step was bogus. I should not have left the magnitude from when a magnitude is equal to zero. e.g. | + x + y | = 0 does not mean that x = - y. It means x = 0, y = 0. whereas if | + x + y | = z then it is ok to say that x = z - y where all values are magnitudes and leaving the magnitude form steps up to the reals with a guarantee that z > x and z > y. > So I graphed it in gnuplot and got some roots. But neither of them > actually worked out so I must have made a mistake along the way, or the > method is bogus. > I think that this method is alright, except for the part where I zoom > in on the zero solutions of a complicated polynomial in gnuplot. Ill > try to spend a little more time with it. > -Tim -Tim === Subject: Re: Polysigned Numbers posting-account=BjC-YAwAAADQ91Zm3XkS3aGs3XlaqZ4X I didnt check on Your calculation. > Or in real values: > 2ad + 2bc = 1 > aa + cc + 2bd = 0 > 2ab + 2cd = 0 > 2ac + bb + dd = 0 (4 equations with 4 unknown) i calculated first a=f(d,b,c) then c =g (a,b, d) insert this in the first. Both in the remaining equations and by comparing a=b=c=d=0 Ive got a nice rule to memorize the sizes in a tetrahedron. On the way to the center start with one corner. Divide the edge or side line of length s 1:1, or go 1/2 of s. Turn right and facing a corner, divide this line 1:2, or go 1/3 of this line (which is sqrt3 / 2 of s long) . Now turn a right angle and face the last corner, divide this line 1:3, or go 1/4 of it ( which is sqrt2/sqrt3 of s long). Have fun Hero === Subject: Re: Double posts > When I notice duplicates, > dont propagate everywhere. Thunderbird, which is also a little bit buggy? -- Karl M. Bunday P.O. Box 1456, Minnetonka MN 55345 Learn in Freedom (TM) http://learninfreedom.org/ remove .de to email === Subject: Re: Double posts >> When I notice duplicates, messages >> dont propagate everywhere. Mozilla > Thunderbird, which is also a little bit buggy? Thunderbird? -- Herman Jurjus === Subject: Re: Double posts Mozilla >> Thunderbird, which is also a little bit buggy? Thunderbird? My problem with Thunderbird, a set of habits I carry over from using a Brand X product, is that I forget the message composer for Thunderbird looks the same whether it is sending email or a Usenet message. So once in a while I see a cool Usenet message and desire to tell an email list about it, and then I click compose (now its write in the current release of Thunderbird) and the address of the recipient is automatically filled in as the newsgroup I am reading at the time. Filling in an email recipient does NOT suppress sending a copy of my message to the newsgroup; to prevent the newsgroup posting, I have to actively delete the newsgroup address. The last brand name of email/newsgroup client I used brought up different compose programs depending on whether I was posting to a newsgroup or to email, so it was a lot harder to make that mistake. so Id like to learn how to send them. Even better will be keeping vigilant to avoid posting mistaken posts in the first place. Technology should make mistakes less likely, not more. http://www.useit.com -- Karl M. Bunday P.O. Box 1456, Minnetonka MN 55345 Learn in Freedom (TM) http://learninfreedom.org/ remove .de to email Supersedes: === Subject: Invariant Galilean Transformations (FAQ) On All Laws Summary: All laws/equations are Galilean invariant when expressed in the generalized cartesian coordinates demanded by basic analytic geometry, vector algebra, and measurement theory. Originator: faqserv@penguin-lust.mit.edu Disclaimer: approval for *.answers is based on form, not content. Opponents of the content should first actually find out what it is, then think, then request/submit-to arbitration by the appropriate neutral mathematics authorities. Flaming the hard- working, selßess, *.answers moderators evidences ignorance and despicable netiquette. Archive-Name: physics-faq/criticism/galilean-invariance Version: 0.04.03 Posting-frequency: 15 days Invariant Galilean Transformations (FAQ) On All Laws (c) Eleaticus/Oren C. Webster Thnktank@concentric.net An obvious typo or two corrected. The Brittanica section revised to less Ôpussy-footing and to more directly anticipate the elementary measurement theory and basic analytic geometry that is applied to the transformation concept. ------------------------------ === Subject: 1. Purpose The purpose of this document is to provide the student of Physics, especially Relativity and Electromagnetism, the most basic princ- iples and logic with which to evaluate the historic justification of Relativity Theory as a necessary alternative to the classical physics of Newton and Galileo. We will prove that all laws are invariant under the Galilean transformation, rather than some being non-invariant, after we show you what that means. We shall also show that another primal requirement that SR exist is nonsense: Michelson-Morley and Kennedy-Thorndike do indeed fit Galilean (c+v) physics. ------------------------------ === Subject: 2. Table of Contents 1. Foreword and Intent 2. Table of Contents 3. The Principle of Relativity 4. The Encyclopedia Brittanica Incompetency. 5. Transformations on Generalized Coordinate Laws 6. The data scale degradation absurdity. 7. The Crackpots Version of the Transforms. 8. What does sci.math have to say about x0=x0-vt? 9. But Doesnt x.c=x.c? 10. But Isnt (x-x.c)=(x-x.c) Actually Two Transformations? 11. But Doesnt (x-x.c+vt) Prove The Transformation Time Dependent? 12. But Isnt (x-x.c)=(x-x.c) a Tautology? 13. But Isnt (x-x.c)=(x-x.c) Almost the Definition of a Linear Transform? 14. But The Transform Wont Work On Time Dependent Equations? 15. But The Transform Wont Work On Wave Equations? 16. But Maxwells Equations Arent Galilean Invariant? 17. First and Second Derivative differential equations. ------------------------------ === Subject: 3. The Principle of Relativity and Transformation If a law is different over there than it is here, it is not one law, but at least two, and leaves us in doubt about any third location. This is the Principle of Relativity: a natural law must be the same relative to any location at which a given event may be perceived or measured, and whether or not the observer is moving. The idea of location translates to a coordinate system, largely because any object in motion could be considered as having a coordinate system origin moving with it. If you perceive me moving relative to you - who have your own coordinate system - will your measurements of my position and velocity fit the same laws my own, different measurements fit? If a law has the same form in both cases it is called covariant. If it is identical in form, var- ables, and output values, it is called invariant. What were asking is that if the x-coordinate, x, on one coordinate axis works in an equation, does the coordinate, x, on some other, parallel axis work? Speaking in terms of the axis on which x is the coordinate, x is the Ôtransformed coordinate. The situation is complicated because were talking about coordinates - locations - but in most mean- ingful laws/equations, it is lengths/distances (and time intervals) the equations are about, and x coord- inates that represent good, ratio scale measures of distances are only interval scale measures on the x axis. [See Table of Contents for discussion of scales.] So, if we have an x-coordinate in one system, then we can call the x value that corresponds to the same point/location the transform of x. In particular, the Principle of Relativity is embodied in the form of the Galilean transformation, which relates the original x, y, z, t to x, y, z, t by the transform equations x=x-vt, y=y, z=z, t=t in the simplified case where attention is focused only on transforming the x-axis, and not y and z. In the case of Special Relativity, the x transform is the same except that x is then divided by sqrt(1-(v/c)^2), and t=(t-xv/cc)/sqrt(1-(v/c)^2). In either case, v is the relative velocity of the coordinate systems; if there is already a v in the equations being trans- formed use u or some other variable name. ------------------------------ === Subject: 4. The Encyclopedia Brittanica Incompetency. One example of the traditional fallacious idea that an equation is not invariant under the galilean transformation comes from the Encyclopedia Brittanica: Before Einsteins special theory of relativity was published in 1905, it was usually assumed that the time coordinates measured in all inertial frames were identical and equal to an Ôabsolute time. Thus, t = t. (97) The position coordinates x and x were then assumed to be related by x = x - vt. (98) The two formulas (97) and (98) are called a Galilean transformation. The laws of nonrelativ- istic mechanics take the same form in all frames related by Galilean transformations. This is the restricted, or Galilean, principle of relativity. The position of a light wave front speeding from the origin at time zero should satisfy x^2 - (ct)^2 = 0 (99) in the frame (t,x) and (x)^2 - (ct)^2 = 0 (100) in the frame (t,x). Formula (100) does not transform into formula (99) using the transform- ations (97) and (98), however. ................................................. Besides the trivially correct statement of what the Galilean Ôtransform equations are, there is exactly one thing they got right. I. Eq-100 is indeed the correct basis for discussing the question of invariance, given that eq-99 is the correct Ôstationary (observer S) equation. [Let observer M be the Ômovingsystem observer.] In particular, eq-100 is of exactly the same form [the square of argument one minus the square of argument two equals zero (argument three).] II. It is nonsense to say eq-99 should be derivable from eq-100; for one thing, the transforms are TO x and t from x and t, not the other way around, and the idea that either observers equation should contain within itself the terms to simplify or rearrange to get to the other is ridiculous. As the transform equations say, the relationship of t, x to t, x is based on the relative velocity between the two systems, but neither the original (eq-99) equation nor the M observer equation is about a relationship between coordinate systems or observers. One might as well expect the two equations to contain banana export/import data; there is no relevancy. The Ôtransform equations are the relationships between x and x, t and t and have nothing to do with what one equation or the other ought to Ôsay. The equations content is the rate at which light emitted along the x-axes moves. III. Most remarkable, the True Believer SR crackpots who most despise the consequences of measurement theory (demonstrable fact) contained in this document are those who want to argue against our saying the Britt- anica got eq-100 right; They insist that the correct equation is derived directly from x=x-vt and t=t. Solve for x=x+vt and replace t with t, then substitute the result in eq-99: (x+vt)^2 - (ct)^2 = 0. Besides the fact that this results in an equation with arguments exactly equal to eq-99, they will insist the transform is not invariant. IV. A major justification they have for their idea of the correct M system equation on which to base the the discussion of invariance, is that the variables are M system variables, never mind the fact that the arguments are S system values. That argument of theirs is arrant nonsense. The velocity v that S sees for the M system relative to herself is the negative of what the M system sees for the S system relative to himself. In other words, x+vt is a mixed frame expression and it is x+(-v)t that would be strictly M frame notation, and that equation is far off base. [Work it out for yourself, but make sure you try out an S frame negative v so as not to mislead yourself.] V. In I. we said: given that eq-99 is the correct Ôstationary equation. Lets look at it closely: x^2 - (ct)^2 = 0 (99) This whole matter is supposed to be about coordinate transforms. Is that what t is, just a coordinate? No. It isnt, in general. Suppose you and I are both modelling the same light event and you are using EST and Im using PST. ÔJust a time coordinate is just a clock reading amd your t clock reading says the light has been moving three hours longer than my clock reading says. Well, thats what the idea that t is a coordinate means. Eq-99 works if and only if t is a time interval, and in particular the elapsed time since the light was emitted. Thus, that equation works only if we understand just what t is, an elapsed time, with emissioon at t=0. However, we dont have to Ôunderstand anything if we use a more intelligent and insightful form of the equation: (x)^2 - [ c(t-t.e) ]^2 = 0, where t.e is anyones clock reading at the time of light emission, and t is any subsequent time on the same clock. Similarly, x is not just a coordinate, but a distance since emission. (x-x.e)^2 - [ c(t-t.e) ]^2 = 0 (99a) VI. In the spirit of Ôthere is exactly one thing they got right, the correct M system version of eq-99a is eq-100a: (x-x.e)^2 - [ c(t-t.e) ]^2 = 0 (100a) Every observer in the universe can derive their eq-100a from eq-99a and vice versa, not to mention to and from every other observers eq-99a. Now, THATs invariance. [You do realize that every eq-100a reduces to eq-99a, when you back substitute from the transforms, right? t.e=t.e, x.e=x.e-vt.] ------------------------------ === Subject: 5. Transformations on Generalized Coordinate Laws The traditional Gallilean transform is correct: t = t x = x - vt. But remember this: a transform of x doesnt effect just some values of x, but all of them, whether they are in the formula or not. This is important if you want to do things right. The crackpot position is strongly against this sci.math verified position, and the apparently standard coordinate pseudo-transformation they suggest is perhaps the result. {See Table of Contents.] Lets use a simple equation: x^2 + y^2 = r^2, which is the formula for a circle with radius r, centered at a location where x=0. But what if the circle center isnt at x=0? Well, wed want to use the form analytic geometry, vector algebra, and elementary measurement theory tells us to use, a form where we make explicit just where the circle center is, even if it is at x=x0=0: (x-x0)^2 + (y-y0)^2 = r^2. The circle center coordinate, x0, is an x-axis coordinate, just like all the x-values of points on the circle. So, in proper generalized cartesian coordinate forms of laws/equations we want to transform every occurence of x and x0 - by whatever name we call it: x.c, x_e, whatever. So, what is the transformed version of (x-x0)? Why, (x-x0); both x and x0 are x-coordinates, and every So, what is the value of (x-x0) in terms of the original x data? is also true for x0=x0-vt: (x-x0)=[ (x-vt)-(x0-vt) ]=(x-x0). In other words, when we use the generalized coordinate form specified by analytic geometry, we find that the value of (x-x0) does not depend on either time or velocity in any way, shape, form, or fashion. Similarly for (y-y0). We can treat time the same way if necessary: (t-t0). The above is a proof that any equation in x,y,z,t is invariant under the galilean transforms. Just use the generalized coordinate form, with (x-x0)/etc, in the transformation process, not the incompetently selected privileged form, with just x/etc. [The form is privileged because it assumes the circle center, point of emission, whatever, is at the origin of the axes instead at some less convenient point. After transform the coordinate(s) of the circle center/origin are also changed but the privileged form doesnt make this explicit and screws up the calculations, which should be based on (x-x0) but are calculated as (x-0).] The value of (x-x0) is the same as (x-x0). That makes sense. Draw a circle on a piece of paper, maybe to the right side of the paper. On a transparent sheet, draw x and y coordinate axes, plus x to the right, plus y at the top. Place this axis sheet so the y-axis is at the left side of the circle sheet. Now answer two questions after noting the x-coordinate of the circle center and then moving the axis sheet to the right: (a) did the circle change in any way because you moved the axis sheet (ie because you transformed the coordin- nate axis)? (b) did the coordinate of the circle center change? The circle didnt change [although SR will say it did]; that means that (x-x0) does indeed equal (x-x0). The coordinate of the circle center did change, and it changed at the same rate (-vt) as did every point on the circle. That means that x0<>x0, and the fact the circle center didnt change wrt the circle, means that the relationship of x0 with x0 is the same as that of any x on the circle with the corresponding x: x=x-vt; x0=x0-vt. This is to prepare you for the True Believer crackpots that say Ôconstant coordinates cant be transformed; some even say they arent coordinates. These crackpots include some that brag about how they were childhood geniuses, btw. QED: The galilean transformation for any law on generalized Cartesian coordinates is invariant under the Galilean transform. The use of the privileged form explains HOW the transformed equation can be messed up, the next Subject explains what the screwed up effect of the transform is, and how use of the generalized form corrects the screwup. ------------------------------ === Subject: 6. The data scale degradation absurdity. The SR transforms and the Galilean transforms both convert good, ratio scale data to inferior interval scale data. The effect is corrected, allowed for, when the transforms are conducted on the generalized coordinate forms specified by analytic geometry and vector algebra. Both sets of transforms are Ôtranslations - lateral movements of an axis, increasing over time in these cases - but with the SR transform also involving a rescaling. It is the translation term, -vt in the x transform to x, and -xv/cc in the t transform to t, that degrades the ratio scale data to interval scale data. In general, rescaling does not effect scale quality in the size-of-units sense we have here. SR likes to consider its transforms just rotations, however - in spite of the fact Einstein correctly said they were Ôtranslations (movements) - and in the case of Ôgood rotations, ratio scale data quality is indeed preserved, but SR violates the conditions of good ro- tations; they are not rigid rotations and they dont appropriately rescale all the axes that must be rescaled to preserve compatibility. The proof is in the pudding, and the pudding is the combination of simple tests of the transformations. We can tell if the transformed data are ratio scale or interval. Ratio scale data are like absolute Kelvin. A measure- ment of zero means there is zero quantity of the stuff being measured. Ratio scale data support add- ition, subtraction, multiplication, and division. The test of a ratio scale is that if one measure looks like twice as much as another, the stuff being measured is actually twice as much. With absolute Kelvin, 100 degrees really is twice the heat as 50 degrees. 200 degrees really is twice as much as 100. Interval scale data are like relative Celsius, which is why your science teacher wouldnt let you use it in gas law problems. There is only one mathematical operation interval scales support, and that has to be between two measures on the same scale: subtraction. 100 degrees relative (household) Celsius is not twice as much as 50; we have to convert the data to absolute Kelvin to tell us what the real ratio of temperatures is. However, whether we use absolute Kelvin or relative Celsius, the difference in the two temperature readings is the same: 50 degrees. Thus, if we know the real quantities of the Ôstuff being measured, we can tell if two measures are on a ratio scale by seeing if the ratio of the two measures is the same as the ratio of the known quant- ities. If a scale passes the ratio test, the interval scale test is automatically a pass. If the scale fails the ratio test, the interval scale test becomes the next in line. It isnt just the bare differences on an interval scale that provides the test, however. Differences in two interval scale measures are ratio scale, so it is ratios of two differences that tell the tale. Lets do some testing, and remember as we do that our concern is for whether or not the data are messed up, not with Ôreasons, excuses, or avoidance. ------------------------------------------------------ Are we going to take a transformed length (difference) and see whether that length fits ratio or interval scale definitions? Of course, not. Interval scale data are ratio after one measure is subtracted from another. That is the major reason the SR transforms can be used in science. Let there be three rods, A, B, C, of length 10, 20, 40, respectively. These lengths are on a known ratio scale, our original x-axis, with one end of each rod at the origin, where x=0, and the other end at the coordinate that tells us the correct lengths. Note that these x-values are ratio scale only because one end of each rod is at x=0. That may remind you of the correct way to use a ruler or yard/meter-stick: put the zero end at one end of the thing you are measuring. Put the 1.00 mark there instead of the zero, and you have interval scale measures. Let A,B,C, be 10, 20, 40. Let a,b,c be x at v=.5, t=10. x=x-vt. A B C a b c ---------------- -------------------- 10 20 40 5 15 35 ---------------- -------------------- B/A = 2 b/a = 3 C/A = 4 c/a = 7 C/B = 2 c/b = 2.333 Obviously, the transformed values are no longer ratio scale. The effect is less on the greater values. C-A = 10 b-a = 10 C-A = 30 c-a = 30 C-B = 20 c-b = 20 Obviously, the transformed values are now interval scale. This will hold true for any value of time or velocity. (C-A)/(B-A) = 3 (c-a)/(b-a) = 3 (C-B)/(B-A) = 2 (c-b)/(b-a) = 2 Obviously, the ratios of the differences are ratio scale, being identical to the ratios of the corresponding original - ratio scale - differences. The main difference between these results and the SR results is that the differences do not correspond so neatly to the original, ratio scale, differences. This is due only to the rescaling by 1/sqrt(1-(v/c)^2). The ratios of the differences on the transformed values do correspond neatly and exactly to the ratio scale results. Using the generalized coordinate form, such as (x-x0), the transform produces an interval scale x and an interval scale x0. That gives us a ratio scale (x-x0), just like - and equal to - (x-x0). ------------------------------ === Subject: 7. The Crackpots Version of the Transforms. It has become apparent - whether misleading or not - that the crackpot responses to the obvious derive from a common source, whether it be bandwagoning or their SR instructors. Below, in the sci.math subject, we see that all sci.math respondents agree with the basic controversial position of this faq: every coordinate is transformed, whether a supposed constant or not. Think about it, the generalized coordinate of a circle center, x0, applies to infinities upon infinities of circle locations (given y and z, too); it is a constant only for a given circle, and even then only on a given coordinate axis. And even variables are often held Ôconstant during either integration or differentiation. The utility of a variable is that you can discuss all possible particular values without having to single out just one. That utility does not make particular - singled out - values on the variables axis not values of the variable just because they have become named values. In any case, all that is preamble to the incompetent idea they have proposed for a transform of coordinates. It is based on the idea that the circle center, point of emission, whatever, has coordinates that cannot be transformed. Let there be an equation, say (x)^2 - (ict)^2 = 0. What is the transformed version of that equation? Answer: (x)^2 - (ict)^2 = 0. Thats the one thing the Brittanica got right. Note that the leading crackpot just criticized this faq for presuming to correct the Britt- anica, but it then and before poses the incompetent pseudo- transform we analyze here in this section. x to x and t to t are obviously coordinate transforms; the x and t coordinates have been replaced by the coord- inates in the primed system. A tranform of an equation from one coordinate system to another is NOT a substitution of the/a definition of x for itself; that is not a coordinate transformation. The most that can said for such a substitution is that it is a change of variable. But the crackpots are calling this a coordinate trans- form of the original equation: (x+vt)^2 - (ict)^2 = 0. It is not a coordinate transform, of course, except accidentally. (x+vt) is not the primed system coordinate, it is another form/expression of x. They get that substitution by solving x=x-vt for x; x=x+vt. So, by incompetent misnomer, they accomplish what they have been railing against all along. It has been the generalized coordinate form in question all this time: (x-x0)^2 - (ict)^2 = 0. Here they substitute for x instead of transforming to the primed frame: (x+vt-x0)^2 - (ict)^2. ----- ^ | ^ | It is still x ^ but see what they have accomplished by their mis/malfeasance: [x+vt-x0]=[x+(vt-x0)]=[x-(x0 -vt)]. =[x-x0] The crackpots have been bragging about how you dont have to transform the circle centers coordinate to transform the circle centers coordinate. Bragging that what they were doing was not what they said they were doing. This does give us insight as to some of the crackpot variations on their x0<>x0-vt theme, which in all the variations will be discussed in later sections.. They are used to seeing the mixed coordinate form, (x+vt-x0) without realizing what it respresented, so - accompanied with a lack of understanding of the term Ôdependent - they are used to seeing just the one vt term, and not the one hidden in the defi- nition of x and are used to imagining it makes the whole expression time dependent and thus not invariant. About which, let x=10, let, x0=20, v=10, and t variously 10 and 23: (x-x0)=-10. Using their (x+vt-x0): For t=10, we have (x+vt-x0) = [ (10-10*10) + (10*10) - (20) ] = -90 + 100 - 20 = -10 = (x-x0) For t=23, we have (x+vt-x0) = [ (10-10*23) + (10*23) - (20) ] = -220 + 230 - 20 = -10 = (x-x0) The result depends in no way on the value of time; we showed the obvious for a couple of instances of t just so you can see that the crackpots not only do not understand the obvious logic of the algebra { (x-x0)=[ (-vt)-(x0-vt) ]=(x-x0) } - which shows that the transform has no possible time term effect - but they dont understand even a simple arithmetic demonstration of the facts. Oh. Their (x+vt-x0) or (x+vt-x0) reduces the same way since t=t: (x-vt+vt-x0)=(x-x0). Their process, which says (x+vt) is the transform of x, says that (x+vt) is the moving system location of x, but it cant be because x is moving further in the negative direction from the moving viewpoint. That formula will only work out with v<0 which is indeed the velocity the primed system sees the other moving at. However, that formula cannot be derived from x=x-vt, the formula for transformation of the coordinates from the unprimed to the primed, ------------------------------ === Subject: 8. What does sci.math have to say about x0=x0-vt? The crackpots positions/arguments were put to sci.math in such a way that at least two or three who posted re- sponses thought it was your faq-er who was on the idiots side of the questions. Their responses: ---------------------------------------------------------- I. x0 = x0. In other words: x0 <> x0-vt, or constant values on the x-axis are not subject to the transform. No. x0 = x0 - vt. Well, if you want, you could define constant values on the but in the context of the question that is not relevant. The relevant fact is that if the unprimed observer holds an object at point x0, then the primed observer assigns to that object a coordinate x0 which is numerically related to x0 by x0= x0 -vt. What does this mean? The line x=x0 will give x=x-v*t=x0-vt, so if x0 is to give the coordinate in the (x,t,)-system, it will be given by x0=x0-v*t: ie., it is not given by a constant. Thus, being at rest (constant x-coordinate) is a coordinate-dependent concept. Sounds very false. We can say that the representation of the point X0 is the number x0 in the unprimed system, and x0 in the primed system. Clearly x0 and x0 are different, if vt is not zero. However one may say that (though it sounds/is stupid) the point X0 itself is the same throughout the transformation. However that expression sounds meaningless, since a transform (ok, maybe we should call it a change of basis) is only a function that takes the points representation in one system into the same points representation in another system. It is preferrable to use three notations: X0 for the point itself and x0 and x0 for the points representations in some coordinate systems. ------------------------------ === Subject: 9. But Doesnt x.c=x.c? That idea is one of the most idiotic to come up, and it does so frequently. And in a number of guises. The idea being that x.c <> x.c-vt, with x.c being what we have called x0 above; the notation makes no difference. Some crackpots have managed to maintain that position even after graphs have illustrated that such an idea means that after a while a circle center represented by x.c could be outside the circle. The leading crackpot just make that explicit, as far as one can tell from his befuddled post in response to a line about active transforms, which are actually moving body situations, not coordinate transformations: ------------------------------------------------------------- ------- e>An active transform is not a coordinate transform, ... Right, it is a transform of the center (in the opposite direction) done to effect the change of coordinates without a coordinate transform. ... E: Transform of the center? Center of a circle? He really is saying a circle center moves in the opposite direction of the circle! Right? ------------------------------------------------------------- ------- If r=10 and x.c was at x.c=0, then the points on the circle (10,0), (-10,0), (0,10) and (0,-10) could at some time become (-10,0), (-30,0), (-20,10), and (-20,-10), but with x.c=x.c, the circle center would be at (0,0) still! The circle is here but its center is way, way over there! Indeed, although a change of coordinate systems is not movement of any object described in the coordinates, the x.c=x.c crackpottery is tantamount to the circle staying put but the center moving away. Or vice versa. ------------------------------ === Subject: 10. But Isnt (x-x.c)=(x-x.c) Actually Two Transformations? One crackpot puts the (x-x.c)=(x-vt - x.c+vt) relationship like this: (x-vt+vt - x.c). See, he says, that is transforming x (with x-vt - x.c) and then reversing the transform (x-vt+vt - x.c). Thats just another crackpot form of the idiocy that x.c <> x.c-vt. Youll have noticed the implication is that there is no transform vt term relating to x.c. ------------------------------ === Subject: 11. But Doesnt (x-x.c+vt) Prove The Transformation Time Dependent? That particular crackpottery is perhaps more corrupt than moronic, since it includes deliberately hiding a vt term from view, and pretending it isnt there. [However, we have seen above that it is a familiar incompetency, and not likely an original.] Look, the crackpots say, there is a time term in the transformed (x - x.c+vt). The transform isnt invariant! Its time dependent! Just put x in its original axis form, also, which reveals the other time term, the one they hide: (x-x.c+vt) = (x-vt - x.c+vt) = (x-x.c). So, at any and all times, the transform reduces to the original expression, with no time term on which to be dependent. Then there is the fact that if you leave the equation in any of the various notation forms - with or without reducing them algebraicly - the arithmetic always comes down to the same as (x-x.c). That means nothing to crack- pots, but may mean something to you. ------------------------------ === Subject: 12. But Isnt (x-x.c)=(x-x.c) a Tautology? My dictionary relates Ôtautology to needless repetition. Thats another form of the x.c <> x.c-vt idiocy. The repetition involved is the vt transformation term. Apply the -vt term to the x term, and it is needless repetition to apply it anywhere again? The Ôagain is to the x.c term. The x.c = x.c crackpot idiocy. The repetition of the vt terms is required by the presence of two x values to be transformed. Be sure to note the next section. ------------------------------ === Subject: 13. But Isnt (x-x.c)=(x-x.c) Almost the Definition of a Linear Transform? Now, how on earth can we relate a tautology to a basic definition in math? we get this definition: -------------------------------------------------------------- A linear transformation, A, on the space is a method of corr- esponding to each vector of the space another vector of the space such that for any vectors U and V, and any scalars a and b, A(aU+bV) = aAU + bAV. ------------------------------------------------------------- Let points on the sphere satisfy the vector X={x,y,z,1}, and the circle center satisfy C={x.c,y.c,z.c,1}. Let a=1, and b=-1. Let A= ( 1 0 0 -ut ) ( 0 1 0 -vt ) ( 0 0 1 -wt ) ( 0 0 0 1 ) A(aX+bC) = aAX + bAC. aX+bC = (x-x.c, y-y.c, z-z.c, 0 ). The left hand side: A( x - x.c , y - y.c, z - z.c, 0 ) = ( x-x.c , y-y.c, z-z.c, 0 ). The right hand side: aAX= ( x-ut, y-vt, z-wt, 1 ). bAC= (-x.c+ut, -y.c+vt, -z.c+wt, -1 ). and aAX+bAC = ( x-x.c, y-y.c, z-z.c, 0 ). Need it be said? Sure: QED. On the galilean transform the definition of a linear transform, A(aU+bV)=aAU + bAV, is completely satisfied. The generalized form transforms exactly and non-redundantly - with ONE TRANSFORM, not a transform and reverse transform - and non- tautologically, just as the very definition of a linear transform says it should. And does so with absolute invariance, with this galilean transformation. ------------------------------ === Subject: 14. But The Transform Wont Work On Time Dependent Equations? The main crackpot that has asserted such a thing was referring to equations such as in Subject 4, above. The Light Sphere equation; for which we have shown repeatedly elsewhere that the numerical calculations are identical for any primed values as for the unprimed values. The presence - before transformation - of a velocity term seems to confuse the crackpots. It turns out there is ex- treme historical reason for this, as you will see in the subject on Maxwells equations. ------------------------------ === Subject: 15. But The Transform Wont Work On Wave Equations? See Subject 17, below, for a discussion of Second Derivative forms and the galilean transforms. ------------------------------ === Subject: 16. But Maxwells Equations Arent Galilean Invariant? Oh? Just what is the magical term in them that prevents (x-x.c)=(x-vt - x.c+vt)=(x-x.c) from holding true? It turns out not to be magic, but reality, that interferes with the application of the galilean transforms to the gen- eralized coordinate form(s) of Maxwell: there are no coordi- nates to transform! When True Believer crackpots are shown the simple demonstration that the galilean transform on generalized cartesian coordinates is invariant, their first defense is usually an incredibly stupid x0=x0, because the coordinate of a circle center, or point of emission, etc, is a constant and cant be transformed. The last defense is but Maxwells equations are not invariant under that coordinate transform. When asked just what magic occurs in Maxwell that would prevent the simple algebra (x-x0)=[ (x-vt)-(x0-vt) ]=(x-x0) from working, and when asked them for a demonstration, they will never do so, however many hundreds of times their defense is asserted. The reason may help you understand part of Einsteins 1905 paper in which he gave us his absurd Special Relativity derivation: THERE ARE NO COORDINATES IN THE EQUATIONS TO BE TRANSFORMED. Einstein gave the electric force vector as E=(X,Y,Z) and the magnetic force vector as B=(L,M,N), where the force components in the direction of the x axis are X and L, Y and M are in the y direction, Z and N in the z direction. Those values are not, however, coordinates, but values very much like acceleration values. BTW, the current fad is that E and B are Ôfields, having been Ôforce fields for a while, after being Ôforces. So, when Einstein says he is applying his coordinate transforms to the Maxwell form he presented, he is either delusive or lying. (a) there are no coordinates in the transform equations he gives us for the Maxwell transforms, where B=beta=1/sqrt(1-(v/c)^2): X=X. L=L. Y=B(Y-(v/c)N). M=B(M+(v/c)Z). Z=B(Z+(v/c)M). N=B(N-(v/c)Y). X is in the same direction as x, but is not a coordinate. Ditto for L. They are not locations, coordinates on the Similarly for Y and M and y, Z and N and z. (b) the v of the coordinate transforms is in Maxwell before any transform is imposed; Einsteins transform v is the velocity of a coordinate axis, not the velocity he touched it. (c) if they were honest Einsteinian transforms, theyd be x, which means it is X and L that are supposed to be transformed, not Y and M, and Z and N. And when SR does transform more than one axis, each axis has its own velocity term; using the v along the x-axis as the v for a y-axis and z-axis transform is thus trebly absurd: the axes perpendicular to the motion are not changed according to SR, the v used is not their v, and the v is not a transform velocity anyway. (d) as everyone knows, the effect of E and B are on the direction. Both the speed and direction are changed by E and B, but v - the speed - is a constant in SR. As absurd as are the previously demonstrated Einsteinian blunders, this one transcends error and is an incredible example of True Believer delusion propagating over decades. The components of E and B do differ from point to point, and in the variations that are not coordinate free, they are subject to the usual invariant galilean trans- formation when put in the generalized coordinate form. ------------------------------------------------------------- The SR crackpots dont know what coordinates are. The various things they call coordinates include coordin- nates, but also include a variety of other quantities. ------------------------------------------------------ 1. One may express coordinates in a one-axis-at-a-time manner [like x^2+y^2=r^2] but it is the use of vector notation that shows us what is going on. In vector notation the triplet x,y,z [or x1,x2,x3, whatever] represents the three spatial coordinates, but there are so-called basis vectors that underlie them. Those may be called i,j,k. Thus, what we normally treat as x,y,z is a set of three numbers TIMES a basis vector each. 2. These e*i, f*j, g*k products can have a lot of meanings. If e, f, j are distances from the origin of i,j,k then e*i, f*j, g*k are coordinates: distances in the directions of i,j,k respectively, from their origin. That makes the triplet a coordinate vector that we describe as being an x,y,z triplet; perhaps X=(x,y,z). The e*i, f*j, g*k products could be directions; take any of the other vectors described above or below and divide the e,f,g numbers by the length of the vector [sqrt(e^2+f^2+g^2)]. That gives us a vector of length=1.0, the e,f,g values of which show us the direction of the original vector. That makes the triplet a direction vector that we describe as being an x,y,z triplet; perhaps D=(x,y,z). The e*i, f*j, g*k products could be velocities; take any of the unit direction vectors described above and multiply by a given speed, perhaps v. That gives a vector of length v in the direction specified. That makes the triplet a velocity vector that we describe as being an x,y,z triplet; perhaps V=(x,y,z). Each of the three values, e,f,g, is the velocity in the direction of i,j,k respectively. The e*i, f*j, g*k products could be accelerations; take any of the unit direction vectors described above and multiply by a given acceleration, perhaps a. That gives a vector of length a in the direction specified. That makes the triplet an acceleration vector that we describe as being an x,y,z triplet; perhaps A=(x,y,z). Each of the three values, e,f,g, is the acceleration in the direction of i,j,k respectively. The e*i, f*j, g*k products could be forces (much like accel- erations); take any of the unit direction vectors described above and multiply by a given force, perhaps E or B. That gives a vector of length E or B in the direction specified. That makes the triplet a force vector that we describe as being an x,y,z triplet; perhaps E=(x,y,z) or B=(x,y,z). Each of the three values, e,f,g, is the force in the direction of i,j,k respectively. Einsteins - and Maxwells - E and B are not coordinate vectors. There is another variety of intellectual befuddlement that misinforms the idea that Maxwell isnt invariant under the galilean transform: confusions about velocities. Velocities With Respect to Coordinate Systems. ----------------------------------------------- Aaron Bergman supplied the background in a post to a sci.physics.* newsgroup: Imagine two wires next to each other with a current I in each. Now, according to simple E&M, each current generates a magnetic field and this causes either a repulsion or attraction between the wires due to the interaction of the magnetic field and the current. Lets just use the case where the currents are parallel. Now, suppose you are running at the speed of the current between the wires. If you simply use a galilean transform, each wire, having an equal number of protons and electrons is neutral. So, in this frame, there is no force between the wires. But this is a contradiction. First of all, the invariance of the galilean transform (x-x.c) =(x-x.c), insures that it is an error to imagine there is any difference between the data and law in one frame and in another; the usual, convenient rest frame is the best frame and only frame required for universal analysis. [Well, (x<>x, x,c<>x.c, but (x-x.c)=(x-x.c).] Second, given that you decide unnecessarily to adapt a law to a moving frame, dont confuse coordinate systems with meaningful physical objects, like the velocity relative to a coordinate system instead of relative to a physical body or field. In other words, what does current velocity with respect to a coordinate system have to do with physics? Nothing. Certainly not anything in the example Bergman gave. What is relevant is not current velocity with respect to a coordinate system, but current velocity with respect to wires and/or a medium. The velocity of an imaginary coordinate sys- tem has absolutely nothing to do with meaningful physical vel- ocity. You can - if you are insightful enough and dont violate item (e) - identify a coordinate system and a relevant physical object, but where some v term in the pre-transformed law is in use, dont confuse it with the velocity of the coordinate transform. Velocities With Respect to ... What? ----------------------------------------------- Albert Einstein opened his 1905 paper on Special Relativity with this ancient incompetency: The equations of the day had a velocity term that was taken as meaning that moving a magnet near a conductor would create a current in the conductor, but moving a conductor near a wire would not. This was belied by fact, of course. The important velocity quantity is the velocity of the magnet and conductor with respect to each other, not to some absolute coordinate frame (as far as we know) and not to an arbitrary coordinate system. One possible cause was the idea: but the equation says the magnet must be moving wrt the coordinate system or ... the absolute rest frame. There not being anything in the equation(s) to say either of those, it is amazing that folk will still insist the velocity term has nothing to do with velocity of the two bodies wrt each other. ----------------------------------------------------------- ------------------------------ === Subject: 17. First and Second Derivative differential equations. One of the intellectually corrupt ways of denying the very simple demonstration of galilean invariance of all laws expressed in the generalized coordinate form demanded by analytic geometry, vector analysis, and measurement theory [ (x-x.c)=[ (x-vt)-(x.c-vt) ]=(x-x.c) ] is the assertion that those equations Ôover there (usually Maxwell or wave) are somehow immune to the elementary laws of algebra used to demon- strate the invariance. [Unfortunately, the assertions are never accompanied by reference to the magical math that makes elementary al- gebra invalid. Wonder why that is?] Part of the time it is based on the old lore based on the incompetent transformation of the privileged form of an equation instead of the correct form. [Evidence of this is any reference to an effect due to the velocity of the transform; it falls out algebraicly metically - as you can see above.] But usually it is just whistling in the dark, waving the cross (zwastika, Id say) at the mean old vampire. The most general equation that could be conjured up is a differential with either First or Second Derivatives. Lets examine the plausibility of such magical magical, non-invariance assertions. (a) to get a Second Derivative you must have a First Derivative. (b) to get a First Derivative you must have a function to differentiate. (c) to get a Second Derivative you must have a function in the second degree. So, let us examine the question as to whether any such common Maxwell/wave equation will differ for (a) the common, privileged form, represented as ax^2, with a being an unknown constant function. (b) the generalized cartesian form, represented as a(x-x.c)^2 = ax^2 -2ax(x.c) + ax.c^2, with a being an unknown constant function. (c) the transformed generalized cartesian form, represented as a(x-vt -x.c+vt)^2, same as for (b), = ax^2 -2ax(x.c) + ax.c^2, of course, with a being an unknown constant function. I. for (a), remembering that x.c is a constant, and that this version is only correct because x.c=0, otherwise (b) is the correct form: d/dx ax^2 = 2ax (d/dx)^2 ax^2 = 2a II. for (b), remembering that x.c is a constant. d/dx (ax^2 -2ax(x.c) + ax.c^2) = 2ax - 2ax.c (d/dx)^2 (ax^2 -2ax(x.c) + ax.c^2) = 2a III. for (c); same as for (b). So, what we have seen so far is (1) differential equations in the second degree - the wave equations - must clearly be the same for all forms: the privileged form in x, the generalized cartesian form in x and the centroid, x.c, or the transformed generalized cartesian form. That is, anyone who imagines that correct usage gives different results for galilean transformed frames is at first showing his ignorance, and in the end showing his intellectual corruption. (2) As far as the First Derivatives are concerned, the only cases in which there really is a difference between the two forms is where x.c <> 0, and in that case, the use of the privileged form is obviously incompetent. So, how do you correctly use the differential equations? If you are using rest frame data with the centroid at x=0, etc, you cant go wrong without trying to go wrong. If you are using rest frame data with the centroid not at x=0, you must use (x-x.c) anyplace x appears in the equation. If you are using moving frame data, you must use the moving frame centroid as well as the light front (or whatever) moving frame data itself, perhaps first calculating (x-x.c), which equals (x-x.c) which is obviously correct, and which is obviously the plain old correct x of the privileged form. Unless, of course, there really is some magical term or expression that invalidates the obvious and elemen- tary algebra of the invariance demonstration. Or maybe you just whistle when you dont want basic algebra to hold true. Eleaticus !---?---!---?---!---?---!---?---!---?---!---?---!---?---!---? ---!---? ! Eleaticus Oren C. Webster ThnkTank@concentric.net ? ! Anything and everything that requires or encourages systematic ? ! examination of premises, logic, and conclusions ? !---?---!---?---!---?---!---?---!---?---!---?---!---?---!---? ---!---? === Subject: Re: Invariant Galilean Transformations (FAQ) On All Laws > Disclaimer: approval for *.answers is based on form, not content. > Opponents of the content should first actually find out what > it is, then think, then request/submit-to arbitration by the > appropriate neutral mathematics authorities. Flaming the hard- > working, selßess, *.answers moderators evidences ignorance > and despicable netiquette. > Archive-Name: physics-faq/criticism/galilean-invariance > Version: 0.04.03 > Posting-frequency: 15 days > Invariant Galilean Transformations (FAQ) On All Laws > (c) Eleaticus/Oren C. Webster > Thnktank@concentric.net [snip 1300 lines of trolled garbage] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Originally trolled across sci.physics sci.physics.relativity alt.physics sci.math sci.answers alt.answers news.answers Psychotic ineducable boring troll Eleaticus, Were there to be internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) that would automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t = t, x = x - vt, y = y, z = z. His refusal to accept that t must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to fields over space and time (electric and magnetic fields for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt = d/dt + v d/dx, d/dx = d/dx, d/dy = d/dy, d/dz = d/dz. This shows the necessity of introducing a new variable t, since partial differentiation with respect to t (constant x, y, z) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt = dt/dt d/dt + dx/dt d/dx + dy/dt d/dy + dz/dt d/dz, d/dx = dt/dx d/dt + dx/dx d/dx + dy/dx d/dy + dz/dx d/dz, d/dy = dt/dy d/dt + dx/dy d/dx + dy/dy d/dy + dz/dy d/dz, d/dz = dt/dz d/dt + dx/dz d/dx + dy/dz d/dy + dz/dz d/dz. The presence of the term involving d/dx in the expression for d/dt is indicative of the fact that x depends on t (x, y, z, being held constant), as can be seen from the fact that the coefficient of d/dx in the expression for d/dt is dx/dt. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt is indicative of t depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwells Equations under the Galilean Transformation. The first advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwells Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x = E_x, E_y = E_y - v B_z, E_z = E_z + v B_y, B_x = B_x, B_y = B_y, B_z = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x = E_x, E_y = E_y, E_z = E_z, B_x = B_x, B_y = B_y + v/c^2 E_z, B_z = B_z - v/c^2 E_y, rho = rho, J_x = J_x - v rho, J_y = J_y, J_z = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwells Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM field for the two cases are inconsistent with each other. The transformation law for the EM field which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM field which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwells equations are invariant under the Lorentz Transformation, with transformation laws: E_x = E_x, E_y = gamma (E_y - v B_z), E_z = gamma (E_z + v B_y), B_x = B_x, B_y = gamma (B_y + v/c^2 E_z), B_z = gamma (B_z - v/c^2 E_y), rho = gamma (rho - v/c^2 J_x), J_x = gamma (J_x - v rho), J_y = J_y, J_z = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arxiv.org/abs/gr-qc/0103044 http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation No aether http://fsweb.berry.edu/academic/mans/clane/ No Lorentz violation http://arXiv.org/abs/gr-qc/0409089 Spin-2 gravitons have problems (so does the proposal) http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect http://arxiv.org/abs/astro-ph/0403292 http://arXiv.org/abs/astro-ph/0310723 WMAP + Sloane Digital Sky Survey http://arxiv.org/abs/hep-ph/0404175 Dark matter candidates Carroll on what it all means. Special Relativity is physics on a topologically trivial Lorentzian manifold with a metric whose curvature tensor is zero. This is a perfectly diffeomorphism-invariant condition and does not require any particular coordinate choice. It is invariant under the full group of diffeomorphisms. The Poincare group is the group of *isometries* of the metric in special relativity. The Special Relativity metric is *non-dynamical* (unlike GR). It defines the coupling *constants* of your theory. If you change the metric in any nontrivial way you are changing your theory. An operation can only be called a symmetry of a special-relativistic (non-gravitational) theory if it preserves the metric, and therefore the symmetry of special-relativistic theories is the Poincare group only. General Relativity (gravitation) has a dynamic metric. NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf Longitudinal and transverse mass http://arxiv.org/abs/gr-qc/0306076.pdf http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: Invariant Galilean Transformations (FAQ) On All Laws > [snip 1300 lines of trolled garbage] > eleaticus, Oren Webster, is a despised and stooopid troll, Schwartz is a despised and stooopid troll too, so who cares? Androcles. === Subject: Re: Invariant Galilean Transformations (FAQ) On All Laws > [snip 1300 lines of trolled garbage] > eleaticus, Oren Webster, is a despised and stooopid troll, > Schwartz is a despised and stooopid troll too, so who cares? > Androcles. http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity Your ignorance, incompetence, and psychosis are not of interest to the world at large. Quite the contrary. You are not even an interesting laughingstock. http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: Invariant Galilean Transformations (FAQ) On All Laws >> [snip 1300 lines of trolled garbage] >> eleaticus, Oren Webster, is a despised and stooopid troll, >> Schwartz is a despised and stooopid troll too, so who cares? >> Androcles. [snip crap] Put this past your sphincter where you can read it. http://www.mazepath.com/uncleal/sunshine.jpg http://www.fourmilab.ch/etexts/einstein/specrel/www/ Androcles. Supersedes: === Subject: (SR) Lorentz t, x = Intervals Summary: The Lorentz transforms themselves are proof t and x cannot possibly be just coordinates. Examination of their derivation verifies their identity as intervals. Originator: faqserv@penguin-lust.mit.edu Disclaimer: approval for *.answers is based on form, not content. Opponents should first actually find out what the content is, then think, then request/submit-to arbitration by the appropriate neutral mathematics authorities. Flaming the hard- working, selßess, *.answers moderators evidences ignorance and atrocious netiquette. Version: 0.02.1 Archive-name: physics-faq/criticism/lorentz-intervals Posting-frequency: 15 days (SR) Lorentz t, x = Intervals (c) Eleaticus/Oren C. Webster Thnktank@concentric.net ------------------------------ === Subject: 1. Introduction with the obvious debunking of the use of Ôjust coordinates in any scientific formula. Defenders of the Special Relativity faith are especially fond of telling opponents of their space-time fairy tales that they do not know the difference between coordinates and magnitudes. That may often be so, but the fault lies ultimately with SR dogma. The Lorentz-Einstein transformations cannot possibly be Ôjust coordinates, which is the interpre- tation required to support the many sideshow carnival acts with which the SR faithful bedazzle the public, and establish their moral and intellectual superiority. If I get in my car and drive steadily for a few hours at 50 kilometers per hour, is 50t the distance I travel? Of course not. The last time my hours-counting Ôjust coord- inates clock was set to zero was when Zeno first reported one of his paradoxes to Parmenides. That was a long time ago, so my t is not useful for such purposes unless you also use my clock to established the starting time, perhaps t0, and use the formula 50(t-t0) to calculate the distance. In any case, my t is even then not Ôjust a coordinate because it always represents particular elapsed times that can be used in the (t-t0) form to calculate perfectly good time intervals (elapsed times). Alternatively, I could (re)set my clock to zero at the start of some meaningful time interval, in which case my t shows a scientifically perfect current and/or end time. In which case, the Lorentz-Einstein t=(t-vx/cc)/g is a function of an elapsed time interval (not Ôjust a coordinate) and a time interval (-vx/cc; the interval amount the t clock is being screwed up at time t) and thus cannot be Ôjust a coordinate since neither of the independent variables is such a Ôjust thing. {Their meaning is shown below, step-by-step.] If it takes me 50 minutes to cross the Interstate highway, was x/50 my velocity crossing it? Of course not. The origin of all my axes is at the very spot where Zeno first presented his first paradox to Parmenides. That makes my x equal a couple of thousands of miles, plus, and is not useful for such purposes unless you establish the starting x value, perhaps x0, and use the formula (x-x0)/50 to calculate my velocity. In any case, even then my x is not Ôjust a coordinate because it always repesents particular distance intervals that can always be used in the (x-x0) form for any and every scientific purose. Alternatively, I could move my x-axis origin to the starting (zero) point of some meaningful distance, in which case my x shows a scientifically perfect current and/or end distance. In which case, the Lorentz-Einstein x=(x-vt)/g is a function of a current/ending distance interval (not Ôjust a coordinate) and a distance interval (-vt; the interval amount the x axis is being screwed up at time t) and thus cannot be Ôjust a coordinate since neither of the independent variables is such a Ôjust thing. {Their meaning is shown below, step-by-step.] ------------------------------ === Subject: 2. Table of Contents 1. Introduction with the obvious debunking of the use of Ôjust coordinates in any scientific formula. 2. Table of Contents. 3. The Lorentz-Einstein transforms. 4. The Ôjust coordinates argument. 5. Single-system, little-purpose ambiguity. 6. Relating two coordinate measures/systems. 7. Distances and moving coordinate axes. 8. Time intervals. 9. Einsteins (1905) derivations. 10. A word about intervals. 11. Intervals versus the Twins Paradox. 12. Summary ------------------------------ === Subject: 3. The Lorentz-Einstein transforms Special Relativitys space-time circus is based on the Ôtransformation equations by which it is believed one can relate a nominally Ôstationary systems space and time coordinates to those of an inertially (not accelerating) moving other observer. That moving observers own physical body and coordinate system might have been identical in size to those of the stationary observer before the traveller began moving, but are Ôseen as very different by the stationary observer when the relative velocity of the two is great enough, a high percentage of the velocity of light. Concerning ourselves - as is customary - with just the spatial coordinate axis that lies parallel to the direction of motion, and with time, Einstein arrived at these formulas that relate the moving system measures or coordinates (x and t) to the stationary system coordinates (x and t): x = (x - vt)/sqrt(1-vv/cc) (Eq 1x) t = (t - vx/cc)/sqrt(1-vv/cc) (Eq 1t) The v is for the two systems relative velocity as seen by the stationary observer, and is positive if the dir- ection is toward higher values of x. By concensus, the moving system x-axis higher values also lie in that direction, and all axes parallel the other systems corresponding axis. We used vv to mean the square of v but might use v^2 for that purpose below. Similarly for c. Because it is believed that no physical object can reach or exceed c, the square-root term in both denominators is presumed always less than one, which means that the formulas say both x and t will tend to be greater than x and t, respectively. However, SRians call the x result Ôcontraction - which means shortening - and the t result Ôdilation - which means increasing. ------------------------------ === Subject: 4. The Ôjust coordinates argument The Ôjust coordinates argument is so patently ridiculous that even opponents have a hard time accepting just how simple and obvious its debunking can be, as shown in this section. However, further sections take a more arithmet- ical approach that youll maybe find more professorial. The Ôjust coordinates argument is that t is mot a duration, not a time interval; its just an arbitrary clock reading. But what if the moving system observer comes speeding by while you make your annual Ôspring forward or Ôfall back change? The formula says that the moving system clocks Ôjust coordinate reading can be calculated from yours: t = (t - vx/cc)/sqrt(1-vv/cc) (Eq 1t) Imagine the moving system obervers confusion if his clock changes its reading while hes looking at it! If his clock doesnt change when yours does, the formula is wrong; if it is truly a Ôjust coordinates formula. And then what happens if you realize you were a day early and put your clock back to what it had said previously? And suppose you are in NYC and your twin in LA and both are watching the moving observer. Youll both be using the same v because you are at rest wrt (with respect to) each other. Youre on Eastern Standard Time and your twin is on Pacific Standard Time maybe. You have three hours more on your clock than does your twin. On which Ôjust coordinate clock will the Lorentz transforms base the Ôjust coordinate time the moving system clock says? The formula applies to both of your t-times: t = (t - vx/cc)/sqrt(1-vv/cc) (Eq 1t) Sure, the idea that you can change someone elses clock with no connection of any kind is really ridiculous, but Eqs 1x and 1t arent MY equations. Are they yours? And we arent the ones to say x, t, x, and t are just coordinates. If the t formula is actually either an elapsed time formula, or the basis of a t/t ratio, then there is no implication that one clocks reading has anything to do with the others. It can only be rates of clock ticking, or how one time INTERVAL compares to the other that the formula is about. ------------------------------ === Subject: 5. Single-system, little-purpose ambiguity. Since were going to be comparing measurements on two coordinate systems in the next section, lets go to our supply cabinet and get our yard-stick (which we use to measure things in inches) and our meter-stick (which we use to measure things in centimeters). Here, Im getting mine. Oh! Oh! Theres an ant on mine, and he ... she ... sure is hanging on, right at the 3.5 inch mark of the yard- stick. Lets see if I can wave the stick around enough that shell let go. Nope. However, before I gave up I waved the stick and the ant Ôall over the place. Always, however, the ant was at the 3.5 mark on the yard-stick, and always 3.5 away from the end of the stick, however far and wide I have transported her. Neither of those 3.5 facts means very much. Of the two, the distance aspect meant almost nothing. So the distance was 3.5 from the end. So what? That length, distance, was not in use. And only maybe the ant might have been concerned with just what location, Ôjust coordinate, on the stick she was at. Just so with x and t. So, is the 3.5 reading just a coordinate? Or a distance/length? Its ambiguous in and of itself, and really makes no difference what you say until you try to make use of the number. Hey, my address is 5047 Newton Street. If you are looking for me and youre at 4120 Newton, it is helpful information, because it tells you which direction to go. Is that Ôjust coordinate? Where it really becomes useful, perhaps, is in telling you how far away I am. Thats not just a coordinate value, thats a distance, length, interval. However, it is subtracting 4120 from 5047 that tells you which direction and how far. It is only because both 5047 and 4120 are distances from the same point - ANY same point - that the result means anything. My x - my yardstick reading - is always a distance or length; it is impossible to be otherwise with an honest, competently designed yardstick. Whether or not its reading is of good use in some particular scientific formula depends on whether I put the zero end of the yardstick at some useful place. As in the introduction, we should either put it at the starting location/end, or use two readings from it: (x-x0). ------------------------------ === Subject: 6. Relating two coordinate measures/systems. Taking care to not damage our brave little ant, I place my yard-stick onto the table, zero end to the left, 36 end to the right. Now I place the Ôjust coordinate meter-stick on the table in the same orientation, in a random location, and find that the ants coordinate on the meter-stick is 51. The formula relating centimeters to inches is cm=i*2.54 but we want a formula similar to x=(x-vt)/sqrt(1-vv/cc). That would be c=i/.03937 approximately, but lets use x for the meter-stick reading, and x for the inch reading: x=x/.3937. 3.5/.3937 = 8.89 Wait a minute. Its not just science but definition that says c=i/.3937=8.89, so something is wrong. 8.89 is not 51. We already knew that 51 cm was just an arbitrary coordinate. Arbitrary not because that point isnt 51 cm from the zero end of the meter-stick, but because the zero point was in an arbitrary position. Lets put the meter-stick in a position where its zero point is at the yard-stick zero point. What is the centimeter coordinate now? Hey. 8.89, just like the formula says. The only way for a Ôtransform like x=x/g to work, whatever g might be, is for both coordinate systems to have their zero points aligned, in which case saying the two measures are not intervals is pure idiocy. Noe that with both zero points at the same position both x and x are great measures for scientific purposes, in any and every case where we were smart enough to put those zero points at a useful location. There is one extension of x=x/g that will let us use the meter-stick in arbitrary position. When the cm reading was 51, the zero point of the yard-stick read (51-8.89=) 42.11 cm. If we call that point x.z we get x = x.z + x/.3937. = 42.11 + 3.5/.3937 = 42.11 + 8.89 = 51. Obviously, in this formula x/.3937 is the distance from the x coordinate of the location where x=0. An interval. Just as obviously, the fact that we now have the correct formula for relating an x interval to an arbitrary x coordinate, does not mean that x is anything more than nonsense for use in any scientific formula. Unless we were smart enough to put the x zero point in a useful location, and use (x-x.z) in the scientific formula. (x-x.z) equals the useful, Ratio Scale value x/.3937. So, we have discovered a basic fact: a transformation formula like x=x/g works only if the two zero points of the coordinate systems coincide. That makes it non- sense to say the two coodinates are only coordinates and not intervals. Both must be values that represent distances from their respective zero points unless you take the proper steps to adjust for the discrepancy. Make sure you understand that although the inclusion of x.z made it possible to correctly calculate x, the result is nonsense when it comes to use of x for general length/distance purposes; it is x-x.z that is a useful number in such cases. It could be that were measuring a sheet of paper with one end at x=0 and the other at x=3.5; x=51 is nonsense as a centimeter measure of the paper. But, you say, the Lorentz transform contain a -vt term. ------------------------------ === Subject: 7. Distances and moving coordinate axes. We discovered x=x.z + x/g as the correct formula for relating one coordinate to another systems. But the Lorentz transform contains another term, -vt/sqrt(1-vv/cc). What is it? Lets start with our x=51 cm, x=3.5, x.z=42.11 example. Every minute, lets move the meter-stick one inch to our right. At minute 0, the cm reading was 51 cm. At minute 1, the cm reading is now 50 cm. At minute 2, the cm reading is now 49 cm. In this instance, v=1 inch/minute. And t was 0, 1, 2. What has happened is that we have made our x.z a lie, and increasingly so. -vt/.3937 is the change in x.z. x = (x.z - vt/.3937) + x/.3937. Obviously, vt/.3937 is not a coordinate; even most SRians wouldnt imagine it was. It is an interval, the distance over which the moving system has moved since t=0. And, of course, x/.3937 is the distance of our brave little ant from the point where x=0 and the centimeter reading is x.z-vt/.3937. Yes, every minute the meter- stick moves to the right and the meter-stick coordinate of the spot where x=0 gets less and less - and eventually negative. Make sure you understand that every minute the x coordinate, because of -vt/g, becomes a better measure of, say, the 3.5 paper we might be measuring with the yard-stick, given that 51 was too big a number and -vt is negative. That is, until the two origins coincide at x=x=0, and then it gets worse and worse. With -vt positive (because v<0) the situation is different. With 51 and -vt positive, x just gets worse and worse over time. Quite obviously, the fact that we now have the correct formula for relating an x interval to an arbitrary x coordinate even when the x axis is moving, does not mean that xis anything more than nonsense for use in any scientific formula. Unless we were smart enough to put the x zero point in a useful location, and use (x-x.z+vt/.3937) in the scientific formula. (x-x.z+vt/.3937) equals the useful, Ratio Scale value x/.3937. ------------------------------ === Subject: 8. Time intervals. Instead of using our sticks, lets get out two clocks. Mind you, were not going to deal with different clock rates here, just establish the same basics as for distance. Your clock says 9:00 Eastern Standard Time (EST) and we note that t=540 minutes when we put down the clock. Blindly, lets turn the setting knob of your twins Pacific Standard Time clock and put it down before us. According to what we see, ESTs 540 minutes (9:00) corre- sponds to PSTs 14:30; t=870. We know the formula relating PST to EST is t (pacific) = t (eastern) - 180 (minutes). Thus, it is not correct that the second clock can have an arbitrary setting, because 870 <> 540-180. We know that the two clocks are related by t = t/1 since both are using the same second, hour, etc units. But 870 (14:30 in minutes) is not 540/1-180, so once again we know something is wrong. However, t=t.z + t/1 works. EST midnight equals PST 0.0 (midnite) - 180, so t.z = -180, and t = -180 + 540/1 = 360. Since EST-180=PST, 9:00 EST is 6:00 PST = 360 minutes. We see thus that like distance measures/coordinates, time axis origins (zero points) must either be Ôlined up or adjusted for. So, the Lorentz/Einstein t=t/sqrt(1-vv/cc) must be the moving system elapsed time interval since the time axes were both at a common zero. There is no t.z adjustment: t = (t - vx/cc)/sqrt(1-vv/cc) (Eq 1t) Make sure you understand that in the clock case, if the EST is showing a good number for elapsed time since the travelling observer passed NYC, then the PST clock is silliness. t.z must be zero or must be taken out of time lapse calculations for the PST clock to be used intelligently, just as was true for x.z. What is lacking as yet for Lorentz t is the -vx/cc term that corresponds to the x formula -vt term. Break it up into two parts: v/c and x/c. v/c is a scaling factor that changes velocity from whatever kind of unit you are using over to fractions of c. x/c is distance divided by velocity, which is time. x/c is thus the time interval since the two time axes had a common zero point - which they have to have in the Lorentz transforms which do not have the t.z term we learned to use above. Thus, (-vx/cc)/sqrt(1-vv/cc) is the interval amount the moving system clock has been changed - since the common/ adjusted time - over and beyond the elapsed time interval represented by x/sqrt(1-vv/cc). We have discovered that the only way for t to be t/g is for t and t to have a common zero point, just as for x and x. It would be otherwise if the t formula contained an adjustment t.z under some name or other, but the necessity to include such a term correlates 100% with t numbers that arent directly usable. As for x and x, our knowledge of how to setup a proper formula relating t and t is of no use unless we use the knowledge in scientific formulas; (t-t.z+xv/gcc) gives us the only directly useful value: t/g. ------------------------------ === Subject: 9. Einsteins (1905) derivations. When we return to Einsteins derivations of the transform formulas with a well-focused eye, we find he was a wee bit confused - or at least self-contradictory. When he set up his (at first unknown) tau=moving system time formulas, he created three particular instances of tau. Tau.0 is the time at which light is emitted at the moving origin toward a mirror to the right that is moving at rest wrt that moving origin and at a constant distance from that origin. He lets the stationary time slot have the value t, a constant, the stationary system starting time. Tau.1 is the time at which the light is reßected. He lets the stationary time be t+x/(c-v); t is still a constant and x/(c-v) is the time interval since t. Tau.2 is the time at which the light gets (back) to the moving origin. The stationary time value is put as t + x/(c-v) + x/(c+v); t is still a constant and x/(c-v) + x/(c+v) is the time interval since t. On the thesis that the moving observer sees the time to the mirror as the same as the time back to the origin, he sets .5[ tau.0 + tau.2 ] = tau.1. Tau.0 completely drops out of the analysis and leaves no trace, and has no effect. Further, the t you see in tau.0, tau.1, and tau.2 also completely drops out with no trace and no effect, leaving us with exactly what youd get if you had explicilty said t is an interval and so is t. What doesnt drop out in the stationary time values is x/(c-v) and x/(c+v), the time interval it takes for light to get to the ßeeing mirror, and the time interval it takes for light to get back to the approaching origin. Thus, his resultant t formula is strictly based on time intervals in the stationary system. Time intervals since some starting time, yes, but time intervals. There is absolutely nothing in the derived formulas that depends on arbitrary coordinates like the constant t in the stationary time arguments. Lets look at the x dimension; it is x=x-vt [as x increases by vt, the effect over time is x=(x+vt)-vt)], which Einstein explicitly sets up as a constant stationary distance. He uses that x not just in the time interval parts of the stationary time arguments, but also in the x (distance) stationary system argument for the tau at the time light is reßected. x cant be the stationary system coordinate of the mirror at that time. That value is x+vt. x is explicitly an interval, distance. Thus, the whole tau derivation of the t formula is fully and explicitly based on x - a spatial length/distance/interval - and the two time interals x/(c-v) and x/(c+v). While were at it, if the starting t is not zero, his x=x-vt formula is complete nonsense also. Given that there was some L that was the mirror x-location and length when the light is emitted, if t was already, say, 500, then x=L-vt could have been a very negative length. ------------------------------ === Subject: 10. A word about intervals. There are intervals, and there are intervals. If we put our yard stick zero point at one end of a piece of paper and read off the coordinate at the other end of the paper, we have a good measure of the papers length, a Ratio Scale measure. [Absolute temperature scales are ratio scale.] If instead we put the one end of the paper at the one inch mark (or the zero end of the stick one inch Ôinto the length of the paper) we get measures that are one inch off the true, ratio scale length. The two messed up measures are still intervals, but they are Interval Scale measures. [Household temperature scales are interval scale, which is why your physics and chemistry professors wont let you use them without first converting to the ratio scale absolute temperatures.) t=t/g and x=x/g represent ratio scale measures, given that t and x were ratio scalae to start with. t=t.z+t/g and t=t/g-vx/gcc are both interval scale measures, even given a good ratio scale t and a good ratio scale x. x=x.z+x/g and x=x/g-vt/g are both interval scale measures, even given a good ratio scale x and a good ratio scale t. Look for the (SR) Lorentz t, x = degraded measures document soon at a newsgroup near you. ------------------------------ === Subject: 11. Intervals versus the Twins Paradox. t=(t-vx/cc)/g shows t being greater than t. The reason Special Relativity will not allow the use of its basic time equation in determining what SR has to say about the twins ages, is that t and x are supposedly just coordinates, and they say you have to take the coordinate pairs (t,x) and (x,t) into consideration in both the time and place the twins separation started and the time and place the twins reunited. Since t and x are actually both intervals, not just coordinates, the Ôexcuse is spurious, and is so even without use of the obvious (x_b-x_a) and (t_b-t_a) usages. However, SR is right to be embarrassed by their transformation formulas. Look for the (SR) Lorentz t, x = degraded measures document at a newsgroup near you. ------------------------------ === Subject: 12. Summary A. t=t/g and x=x/g can be almost Ôjust coordinates in the sense that the values obtained may not be of much use except in the most primal and useless way: how long and how far since/from the time/ place they were zero. Even here, however, the zero points within each of the two scale pairs (t,t) and (x.x) must have been lined up. If the zero points have been intelligently selected (such as at the starting point and time of a trip) they can be rationally used Ôas is in any valid sci- entific equation. B. Even the interval scale t=t.z - xv/gcc + t/g and x=x.z - vt/g + x/g are not Ôjust coordinates. They can be used to good effect by establishing the relevant starting times/points and using (t-t.z+xv/gcc) and (x-x.z+vt/g), as the situation may require. C. When you see vx/gcc or vt/g in use in any guise with non-zero values, you know the resultant t or x is a degraded, interval scale value. E-X: Anytime you do not see what amounts to t.z and xv/gcc in the time case, or x.z and vt/g in the distance case, you know that the t and/or x in use are intervals. Period. Y: Either set your clock to zero at the start of the relevant time interval, or use (t-t0), with both being readings on the same clock. Either move your x-axis origin to the starting end or point, or use (x-x0), with both being readings on the same axis. Z: In _(SR) Lorentz t, x = Degraded (Interval) Scales_ we see that t and x satisfy the mathematical tests for/of interval scales when -vt and -vx/cc are not zero; thus, they must be intervals. When -vt and -vx/cc are zero, t and x satisfy the much better mathematical definition of ratio scales, and are thus not just mere intervals, but (rescaled) good ones. Eleaticus !---?---!---?---!---?---!---?---!---?---!---?---!---?---!---? ---!---? ! Eleaticus Oren C. Webster ThnkTank@concentric.net ? ! Anything and everything that requires or encourages systematic ? ! examination of premises, logic, and conclusions ? !---?---!---?---!---?---!---?---!---?---!---?---!---?---!---? ---!---? === Subject: Re: (SR) Lorentz t, x = Intervals [snip lies] > (SR) Lorentz t, x = Intervals > (c) Eleaticus/Oren C. Webster > Thnktank@concentric.net [snip 700 lines of trolled garbage] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Originally trolled across sci.physics sci.physics.relativity alt.physics sci.math sci.answers alt.answers news.answers Psychotic ineducable boring troll Eleaticus, Were there to be internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) that would automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t = t, x = x - vt, y = y, z = z. His refusal to accept that t must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to fields over space and time (electric and magnetic fields for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt = d/dt + v d/dx, d/dx = d/dx, d/dy = d/dy, d/dz = d/dz. This shows the necessity of introducing a new variable t, since partial differentiation with respect to t (constant x, y, z) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt = dt/dt d/dt + dx/dt d/dx + dy/dt d/dy + dz/dt d/dz, d/dx = dt/dx d/dt + dx/dx d/dx + dy/dx d/dy + dz/dx d/dz, d/dy = dt/dy d/dt + dx/dy d/dx + dy/dy d/dy + dz/dy d/dz, d/dz = dt/dz d/dt + dx/dz d/dx + dy/dz d/dy + dz/dz d/dz. The presence of the term involving d/dx in the expression for d/dt is indicative of the fact that x depends on t (x, y, z, being held constant), as can be seen from the fact that the coefficient of d/dx in the expression for d/dt is dx/dt. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt is indicative of t depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwells Equations under the Galilean Transformation. The first advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwells Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x = E_x, E_y = E_y - v B_z, E_z = E_z + v B_y, B_x = B_x, B_y = B_y, B_z = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x = E_x, E_y = E_y, E_z = E_z, B_x = B_x, B_y = B_y + v/c^2 E_z, B_z = B_z - v/c^2 E_y, rho = rho, J_x = J_x - v rho, J_y = J_y, J_z = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwells Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM field for the two cases are inconsistent with each other. The transformation law for the EM field which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM field which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwells equations are invariant under the Lorentz Transformation, with transformation laws: E_x = E_x, E_y = gamma (E_y - v B_z), E_z = gamma (E_z + v B_y), B_x = B_x, B_y = gamma (B_y + v/c^2 E_z), B_z = gamma (B_z - v/c^2 E_y), rho = gamma (rho - v/c^2 J_x), J_x = gamma (J_x - v rho), J_y = J_y, J_z = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arxiv.org/abs/gr-qc/0103044 http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation No aether http://fsweb.berry.edu/academic/mans/clane/ No Lorentz violation http://arXiv.org/abs/gr-qc/0409089 Spin-2 gravitons have problems (so does the proposal) http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect http://arxiv.org/abs/astro-ph/0403292 http://arXiv.org/abs/astro-ph/0310723 WMAP + Sloane Digital Sky Survey http://arxiv.org/abs/hep-ph/0404175 Dark matter candidates Carroll on what it all means. Special Relativity is physics on a topologically trivial Lorentzian manifold with a metric whose curvature tensor is zero. This is a perfectly diffeomorphism-invariant condition and does not require any particular coordinate choice. It is invariant under the full group of diffeomorphisms. The Poincare group is the group of *isometries* of the metric in special relativity. The Special Relativity metric is *non-dynamical* (unlike GR). It defines the coupling *constants* of your theory. If you change the metric in any nontrivial way you are changing your theory. An operation can only be called a symmetry of a special-relativistic (non-gravitational) theory if it preserves the metric, and therefore the symmetry of special-relativistic theories is the Poincare group only. General Relativity (gravitation) has a dynamic metric. NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf Longitudinal and transverse mass http://arxiv.org/abs/gr-qc/0306076.pdf http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: About Ancle assAls response to: (SR) Lorentz t, x = Intervals > The transformation law for the differential operators under the > Galilean transformation is given by: > d/dt = d/dt + v d/dx, > d/dx = d/dx, > d/dy = d/dy, > d/dz = d/dz. > This shows the necessity of introducing a new variable t, since > partial differentiation with respect to t (constant x, y, z) is a > different operation to partial differentiation with respect to t > (constant x, y, z). The above transformation law is determined by the > Chain Rule: Actually, I am soOOO surprized you miss the necessity of introducing a new variable v since partial differentiation wrt v is a different operation to partial differentiation with respect to v. Hey, violating the rules of logic by asserting t=t when there is no t in the newtonian theoretic material you have such a problem with is one thing, but how about justifying the idiocy of not imposing the actual, factual, not-so-satisfactual (to SR) v=-v transform? Not to mention, justifying not differentiating wrt v in terms that don;t also apply to t. eleaticus === Subject: Re: About Ancle assAls response to: (SR) Lorentz t, x = Intervals >> The transformation law for the differential operators under the >> Galilean transformation is given by: >> d/dt = d/dt + v d/dx, >> d/dx = d/dx, >> d/dy = d/dy, >> d/dz = d/dz. >> This shows the necessity of introducing a new variable t, since >> partial differentiation with respect to t (constant x, y, z) is a >> different operation to partial differentiation with respect to t >> (constant x, y, z). The above transformation law is determined by >> the >> Chain Rule: > Actually, I am soOOO surprized you miss the necessity of introducing a > new > variable v since partial differentiation wrt v is a different > operation to > partial differentiation with respect to v. > Hey, violating the rules of logic by asserting t=t when there is no > t in > the newtonian theoretic material you have such a problem with is one > thing, > but how about justifying the idiocy of not imposing the actual, > factual, > not-so-satisfactual (to SR) v=-v transform? > Not to mention, justifying not differentiating wrt v in terms that > don;t > also apply to t. > eleaticus I think you are trying to teach an old dog new tricks. Even a street whore wouldnt trick with him, and she was desperate. Androcles. === Subject: Re: (SR) Lorentz t, x = Intervals sci.answers,alt.answers and news.answers pruned. Followups set exclusively to sci.physics.relativity. And this has probably been debunked somehwere before. But Im in a mood to vent at somebody; its been one of those weeks. :-) In sci.math, Eleaticus : > Disclaimer: approval for *.answers is based on form, not content. > Opponents should first actually find out what the content is, > then think, then request/submit-to arbitration by the > appropriate neutral mathematics authorities. Flaming the hard- > working, selßess, *.answers moderators evidences ignorance > and atrocious netiquette. > Version: 0.02.1 > Archive-name: physics-faq/criticism/lorentz-intervals > Posting-frequency: 15 days > > (SR) Lorentz t, x = Intervals > (c) Eleaticus/Oren C. Webster > Thnktank@concentric.net > ------------------------------ === > Subject: 1. Introduction with the obvious debunking > of the use of Ôjust coordinates in any > scientific formula. > Defenders of the Special Relativity faith are especially > fond of telling opponents of their space-time fairy tales > that they do not know the difference between coordinates > and magnitudes. > That may often be so, but the fault lies ultimately with > SR dogma. The Lorentz-Einstein transformations cannot > possibly be Ôjust coordinates, which is the interpre- > tation required to support the many sideshow carnival acts > with which the SR faithful bedazzle the public, and establish > their moral and intellectual superiority. > If I get in my car and drive steadily for a few hours at 50 > kilometers per hour, is 50t the distance I travel? Assuming t is in hours, you will be driving 166.6 * t microseconds distance. And yes, this is a weird way of putting it -- but because of the invariance of x^2 - c^2*t^2, perfectly correct as far as SR is concerned. But dont tell the speedometer manufacturers... :-) If you prefer, you can use units such as light-second for distance. The velocity can then be expressed as 1.666 light-microseconds per hour, and of course c = 1 in such units. However, there are some minor inconveniences -- this is, after all, the population which still clings to so-called Imperial Units. :-) One might have better luck in Europe. > Of course not. The last time my hours-counting Ôjust coord- > inates clock was set to zero was when Zeno first reported > one of his paradoxes to Parmenides. Well, if you want to move your origin, as opposed to the goalposts, fine...just be aware youre doing it. :-) > That was a long time ago, so my t is not useful for such > purposes unless you also use my clock to established the starting > time, perhaps t0, and use the formula 50(t-t0) to calculate the > distance. > In any case, my t is even then not Ôjust a coordinate because > it always represents particular elapsed times that can be > used in the (t-t0) form to calculate perfectly good time > intervals (elapsed times). > Alternatively, I could (re)set my clock to zero at the start > of some meaningful time interval, in which case my t shows a > scientifically perfect current and/or end time. > In which case, the Lorentz-Einstein t=(t-vx/cc)/g is a function > of an elapsed time interval (not Ôjust a coordinate) and a time > interval (-vx/cc; the interval amount the t clock is being > screwed up at time t) and thus cannot be Ôjust a coordinate > since neither of the independent variables is such a Ôjust thing. > {Their meaning is shown below, step-by-step.] An interesting point, but again, beware the shifting origin. [identical dist case snipped for brevity] > ------------------------------ === > Subject: 2. Table of Contents > 1. Introduction with the obvious debunking > of the use of Ôjust coordinates in any > scientific formula. > 2. Table of Contents. > 3. The Lorentz-Einstein transforms. > 4. The Ôjust coordinates argument. > 5. Single-system, little-purpose ambiguity. > 6. Relating two coordinate measures/systems. > 7. Distances and moving coordinate axes. > 8. Time intervals. > 9. Einsteins (1905) derivations. > 10. A word about intervals. > 11. Intervals versus the Twins Paradox. > 12. Summary > ------------------------------ Silly. Usually the TOC (a) goes at the top of the doc and (b) doesnt need an entire subject dedicated thereto. === > Subject: 3. The Lorentz-Einstein transforms > Special Relativitys space-time circus is based on > the Ôtransformation equations by which it is believed > one can relate a nominally Ôstationary systems space > and time coordinates to those of an inertially (not > accelerating) moving other observer. > That moving observers own physical body and coordinate > system might have been identical in size to those of the > stationary observer before the traveller began moving, > but are Ôseen as very different by the stationary observer > when the relative velocity of the two is great enough, a > high percentage of the velocity of light. Actually, its seen in all velocities -- though its hard to observe at standard highway speeds. A car travelling 30 km/s = 67.1 mph will have a shrinkage factor of about 5 * 10^-15. Since thats about the width of an atomic nucleus (per meter), theres a vanishingly small chance of it being observed directly -- but thats what SR predicts. > Concerning ourselves - as is customary - with just > the spatial coordinate axis that lies parallel to > the direction of motion, and with time, Einstein > arrived at these formulas that relate the moving > system measures or coordinates (x and t) to the > stationary system coordinates (x and t): > x = (x - vt)/sqrt(1-vv/cc) (Eq 1x) > t = (t - vx/cc)/sqrt(1-vv/cc) (Eq 1t) This equation assumes that both origins are coincident. Of course, you then go on a long-winded tirade about how the origins need to be coincident. So well schlog through here for awhile... :-) > The v is for the two systems relative velocity as seen > by the stationary observer, and is positive if the dir- > ection is toward higher values of x. By concensus, > the moving system x-axis higher values also lie in > that direction, and all axes parallel the other systems > corresponding axis. v = -v. To argue otherwise invites much silliness. > We used vv to mean the square of v but might use v^2 > for that purpose below. Similarly for c. > Because it is believed that no physical object can > reach or exceed c, the square-root term in both > denominators is presumed always less than one, which > means that the formulas say both x and t will tend to > be greater than x and t, respectively. However, > SRians call the x result Ôcontraction - which means > shortening - and the t result Ôdilation - which > means increasing. > ------------------------------ === > Subject: 4. The Ôjust coordinates argument > The Ôjust coordinates argument is so patently ridiculous > that even opponents have a hard time accepting just how > simple and obvious its debunking can be, as shown in this > section. However, further sections take a more arithmet- > ical approach that youll maybe find more professorial. > The Ôjust coordinates argument is that t is mot a > duration, not a time interval; its just an arbitrary > clock reading. But what if the moving system observer > comes speeding by while you make your annual Ôspring > forward or Ôfall back change? The formula says that > the moving system clocks Ôjust coordinate reading > can be calculated from yours: > t = (t - vx/cc)/sqrt(1-vv/cc) (Eq 1t) > Imagine the moving system obervers confusion if his > clock changes its reading while hes looking at it! Hence such artifices as UTC, which doesnt have time zones. It does have leap-second adjustments, however, which can cause minor confusion. > If his clock doesnt change when yours does, the formula > is wrong; if it is truly a Ôjust coordinates formula. > And then what happens if you realize you were a day > early and put your clock back to what it had said > previously? > And suppose you are in NYC and your twin in LA and > both are watching the moving observer. Youll both be > using the same v because you are at rest wrt (with > respect to) each other. Youre on Eastern Standard > Time and your twin is on Pacific Standard Time > maybe. You have three hours more on your clock than > does your twin. > On which Ôjust coordinate clock will the Lorentz > transforms base the Ôjust coordinate time the moving > system clock says? The formula applies to both of > your t-times: > t = (t - vx/cc)/sqrt(1-vv/cc) (Eq 1t) > Sure, the idea that you can change someone elses > clock with no connection of any kind is really > ridiculous, but Eqs 1x and 1t arent MY equations. > Are they yours? And we arent the ones to say x, t, > x, and t are just coordinates. > If the t formula is actually either an elapsed > time formula, or the basis of a t/t ratio, then > there is no implication that one clocks reading > has anything to do with the others. > It can only be rates of clock ticking, or how one > time INTERVAL compares to the other that the formula > is about. The origin shifts again -- hopefully predictably. > ------------------------------ === > Subject: 5. Single-system, little-purpose ambiguity. > Since were going to be comparing measurements on two > coordinate systems in the next section, lets go to > our supply cabinet and get our yard-stick (which we > use to measure things in inches) and our meter-stick > (which we use to measure things in centimeters). > Here, Im getting mine. Oh! Oh! > Theres an ant on mine, and he ... she ... sure is > hanging on, right at the 3.5 inch mark of the yard- > stick. > Lets see if I can wave the stick around enough that > shell let go. Nope. > However, before I gave up I waved the stick and the > ant Ôall over the place. > Always, however, the ant was at the 3.5 mark on the > yard-stick, and always 3.5 away from the end of the > stick, however far and wide I have transported her. You are now getting into rotational tensor territory, which is unfamiliar to me. > Neither of those 3.5 facts means very much. Of the > two, the distance aspect meant almost nothing. So > the distance was 3.5 from the end. So what? That > length, distance, was not in use. And only maybe > the ant might have been concerned with just what > location, Ôjust coordinate, on the stick she was > at. > Just so with x and t. > So, is the 3.5 reading just a coordinate? Or a > distance/length? Neither. Its a *vector*. Specifically, its a direction, within an established coordinate system, from the origin to a desired location. Since youve established *two* coordinate systems (C1: you, standing there waving the stick all over the place; C2: the stick, where 0 = the endpoint and the x-axis is the stick itself [the other two axes can be defined in a compatible but consistent fashion; e.g., z might be to the sticks left, and y might be through the stick going up]), you now get to relate them. Lucky you! Fortunately, tensors are available, although all over the place isnt exactly the easiest one to use, mathematically. > Its ambiguous in and of itself, > and really makes no difference what you say until > you try to make use of the number. > Hey, my address is 5047 Newton Street. If you > are looking for me and youre at 4120 Newton, it > is helpful information, because it tells you which > direction to go. Is that Ôjust coordinate? Actually, it does not. For starters, there are multiple Newton Streets. Is your city the same as mine? Even if it is, there are some issues relating to the direction of travel; the best one can do here is start at 4120 (if one can see the numbers!), travel a few meters, then establish whether one is going up (4130) or down (4110). And heaven help you if youre on a city boundary; many streets do that, which makes for possibly different numbering schemes depending on which side of the street one is on. > Where it really becomes useful, perhaps, is in > telling you how far away I am. Thats not just > a coordinate value, thats a distance, length, > interval. Thats another subproblem, as well. > However, it is subtracting 4120 from 5047 that > tells you which direction and how far. Uh, no it doesnt. Ive neglected to mention that the street can curve, as well. However, thats more GR than SR territory, but if youre going to wave your stick around GR is probably the way to go, as it is a more general theory for, among other things, rotations and gravitational stresses. > It is only > because both 5047 and 4120 are distances from the > same point - ANY same point - that the result means > anything. Well, one could conceivably use the house numbers as a (rather crude) metric for one coordinate-space, with the ground (actually, the oblate spheroid) as being another coordinate-space, relating the two with a (rather complicated) tensor patch -- and of course that patch would only be valid for the length of the street (if the street crosses city boundaries it may change names, as well -- yet another complication). I dont know how companies such as Etak (are they in existence anymore?) and Yahoo! do it, at this point. GPS isnt all that useful unless one knows where one needs to be in both coordinate systems -- basically, Im at 32 degrees 49 minutes north, 96 degrees 43 minutes west. Where am I? Probably where Im not supposed to be, as that coordinate point is associated with White Rock Lake, Texas (in the middle of Dallas), and with all of the terrorist activity they might think Im doing something naughty in there. (Fortunately, Im nowhere near Dallas anyway, so if the FBI is even bothering to read this, Im (a) nowhere near there, and (b) I wouldnt want to anyway; Ive more interesting things to do -- like posting rebuttals on Usenet -- than trying to poison the water/plug up the piping/convert water into wine/etc.) Good luck figuring that out from Yahoo! Maps, though -- the system may use that coordinate pair internally (I cant say), but the user is expected to use the address/city form. If one only specifies the city, one apparently gets the city marker -- usually a small bronze marker somewhere downtown. However, GPS is very good at giving the coordinates degrees N/S degrees E/W, to a precision of about 100 m (in civilian use), or, put another way, about 3.23/cos(latitude) arc-seconds longitude, 1.62 arc-seconds latitude. (hairy ball and orange peel get in the way here. One interesting illustration of the mapping problem can be had at http://octopus.gma.org/surfing/imaging/mapproj.html which uses a 2-liter soda bottle (cut in a certain fashion), a marking pen, a ßashlight, and some tracing paper. But this is a bit of a digression.) > My x - my yardstick reading - is always a distance > or length; it is impossible to be otherwise with > an honest, competently designed yardstick. Depends on whether it breaks or not as youre waving it around. Oops. (Youre probably making the poor ant sticksick, as well...) > Whether or not its reading is of good use in some > particular scientific formula depends on whether > I put the zero end of the yardstick at some useful > place. As in the introduction, we should either > put it at the starting location/end, or use two > readings from it: (x-x0). And I thought *I* was long-winded about reaching a point. :-) > ------------------------------ === > Subject: 6. Relating two coordinate measures/systems. > Taking care to not damage our brave little ant, I place > my yard-stick onto the table, zero end to the left, 36 > end to the right. Left and right of you, presumably. Be very careful here, though. Take, for example, an ordinary Earthglobe -- available presumably at any good science shop. Rotate it west-to-east (the real Earth rotates west-to-east, as it turns out). Now stare at it from the North Pole. Which way is it rotating? Now stare at it from the *South* Pole. Does it rotate the same way? In your example, of course, have you and a friend observe the stick on a (smallish) table. You have positioned the stick in front of you as specified. Your friend is staring at you from the other side of the table, behind the stick. Does your friend observe the sticks ticks increasing left to right? A second friend is to your left, observing the stick. Which way is it pointing to him or her? A third friend is to your right. How about him or her? At this point its probably best to put away the stick and shufße a deck of cards for bridge -- or maybe have a round of golf. And of course you did cover the sugar bowl, right? I think the ants wandered off that crazy stick by now and into said bowl. Oh, I think shes [*] disappeared through a crack in the wall back to her queens nest... :-) Ill leave it to the interested reader on which way the stick is pointing relative to our intrepid six-legged explorer. > Now I place the Ôjust coordinate meter-stick on the table > in the same orientation, in a random location, and find > that the ants coordinate on the meter-stick is 51. Youve moved the origin again. Naughty. > The formula relating centimeters to inches is cm=i*2.54 > but we want a formula similar to x=(x-vt)/sqrt(1-vv/cc). > That would be c=i/.03937 approximately, but lets use x > for the meter-stick reading, and x for the inch reading: > x=x/.3937. > 3.5/.3937 = 8.89 > > Wait a minute. Its not just science but definition > that says c=i/.3937=8.89, so something is wrong. 8.89 > is not 51. > We already knew that 51 cm was just an arbitrary coordinate. > Arbitrary not because that point isnt 51 cm from the zero > end of the meter-stick, but because the zero point was in an > arbitrary position. > Lets put the meter-stick in a position where its > zero point is at the yard-stick zero point. > What is the centimeter coordinate now? Hey. 8.89, > just like the formula says. > The only way for a Ôtransform like x=x/g to work, > whatever g might be, is for both coordinate systems > to have their zero points aligned, in which case > saying the two measures are not intervals is pure > idiocy. > Noe that with both zero points at the same position > both x and x are great measures for scientific > purposes, in any and every case where we were smart > enough to put those zero points at a useful location. Actually, theyre not all that great. The meter is defined as the interval that light travels in vacuo during 1/299792458th of a second. Good luck verifying that with a simple meter stick; the marks might be as much as a tenth of a millimeter wide. (Even the old KR-86 meter standard -- 1,650,763.73 vacuum wavelengths -- had trouble measuring the speed of light. Hence, the change in 1983. http://www.mel.nist.gov/div821/museum/timeline.htm) > There is one extension of x=x/g that will let us > use the meter-stick in arbitrary position. > When the cm reading was 51, the zero point of the > yard-stick read (51-8.89=) 42.11 cm. If we call that > point x.z we get > x = x.z + x/.3937. > = 42.11 + 3.5/.3937 > = 42.11 + 8.89 > = 51. > Obviously, in this formula x/.3937 is the distance > from the x coordinate of the location where x=0. > An interval. > Just as obviously, the fact that we now have the > correct formula for relating an x interval to an > arbitrary x coordinate, does not mean that x > is anything more than nonsense for use in any > scientific formula. > Unless we were smart enough to put the x zero > point in a useful location, and use (x-x.z) in > the scientific formula. (x-x.z) equals the useful, > Ratio Scale value x/.3937. > So, we have discovered a basic fact: a transformation > formula like x=x/g works only if the two zero points > of the coordinate systems coincide. That makes it non- > sense to say the two coodinates are only coordinates > and not intervals. Both must be values that represent > distances from their respective zero points unless you > take the proper steps to adjust for the discrepancy. > Make sure you understand that although the inclusion > of x.z made it possible to correctly calculate x, > the result is nonsense when it comes to use of x > for general length/distance purposes; it is x-x.z > that is a useful number in such cases. It could be > that were measuring a sheet of paper with one end > at x=0 and the other at x=3.5; x=51 is nonsense as > a centimeter measure of the paper. > But, you say, the Lorentz transform contain a -vt term. Ill refer you to some of my earlier posts -- Id have to find them myself -- as to why there are two v-terms in the standard Lorentz. Its not a difficult calculation, and both are required because of the hypothesis that lightspeed is constant for all observers, no matter what source and destination are doing. Brießy put, try modeling the speed of a lightßash in (x, t) space using various quasi-tensors in a 2-D space. *** Galilean: x = (x - vt) t = t Modified Galilean: x = (x - vt) t = (t - vx/c^2) Misconstrued Lorentz: x = (x - vt) / sqrt(1-v^2/c^2) t = t / sqrt(1-v^2/c^2) Correct Lorentz: x = (x - vt) / sqrt(1-v^2/c^2) t = (t - vx/c^2) / sqrt(1-v^2/c^2) *** The easiest method is to substitute x = ct in each of these tensors (modeling a light ßash at the double-origin) and then see how x and t relate. For example, with the Galilean, one gets: x = (ct - vt) = (c-v)t = (c-v)t therefore the predicted velocity of light is (c-v). The Modified Galilean gets trickier: x = (c-v)t t = (t - vt/c) = (1 - v/c)t t = t/(1-v/c) x = (c-v)t/(1-v/c) = ct It turns out the Modified Galiliean and Correct Lorentz predict the correct result with respect to light. A second test is to hypothesize an object moving in the (x,t) space such that x = vt, and see what it does. A third test involves computing x,t with respect to x, t using the tensor with vs sign reversed. After all, if A is moving +v with respect to B, B has to be moving -v with respect to A, right? The Modified Galilean gets: x = (x + vt) = (x - vt) + v(t - vx/c^2) = x - vt + vt - vx/c^2 = x(1 - v^2/c^2) Oops. Ill leave verification of the others to the interested reader. This is of course a purely mathematical exercise only; the real verification of SR and GR are with experiments such as the MMX, Hafele/Keating, NST-2, and Gravity Probe B -- and a whole slew of others. > ------------------------------ === > Subject: 7. Distances and moving coordinate axes. > We discovered x=x.z + x/g as the correct formula > for relating one coordinate to another systems. Your nomenclature is atrocious. A slightly more conventional form might have x = x_0 + K(x - x_0) where K is the interval conversion factor. (And this typesets nicely in LaTeX, too! :-) ) If you really must use a divisor, then try x = x_0 + (x - x_0)/k The main problem with Ôg is that it is conventionally used to represent 9.805 m/s/s. The main problem with Ôx.z is that, from an algebraic standpoint, its either a dot product or something equally strange-looking. (In C++ or Java its a structure field accessor, making it even weirder for those of us with a programming language background.) > But the Lorentz transform contains another term, > -vt/sqrt(1-vv/cc). What is it? > Lets start with our x=51 cm, x=3.5, x.z=42.11 example. > Every minute, lets move the meter-stick one inch to our > right. > At minute 0, the cm reading was 51 cm. > At minute 1, the cm reading is now 50 cm. > At minute 2, the cm reading is now 49 cm. > In this instance, v=1 inch/minute. And t was 0, 1, 2. > What has happened is that we have made our x.z a lie, > and increasingly so. -vt/.3937 is the change in x.z. > x = (x.z - vt/.3937) + x/.3937. > Obviously, vt/.3937 is not a coordinate; even most SRians > wouldnt imagine it was. It is an interval, the distance > over which the moving system has moved since t=0. > And, of course, x/.3937 is the distance of our brave > little ant from the point where x=0 and the centimeter > reading is x.z-vt/.3937. Yes, every minute the meter- > stick moves to the right and the meter-stick coordinate > of the spot where x=0 gets less and less - and eventually > negative. > Make sure you understand that every minute the x > coordinate, because of -vt/g, becomes a better measure > of, say, the 3.5 paper we might be measuring with > the yard-stick, given that 51 was too big a number and > -vt is negative. That is, until the two origins coincide > at x=x=0, and then it gets worse and worse. > With -vt positive (because v<0) the situation is different. > With 51 and -vt positive, x just gets worse and worse > over time. > Quite obviously, the fact that we now have the > correct formula for relating an x interval to an > arbitrary x coordinate even when the x axis is > moving, does not mean that xis anything more than > nonsense for use in any scientific formula. > Unless we were smart enough to put the x zero point > in a useful location, and use (x-x.z+vt/.3937) in > the scientific formula. (x-x.z+vt/.3937) equals the > useful, Ratio Scale value x/.3937. > ------------------------------ === > Subject: 8. Time intervals. > Instead of using our sticks, lets get out two clocks. > Mind you, were not going to deal with different clock > rates here, just establish the same basics as for distance. > Your clock says 9:00 Eastern Standard Time (EST) and we > note that t=540 minutes when we put down the clock. > Blindly, lets turn the setting knob of your twins Pacific > Standard Time clock and put it down before us. > According to what we see, ESTs 540 minutes (9:00) corre- > sponds to PSTs 14:30; t=870. > We know the formula relating PST to EST is t (pacific) >= t (eastern) - 180 (minutes). Thus, it is not correct > that the second clock can have an arbitrary setting, > because 870 <> 540-180. > We know that the two clocks are related by t = t/1 since > both are using the same second, hour, etc units. But 870 > (14:30 in minutes) is not 540/1-180, so once again we know > something is wrong. > However, t=t.z + t/1 works. EST midnight equals PST 0.0 > (midnite) - 180, so t.z = -180, and > t = -180 + 540/1 = 360. > Since EST-180=PST, 9:00 EST is 6:00 PST = 360 minutes. > We see thus that like distance measures/coordinates, time > axis origins (zero points) must either be Ôlined up or > adjusted for. > So, the Lorentz/Einstein t=t/sqrt(1-vv/cc) must be the moving > system elapsed time interval since the time axes were both at > a common zero. There is no t.z adjustment: > t = (t - vx/cc)/sqrt(1-vv/cc) (Eq 1t) > Make sure you understand that in the clock case, if the > EST is showing a good number for elapsed time since the > travelling observer passed NYC, then the PST clock is > silliness. t.z must be zero or must be taken out of > time lapse calculations for the PST clock to be used > intelligently, just as was true for x.z. > What is lacking as yet for Lorentz t is the -vx/cc term that > corresponds to the x formula -vt term. > Break it up into two parts: v/c and x/c. > v/c is a scaling factor that changes velocity from whatever > kind of unit you are using over to fractions of c. > x/c is distance divided by velocity, which is time. x/c > is thus the time interval since the two time axes > had a common zero point - which they have to have in the > Lorentz transforms which do not have the t.z term we > learned to use above. > Thus, (-vx/cc)/sqrt(1-vv/cc) is the interval amount the > moving system clock has been changed - since the common/ > adjusted time - over and beyond the elapsed time interval > represented by x/sqrt(1-vv/cc). > We have discovered that the only way for t to be t/g > is for t and t to have a common zero point, just as > for x and x. It would be otherwise if the t formula > contained an adjustment t.z under some name or other, > but the necessity to include such a term correlates > 100% with t numbers that arent directly usable. > As for x and x, our knowledge of how to setup a proper > formula relating t and t is of no use unless we use > the knowledge in scientific formulas; (t-t.z+xv/gcc) > gives us the only directly useful value: t/g. Well, youve spent how many words beating about the obvious? And I thought I was bad... :-) [rest snipped -- its more of the same.] People, make sure your origins are compatible! :-) [*] worker and soldier ants are all female. -- #191, ewill3@earthlink.net Its still legal to go .sigless. === Subject: 1/x + x = y Solve for x: (1/x) + x = y The problem came up earlier this year when I was doing an abstract algebra problem involving this equation in a completely incorrect manner. I attempted to solve for x, found I couldnt, asked a friend, he found he couldnt, and we collectively beat our heads against the wall. Of course, show your work. :) Best, Will === Subject: Re: 1/x + x = y ETAtAhRf2bgs40y/TZZXURyH8caA5rEs+AIVAKf4ngN0AfvmYKbahP5qtxX/ dxU9 Uh, x^2 - xy + 1 = 0, with y as a parameter to be used in the Quadratic Formula? --OL === Subject: Re: 1/x + x = y Will Oram a .8ecrit : > Solve for x: > (1/x) + x = y > The problem came up earlier this year when I was doing an abstract algebra > problem involving this equation in a completely incorrect manner. I > attempted to solve for x, found I couldnt, asked a friend, he found he > couldnt, and we collectively beat our heads against the wall. > Of course, show your work. :) Show yours :-) Did you try multiplying by x both sides? Have you heard of quadratics (second-degree equations)? > Best, > Will === Subject: Re: 1/x + x = y > Will Oram a .8ecrit : >> Solve for x: >> (1/x) + x = y >> The problem came up earlier this year when I was doing an abstract algebra >> problem involving this equation in a completely incorrect manner. I >> attempted to solve for x, found I couldnt, asked a friend, he found he >> couldnt, and we collectively beat our heads against the wall. >> Of course, show your work. :) > Show yours :-) Did you try multiplying by x both sides? Have you heard > of quadratics (second-degree equations)? Yes, of course. Now that Im reading the solution people posted here, Im slapping my forehead. I did not actually stop to consider the QuadFormula; I struggled using only algebraic manipulation. To all responders of this thread: Come now, I am a maths major in uni. I struggled with it for 10 minutes with a friend (also a maths major) and failed to solve for x. Before anyone laughs at me for something so Ôobvious, dont forget that youve probably had a Ôduh mathematical moment yourself. Will === Subject: Re: 1/x + x = y >Solve for x: >(1/x) + x = y >The problem came up earlier this year when I was doing an abstract algebra >problem involving this equation in a completely incorrect manner. I >attempted to solve for x, found I couldnt, asked a friend, he found he >couldnt, and we collectively beat our heads against the wall. >Of course, show your work. :) (1/x) + x = (1/x) + (x^2/x) = (1+(x^2))/x. (1 + (x^2))/x = y 1 + (x^2) = yx x^2 - yx + 1 = 0 a = 1, b = -1, c = 1... in (-b +/- sqrt(b^2-4ac))/2a. John Savard http://home.ecn.ab.ca/~jsavard/index.html === Subject: Re: 1/x + x = y > Solve for x: > (1/x) + x = y > The problem came up earlier this year when I was doing an abstract algebra > problem involving this equation in a completely incorrect manner. I > attempted to solve for x, found I couldnt, asked a friend, he found he > couldnt, and we collectively beat our heads against the wall. hint: reduce to solving a quadratic equation. Bob Kolker === Subject: Re: 1/x + x = y > Solve for x: > (1/x) + x = y Hint: (1/x) + x = Y <=> 1 + x^2 = yx <=> x^2 - yx + 1 = 0. Jose Carlos Santos === Subject: Re: 1/x + x = y > Solve for x: > (1/x) + x = y (1+x^2)/x = y x^2 + 1 = yx x^2 - yx + 1 = 0 Use the Quadratic Formula. x = (y +- sqrt(y^2-4))/2 x = (1/2)(y +- sqrt(y^2-4)) === Subject: Re: Schrodingers equation project posting-account=VrpLFAwAAACa6GkV_jrhgeb1Ocd9vzzh Prove that the Schroedingers equation for n bodies is invariant with respect to the transformation: m -> z m, for all masses involved h -> z h p -> z p, for all momenta involved H -> z H, for the Hamiltonian U -> z U, for all other energies involved, such as potentials. x -> x psi -> psi. Prove that the same psi that is the solution to any of the equations obtained after the transformation for z > 0, is the solution to them all. Discuss the case z = 10 to the -1000000000 power and the case z = 0 and the case z = -1. Explain the difference between them. Discuss the objectivity of any value assigned to Plancks constant, h. === Subject: Analysis from Rudin 2. Consider the linear homogeneous differential equation u(x) + p(x)u(x) + q(x)u(x) = 0 where p(x) and q(x) are continuous functions on an interval (a, b). Suppose that u_1(x) and u_2(x) are solutions of this equation on (a, b). Define the Wronskian by W(x) = u_1(x)u_2(x) - u_1(x)u_2(x) (a) Suppose that u1(x) and u2(x) are dependent. Show that W(x) = 0 for all x in (a, b). This was not bad. Here is what I got: u_1(x) and u_2(x) dependent--> there exists c_1 and c_2 not both 0 (wolog c_1 /= 0) s/t c_1*u_1(x) + c_2*u_2(x) =0 --> u_1(x) =( -c_2/ c_1)*u_2(x) -->u_1(x) =( -c_2/ c_1)*u_2(x) W(x) = u_1(x)u_2(x) - u_1(x)u_2(x) = (-c_2/c_1)*u_2(x)*u_2(x) - (-c_2/c_1)*u_2(x)*u_2(x) = (-c_2/c_1)*u_2(x)*u_2(x) + (c_2/c_1)*u_2(x)u_2(x) = 0 (b) Suppose that W(x_0) = 0 for some x_0 in (a, b). Show that u_1(x) and u_2(x) are dependent. I am not clear why W(x_0) = 0 for some x_0 in (a, b) is enough for u_1(x) and u_2(x) to be dependent. Can someone please give me a brief lecture on this? === Subject: Re: Analysis from Rudin > (b) Suppose that W(x_0) = 0 for some x_0 in (a, b). Show that u_1(x) and > u_2(x) are dependent. > I am not clear why W(x_0) = 0 for some x_0 in (a, b) is enough for u_1(x) > and u_2(x) to be dependent. > Can someone please give me a brief lecture on this? For two functions in general, it is not enough. BUT for two solutions of your differential equation, it is. See if your Wronskian itself satisfies something. Show that if W(x_0)=0 for SOME x_0, then W(x)=0 for ALL x. === Subject: Re: Analysis from Rudin > (b) Suppose that W(x_0) = 0 for some x_0 in (a, b). Show that u_1(x) and > u_2(x) are dependent. > I am not clear why W(x_0) = 0 for some x_0 in (a, b) is enough for u_1(x) > and u_2(x) to be dependent. > Can someone please give me a brief lecture on this? The system: r*u_1(x_0) + s*u_2(x_0) = 0 t*u_1(x_0) + u*u_2(x_0) = 0 has a solution with (r_0, s_0, t_0, u_0) <> (0,0,0,0) (because (0,0,0,0) is already a solution, and the determinant of the system is 0), whence: t = r_0*u_1 + s_0*u_2 is a solution of the equation with t(x_0) = 0 and t(x_0) = 0. is unique, and then you can conclude: t = 0, and u_1 and u_2 are linearly dependent. -- Julien Santini === Subject: More on groups of order 16 posting-account=jcZk7AwAAADXpPEyHtVyWC264SxtppRB I am still having some trouble with 1 of the 14 groups of order 16. It is the one with 2 generators G = Someone said this is (Z_2 x Z_2) x| Z_4, but I have not been able to verify this, and wonder if anyone could help. I have done the central product Z_4 o D_4 which has 3 generators and x^2 = z^2, where Z_4 = , D_4 = with yxy^-1 = x^-1. The above group is called G(2,2) sometimes, and and arent normal. I thought perhaps that the normal subgroup was (1,x^2,y^2,x^2y^2), but have not been able to show this either. Any help would be welcome. Van === Subject: Re: More on groups of order 16 > I am still having some trouble with 1 of the 14 groups of order 16. > It is the one with 2 generators G = xy^3 = yx^3 Someone said this is (Z_2 x Z_2) x| Z_4, but I have not been able to > verify this, and wonder if anyone could help. > I have done the central product Z_4 o D_4 which has 3 generators and > x^2 = z^2, where Z_4 = , D_4 = with yxy^-1 = x^-1. > The above group is called G(2,2) sometimes, and and arent > normal. > I thought perhaps that the normal subgroup was (1,x^2,y^2,x^2y^2), but > have not been able to show this either. > Any help would be welcome. Thinking about this some more, I came up with a more direct approach. Since |G| = 16, || = || = 4 and ^ = 1, we have that G = , i.e., every element of G can be expressed as a power of x times a power of y, in that order. So lets see if we can find a way to multiply any two such elements, (x^k y^l)(x^m y^n), using the given presentation. What we need is a way to Ôpull x^m through y^l, or alternatively to Ôpush y^l through x^m. One obvious way to do this is to see if we can determine the conjugation action of any power of y on any power of x, and of course we can (if not, the group wouldnt have order 16). Since xyxy = 1 then yxy^-1 = x^3 y^2, and since xy^3 = yx^3 then y x^3 y^-1 = xy^2, so y^2 x y^-2 = y (x^3 y^2) y^-1 = xy^2 y^2 = x, so y^2 commutes with x and thus y^3 acts the same way on x that y does. Also, y x^2 y^-1 = (yxy^-1)^2 = (x^3 y^2)^2 = x^2 (since y^2 commutes with x), so y commutes with x^2, so y and y^3 act the same way on x^3 that they do on x. Now that we know how to multiply any two elements in G = , its straightforward to write down all the conjugacy classes and cyclic subgroups, determine the complete subgroup structure, and see that G is in fact (Z_2 x Z_2) x| Z_4. -- Jim Heckman === Subject: Re: More on groups of order 16 <10sdfcrtmei0125@corp.supernews.com> posting-account=jcZk7AwAAADXpPEyHtVyWC264SxtppRB > I am still having some trouble with 1 of the 14 groups of order 16. > It is the one with 2 generators G = xy^3 = yx^3 Someone said this is (Z_2 x Z_2) x| Z_4, but I have not been able to > verify this, and wonder if anyone could help. > The above group is called G(2,2) sometimes, and and arent > normal. > I thought perhaps that the normal subgroup was (1,x^2,y^2,x^2y^2), but > have not been able to show this either. > Any help would be welcome. > Thinking about this some more, I came up with a more direct > approach. Since |G| = 16, || = || = 4 and ^ = 1, > we have that G = , i.e., every element of G can be > expressed as a power of x times a power of y, in that order. So > lets see if we can find a way to multiply any two such > elements, (x^k y^l)(x^m y^n), using the given presentation. What > we need is a way to Ôpull x^m through y^l, or alternatively to > Ôpush y^l through x^m. One obvious way to do this is to see if > we can determine the conjugation action of any power of y on any > power of x, and of course we can (if not, the group wouldnt > have order 16). Since xyxy = 1 then yxy^-1 = x^3 y^2, and since > xy^3 = yx^3 then y x^3 y^-1 = xy^2, so y^2 x y^-2 = > y (x^3 y^2) y^-1 = xy^2 y^2 = x, so y^2 commutes with x and thus > y^3 acts the same way on x that y does. Also, y x^2 y^-1 = > (yxy^-1)^2 = (x^3 y^2)^2 = x^2 (since y^2 commutes with x), so y > commutes with x^2, so y and y^3 act the same way on x^3 that > they do on x. > Now that we know how to multiply any two elements in G = , > its straightforward to write down all the conjugacy classes and > cyclic subgroups, determine the complete subgroup structure, and > see that G is in fact (Z_2 x Z_2) x| Z_4. > -- > Jim Heckman Jim, I am going thru this now, but what do you mean by ^ = 1? { y^i x^m y^(-i) = ?} I will look at this too, but is {y^i x^m y^(-i) | i,m in Z_4} what you mean by ^ ? And how can you say this is 1? Van === Subject: Re: More on groups of order 16 > I am still having some trouble with 1 of the 14 groups of order 16. > It is the one with 2 generators G = xy^3 = yx^3 Thinking about this some more, I came up with a more direct > approach. Since |G| = 16, || = || = 4 and ^ = 1, > we have that G = , i.e., every element of G can be > expressed as a power of x times a power of y, in that order. So > lets see if we can find a way to multiply any two such > elements, (x^k y^l)(x^m y^n), using the given presentation. What > we need is a way to Ôpull x^m through y^l, or alternatively to > Ôpush y^l through x^m. One obvious way to do this is to see if > we can determine the conjugation action of any power of y on any > power of x, and of course we can (if not, the group wouldnt > have order 16). Since xyxy = 1 then yxy^-1 = x^3 y^2, and since > xy^3 = yx^3 then y x^3 y^-1 = xy^2, so y^2 x y^-2 = > y (x^3 y^2) y^-1 = xy^2 y^2 = x, so y^2 commutes with x and thus > y^3 acts the same way on x that y does. Also, y x^2 y^-1 = > (yxy^-1)^2 = (x^3 y^2)^2 = x^2 (since y^2 commutes with x), so y > commutes with x^2, so y and y^3 act the same way on x^3 that > they do on x. > Now that we know how to multiply any two elements in G = , > its straightforward to write down all the conjugacy classes and > cyclic subgroups, determine the complete subgroup structure, and > see that G is in fact (Z_2 x Z_2) x| Z_4. > Jim, I am going thru this now, but what do you mean by ^ = 1? / or intersection What does x| mean? x = 1 no x = y no x = y^2 gives x^2 = 1 x = y^3 gives x = y^-1 x^2 = 1 no x^2 = y gives y^2 = 1 x^2 = y^2 hm x^2 = y^3 gives 1 = x^4 = y^6 = y^2 x^3 = 1 no x^3 = y gives x^-1 = y x^3 = y^2 gives x^2 = x^6 = y^4 = 1 x^3 = y^3 gives x = y > { y^i x^m y^(-i) = ?} I will look at this too, but is > {y^i x^m y^(-i) | i,m in Z_4} what you mean by ^ ? > And how can you say this is 1? > Van === Subject: Re: More on groups of order 16 <10sdfcrtmei0125@corp.supernews.com> posting-account=jcZk7AwAAADXpPEyHtVyWC264SxtppRB I am still having some trouble with 1 of the 14 groups of order 16. > It is the one with 2 generators G = xy^3 = yx^3 > Thinking about this some more, I came up with a more direct > approach. Since |G| = 16, || = || = 4 and ^ = 1, > we have that G = , i.e., every element of G can be > expressed as a power of x times a power of y, in that order. So > lets see if we can find a way to multiply any two such > elements, (x^k y^l)(x^m y^n), using the given presentation. What > we need is a way to Ôpull x^m through y^l, or alternatively to > Ôpush y^l through x^m. One obvious way to do this is to see if > we can determine the conjugation action of any power of y on any > power of x, and of course we can (if not, the group wouldnt > have order 16). Since xyxy = 1 then yxy^-1 = x^3 y^2, and since > xy^3 = yx^3 then y x^3 y^-1 = xy^2, so y^2 x y^-2 = > y (x^3 y^2) y^-1 = xy^2 y^2 = x, so y^2 commutes with x and thus > y^3 acts the same way on x that y does. Also, y x^2 y^-1 = > (yxy^-1)^2 = (x^3 y^2)^2 = x^2 (since y^2 commutes with x), so y > commutes with x^2, so y and y^3 act the same way on x^3 that > they do on x. Now that we know how to multiply any two elements in G = , > its straightforward to write down all the conjugacy classes and > cyclic subgroups, determine the complete subgroup structure, and > see that G is in fact (Z_2 x Z_2) x| Z_4. > Jim, I am going thru this now, but what do you mean by ^ = 1? > / or intersection x = 1 no > x = y no > x = y^2 gives x^2 = 1 > x = y^3 gives x = y^-1 > x^2 = 1 no > x^2 = y gives y^2 = 1 > x^2 = y^2 hm > x^2 = y^3 gives 1 = x^4 = y^6 = y^2 > x^3 = 1 no > x^3 = y gives x^-1 = y > x^3 = y^2 gives x^2 = x^6 = y^4 = 1 > x^3 = y^3 gives x = y > { y^i x^m y^(-i) = ?} I will look at this too, but is > {y^i x^m y^(-i) | i,m in Z_4} what you mean by ^ ? > And how can you say this is 1? > Van not the intersection, but the action of Y = on X = by conjugation. Putting this aside, the rest is true. If yxy^(-1) = x = y^2 x^3, then y^2 x y^2 = = y^4 x^9 = x, and y^2 is in the center Z. So is x^2, so Z = . Also, one can write any element of G in the form x^i y^j, with i,j in Z_4. I hesitate to post this, as I have yet to work it out clearly, but apart from the ^ = 1 statement, which I dont see, I think the rest of what is said is true. I too would like to say more about what this statement means: G is in fact (Z_2 x Z_2) x| Z_4. Usually this means that (Z_2 x Z_2) is a normal subgroup, and that Z_4 is acting by conjugation, is this not right? The only normal subgroup of order 4 I have found is the center Z, in which case the x| would reduce to the direct product, and we would be talking about an Abelian group, which we arent. I question if this is true; G = (Z_2 x Z_2) x| Z_4 If it is, I dont understand in what sense it is true, i.e., what the normal subgroup of G is, and what the action of Z_4 on the normal subgroups giving the structure is. I have been fiddling with this for a while and this is still about all I can say about this group. Van === Subject: Re: More on groups of order 16 > What does x| mean? Its an ASCII rendition of the semidirect product sign (like a multiplication sign, but with a vertical line joining the right-hand extremities of the cross). Information on semidirect products here: http://en.wikipedia.org/wiki/Semidirect_product http://planetmath.org/encyclopedia/ SemidirectProductOfGroups.html === Subject: Re: More on groups of order 16 > I am still having some trouble with 1 of the 14 groups of order 16. > It is the one with 2 generators G = xy^3 = yx^3 Someone said this is (Z_2 x Z_2) x| Z_4, but I have not been able to > verify this, and wonder if anyone could help. > I have done the central product Z_4 o D_4 which has 3 generators and > x^2 = z^2, where Z_4 = , D_4 = with yxy^-1 = x^-1. > The above group is called G(2,2) sometimes, and and arent > normal. > I thought perhaps that the normal subgroup was (1,x^2,y^2,x^2y^2), but > have not been able to show this either. Try going at it backwards. A non-abelian (i.e., non-direct) G = (Z_2 x Z_2) x| Z_4 must have a presentation . Write down all the cyclic subgroups of G, i.e., {1}, {a,1}, {b,1}, {ab,1}, {c,c^2,c^3,1}, etc., and see if you can find elements that satisfy the conditions of your x and y above. -- Jim Heckman === Subject: Re: More on groups of order 16 === Subject: More on groups of order 16 > I am still having some trouble with 1 of the 14 groups of order 16. > It is the one with 2 generators > G = been able to verify this, and wonder if anyone could help. I dont see why. Whats x| ? > This group is symmetric in x and y, > and while and arent normal yxy^3 = y^2 x^3 = 1; yx = y; x = 1 = x; yx = xy; y^2 = x^2 = x^2; y^2 = x^3; 1 = x^2 = x^3; y^2 = 1 Why? Because if xy = yx, then x^2 = y^2 would make G have fewer than 16 elements? Are all 16 of these unique? 1, x, x^2, x^3 y, yx, yx^2, yx^3 y^2, y^2 x, y^2 x^2, y^2 x^3 y^3, y^3 x, y^3 x^2, y^3 x^3 > one can use xyxy = 1 and xy^3 = yx^3 ==> (x/y)^2 = 1, > so that a = xy and b = xy^-1 have order 2, and > so does c = yx, so cb = y x^2 y^-1 and bc = x^2 and > [c,b] = cbcb = x^4 = 1 ==> cb = bc ==> x^2 in center, > and by symmetry of x and y y^2 aso in center and so > center Z = Z_2 x Z_2 = , and G/Z = Z_2 x Z_2. > I would like to look at the subgroups a little more, > but I think this is a start. ---- === Subject: Re: More on groups of order 16 posting-account=jcZk7AwAAADXpPEyHtVyWC264SxtppRB This group is symmetric in x and y, and while and arent normal, one can use xyxy = 1 and xy^3 = yx^3 ==> (x/y)^2 = 1, so that a = xy and b = xy^-1 have order 2, and so does c = yx, so cb = y x^2 y^-1 and bc = x^2 and [c,b] = cbcb = x^4 = 1 ==> cb = bc ==> x^2 in center, and by symmetry of x and y y^2 aso in center and so center Z = Z_2 x Z_2 = , and G/Z = Z_2 x Z_2. I would like to look at the subgroups a little more, but I think this is a start. Van === Subject: 2 kinds of rounding: terminology question Examples of one kind of rounding: 123.123456789 --> 123.1234 0.00123456789 --> 0.0012 Another: 123.123456789 --> 123.1 0.00123456789 --> 0.001234 If memory serves, The first rounds to four significant The second rounds to four significant Please tell me word A and word B. Jack === Subject: Re: 2 kinds of rounding: terminology question posting-account=Glvc4AwAAADzVCZ73XnxpzMhXir6xVzs I thought at first you were talking about rounding down because you didnt change the last 4 to a 5 when you truncated. > Examples of one kind of rounding: > 123.123456789 --> 123.1234 123.1235 > 0.00123456789 --> 0.0012 > Another: > 123.123456789 --> 123.1 > 0.00123456789 --> 0.001234 0.001235 > If memory serves, > The first rounds to four significant The second is to four significant figures. I suppose you could call the first rounding to four decimal places, or rounding to the nearest 0.0001. - Randy === Subject: Re: 2 kinds of rounding: terminology question > I thought at first you were talking about rounding down because > you didnt change the last 4 to a 5 when you truncated. >> Examples of one kind of rounding: >> 123.123456789 --> 123.1234 > 123.1235 >> 0.00123456789 --> 0.0012 >> Another: >> 123.123456789 --> 123.1 >> 0.00123456789 --> 0.001234 > 0.001235 >> If memory serves, >> The first rounds to four significant The second rounds to four significant could call the first rounding to four decimal places, > or rounding to the nearest 0.0001. > - Randy Jack === Subject: Re: [OT] Double posts posting-account=hXoQ7w0AAADSdZxlCHUb3O5k5oe4oxj9 > At least in my news reader (Netscape 7.2, fed from optonline.net), I > seem to be seeing a lot more doube posts lately. I refer to the exact > same post posted at least twice, usually with the same time or perhaps a > minute or two apart. This has happened to at least one of my posts > lately, too, and that may have happened when I posted from > -- > Stephen J. Herschkorn sjherschko@netscape.net I have endless problems with the new Google Groups. I frequently get server errors indicating that the post has failed. Then I re-post, but it later turns out that the first posting worked after all (according to the Google listing anyway). The whole Gooogle groups-beta thing is a disaster, and I cannot possibly imagine what they think they are doing. I have mailed them a long list of problems but nothing has improved (yet). Its like they gave it to a couple of summer vacation students to do over a weekend. Still, I guess its free. Can anyone recommend an alternative web-based newsreader that ... er ... works? === Subject: Re: [OT] Double posts === >Subject: Re: [OT] Double posts >> At least in my news reader (Netscape 7.2, fed from optonline.net), I >> seem to be seeing a lot more doube posts lately. I refer to the >exact >> same post posted at least twice, usually with the same time or >perhaps a >> minute or two apart. This has happened to at least one of my posts >> lately, too, and that may have happened when I posted from >> -- >> Stephen J. Herschkorn sjherschko@netscape.net >I have endless problems with the new Google Groups. I frequently get >server errors indicating that the post has failed. Then I re-post, but >it later turns out that the first posting worked after all (according >to the Google listing anyway). Did you ever use the old Google Groups? Server errors were so common in the old system that I always composed my messages in Notepad and then pasted them in so I wouldnt have to re-type them. And how is a false error message a bad thing? Now that you dont have to wait hours to see your message, those type of errors dont even bother me anymore. If you want to complain about something, I had a couple messages accepted without error only to get stuck in limbo somewhere and not appear in the Google archive for 24 hours. They did get broadcast to the rest of the Internet as I saw replies before I saw my messages. >The whole Gooogle groups-beta thing is a disaster, and I cannot >possibly imagine what they think they are doing. I have mailed them a >long list of problems but nothing has improved (yet). Ive been using the new Google Groups long before they dumped the old version. To say that nothing has improved is completely wrong, there have been significant improvements. Maybe not the ones youre looking for yet, but its not like theyre sitting around doing nothing. >Its like they >gave it to a couple of summer vacation students to do over a weekend. Now you know what you get by recruiting programmers with puzzles on billboards. >Still, I guess its free. >Can anyone recommend an alternative web-based newsreader that ... er >... works? -- Mensanator Ace of Clubs === Subject: Average, standard deviation and max of a set I hope my question is not OT: having a set of numeric values X_1, ... X_N I can compute the average value A and the standard deviation S. But if I have only A, S and the number N of the values in the set, exist a method for the estimation of the maximum (or the minimum) value of the set? replies. Robert === Subject: Re: Average, standard deviation and max of a set > having a set of numeric values X_1, ... X_N I can compute the average > value A and the standard deviation S. > But if I have only A, S and the number N of the values in the set, > exist a method for the estimation of the maximum (or the minimum) > value of the set? Without knowing anything about the distribution of the (X_i) values, the best you can do is a bound: the minimum lies between A - S sqrt(N-1) and A - S / sqrt(N-1), and the maximum between A + S sqrt(N-1) and A + S / sqrt(N-1). You can derive these results by looking at the possible values of (X_i) for a given average and standard deviation. The extremes are reached when (N-1) of the values are the same, and the other is different. Getting any more information (like an unbiased estimator for minimum and maximum) depends on knowing more about the distribution of (X_i). - Tim === Subject: Re: Average, standard deviation and max of a set >having a set of numeric values X_1, ... X_N I can compute the average >value A and the standard deviation S. >But if I have only A, S and the number N of the values in the set, >exist a method for the estimation of the maximum (or the minimum) >value of the set? Not an estimate, but a lower bound on the maximum (or upper bound on the minimum). Use the fact that the if the points lie in the interval [A-c, A+c], then the standard deviation is maximized when all the points are at the endpoints of the intervals. -- Stephen J. Herschkorn sjherschko@netscape.net === Subject: Re: Average, standard deviation and max of a set >having a set of numeric values X_1, ... X_N I can compute the average >value A and the standard deviation S. >But if I have only A, S and the number N of the values in the set, >exist a method for the estimation of the maximum (or the minimum) >value of the set? > > Not an estimate, but a lower bound on the maximum (or upper bound on the > minimum). Use the fact that the if the points lie in the interval > [A-c, A+c], then the standard deviation is maximized when all the > points are at the endpoints of the intervals. But for a finite set, the range is maximized, for a given fixed SD and N, when all but one item have the same value. Letting R be that range, then A +/- R*(N-1)/N will give the maximum possible and minimum possible values for a given R. The maximum value of R is S times some function of N. Which function depends on which standard deviation formula you use, population or sample. === Subject: Re: Poll: Are PCs Turing Machines? <8KAsd.54752$QJ3.37736@newssvr21.news.prodigy.com> <41b65ebf_2@newsfeed.slurp.net> <31nubiF3d9i8aU1@news.dfncis.de> <%QPtd.160138$V41.69674@attbi_s52> <31qji2F3dhfulU1@news.dfncis.de> posting-account=sASPfg0AAAB32ck2Ys0CgbD_dk7GKPYH I understand your argument. It seems to be an instrumentalist point of view. -- Eray Ozkural === Subject: Re: Poll: Are PCs Turing Machines? <32fmsoF3lf922U1@news.dfncis.de> posting-account=sASPfg0AAAB32ck2Ys0CgbD_dk7GKPYH Hi Fabian, No, it doesnt avoid discussions as you can tell :) I couldnt keep myself away from the discussions either. PC does not necessarily mean a personal computer. We were thinking about possible Physical Computers, that is more precise. The question also needs to be asked in the following way. Take a PC, is this computationally equivalent to a particular TM? (Does your answer change in this case? I assume no in the discussion below) As for your first argument consider then the following question. (It is the one that urged me to make the poll in the first place) A Finite State Transducer (FST) is a finite state machine that recodes an input string to an output string, the next state is determined by the current symbol and state only and the output is calculated from left to right. (So, its just an FSM with rules like a/b, 2 meaning when input a, output b, and go to state 2.) Now, the FST also works on unbounded tapes, there is absolutely no limit to the length of the string it can process and output. (Important) Are there physical examples to FSTs in the world, or should we apply your argument and conclude negatively: an FST has one infinite band on which it is able to read, and one infinite band on which it is able to write. This would mean a Physical FST should have infinite memory. Now, this brings us to a dilemma, because many people think that when they implement FSTs, they have physical models of these abstract machines, which work in the real world. The dilemma is this: you are going to have trouble answering either way, because: If you say, yes there are physical FSTs, then you would be at a loss to explain why your infinite band argument holds for TMs but not for FSTs. If on the other hand, you say no, then you would be consistent, but you would upset researchers who routinely program FSTs to achieve such mundane tasks as NLP, etc. (For instance, it is used for morphological analysis) How do you propose to solve this dilemma? -- Eray Ozkural PS: My humble observation: the programmer types are more inclined to answer yes to my question, and the mathematician types are more inclined to say no. The programmers might prefer to shun away from idealism. === Subject: Re: Poll: Are PCs Turing Machines? > Hi! > Are PCs physical examples to Turing Machines? [*] > Please write only Yes/No to avoid discussion. > As you can see, answering only Ôyes or Ôno does not avoid discussions ;-) > So Ill answer a little more: > PCs are not physical examples to TMs. A TM has one (or more) infinite > band on which it is able to write and read. This would mean a PC should > have infinite memory. > Another difference is, that a PC can write/read a bigger number of bits > (normaly 32) per cycle. I know that this argument does not count much, > because using a kind of compression (new alphabet) on a TM would give > the TM the same power. > But following this, PCs are more a physical example to the so called > able to add/operate arbitrarily long words in one cycle. The theoretical > the function of TMs is. > Fabian Right! The PC is NOT a good example of a TM. But it IS a TM. The PC is a generic finite-memory function evaluator. This is a particular algorithm (class). All algorithms can be handled by a TM. Is a set of traffic lights an automation? Yes but an automation can be much more powerful. Is a PC a TM? Yes but a TM can be much more powerful. The PC is not a UTM, but is is equivalent to a particular TM. Tricky subject title! Herc === Subject: Re: Poll: Are PCs Turing Machines? >> Hi! >> Are PCs physical examples to Turing Machines? [*] >> Please write only Yes/No to avoid discussion. >> As you can see, answering only Ôyes or Ôno does not avoid discussions >> ;-) >> So Ill answer a little more: >> PCs are not physical examples to TMs. A TM has one (or more) infinite >> band on which it is able to write and read. This would mean a PC should >> have infinite memory. >> Another difference is, that a PC can write/read a bigger number of bits >> (normaly 32) per cycle. I know that this argument does not count much, >> because using a kind of compression (new alphabet) on a TM would give >> the TM the same power. >> But following this, PCs are more a physical example to the so called >> able to add/operate arbitrarily long words in one cycle. The theoretical >> the function of TMs is. >> Fabian > Right! The PC is NOT a good example of a TM. But it IS a TM. > The PC is a generic finite-memory function evaluator. This is a > particular algorithm (class). > All algorithms can be handled by a TM. > Is a set of traffic lights an automation? Yes but an automation can be > much more powerful. > Is a PC a TM? Yes but a TM can be much more powerful. > The PC is not a UTM, but is is equivalent to a particular TM. > Tricky subject title! > Herc Some PCs can compute the same problems that a TM can compute. But that is not the question asked in the subject which due to the sentence structure asks Do all PCs have a TM correspondence and Ive already seen you answer the question no. You converted the question in the subject, to a singular Is there a (or even some) PCs equivalent to TMs? The answer is yes. But the person who originally asked the question insists that there is a PC match for every possible TM. Also you have converted the question to what class of problems can be computed for the comparison. The way the question is actually worded the answer is entirely no, because TMs are defined as non-physical and PCs are defined as physical. The question does not ask if a TM were physically constructed, without the endless tapes, but a some physical substitute for the tapes memory function, would PCs in that case be TMs computationally. Yes, in that sense because they would both be finite state machines. The question is deliberately tricky because the author is trying to confuse the issue by rewording his earlier lunacy so that he can say Ôthis is what I really meant. But that PCs could compute some part of the range of TMs had already been pointed out to the OP before he posted this desperate escape mechanism. I use that terminology because Eray is a simpering arrogant useless nutcase who has managed to waste the time of his superiors before his pretending to have some knowledge was exposed as a lie. It is too bad he was not incarnated as a baby seal. === Subject: Re: Poll: Are PCs Turing Machines? > But the person who originally asked the question insists > that there is a PC match for every possible TM. That is completely wrong. The question is specifically about PCs, not TMs. Are PCs big? Are PCs power hungry? Are PCs automations? Are automations TMs? Are traffic lights automations? Are PCs TMs? Were not interested if TMs are power hungry, were interested if PCs are power hungry. > Also you have converted the question to what class of > problems can be computed for the comparison. No, *a* TM is a representation of an algorithm with a built in computing actuation. A computer contains an algorithm and has hardware computing actuators. The only difference is the computer only handles finite memory algorithms, but f(a,b) = a+b is a TM, and it only uses finite memory too. > The way the question is actually worded the answer > is entirely no, because TMs are defined as non-physical > and PCs are defined as physical. Again this is completely wrong! Is the sun yellow? YES One is physical, one is abstract. Herc -- YOU CANT PROVE ME If you prove its true then it has a proof, which makes it false. If you dont prove it, then its true. 10,000 people in sci.math ALL believe that it means mathematics will always be incomplete. === Subject: Re: Poll: Are PCs Turing Machines? <32fmsoF3lf922U1@news.dfncis.de> <32hqvlF3n0keuU1@individual.net> <32ju89F3mp0ldU1@individual.net> posting-account=sASPfg0AAAB32ck2Ys0CgbD_dk7GKPYH Once upon a time, I started a thread titled Misunderstanding Computability which specifically targeted one of the few ideas of Stephen that defies change. Back then, I again emphasized that an infinite tape is not a necessary component of a formalization of computation. Simply the notion of a general purpose physical machine is sufficient. Now, I realize that there are deeper problems with those views. They talk about things that do not exist, and demons follow! The problem is simple, Herc, very very elementary. Abstract does not require non-physical, because immaterial things do *not* exist. This is nominalism. This is physicalism. This is 21st century. They are conßating knowlege with existence. And they are implicitly defending a sillier version of Cartesian dualism, but they do not know what they are saying because they have no clue about philosophy of psychology! Lets get rid of those religious views. They stain our intellect. -- Eray Ozkural === Subject: Re: Poll: Are PCs Turing Machines? > is entirely no, because TMs are defined as non-physical > and PCs are defined as physical. > Again this is completely wrong! Is the sun yellow? YES Technically its not completely wrong. there is a TM for every FSM that doesnt use more than a fixed amount of its memory tape. Even though literally TMs have an infinite tape, FSMs are TMs Turing Machines plural isnt any particular device, its a class of devices. There is a Turing Machine that does the same computations as my PC. Herc -- YOU CANT PROVE ME If you prove its true then it has a proof, which makes it false. If you dont prove it, then its true. 10,000 people in sci.math ALL believe that it means mathematics will always be incomplete. === Subject: Re: Poll: Are PCs Turing Machines? <32fmsoF3lf922U1@news.dfncis.de> <32hqvlF3n0keuU1@individual.net> posting-account=sASPfg0AAAB32ck2Ys0CgbD_dk7GKPYH Stephen, I do not insist that there is a PC match for every possible TM, you misunderstand... There are obviously TMs that are too large to have a physical correlate, that is Kolmogorov complexity 101. I insist that if a PC X is computationally equivalent to a TM Y this means: 1. I can map every computational mechanism in X to Y 2. I can map every computational mechanism in Y to X That is I require a 1-1 correspondence between every computational unit of X and Y. I ask the question: Are physical computers examples to Turing Machines? Which means: Given *any* physical computer X, is X computationally equivalent to any TM? I could not have possibly asked it any other way. The mistake has always been yours, unfortunately. And I am not a simpering arrogant useless nutcase, that is you, because you have asserted that Pi is computable by TMs but not by PCs therefore TMs can do things that are *in principle* beyond the capabilities of PCs, which is among the stupidest things ever said about computation. TMs as abstract things DO NOT EXIST. Again, a PC has no principle difference from a TM. TMs tape is not infinite, it is unbounded Stephen. And that took you 3 years to understand. You improve, but not fast. -- Eray Ozkural === Subject: Re: Poll: Are PCs Turing Machines? <32fmsoF3lf922U1@news.dfncis.de> <32hqvlF3n0keuU1@individual.net> posting-account=sASPfg0AAAB32ck2Ys0CgbD_dk7GKPYH Hi Herc, I agree with most of that you say above, and I hope Fabian assesses the replies of us both. There is one point, however. You need to explain what you mean by universality. It is something that I thought of as well, and it is one of the interesting arguments related to this discussion. The PC can be a UTM in the technical sense, if it is a physical model of a particular TM as we suggest. (Otherwise, we would contradict ourselves) For instance, my pc that stands 35 centimeters away from me is a UTM by virtue of its instruction set. If I physically transcribe within its processing *capacity*. (That is, UTMs are particular computers, too, but they are rather rich in their simulation capability) However, it is not universal in the sense that it can emulate only a bounded number of computers, e.g. space-time is practically finite when it comes to constructing computing machinery, and my pc is a very good example of a finite computer. But it can simulate other things, for instance it can simulate a C64 perfectly well, with absolutely nothing missing from the computational picture of a C64. On the other hand, there is a third sense of universality which is sometimes conßated with these other senses: that a particular PC means a finite control together with an actually infinite set of input tapes. Thats not a good conception of identity as I argue in Theories of general machines thread, which I believe you should have a look. Harriss misconceptions lead us to rather nonsensical arguments about machines of other kinds like aircraft if we are to take this notion of identity seriously as it concerns generalizing theories of machines. -- Eray Ozkural === Subject: Re: Counting set covers >>Hello all. I was wondering if there is some relatively simple way >>to count the number of set covers of a set of size n that satisfy >>the following properties: >>1. No set in the cover is a subset of another set in the cover >>2. For all sets A(i) in the cover: >> A(i) (union of all A(k) (k != i)) = {} >S = /_j A_j >nulset = A_k - (/_j A_j - A_k) = A_k - SA_k = A_k >>Unfortunately (/_j A_j - A_k) != SA_k. > Actually, the problem is that > /_{j != k} A_j != /_j A_j - A_k. > Consider the cover {{1, 2}, {2, >>3}, {1, 3}} of {1, 2, 3}. It satisfies the above two properties, yet >>none of the sets are empty. It is incidentally the only such cover of >>{1, 2, 3} besides {{1, 2, 3}}. > It looks like {{1, 2, 3}} doesnt satisfy the second condition, > since the union of an empty collection is empty and this would > force {1, 2, 3} to be included in the empty set. Ah, yes. I meant to include Ôthe set of the set into the count as well, so I should have mentioned that. But, the problem is largely the same anyway. -- Daniel Sj.9ablom === Subject: Re: Counting set covers >>Hello all. I was wondering if there is some relatively simple way to >>count the number of set covers of a set of size n that satisfy the >>following properties: >>1. No set in the cover is a subset of another set in the cover >>2. For all sets A(i) in the cover: >> A(i) (union of all A(k) (k != i)) = {} >>The second property could also be formulated as: There is no set in the >>cover that contains an element not contained in another set in the cover. > Or in other words, each element is contained in at least two sets of > the cover. > Property (1.) says that the cover is an antichain. AFAIK there is > no closed-form formula for the number of antichains of subsets of > an n-set, but a complicated asymptotic formula is known. In > particular it is less than 2^((n choose ßoor(n/2))(1 + O(log n/n))). > See Ian Anderson, Combinatorics of Finite Sets, Oxford 1987, section > 3.4.1. So this is an upper bound for your number. I suspect that it > is a fairly good upper bound when n is large, i.e. most antichains will > satisfy property (2.). -- Daniel Sj.9ablom at 07:13 PM, pubkeybreaker@aol.comstuff (Bob Silverman) said: >(3) Unmotivated students. Children start out wanting to learn. The public schools systematically undermine that desire by emphasis on drill and uniformity at the expense of content and challenge. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolicited bulk E-mail subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not > at 07:13 PM, pubkeybreaker@aol.comstuff (Bob Silverman) said: >>(3) Unmotivated students. >Children start out wanting to learn. The public schools systematically >undermine that desire by emphasis on drill and uniformity at the >expense of content and challenge. The kids are bored to death. When they begin twitching in protest, they get drugged to death. /BAH Subtract a hundred and four for e-mail. ----- Original Message ----- > Children start out wanting to learn. The public schools systematically > undermine that desire by emphasis on drill and uniformity at the > expense of content and challenge. And yet I have students who are so weak on this issue that they cannot understand the difference between 2/3 and 2*(1/3). DM > ----- Original Message ----- > Asia >> Children start out wanting to learn. The public schools systematically >> undermine that desire by emphasis on drill and uniformity at the >> expense of content and challenge. > And yet I have students who are so weak on this issue that they cannot > understand the difference between 2/3 and 2*(1/3). Let me rephrase. They are convinced there is a distinction between 2/3 and 2*(1/3). DM > ----- Original Message ----- > Asia >> Children start out wanting to learn. The public schools systematically >> undermine that desire by emphasis on drill and uniformity at the >> expense of content and challenge. > And yet I have students who are so weak on this issue that they cannot > understand the difference between 2/3 and 2*(1/3). > Let me rephrase. They are convinced there is a distinction between 2/3 and > 2*(1/3). Imagine a bar one foot long. (2/3) of it is a bar 8 inches long 2*(1/3) of it is two bars, each 4 inches long. They have a point. The trick is to get them to put it aside for the time being, without trying to convince them that their point is eeevul. -- Chris Henrich God just doesnt fit inside a single religion. > Imagine a bar one foot long. > (2/3) of it is a bar 8 inches long > 2*(1/3) of it is two bars, each 4 inches long. > They have a point. The trick is to get them to put it aside for the > time being, without trying to convince them that their point is eeevul. They do not have a point. We are not talking about engineering where they are concerned with the distinct difference between the physical properties of a single 8 inch solid piece of steel and two 4 inch pieces of steel. Further, when the discussion is radians (as was the case here except I left off the pi from the expression), your analogy, to me at least, is more confusing than the issue. Which is the basics of fraction multiplication. I seen a number of HS graduates who cannot add 1/3 and 1/2 without a calculator. And when they do they feel that 0.833 is a better answer than 5/6. DM <41c38e1b$18$fuzhry+tra$mr2ice@news.patriot.net> <9eudnR0UuP-P-1ncRVn-jQ@comcast.com> posting-account=BjC-YAwAAADQ91Zm3XkS3aGs3XlaqZ4X Translating the example of one bar of 8 inches different from two bars of 4 inches: An equality like 2*(1/3)=2/3 gives equal values for different expressions. In this example an multiplication of two numbers is an operation and that is different from a value, which is not an operation. I do not understand, why You dont understand me. says the teacher. Math aint that easy. Hero > An equality like > 2*(1/3)=2/3 gives > equal values > for different expressions. > In this example > an multiplication of two numbers > is an operation and that > is different > from a value, which is not an operation. > I do not understand, why You dont understand me. > says the teacher. > Math aint that easy. Yawn. The multiplication operator * : RxR -> R is a binary map. The student was comparing *(2,1/3), a point in the image space of the map, with 2/3, a different notational representation of the same rational number in R. There is NO distinction. There is a distinction between the binary operation and the image of that operation on a pair of elements in R. But that was not the point of discussion. The class was precalc and not group theory or some discussion growing out of Halmos Naive Set Theory. DM <41c38e1b$18$fuzhry+tra$mr2ice@news.patriot.net> <9eudnR0UuP-P-1ncRVn-jQ@comcast.com> posting-account=BjC-YAwAAADQ91Zm3XkS3aGs3XlaqZ4X Yawn. The multiplication operator * : RxR -> R is a binary map. The student was comparing *(2,1/3), a point in the image space of the map, with 2/3, a different notational representation of the same rational number in R. There is NO distinction. What You first posted can be compared to : The students think the mapping of (2,1/3)by * is different from the image-point *(2,1/3) Hero > Yawn. The multiplication operator * : RxR -> R is a binary > map. The student was comparing *(2,1/3), a point in the image > space of the map, with 2/3, a different notational representation of > the same rational number in R. There is NO distinction. > What You first posted can be compared to : > The students think the mapping of (2,1/3)by * > is different from the image-point *(2,1/3) Based on my conversations with many students, it is not this subtlety that is the cause of confusion. It was the fact that, as elements of Q, there is no distinction between 2/3, 2*(1/3), 6/9, 1/3 + 1/3, etc. That is, these are all different representations of the exact same point in Q -- some of which may have been viewed as an image point of the + operator and some an image point of the * operator, and some just viewed as elements of Q, as constructed from N. Another issue I have come across is a basic lack of understanding of how to understand and implement the algebraic rules within Q. It is quite common for students to believe that a/(b+c) = (a/b) + (a/c) -- which tends to hamper their ability to rewrite sums of algebraic expressions over a common denominator, among other useful ideas. DM understanding of how to >understand and implement the algebraic rules within Q. >It is quite common >for students to believe that a/(b+c) = (a/b) + (a/c) -- Of course they will. Dont use slanty lines. Straight horizontal lines help convey the terms and where they belong. >which tends to hamper their >ability to rewrite sums of algebraic expressions over a common denominator, >among other useful ideas. My high school algebra teacher counted a correct solution wrong if the equation used slanty lines. It didnt take long for everybody to stop that. Its easier to separate terms and whole divisors if horizontal lines are when drawing fractions on paper. This is especially true when stuff below a line has shorter lines. /BAH Subtract a hundred and four for e-mail. > Another issue I have come across is a basic lack of >>understanding of how to >>understand and implement the algebraic rules within Q. >>It is quite common >>for students to believe that a/(b+c) = (a/b) + (a/c) -- > Of course they will. Dont use slanty lines. Straight > horizontal lines help convey the terms and where they > belong. Uh.. I was using the slanty lines (aka forward slashes) to post to this board. Normally I write in LaTeX where the notion is quite clear. I.e., $$frac{a}{b+c} = frac{a}{b} + frac{a}{c}$$ > My high school algebra teacher counted a correct solution > wrong if the equation used slanty lines. It didnt take long > for everybody to stop that. Its easier to separate terms > and whole divisors if horizontal lines are when drawing > fractions on paper. This is especially true when stuff > below a line has shorter lines. See above. DM >> understanding of how to >understand and implement the algebraic rules within Q. >It is quite common >for students to believe that a/(b+c) = (a/b) + (a/c) -- >> Of course they will. Dont use slanty lines. Straight >> horizontal lines help convey the terms and where they >> belong. >Uh.. I was using the slanty lines (aka forward slashes) >to post to this board. Normally I write in LaTeX where the >notion is quite clear. I.e., >$$frac{a}{b+c} = frac{a}{b} + frac{a}{c}$$ >> My high school algebra teacher counted a correct solution >> wrong if the equation used slanty lines. It didnt take long >> for everybody to stop that. Its easier to separate terms >> and whole divisors if horizontal lines are when drawing >> fractions on paper. This is especially true when stuff >> below a line has shorter lines. >See above. Do arithmetic and algebra teachers also use LaTex or do the kids see these things ala ASCII? I bought my mother an algebra book and some of it has horizontal lines but not the pages that teach BASIC programming. I havent seen her workbook but I spent a whole phone call trying to get her to write straight horizontal lines with her pencil. /BAH Subtract a hundred and four for e-mail. There *is* a distinction between 2*(1/3) and 2/3, though of course the two quantities are equal. Admittedly, Mr. Masons students are probably not arguing that subtlety. Sheesh, if you cant convince them that 2*(1/3) = 2/3, how will they ever understand 0.999... = 1? -- Stephen J. Herschkorn sjherschko@netscape.net ^OX9W/.#XpUmm`>TD2zNE-t}emfPkFR.Z5`ßY:3QYT$>dUwN^sm;MBV: F7aL9x*q!` ln!l}>Y6_45$%R|P7DSrBkEph@1-;P*s~F_28vO@e4p/>}Pc?@rl8cz] d9RXOtSheesh, if you cant convince them > that 2*(1/3) = 2/3, how will they ever understand 0.999... = 1? Oh, is that something that students are supposed to learn? Ive always wanted to make this a test question at the end of the calculus sequence, to get exact data on who gets it and who doesnt, but I guess it would only be embarrassing all around. > There *is* a distinction between 2*(1/3) and 2/3, though of course > the two quantities are equal. Admittedly, Mr. Masons students are > probably not arguing that subtlety. I have frequently run across people who think of something like Ô2*(1/3) as an un-evaluated expression that can be simplified to give a number, in this case 2/3. The idea that an expression actually denotes its value is not immediately obvious to everyone. My observation of the local school system -- which sends a large fraction of its graduates to selective and highly-selective universities -- is that this kind of basic abstraction is not taught; it is mentioned and some kids will get it or otherwise puzzle it out on their own. Nobody notices or cares that many dont ever get it since it doesnt hurt their state proficiency test or SAT scores. > Children start out wanting to learn. The public schools systematically > undermine that desire by emphasis on drill and uniformity at the > expense of content and challenge. Square pegs are ground down to fit in round holes. The motto of the Administration is the opposite of that of the Black Knight: All shall pass! Bob Kolker > at 07:13 PM, pubkeybreaker@aol.comstuff (Bob Silverman) said: >>(3) Unmotivated students. >Children start out wanting to learn. The public schools systematically >undermine that desire by emphasis on drill and uniformity at the >expense of content and challenge. Many schools (certainly including many non-public schools) spend much effort on stupefying children, with enormous success. This doesnt mean that there arent also students who arrive at school either stupid (for genetic or non-human-environmental reasons, e.g., heavy metal poisoning) or stupefied (by their pre-school human environment). There are many paths into stupidity/stupefaction, and very few out. Lee Rudolph >> When I teach pre-calc, I have two major uses for graphing calculators. >> First, students can use them to solve optimization word problems without >> the use of calculus. > For example? > Suppose that an aluminum can must hold 12 ounces of ßuid. It costs $0.03 > per square inch to produce/manufacture the top and bottom portion of the can > and $0.02 per square inch to produce/manufacture the cylindrical side of the > can. Find the dimensions of the can with the least cost. Then consider how > your answer depends on the differential cost between top/bottom construction > costs and side construction costs. > Obviously, there are many other examples of these style (like designing > Norman windows). 12 oz * in^3/oz = pi.r^2 h C = 2pi.rh.c_s + 2pi.r^2 c_e Youre expecting the graphic calculator to set up the equations??? >> Second, students can numerically solve equations of the form Sin(x) = x >> or 1-x = lnx. > Unless the class is numerical analysis or the topic being taught is > Newtons method. > I dont cover numerical analysis or Newtons method in pre-calc. I > typically use Mathematica or Matlab in numerical analysis courses. Practical applications of numerical analysis would benefit from computers, but to teach the basic concepts? > So have class, homework or graphic calculator contest, dream up wow graphs > and give equations. Where intuition is important is look at > x^2 cos 1/x > And then what? Clearly the issue here is that you are considering f(x)g(x) > where one function has a constant limit at 0 and the other at infinity. > Dont you think that a student could play these mental games with pencil, > paper, and a basic understanding of the graph/periodicity/boundedness of > cos(x), x^2, and the concept of composition? I see those fundamental > underlying ideas as being lost. Yes. I do too. > That said, I have no problem with students using a calculator and this > type of problem to think their way through a rigorous understanding of > these concepts. I do this type of laboratory as group work. > And interesting question that does not require a calculator at all is to > give a fairly asymmetric graph and say it corresponds to a function w(x). > Then ask the student to graph f(x) = -2w(4(x+3))+6. ;-) Talk about electronic engineering and wave equations. Does not require? Do you mean, cannot be solved graphic calculator? Any other problems to demostrate the inability of calculators? === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem <4ujtr05euj9l4q0fcpb8q2sbp141r399op@4ax.com> posting-account=9wVPIwwAAAAonf5Dj39AQaTL2sJYvErF >[questions that have already been answered at great length, >misconceptions that have been abundantly clarified and >falsehoods that have been conclusively refuted snipped.] Thats just more of the same: off-the-cuff, unsubstantiated, all-encompassing. Thats what got you in trouble in the first place! There is no explanation for your statement other than what Smullyan and I are doing. Even if we assume that you were misinterpreted and meant something else, there is no something else. You are unable to provide a detailed alternate explanation of your statement about ignorance other than what Smullyan and I are doing. You are not substantiating your statements, preferring to bounce from claim to claim, leaving a trail of unattended debris like a bad dog. I quoted a reputable source that what you said was wrong. Now show a quote that proves me wrong. C-B > ************************ > David C. Ullrich === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem Charlie-Boo says... >I quoted a reputable source that what you said was wrong. Now show a >quote that proves me wrong. That quote did not contradict what David Ullrich was saying. David is not disagreeing with Smullyan, hes disagreeing with *you*. You are misinterpreting what Smullyan said. Once again, truth and provability are different things *unless* you are dealing with a complete theory (which is the case for the theory of true arithmetic that Smullyan was talking about). -- Daryl McCullough Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem posting-account=9wVPIwwAAAAonf5Dj39AQaTL2sJYvErF > Charlie-Boo says... >I quoted a reputable source that what you said was wrong. Now show a >quote that proves me wrong. > That quote did not contradict what David Ullrich was saying. > David is not disagreeing with Smullyan, hes disagreeing with > *you*. You are misinterpreting what Smullyan said. > Once again, truth and provability are different things *unless* > you are dealing with a complete theory (which is the case for > the theory of true arithmetic that Smullyan was talking about). In that theory, is Smullyan defining provability to be truth? C-B > -- > Daryl McCullough > Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem Charlie-Boo says... >> Once again, truth and provability are different things *unless* >> you are dealing with a complete theory (which is the case for >> the theory of true arithmetic that Smullyan was talking about). >In that theory, is Smullyan defining provability to be truth? No, hes not. Provability always means the same thing: derivability from the axioms by the rules of inference of first-order logic. What Smullyan is doing is choosing the *axioms* to be all true sentences of arithmetic. -- Daryl McCullough Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem posting-account=9wVPIwwAAAAonf5Dj39AQaTL2sJYvErF > Charlie-Boo says... >> Once again, truth and provability are different things *unless* >> you are dealing with a complete theory (which is the case for >> the theory of true arithmetic that Smullyan was talking about). >In that theory, is Smullyan defining provability to be truth? > No, hes not. Provability always means the same thing: derivability > from the axioms by the rules of inference of first-order logic. What > Smullyan is doing is choosing the *axioms* to be all true sentences > of arithmetic. Is Smullyan defing provability in that theory? If so, what is he defining it to be? > -- > Daryl McCullough > Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem Charlie-Boo says... >>In that theory, is Smullyan defining provability to be truth? >> No, hes not. Provability always means the same thing: derivability >> from the axioms by the rules of inference of first-order logic. What >> Smullyan is doing is choosing the *axioms* to be all true sentences >> of arithmetic. >Is Smullyan defing provability in that theory? No, hes not. Provability always means the same thing: derivability from the axioms by the rules of inference of first-order logic. What Smullyan is doing is choosing the *axioms* to be all true sentences of arithmetic. -- Daryl McCullough Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem posting-account=9wVPIwwAAAAonf5Dj39AQaTL2sJYvErF > Charlie-Boo says... >>In that theory, is Smullyan defining provability to be truth? >> No, hes not. Provability always means the same thing: derivability >> from the axioms by the rules of inference of first-order logic. What >> Smullyan is doing is choosing the *axioms* to be all true sentences >> of arithmetic. >Is Smullyan defing provability in that theory? > No, hes not. Provability always means the same thing: derivability > from the axioms by the rules of inference of first-order logic. > What Smullyan is doing is choosing the *axioms* to be all true > sentences of arithmetic. How would one define provability to be truth in a system like N if one wanted to do so? C-B > -- > Daryl McCullough > Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem Charlie-Boo says... >How would one define provability to be truth in a system like N if one >wanted to do so? I guess you could do so as follows: By the word provability I dont mean provability, I mean truth in a system like N. -- Daryl McCullough Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem posting-account=9wVPIwwAAAAonf5Dj39AQaTL2sJYvErF > Charlie-Boo says... >How would one define provability to be truth in a system like N if one >wanted to do so? > I guess you could do so as follows: > By the word provability I dont mean provability, I > mean truth in a system like N. And then the provable sentences would coincide with the true sentences? C-B > -- > Daryl McCullough > Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem Charlie-Boo says... >>How would one define provability to be truth in a system like N if >one >>wanted to do so? >> I guess you could do so as follows: >> By the word provability I dont mean provability, I >> mean truth in a system like N. >And then the provable sentences would coincide with the true sentences? If your axioms include all true sentences, then the provable sentences will coincide with the true sentences. That doesnt mean that you have redefined provability. -- Daryl McCullough Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem posting-account=9wVPIwwAAAAonf5Dj39AQaTL2sJYvErF > Charlie-Boo says... >>How would one define provability to be truth in a system like N if >one >>wanted to do so? >> I guess you could do so as follows: >> By the word provability I dont mean provability, I >> mean truth in a system like N. >And then the provable sentences would coincide with the true sentences? > If your axioms include all true sentences, then the provable sentences > will coincide with the true sentences. That doesnt mean that you have > redefined provability. 1. You say above that if we define provability to be truth in a system like N . . . then the provable sentences will coincide with the true sentences. 2. In Smullyans system N, the provable sentences coincide with the true sentences. 3. Therefore Smullyan is defining provability to be truth. 4. Therefore DUs statement Truth and provability are _different_ things when you define one to be the other you exhibit amazing ignorance of the most basic issues. refers to Raymond Smullyans work. C-B Nice chatting with you. Maybe we can do something more productive than playing cat and mouse? > -- > Daryl McCullough > Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem Charlie-Boo says... >1. You say above that if we define provability to be truth in a system >like N . . . then the provable sentences will coincide with the true >sentences. But Smullyan is *not* doing that. He is not defining provability to be truth. >2. In Smullyans system N, the provable sentences coincide with the >true sentences. >3. Therefore Smullyan is defining provability to be truth. No, hes not. Look, suppose that all the coins in my pocket are pennies. Does that many that penny has been redefined to mean the same thing as coin? No, of course not, although in the restricted context of coins in my pocket, every coin is also a penny, and every penny is also a coin. In Smullyans system, he is not defining provable to mean the same thing as true, but it happens to be the case that for his system, every true sentence is provable, and vice-versa. Heres the quote from Smullyan: We call a formula F(v1,. . .,vn) correct if for every n-tuple (a1,...,an), the sentence F(a1,. . .,an) is true. We let N be the first-order system whose axioms are all the correct formulas (this includes all logically valid formulas.) Thus, the provable formulas of N are nothing more than the axioms of N. Hes saying that the *axioms* of N are all true sentences. It *follows* from this that a formula is true if and only if it is provable in N. -- Daryl McCullough Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem posting-account=9wVPIwwAAAAonf5Dj39AQaTL2sJYvErF > In Smullyans system, he is not defining provable to mean the > same thing as true > but it happens to be the case that for his > system, every true sentence is provable, and vice-versa. That is simply false. You are not describing anything different - it is the exact same system with the same axioms, the same rules (none) and the same theorems. Wheres the difference? It is mathematically identical. You are quibbling over descriptions which are mathematically equivalent. > Hes saying that the *axioms* of N are all true sentences. It > *follows* from this that a formula is true if and only if it > is provable in N. Same axioms, same rules, same theorems. Same Theory. The only system that meets DUs condition for being ignorant is Smullyans System N. C-B > -- > Daryl McCullough > Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem Charlie-Boo says... >> In Smullyans system, he is not defining provable to mean the >> same thing as true >> but it happens to be the case that for his >> system, every true sentence is provable, and vice-versa. >That is simply false. No, its not. Smullyan is saying that for his choice of axioms, the provable sentences are exactly the true sentences. Thats a *conclusion*, not a *definition*. Thats clear from the Smullyan quote. As David Ullrich says, Smullyan uses the word thus, which is a sign that he is drawing a conclusion. His choice of axioms, together with the *standard* definition of provability implies that the provable sentences for his system are exactly the true sentences. Smullyan is clearly taking provability to have been already understood by the reader. Hes not defining it. -- Daryl McCullough Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem Why did you snip the following from the message youre replying to? >>3. Therefore Smullyan is defining provability to be truth. >No, hes not. Look, suppose that all the coins in my pocket are >pennies. Does that many that penny has been redefined to mean >the same thing as coin? Enquiring minds want to know whether or not this means that coin has been redefined to mean penny. (Yes, the rest of us all know the answer is no. But were curious what _your_ answer is.) >> In Smullyans system, he is not defining provable to mean the >> same thing as true >> but it happens to be the case that for his >> system, every true sentence is provable, and vice-versa. >That is simply false. You are not describing anything different - it >is the exact same system with the same axioms, the same rules (none) >and the same theorems. Wheres the difference? It is mathematically >identical. You are quibbling over descriptions which are >mathematically equivalent. >> Hes saying that the *axioms* of N are all true sentences. It >> *follows* from this that a formula is true if and only if it >> is provable in N. >Same axioms, same rules, same theorems. Same Theory. The only system >that meets DUs condition for being ignorant Gorbkle. Where did I say anything about formal systems being ignorant? >is Smullyans System N. >C-B >> -- >> Daryl McCullough >> Ithaca, NY ************************ David C. Ullrich === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem Charlie-Boo says... >1. You say above that if we define provability to be truth in a system >like N . . . then the provable sentences will coincide with the true >sentences. But Smullyan did *not* define provability to be truth. >2. In Smullyans system N, the provable sentences coincide with the >true sentences. >3. Therefore Smullyan is defining provability to be truth. No, he isnt. -- Daryl McCullough Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem posting-account=9wVPIwwAAAAonf5Dj39AQaTL2sJYvErF > Charlie-Boo says... >1. You say above that if we define provability to be truth in a system >like N . . . then the provable sentences will coincide with the true >sentences. > But Smullyan did *not* define provability to be truth. >2. In Smullyans system N, the provable sentences coincide with the >true sentences. >3. Therefore Smullyan is defining provability to be truth. > No, he isnt. CAT: Does Smullyans system N meet the condition after the ellipsis in # 1? C-B > -- > Daryl McCullough > Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem Charlie-Boo says... >> Charlie-Boo says... >>1. You say above that if we define provability to be truth in a >system >>like N . . . then the provable sentences will coincide with the true >>sentences. >> But Smullyan did *not* define provability to be truth. >>2. In Smullyans system N, the provable sentences coincide with the >>true sentences. >>3. Therefore Smullyan is defining provability to be truth. >> No, he isnt. >CAT: Does Smullyans system N meet the condition after the ellipsis in ># 1? You seem to be under the impression that if A imples B, then it follows that B implies A. A = provability is defined to be the same as truth B = the provable statements are exactly the true statements It is certainly the case that A implies B. But it is not the case that B implies A. So the truth of B implies nothing about the truth of A. -- Daryl McCullough Ithaca, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem posting-account=9wVPIwwAAAAonf5Dj39AQaTL2sJYvErF > Charlie-Boo says... >CAT: Does Smullyans system N meet the condition after the ellipsis in ># 1? Well? > You seem to be under the impression that if A imples B, then > it follows that B implies A. > A = provability is defined to be the same as truth > B = the provable statements are exactly the true statements > It is certainly the case that A implies B. But it is not the case > that B implies A. So the truth of B implies nothing about the truth > of A. They are Mathematically identical. There is only one system that meets this condition: AXIOMS = THEOREMS = TRUE SENTENCES. Only this structure satisfies the DU/Raymond Smullyan description. It has to be the same system. C-B > Daryl McCullough > Ithica, NY === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem >> Charlie-Boo says... >In that theory, is Smullyan defining provability to be truth? No, hes not. Provability always means the same thing: >derivability > from the axioms by the rules of inference of first-order logic. >What > Smullyan is doing is choosing the *axioms* to be all true >sentences > of arithmetic. >>Is Smullyan defing provability in that theory? >> No, hes not. Provability always means the same thing: derivability >> from the axioms by the rules of inference of first-order logic. >> What Smullyan is doing is choosing the *axioms* to be all true >> sentences of arithmetic. >How would one define provability to be truth in a system like N if one >wanted to do so? Its really hard to understand what youre trying to prove by asking the same question over and over. Provability has already been defined in that system - it means derivability from the axioms, as always. Hint: although its hard to see what youre _trying_ to prove, what you _are_ proving is clear to everyone but you. >C-B >> -- >> Daryl McCullough >> Ithaca, NY ************************ David C. Ullrich === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem <14ras09md0bvs1r3grod1q6d948ecjsjhu@4ax.com> posting-account=9wVPIwwAAAAonf5Dj39AQaTL2sJYvErF > Its really hard to understand what youre trying to prove by > asking the same question over and over. It was the answer that was repeated, not the question. > Provability has already > been defined in that system - it means derivability from the > axioms, as always. Far from being always, that isnt even what Smullyan is doing. As you can see from my quote alone, he makes no reference to derivation rules in his definition of provability, nor does he use any - anywhere in system N. He defines provability solely in terms of truth. (He uses derivation rules in N as much as he uses a straight edge and compass.) Derivation rules (with reasonable assumptions) produce only recursively enumerable sets of provable sentences. Since the set of provable sentences in N is not r.e., then naturally he had to simply declare the provable sentences to be the true sentences instead of using derivation rules. But even if he were using derivation rules as you describe, that would not represent what Smullyan is talking about - the provable sentences coinciding with the true sentences. That is what he added (in place of derivation rules) and in fact is the very reason Smullyan created system N: to define provability to be truth. (Unmentioned to date is the fact that system N is the system in which the representable relations are precisely the Arithmetic relations.) It sounds like a number of proofs are hard for you to understand. > Hint: although its hard to see what youre _trying_ to prove, > what you _are_ proving is clear to everyone but you. Off-the cuff (afterthought), unsubstantiated (only the claim is given), all-encompassing (everyone). Yes, some things do seem to be keep happening over and over around here. You know, if we all agreed that off-the-cuff, unsubstantiated, all-encompassing statements are the work of idiots, we could be a lot more efficient. I vote for that derivation rule. C-B Actually, a much more interesting question is to consider 3 problems concerning a wff: 1. How to prove it? 2. How to determine if it is true? 3. How to develop a computer program that determines if it is true? Heres a first step in developing a single system to define both truth (2) and provability (1) - as well as the constructive (combinator) proof - program creation (3): Apply 1-3 to P^Q: a. |- P^Q <= > |- P and |- Q b. |= P^Q <=> |= P and |= Q c. A program to evaluate P plus a program to evaluate Q can be combined to create a program that evaluates P^Q (but not vice-versa.) (Notice the lack of a standard syntax for (c) - thats another problem that my axiomatization fixes.) and PvQ: d. |- P or |- Q => |- PvQ e. |= P or |= Q => |= PvQ f. A P program plus a Q program can be combined to produce a PvQ program. and (eA)P(A) and (aA)P(A): g. |- (aA)P(A) => (aA)|-P(A) h. (eA)|-P(A) => |- (eA)P(A) i. (aA)|-P(A) => ~ |- ~(aA)P(A) j. P |- Q <=> |= P -> Q k. A P(x) enumeration program can be transformed into a (eA)P(A) partial solution program. I believe that examining the exact relationships between these problems and their solutions (e.g. how each handles each special case of a wff) is one of the most fundamental problems lying in the intersection of Mathematics, Logic and Computer Science. (Dont worry. Even after Toto exposed the Wizard of Oz as being a big fake, Dorothy still liked him.) > ************************ > David C. Ullrich === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem >> Its really hard to understand what youre trying to prove by >> asking the same question over and over. >It was the answer that was repeated, not the question. >> Provability has already >> been defined in that system - it means derivability from the >> axioms, as always. >Far from being always, that isnt even what Smullyan is doing. As >you can see from my quote alone, he makes no reference to derivation >rules in his definition of provability, nor does he use any - anywhere >in system N. He defines provability solely in terms of truth. (He >uses derivation rules in N as much as he uses a straight edge and >compass.) Maybe you didnt bother to read the quote that you posted: We call a formula F(v1,. . .,vn) correct if for every n-tuple (a1,...,an), the sentence F(a1,. . .,an) is true. We let N be the first-order system whose axioms are all the correct formulas (this includes all logically valid formulas.) Thus, the provable formulas of N are nothing more than the axioms of N. Note the phrase We let N be the first-order system whose axioms are.... Thats quite explicit: hes defining a set of axioms. Also note the sentence Thus, the provable formulas of N are nothing more than the axioms of N. If this were a definition of provable then that Thus would make no sense - the word Thus means that what hes saying here _follows_ _from_ the definition hes just given. It cant follow from that if provable has not yet been defined - the only way it can follow from the previous part of the paragraph is if we already know what provable means. You know this really is hilarious: Before you posted that quote people were explaining to you that no, hes not defining provability to be the same as truth - people whod never read the book were explaining that, basing their assertions solely on the fact that Smullyan knows what hes talking about! Now you post that quote, thinking it shows youre right. But if you read it you see it shows just the opposite. Yes, you have to read it carefully, paying attention to exactly whats written. Logic is like that. ************************ David C. Ullrich === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem >>[...] >> Hint: although its hard to see what youre _trying_ to prove, >> what you _are_ proving is clear to everyone but you. >Off-the cuff (afterthought), unsubstantiated (only the claim is given), >all-encompassing (everyone). Giggle. Its not the sort of assertion thats susceptible to mathematical proof. Thought you might be interested because its true nonetheless (as we well know, truth and provability are different things...) ************************ David C. Ullrich === Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem Charlie-Boo says... >> Provability has already >> been defined in that system - it means derivability from the >> axioms, as always. >Far from being always, that isnt even what Smullyan is doing. Yes, he is. >As you can see from my quote alone, he makes no reference to derivation >rules in his definition of provability, nor does he use any - anywhere >in system N. He assumes that the reader is already familiar with the notion of provability, at least to the extent that if you choose all true sentences as your axioms, then every true sentence will be provable. >He defines provability solely in terms of truth. No, he does not. He defines the *axioms* of his theory N in terms of truth. It *follows* from this that a formula of N is true if and only if it is provable. -- Daryl McCullough Ithaca, NY === Subject: Re: how to solve the problem? <23829-41C2F55F-448@storefull-3254.bay.webtv.net> posting-account=XKIvcAwAAABjV0_KSzxujBgt25t7XOUn > For n = 2 there is no unique solution; you cant define two numbers from > just their average. The problem is underdetermined. For n = 3 you can > set up a linear solution thats easy to solve. To wit, x_1+x_2 = 2*x_12 > and similarly for the pairs {1, 3} and {2, 3}. This easily gives x_1 = > x_12 + x_13 - x_23 and cyclic permutations. For n >= 4 the problem as > stated is overdetermined because the diagonal entries are unavoidably > dependent on one another. There are only n inputs entering into > n*(n-1)/2 outputs where, for n >= 4, (n-1)/2 > 1. One must select an > appropriate subset of n out of the nondiagonal entries to specify. > --OL I dont think thats quite right (or Im misunderstanding something -- which happens a lot lately ... alas ... ): If you sum the nondiagonal entries of (say) the 1st row and multiply the result by 2, you generate the linear equation (n-1)x_1 + x_2 + ... + x_n = what you just calculated ; doing the same for all of the other rows, you end up with a system of n linear equations in n unknowns with the coefficient matrix A having (n-1)s down the diagonal and 1s elsewhere. If n = 2, the matrix A is singular, but for n > 2 it is _not_ (so the problem has a unique solution for n > 2). To see that my claim is true, note that A = J_n + (n-2)I_n with J_n the nxn matrix with all entries 1 and I_n the nxn identity matrix. It follows that det(A) = det(-((2-n)I_n - J_n)) = (-1)^n det((2-n)I_n - J_n) = (-1)^n j_n(2-n) where j_n denotes the characteristic polynomial of J_n. But J_n has 0 as an eigenvalue of multiplicity (n-1) and n as an eigenvalue of multiplicity 1, so j_n(t) = t^{n-1}(t - n). Hence, det(A) = (-1)^n (2-n)^{n-1} (2-2n) = 2(n-1)(n-2)^{n-1} and the claim follows ... === Subject: Re: Unknown Functions & Einsteins Incompetence [snip lies] > Unknown Functions & Einsteins Incompetence (FAQ) > (c) Eleaticus/Oren C. Webster > Thnktank@concentric.net [snip trolled garbage] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Originally trolled across sci.physics sci.physics.relativity alt.physics sci.math sci.answers alt.answers news.answers Psychotic ineducable boring troll Eleaticus, Were there to be internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) that would automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t = t, x = x - vt, y = y, z = z. His refusal to accept that t must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to fields over space and time (electric and magnetic fields for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt = d/dt + v d/dx, d/dx = d/dx, d/dy = d/dy, d/dz = d/dz. This shows the necessity of introducing a new variable t, since partial differentiation with respect to t (constant x, y, z) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt = dt/dt d/dt + dx/dt d/dx + dy/dt d/dy + dz/dt d/dz, d/dx = dt/dx d/dt + dx/dx d/dx + dy/dx d/dy + dz/dx d/dz, d/dy = dt/dy d/dt + dx/dy d/dx + dy/dy d/dy + dz/dy d/dz, d/dz = dt/dz d/dt + dx/dz d/dx + dy/dz d/dy + dz/dz d/dz. The presence of the term involving d/dx in the expression for d/dt is indicative of the fact that x depends on t (x, y, z, being held constant), as can be seen from the fact that the coefficient of d/dx in the expression for d/dt is dx/dt. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt is indicative of t depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwells Equations under the Galilean Transformation. The first advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwells Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x = E_x, E_y = E_y - v B_z, E_z = E_z + v B_y, B_x = B_x, B_y = B_y, B_z = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x = E_x, E_y = E_y, E_z = E_z, B_x = B_x, B_y = B_y + v/c^2 E_z, B_z = B_z - v/c^2 E_y, rho = rho, J_x = J_x - v rho, J_y = J_y, J_z = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwells Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM field for the two cases are inconsistent with each other. The transformation law for the EM field which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM field which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwells equations are invariant under the Lorentz Transformation, with transformation laws: E_x = E_x, E_y = gamma (E_y - v B_z), E_z = gamma (E_z + v B_y), B_x = B_x, B_y = gamma (B_y + v/c^2 E_z), B_z = gamma (B_z - v/c^2 E_y), rho = gamma (rho - v/c^2 J_x), J_x = gamma (J_x - v rho), J_y = J_y, J_z = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arxiv.org/abs/gr-qc/0103044 http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation No aether http://fsweb.berry.edu/academic/mans/clane/ No Lorentz violation http://arXiv.org/abs/gr-qc/0409089 Spin-2 gravitons have problems (so does the proposal) http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect http://arxiv.org/abs/astro-ph/0403292 http://arXiv.org/abs/astro-ph/0310723 WMAP + Sloane Digital Sky Survey http://arxiv.org/abs/hep-ph/0404175 Dark matter candidates Carroll on what it all means. Special Relativity is physics on a topologically trivial Lorentzian manifold with a metric whose curvature tensor is zero. This is a perfectly diffeomorphism-invariant condition and does not require any particular coordinate choice. It is invariant under the full group of diffeomorphisms. The Poincare group is the group of *isometries* of the metric in special relativity. The Special Relativity metric is *non-dynamical* (unlike GR). It defines the coupling *constants* of your theory. If you change the metric in any nontrivial way you are changing your theory. An operation can only be called a symmetry of a special-relativistic (non-gravitational) theory if it preserves the metric, and therefore the symmetry of special-relativistic theories is the Poincare group only. General Relativity (gravitation) has a dynamic metric. NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf Longitudinal and transverse mass http://arxiv.org/abs/gr-qc/0306076.pdf http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: Unknown Functions & Einsteins Incompetence > [snip lies] [snip lies] Androcles. === Subject: Re: Unknown Functions & Einsteins Incompetence > [snip lies] > [snip lies] > Androcles. Your ignorance, incompetence, and psychosis are not of interest to the world at large. Quite the contrary. You are not even an interesting laughingstock. http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: Unknown Functions & Einsteins Incompetence >> [snip lies] >> [snip lies] >> Androcles. > Your ignorance, incompetence, and psychosis are not of interest to the > world at large. Quite the contrary. You are not even an interesting > laughingstock. Repetitive boring fucking moron. [snip crap] Androcles === Subject: Probability-continuous random variables posting-account=__WCMw0AAACDTl8muX4MFuov_vIZutrh I just got half way comfortable with continuous random variables and now my professor has assigned this homework problem which I dont understand well enough to complete. X is a random variable with density f(x)= e^5x x<0 .2x 0<=x<=2 c 2I just got half way comfortable with continuous random variables and >now my professor has assigned this homework problem which I dont >understand well enough to complete. X is a random variable with density >f(x)= e^5x x<0 >.2x 0<=x<=2 >c 20 elsewhere >a.) Find c Hint: If you integrate f(x) from -inf to inf, what must you get? So c=? >b.) Find P(-1<=x<=1 >My first approach is that I integrate each of the above functions using >-1 through 1 and add their answers to get a cumulative distribution >function, but Im not really sure. Please help! P(-1 <= x <=1) = integral(-1..1) f(x) dx, no? --Lynn === Subject: Re: Probability-continuous random variables <1m=EQT6l66iZgqKgfOt9NbluR4iL@4ax.com> posting-account=__WCMw0AAACDTl8muX4MFuov_vIZutrh === Subject: Re: Einstein (1905) Absurdities [snip lies] > Einstein (1905) Absurdities > (c) Eleaticus/Oren C. Webster > Thnktank@concentric.net [snip 1300 lines of trolled garbage] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ Crimes.html Several crimes against logic and science Ha ha ha! Originally trolled across sci.physics sci.physics.relativity alt.physics sci.math sci.answers alt.answers news.answers Psychotic ineducable boring troll Eleaticus, Were there to be internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) that would automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t = t, x = x - vt, y = y, z = z. His refusal to accept that t must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to fields over space and time (electric and magnetic fields for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt = d/dt + v d/dx, d/dx = d/dx, d/dy = d/dy, d/dz = d/dz. This shows the necessity of introducing a new variable t, since partial differentiation with respect to t (constant x, y, z) is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt = dt/dt d/dt + dx/dt d/dx + dy/dt d/dy + dz/dt d/dz, d/dx = dt/dx d/dt + dx/dx d/dx + dy/dx d/dy + dz/dx d/dz, d/dy = dt/dy d/dt + dx/dy d/dx + dy/dy d/dy + dz/dy d/dz, d/dz = dt/dz d/dt + dx/dz d/dx + dy/dz d/dy + dz/dz d/dz. The presence of the term involving d/dx in the expression for d/dt is indicative of the fact that x depends on t (x, y, z, being held constant), as can be seen from the fact that the coefficient of d/dx in the expression for d/dt is dx/dt. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt is indicative of t depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwells Equations under the Galilean Transformation. The first advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwells Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x = E_x, E_y = E_y - v B_z, E_z = E_z + v B_y, B_x = B_x, B_y = B_y, B_z = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x = E_x, E_y = E_y, E_z = E_z, B_x = B_x, B_y = B_y + v/c^2 E_z, B_z = B_z - v/c^2 E_y, rho = rho, J_x = J_x - v rho, J_y = J_y, J_z = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwells Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM field for the two cases are inconsistent with each other. The transformation law for the EM field which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM field which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwells equations are invariant under the Lorentz Transformation, with transformation laws: E_x = E_x, E_y = gamma (E_y - v B_z), E_z = gamma (E_z + v B_y), B_x = B_x, B_y = gamma (B_y + v/c^2 E_z), B_z = gamma (B_z - v/c^2 E_y), rho = gamma (rho - v/c^2 J_x), J_x = gamma (J_x - v rho), J_y = J_y, J_z = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arxiv.org/abs/gr-qc/0103044 http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation No aether http://fsweb.berry.edu/academic/mans/clane/ No Lorentz violation http://arXiv.org/abs/gr-qc/0409089 Spin-2 gravitons have problems (so does the proposal) http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect http://arxiv.org/abs/astro-ph/0403292 http://arXiv.org/abs/astro-ph/0310723 WMAP + Sloane Digital Sky Survey http://arxiv.org/abs/hep-ph/0404175 Dark matter candidates Carroll on what it all means. Special Relativity is physics on a topologically trivial Lorentzian manifold with a metric whose curvature tensor is zero. This is a perfectly diffeomorphism-invariant condition and does not require any particular coordinate choice. It is invariant under the full group of diffeomorphisms. The Poincare group is the group of *isometries* of the metric in special relativity. The Special Relativity metric is *non-dynamical* (unlike GR). It defines the coupling *constants* of your theory. If you change the metric in any nontrivial way you are changing your theory. An operation can only be called a symmetry of a special-relativistic (non-gravitational) theory if it preserves the metric, and therefore the symmetry of special-relativistic theories is the Poincare group only. General Relativity (gravitation) has a dynamic metric. NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf Longitudinal and transverse mass http://arxiv.org/abs/gr-qc/0306076.pdf http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Re: Einstein (1905) Absurdities posting-account=-x-CNg0AAABT6_BwYPRSClG5m9scXgEw mister uncle al I know your not an uncle, your name dont fool me thank you for the links anyway have a nice day === Subject: Re: Einstein (1905) Absurdities > mister uncle al > I know your not an uncle, your name dont fool me > thank you for the links anyway > have a nice day Uncle Als sister whelped four times: one anencephalic female (like mother like daughter); three surviving males whose genitalia were permanently mutilated six days later. Said severed ßesh was ceremonially buried in the backyard. You cannot be fooled any more then a holed bucket can be filled. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: Probability-joint uniform distribution posting-account=__WCMw0AAACDTl8muX4MFuov_vIZutrh Mike and Jeff walk independently. The distance that Mike walks is uniformly distributed between 0 and 2 miles,and the distance Jeff walks is unformly distributed between 0 and 5 miles. Graphically I can picture whats happening along the X-axis but Im lost on what I need to do. My first idea is to complete a double integral but Im not sure how to set the integral up. 0-------------------------5 miles Jeff 0--------2 miles Mike a.) Give the joint density function of X and Y, where X is the distance that Mike walks and Y is the distance Jeff walks. ****(Include the support) b.) find the probability that Jeff walks at least twice as far as Mike does. === Subject: Re: Probability-joint uniform distribution >Mike and Jeff walk independently. The distance that Mike walks is >uniformly distributed between 0 and 2 miles,and the distance Jeff walks >is unformly distributed between 0 and 5 miles. Graphically I can >picture whats happening along the X-axis but Im lost on what I need >to do. My first idea is to complete a double integral but Im not sure >how to set the integral up. >0-------------------------5 miles Jeff >0--------2 miles Mike >a.) Give the joint density function of X and Y, where X is the distance >that Mike walks and Y is the distance Jeff walks. Hint: How do you get the joint density given independence of X and Y? And for what values of x and y is the joint density non-zero? >****(Include the support) >b.) find the probability that Jeff walks at least twice as far as Mike >does. Hint: Shade the region in the xy plane where y >= 2x. That should help you with your limits. --Lynn === Subject: New from Akronos: What is Dark Energy? Akronos Publishing is pleased to announce the addition to its website of the following feature: WHAT IS DARK ENERGY? (What Is, and Is Not, Dark Massfree Energy) by Paulo N. Correa and Alexandra N. Correa http://www.aetherometry.com/dark_energy.html What is Dark Energy? Does it exist? Is there a Massless Dark Energy that was left over from the Big Bang? Is this Massless Dark Energy the mass of ordinary Matter - leptons and baryons - when they do not even explain their own (super)mass? Why havent these supermassive costliest of searches for their existence? Could this failure signal the bankrupcy of the Standard Model and underline the misguided scientific direction and expenditures of institutions such as NASA and the DOE? Could the Big Bang have never taken place and Dark Energy be that has existed as of all time? Could it be Dark Massfree Energy Massfree Energy lie at the opposite end of the energy spectrum from where the search for the Higgs still goes on? Could physics be laboring on a colossal mistake - one that has served only for the sensationalist promotion of Star Wars and Exotic Bomb projects? These are the provocative questions which this straightforward communication addresses, from the physical and micropolitical viewpoints of Aetherometry. Yours, Laura McFinlay Akronos Publishing === Subject: nonstandard models of some of the ordinals posting-account=nrmAfQ0AAAAVEvs440MQyHc_cv3FW6ZR I have been having fun reading Robert Goldblatts book on the hyperreal numbers. Although I am older, and am a geneticist now, I might be considered at the level of an advanced undergraduate. As such, I have a question which I hope some of you can help me with. I have been thinking of the hypernatural numbers as constructible models for some of the smaller ordinal numbers, in a very elementary fashion as might be explained to advanced high school students, perhaps Thus, omega = {1,2,3,...}, i.e. the sequence of natural numbers, as he described. Then, as a first grader looking for a bigger hypernatural number would say omega+1 = {2,3,4, ...} 2*omega = {2,4,6, ...} 2*omega +1 ={3,5,7, ...} omega^2 = (1,4,9,16, ...}, omega^m = {1,2^m,3^m, ...}. Now comes my first question. I want to get to omega^omega. Suppose I first look at {2,4,8,16, ...,2^n, ...}. What is this? 2^omega in the hypernaturals? If so, then form 3^omega, 4^omega, ... . What about {1^1, 2^2, 3^3, ...} ? Is this omega^omega? Then as usual {2^(2^1), 2^(2^2),2^(2^3), ...} Is this 2^(2^omega) ? Then {1^(1^1), 2^(2^2), 3^(3^3), ...} Is this omega^(omega^omega)) ? Then {1, 2^2, 3^(3^3), 4^(4^(4^4)), ...} Is this omega^(omega^(omega^( ...))) in the hypernaturals? Second question: Suppose I look at {Ack(1), Ack(2), Ack(3), ...} where Ack is the unitary Ackerman function. What ordinal does this correspond to? Are there any very elementary references in this regard? === Subject: Re: nonstandard models of some of the ordinals posting-account=tdYrvA0AAACTm02P3kgbrEwRzJI8b08S Isnt everything defined componentwise? I.e. (A,B,...)^(a,b,...)=(A^a,B^b,...) (A,B,...)^(2,2,...), because 2 corresponds to (2,2,...) (or the equivalence class containing (2,2,...) anyway ) ) === Subject: Re: nonstandard models of some of the ordinals > Isnt everything defined componentwise? If you wish, or if someone wishes. But if you use ordinal and omega near one another, people[1] will think that omega is the ordinal of that name, and ordinal arithmetic is not defined componentwise (there are no components). [1: I did, sorry if I got you wrong.] === Subject: Re: nonstandard models of some of the ordinals posting-account=tdYrvA0AAACTm02P3kgbrEwRzJI8b08S > If you wish, or if someone wishes. But if you use ordinal and omega > near one another, people[1] will think that omega is the ordinal of that > name, and ordinal arithmetic is not defined componentwise (there are no > components). But then dont you lose the whole ultraproduct structure? === Subject: Re: nonstandard models of some of the ordinals posting-account=nrmAfQ0AAAAVEvs440MQyHc_cv3FW6ZR Your comments have all been helpful, and I now I can say things a little differently. A few points. First, two apologies. A. For now, as George Cox mentioned above, I was unfortunately using brackets to designate sequences not sets; I will try to make it clearer in the future and less confusing. (I borrowed the notation from the book.) that omega, the smallest infinite ordinal of set theory = sequence{1,2,3, ...}. This was an overenthusiatic error of my own, and as pointed out by Prof. Ullrich above, cannot be correct in the naive form in which it was written, Second, that out of the way, what am I trying to say? Suppose, inspired by the construction of the hyperreal numbers in non standard analysis, we choose a particular integer sequence as a name for the smallest infinite ordinal of set theory, which is usually called omega. This sequence name is not uniquely specified, as pointed out by Prof. Ullrich above, but my hunch is that the structure of what follows will be invariant with respect to different initial choices of otherwise equally good one sided sequences as names for omega. In particular, suppose we choose (my hunch above is without loss of generality) the particular sequence (not set) {1,2,3, ...} as the new fixed name for omega, the smallest infinite ordinal of set theory. Then, in the ring of hyperinteger sequence names, other names suggest themselves for other ordinals, as indicated in my original post, above. For example,there is of course in set theory an ordinal sucessor to omega, often called omega+1. The sequence (not set) {2,3,4, ...} suggests itself as a name for this ordinal, under this naming convention, and so on as suggested above. Whats the point? If the guess of invariance with respect to naming convention is right, then the set of names under fixed convention have the structure one might have guessed when one was 9 years old and wondering about infinity, i.e. a commutative ring, just like the integers. So in the age old discussion, one could have said, No, infinity is not a number, but its name is a hypernumber, or something. E.g seq{1,2,3, ...} - seq {2,4,6, ...} = - seq {1,2,3, ...}, etc. This seems cool. The question is, is it ever at variance with the actual structure of the ordinary ordinals, or as I assumed, can the ordinals be embedded in the hyperintegers with naming convention, in the same way that the reals can be embedded in the hyperreals? P.S. Why the guess of invariance with respect to the initial choice of names for omega? Because whatever name we choose, the ring structure still applies. === Subject: Re: nonstandard models of some of the ordinals (I shortened the lines here.) |In particular, suppose we choose (my hunch above is without loss |of generality) the particular sequence (not set) {1,2,3, ...} Probably (1,2,3,...) would be better. |as the new fixed name for omega, the smallest infinite ordinal |of set theory. Then, in the ring of hyperinteger sequence names, |other names suggest themselves for other ordinals, as indicated |in my original post, above. Ordinals correlate to well-orderings. So if you want to relate them to the hyperintegers, what you want to do is find a well-ordered subset of the hyperintegers. I think this is what you want to do. :-) The hyperintegers >0 are not well-ordered. You have for example an infinite descending sequence (1,2,3,...)>(1,1,2,3,...)> (1,1,1,2,3,...)>.... So if you want to have a well-ordered subset of the hyperintegers, you have to just decide to take only some of them. Someone pointed out already that the operations on the hyperintegers and the operations on the ordinals dont correspond. Ill give you another example of that. As ordinals, 2^omega=omega. This is different from how hyperintegers work, where 2^omega>omega, and is also different from how operations on infinite cardinals work. So you need to be careful. If I were you, Id pick a different name for (1,2,3,...), actually, than omega just to be sure I didnt confuse the two. The sum, product, or exponential of two ordinals will not generally map to the sum, product, or exponential of the hyperintegers you mapped them to. But thats okay as long as you remember it. Given a countable collection of hyperintegers, there exists a hyperinteger greater than all of them. (Exercise!) So any countable ordinal can be embedded in them, and even aleph_1. I dont know what ordinals can be embedded in them; I dont see offhand whether aleph_1+1 embeds in them. Keith Ramsay === Subject: Re: nonstandard models of some of the ordinals > For example,there is of course in set theory an ordinal sucessor to > omega, often called omega+1. > The sequence (not set) {2,3,4, ...} suggests itself as a name for this > ordinal, > under this naming convention, and so on as suggested above. No, if omega is the smallest infinite ordinal, omega + 1 does not equal {2,3,4, ...} (sequence or set). If omega is 1,2,3,... then omega + 1 is 1,2,3,...,1. === Subject: Re: nonstandard models of some of the ordinals > Because whatever name we choose, the ring structure still applies. You know, addition and multiplication in the hyperreals satisfy the usual identities, addition and multiplication in the ordinals do not... not commutative, for example. There is a scheme used by logicians where rapidly-growing sequences if natural numbers correspond to ordinals; but they do not bring in nonstandard analysis as an intermediary. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Re: nonstandard models of some of the ordinals posting-account=7ryOqgsAAABSV_46k1efyFxO01THH4J8 You can visualize those numbers in that way, they are names that you assign to those constructions. 1, 2, 3, ...} = omega, thus any algebaric operation on omega, the number or ordinal, applies to each element of the set that comprises omega. Then, for example with the case 2 * omega, a resulting aspect of the set, now being the even numbers, is that the asymptotic density has been halved, its the reciprocal and in this case inverse of the scalar multiplier of the ordinal. Thus, in a way you have the same number, infinity is immutable. While that is so, infinite sets are equivalent, while that is so, theres still the notion that you can manipulate the symbol omega, little Greek w, just as if it were the scalar unity. For the finite scalar multiplier the asymptotic density is only the inverse, but with the infinite scalar multiplier, or finite exponential, then the asymptotic density of the resulting set goes to zero. It is yet positive: its infinitesimal. In another way, the density of the prime number is known, leading to an infinite ordinal that is the ordinal formed by that set of natural integers. Thus, while infinity is in a way immutable, you can consider performing operations on it as if it were a number, where it automatically equalizes to itself with the accounting in the second column. Dont mind me too much, Im well-known for discussing infinity. Basically, the notion is that infinity is in various ways usable and conincident and coexistent with zero, one and after the negative numbers negative one. Thats where at the deep foundation of infinity, it is the same as the void, and the difference subsumes all inbetween. I, and sometimes we, can consider infinity and null as the same or indistinguishable things, because they share common properties of the necessarily unique and existent non-entity (entities). That enables the mathematical discussion to neatly dovetail with the logical and even philosophical, and for some, the epistemological and existential. Ross Finlayson === Subject: Re: nonstandard models of some of the ordinals >I have been having fun reading Robert Goldblatts book on the hyperreal >numbers. Although I am older, and am a geneticist now, I might be >considered at the level of an advanced undergraduate. As such, I have >a question which I hope some of you can help me with. >I have been thinking of the hypernatural numbers as constructible >models for some of the smaller ordinal numbers, in a very elementary >fashion as might be explained to advanced high school students, perhaps >Thus, omega = {1,2,3,...}, i.e. the sequence of natural numbers, as he >described. >Then, as a first grader looking for a bigger hypernatural number would >say >omega+1 = {2,3,4, ...} >2*omega = {2,4,6, ...} >2*omega +1 ={3,5,7, ...} >omega^2 = (1,4,9,16, ...}, omega^m = {1,2^m,3^m, ...}. >Now comes my first question. I want to get to omega^omega. >Suppose I first look at {2,4,8,16, ...,2^n, ...}. >What is this? 2^omega in the hypernaturals? >If so, then form 3^omega, 4^omega, ... . >What about {1^1, 2^2, 3^3, ...} ? >Is this omega^omega? >Then as usual {2^(2^1), 2^(2^2),2^(2^3), ...} >Is this 2^(2^omega) ? >Then {1^(1^1), 2^(2^2), 3^(3^3), ...} >Is this omega^(omega^omega)) ? >Then {1, 2^2, 3^(3^3), 4^(4^(4^4)), ...} >Is this omega^(omega^(omega^( ...))) in the hypernaturals? >Second question: >Suppose I look at {Ack(1), Ack(2), Ack(3), ...} where Ack is the >unitary Ackerman function. >What ordinal does this correspond to? >Are there any very elementary references in this regard? Well, this makes a little more sense after your second post on the topic. Enough sense that its clear that your questions about which ordinal various sequences correspond to do not have answers, because you have not _specified_ what the correspondence _is_. Its true that youve defined a few hyperreals that are ordered in the same way as a few infinite ordinals. But there are many other ways you could have done this - theres nothing unique about your choice of which ordinal corresponds to omega+1, so theres really no answer to the question of which ordinals those other hyperreals correspond to until you _define_ the correspondence. (If thats not clear: Even if we restrict to just sequences of positive integers, as you seem to be doing, the hyperreal you say is omega is not the smallest hyperreal larger than every natural number. For example (1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,...) is larger than every natural number but smaller than the thing youre saying corresponds to omega. Why does the sequence above correspond to omega, why isnt it this one?) ************************ David C. Ullrich === Subject: Re: nonstandard models of some of the ordinals <1i39s0l3dbd1mpnptspjupnafgj70c56c9@4ax.com> posting-account=nrmAfQ0AAAAVEvs440MQyHc_cv3FW6ZR Yes, you are right; I didnt think of that. But suppose we do everything modulo a particular choice of a representative sequence for omega. Since the integer sequences are constant, the first few examples seem to go through OK. Then, for the, more advanced examples of larger ordinals (i.e. each time we exponentiate) maybe we have to choose a representative again. Admittedly, this only gives a branching tree of models, but still interesting, if true. === Subject: Re: nonstandard models of some of the ordinals >I have been having fun reading Robert Goldblatts book on the hyperreal >numbers. ... >Thus, omega = {1,2,3,...}, i.e. the sequence of natural numbers, as he >described. Okay, thats standard enough. >Then, as a first grader looking for a bigger hypernatural number would >say >omega+1 = {2,3,4, ...} >2*omega = {2,4,6, ...} >2*omega +1 ={3,5,7, ...} >omega^2 = (1,4,9,16, ...}, omega^m = {1,2^m,3^m, ...}. >Now comes my first question. No, before it comes *my* question: are these first grader encodings of bigger hypernatural numbers than omega being done according to a scheme from Goldblatts book (which Ive never seen, nor even heard of before)? If so, could you explain his scheme to those of us who havent seen it? If not, can you provide some meaningful explanation of your own? Not a one of those equations makes sense to me, from what I learned (long ago, from a book by Szierpinski, I think) about === ordinals. (Since your Subject: header uses the word ordinals, and omega+1,..., omega^2 are the sorts of names ordinals have, I assume you are trying to write equations in ordinals. If not--if, indeed, youre writing equations for some kind of hypernatural numbers that dont purport to be ordinals--then please clarify further.) Lee Rudolph === Subject: Re: nonstandard models of some of the ordinals >I have been having fun reading Robert Goldblatts book on the hyperreal >numbers. > ... >Thus, omega = {1,2,3,...}, i.e. the sequence of natural numbers, as he >described. > Okay, thats standard enough. The notation is confusing. The op means the sequence (1,2,3,...) not the set {1,2,3,...}. So omega is not the smallest infinite ordinal. === Subject: Re: nonstandard models of some of the ordinals posting-account=nrmAfQ0AAAAVEvs440MQyHc_cv3FW6ZR Robert Goldblatts book Lectures on the Hyperreals (Springer 1998), describes aspects of the theory of nonstandard analysis. It is easy and fun to read. Roughly speaking, consider a system in which numbers are replaced by equivalence classes of infinite sequences, two sequences being equivalent iff they differ at only a finite number of positions. Drastically oversimplifying, this forms a ring under pointwise addition and multiplication of sequence elements. However, the product of two non-zero elements can equal zero. (e.g. {0,1,0,1, ...} * {1,0,1,0,, ...} = 0) Ordinary numbers correspond to constant sequences. Infinite numbers correspond to divergent sequences. Eventually the ordinary reals embed in an extension of such a system, as well as infinitesimals (e.g. {0,0,0, ...} < {1,1/2, 1/3, ...} < epsilon for any ordinary real number epsilon > 0.) and infininite numbers. Hope this helps Ordinary === Subject: Is there a footprint of intrinsic geometry in the Levi-Civita connection? The Question is: What is The Question? J.A. Wheeler The {LC} connection field in GR curved spacetime is analogous to the EM vector potential A connection in internal space. The tidal stretch-squeeze GCT tensor field = {LC} curl of itself is analogous to the Maxwell EM Fuv field tensor. {LC} and A are both Cartan 1-forms. Curvature and Fuv are both Cartan 2-forms. Zs hullaballo bruhaha has been a search to find the GR analog to the Maxwell decomposition F = -GradU + CurlA Note Cartan identities d^2 = 0 CurlGradU = 0 DivCurlA = 0 GradU is a Cartan 1-form = dS Curl 1-form = d(1-form) dS is an exact 1-form CurlA =/= 0 if the 1-form A is NOT exact. CurlA =/= 0 is an exact 2-form = dA DivCurlA is d^2A = 0 vanishing 3-form All vector fields in 3D are UNIQUELY defined if their circulation densities (curl) and source densities (divergence) are given functions of the coordinates at all points in space, and if the totality of the sources, as well as the source density, is zero at infinity. Panofsky & Phillips Classical Electricity and Magnetism p. 2 Note an infinite ßat plate (vacuum domain wall) violates the required asymptotic ßatness in the GR application. Therefore, The Question is, is there an analogous decomposition for GR at the level, not of the tidal curvature, but of the {LC} itself? That is, thinking of {LC} as a vector field does it have a COORDINATE INDUCED (INERTIAL) divergence part from accelerating LNIF non-geodesic observers + INTRINSIC GEOMETRY curl part? Z says yes. However, Z has failed to produce explicit formulae in even the simplest case of the Schwarzschild vacuum solution. Now in the above analogy {LC} the connection of 1916 GR is a 1-form. Therefore, The Question is, is there a decomposition LC 1-form = d(Zero Form) + 1-form = exact 1-form + non-exact 1-form The exact 1-form is the INERTIAL FIELD coordinate-dependent part. The non-exact 1-form is the INTRINSIC GEOMETRY part. Note that the CURVATURE 2-form is d{LC} = d(non-exact 1-form) However, in non-Abelian GR d{LC} = {LC} covariant curl of itself! Back to EM U = Integral over a Greens function of a scalar density d = I(Gs) A = Integral over the same Greens function of a vector density B = I(GB) Therefore if {LC} = GradU + CurlA Curl{LC} = CurlCurlA But self-consistency requires that B = Curl{LC} A = I(Gcurl{LC}) Therefore, the CONJECTURE is, in analog form: {LC} = -GradI[Gs] + CurlI(GCurl{LC}) ? The GLOBAL boundary conditions are in the Greens function G. INERTIAL FORCE coordinate part of {LC} = -GradI(Gs) INTRINSIC GEOMETRY PART of {LC} = CurlI(GCurl{LC}) The Curl and Grad are of course {LC} covariant operations so that this is all highly nonlinear. There is also the problem of the definition of the Greens functions as well as the Integrals over the curved manifold. It is not clear if Zs idea can be carried out. There is also the side issue of whether a stationary homogeneous g-field i.e. mc^2{LC}^ztt + External Non-Gravity Force^z = 0 In the LNIF rest frame of a HOVERING non-geodesic observer at FIXED DISTANCE z from the FLAT PLATE source Tuv =/= 0, where {LC}^ztt = g/c^2 {LC} Curl of {LC} = 0 where Tuv = 0 Can be an EXACT SOLUTION of Einsteins Guv = (8piG/c^4)Tuv ? Z claims Vilenkens vacuum domain wall is an example. === Subject: Gravity Bohm-Aharonov Effect in Vacuum Domain Wall? A. Vilenken Phys Letters Dec 15, 1983 Gravity Field of a Vacuum Domain Wall Ah BUT the solution does not cover ALL of spacetime - its a LOCAL spacetime region - maximal finite proper distance so that Ruvwl =/= 0 outside it. Also its not an EXACT UNIFORM g-field. So it shows a kind of Bohm-Aharonov nonlocality in which {LC} =/= 0 where Ruvwl = 0 like A =/= 0 where CurlA = B = 0. This {LC} is only measured for HOVERING LNIF non-geodesic observers not for geodesic LIF observers. Its curvature without curvature i.e. A truly NONLOCAL MACRO-QUANTUM EFFECT consistent with NONLOCALITY of pure gravity energy! So, it is beginning to look to me that Taubs surprising result is the gravity analog of the Josephson-Bohm-Aharonov nonlocal effect. Curvature without curvature? this is the GR nonlocality analog to magnetic field without magnetic field of the Bohm-Aharonov effect also seen in the Josephson effect. That is, both the {LC} connection of gravity and the vector potential fiber connection of electro-magnetism have a nonlocal macro-quantum observability in regions where their respective covariant curls locally vanish! A distant curved region where conformal Cuvwl =/= 0 makes a non-vanishing {LC} =/= 0 for HOVERING LNIF observers at fixed distance x from unstable vacuum domain wall (repulsive gravity BTW). Normally this would require local conformal vacuum curvature so that non-geodesic LNIF observers can hover at fixed distance from source by applying non-gravity forces (e.g. ejecting propellent - see Kip Thornes Black Holes and Time Warps on hovering near event horizon of a small black hole and see picture in Hawkings Universe in a Nutshell of two antipodal LNIF observers accelerating directly away from each other but staying at FIXED separation in curved Schwarzschild spacetime. So what we have here is a NONLOCALITY from the non-trivial topology of the single-valued macro-quantum vacuum local (zero entropy) OLDRO parameter out of which Einsteins Guv + /zpfguv = 0 emerges. surprise. The local {LC} =/= 0 is like the Bohm-Aharonov fringe shift where the two paths come together to make an interference pattern. In any case thats how its beginning to look to me at this moment. This is one more argument for the macro-quantum physical reality of the nonlocality of pure gravity energy as explained by Roger Penrose in The Road to Reality. Here is a facsimile PDF of Vilenkins 1983 Article. === Subject: Looking for the field equation. Im looking for a field equation that has a similar plot with the electric field generated by a pair of parallel plates(including the edge effects). May someone give me the equation or point me out the direction of derivation of the equation? Technetium *-----------------------* www.GroupSrv.com *-----------------------* === Subject: Re: Looking for the field equation. posting-account=Ox4sVgwAAACU0CW2pzCV4EMRCSoR-oeA hi, This would be Poissons equation: div(-sigma*grad(phi))=rho here sigma would be the conductivity of your medium and rho would be charge density. In 2-D this equation is easily solved using finite-differencing or by finite-elements. Rai > Im looking for a field equation that has a similar plot with the > electric field generated by a pair of parallel plates(including the > edge effects). May someone give me the equation or point me out the > direction of derivation of the equation? > Technetium > *-----------------------* > www.GroupSrv.com > *-----------------------* === Subject: Curvature without curvature GR nonlocality Paul A. Vilenken (15 Dec 1983 Physics Letters) makes NO CLAIM this is a SHgF solution! The really interesting physics in it is the new Bohm-Aharonov nonlocality of Conformal curvature without conformal curvature, OR conformal curvature acting nonlocally at a distance to make a non-trivial {LC} field requiring HOVERING fixed x LNIF observers to fire their rockets AWAY geodesics away from the wall that look like hyperbolic motion to the HOVERING LNIF non-geodesic observer who is REALLY accelerating i.e. ejecting propellent to keep hovering at fixed distance from the wall at x = 0. The {LC}^uvw field is like the EM vector potential A. The Conformal Curvature field C^uvwl is like the magnetic field B ~ Fij, i,j = 1,2,3 in the Bohm-Aharonov effect confined to the inside of the solenoid. In Vilenkens case the inside of the solenoid is OUTSIDE the FINITE PROPER VOLUME of the horizon limited SPACE-TIME VOLUME of his solution. The vacuum wall has limited proper support both in space and time. Its a kind of solitonic instanton - a spacetime blob. Vilenkens solution in context of Taubs surprising remark is evidence AGAINST the locality of gravity energy and is evidence FOR the macro-quantum coherent emergence of Einsteins local tensor field equations with the footprint of nonlocality in the topology of the order parameter. So is the hedgehog Pioneer 10 & 11 anomaly. === Subject: Re: JSH: Funding, real world, not fantasy <41c24907$1_2@newsfeed.slurp.net> posting-account=Q2zO6wwAAABSLuGzZIjG0efOtB9n8fUY > [snipped another repetition of JSHs standard Ullrich rant] > ... This reply is distinctive in that David Ullrich replied to it claiming it represented his actual thinking. So, I think it worthy to step out whats being said. > [Will Twentyman] the > facts for ourselves. You have been proven to be less than credible about > matters of (recent) history. > Of course theres no slur to be found. The incident referred to was in > early October of 1999. You can find it easily. David Ullrich was truly > pissed at JSH for calling him a liar repeatedly, and a lapdog at one > point. JSH even apologized for that. As David has explained endlessly ever > since, he thought that delivering some sort of racial slur (thats as > specific as it ever got) would be an object lesson in *why* people shouldnt > talk about other people the way JSH did. But he didnt do so. He said he > thought it would have been appropriate to do so, and thats the extent of > it. So, according to Tim Peters, David Ullrich justifiably introduced race, in a context where he noted he was angry, to try and explain to me how NOT to talk to people! But, why pick a racial slur? Obviously David Ullrich knew that a racial slur could be applied to me, as in another post some time before, in a discussion with a South African, I pointed out that I was black. So he probably was thinking of the word nigger. Now then, his claim is that he wanted to teach me a lesson, and now in context his full claim then is that he thought that using the racial slur nigger would teach me a lesson. How is that better? > I dont agree it would have been appropriate, but theres nothing > objectionable about discussing its appropriateness. However, why does race matter? And why is it so important to teach me a lesson, when race hadnt been the subject at hand? After all, Id said that David Ullrich had *acted* as my lapdog in an instance, which is a far cry from a demeaning racial insult meant to indicate that someone is some degraded thing. My comment was graded, and indicated that Ullrich was acting in a particular way, in an instance, while he thought it fit to hurl a racial epithet in reply, by his own words. Later he claims it was to teach me a lesson? And remember, David Ullrich is an actual professor at a state school. He *does* in fact teach students there lessons. His judgement is clearly questionable, at a minimum. > Well, except, apparently, to JSH. Of course theres no shortage of people > who have slung actual racial insults at JSH. He doesnt rant about them. I > view this as another manifestation of his extraordinary talent for deftly > avoiding pesky facts to cut straight to the heart of a fantasy . Now theres a paternalistic nature to the comments here, and theres also a paternalistic slant to the idea that Ullrich wished to teach me a lesson. However, the reality is that others hurling racial insults is not an excuse for Ullrichs own comments. And its worth noting that NO ONE did ever call me nigger on the newsgroup until David Ullrich came here posting about my *private* communication to Oklahoma State University when I made my complaint. So, he actually created the very situation that he talked about, by proxy, as other posters chose to use the racial slur that hed talked of thinking appropriate. I challenge you to find any response from David Ullrich to those people. As why *should* he challenge them, when he himself said he thought a racial slur the appropriate reply? Now then, others did for Ullrich what he was too afraid to do himself, though he tried in a backhanded manner. Ullrich introduced the subject of racial slurs. Ullrich whined on the newsgroup about my private complaint. Ullrich is the one who ßeshed out his thinking with another post talking about when he felt racial slurs would be appropriate. His example was of someone breaking into his house to rape his daughter! Now as an American citizen, I have the right to complain about some professor at a state university publicly posting such things on Usenet. I think that David Ullrich reßects badly not only on his school, but on Americans in general, as I doubt anyone who looks at this objectively, can figure out how a professor at a state university could behave in such a way, and get away with breaking so many rules--like publicizing my private complaint. Then again, I fear that many will just say, yes, thats those Americans. James Harris === Subject: Re: JSH: Funding, real world, not fantasy > But, why pick a racial slur? > Obviously David Ullrich knew that a racial slur could be applied to me, > as in another post some time before, in a discussion with a South > African, I pointed out that I was black. So he probably was thinking > of the word nigger. Im a South African you insensitive clod!! Not all non-black South Africans are racists, fucking idiot. BTW, we hardly know the word n*gg*r. This reverse racism is getting me down. Its ok for non-white people to bring up race in a conversation, but as soon as a white man says anything about race, hes considered a racist. Fokken Doos, keep your hands of my country, were proud of what we achieved in the last 10 years. Comments like these add to the few problems we still have. People like you! Bringing up the issue of South Africa and racism just shows how racist your thoughts really are. Prick. kalix === Subject: Re: JSH: Funding, real world, not fantasy > But, why pick a racial slur? > Obviously David Ullrich knew that a racial slur could be > applied to me, as in another post some time before, in a > discussion with a South African, I pointed out that I was black. > So he probably was thinking of the word nigger. > Im a South African you insensitive clod!! Not all non-black South > Africans are racists, fucking idiot. BTW, we hardly know the word > n*gg*r. This is a natural point of confusion. With a South African accent, that sounds like Kaffir. > This reverse racism is getting me down. Its ok for non-white > people to bring up race in a conversation, but as soon as a > white man says anything about race, hes considered a racist. Even writing as an American white, I think I can say that its a tricky situation for American blacks (and, presumably, South African blacks). As a group, they remember a time when solidarity was close to the only weapon they had. It would be difficult to give that up by refusing to back an individuals complaint, even if they realize that individual is abusing that solidarity, playing the race card for non-race reasons (like trying to get a critic to go away). I think thats a big mistake. Recognition of the legitimacy of their complaints was slowly won, at great cost, but it can be quickly piddled away again if they dont police their own ranks. But, then, its not my decision, is it? > Fokken Doos, keep your hands of my country, were proud of what we > achieved in the last 10 years. Comments like these add to the few > problems we still have. People like you! Bringing up the issue of > South Africa and racism just shows how racist your thoughts > really are. Prick. Even from half-way around the world, I was and am proud of South Africa (as a human being). Its because of you all (and other stories in the same vein) that I sometimes think were going to get out of the 21st century alive. However, many as the sins are that I would accuse Harris of, I have not seen him accuse any individual South African of racism, justly or otherwise. He did say he told a South African he was black. It looks to me like you just did what you just complained about, only with the name-plates of the positions reversed. Double-reverse racism? Jim Burns === Subject: Re: JSH: Funding, real world, not fantasy <41c24907$1_2@newsfeed.slurp.net> <41C58D35.2E458A78@osu.edu> posting-account=Q2zO6wwAAABSLuGzZIjG0efOtB9n8fUY achieved in the last 10 years. Comments like these add to the few > problems we still have. People like you! Bringing up the issue of > South Africa and racism just shows how racist your thoughts > really are. Prick. > Even from half-way around the world, I was and am proud of South > Africa (as a human being). Its because of you all (and other > stories in the same vein) that I sometimes think were going > to get out of the 21st century alive. > However, many as the sins are that I would accuse Harris of, I > have not seen him accuse any individual South African of racism, > justly or otherwise. He did say he told a South African he was black. > It looks to me like you just did what you just complained about, > only with the name-plates of the positions reversed. > Double-reverse racism? > Jim Burns Yup. I wasnt accusing South Africans of racism. I was giving information relevant to context, like how it turns out that I ended up mentioning my race on the newsgroup. It was not an angry conversation, and I dont think there was much of a stir on the newsgroup at the time. We just chatted about a few things--that ended up being racially related--and went on our separate ways. However, David Ullrich probably pulled from that discussion that I am what Americans typically call black, as I cant think of any other way that he got the information, and he used that information later, when he posted talking about the apropriateness of racial slurs, and remember he was replying to me. So he posted in reply to me that hed been angry at my talking of him acting as my lapdog in an instance, and had thought the appropriate reply would have been a racial slur, but he says he was talked out of it. The blatancy of the statement makes it indefensible, as most of you are adults, and even a kid couldnt get away with, say, telling his father that he thought to disparage him with some insult about his anatomy but a school friend talked him out of it! Its not even vague what Ullrich was doing. And, after I communicated with his school--a private communication--he broke the rules by posting about it on the newsgroup, and in response there were posters who did then use racial slurs against me. How dumb do those of you who defend Ullrich really believe everyone else is? Ullrich introduced race, in a context of anger, and talked of the appropriateness of racial slurs. Ullrich came whining on the newsgroup about my *private* complaint to Oklahoma State University, and got a lot of sympathy as an outpouring of hatred went against me, where some posters actually used racial slurs. Ullrichs supporters keep bringing this issue up, repeatedly making posts saying that I tried to get him fired, or that I contact peoples employers, or other statements of that effect, not giving the full story, as they wage a campaign of disinformation. In response Ive been posting the full story. Now theres a problem I think with people who dont like the truth, but believe that all that matters is what the majority presents as the truth, and Ullrich has a lot of people with him, while Im basically by myself. So to you people, its perfectly fair that Ullrich introduced race, used the newsgroup, talked of private communications with his school, and did whatever--as long as hes part of the majority! And he knows that, Im sure. Why else did he use you as he did? He does have tenure at Oklahoma State University. His job was never threatened. He couldnt have worried too much about sneakily introducing race--as long as he didnt actually hurl a racial slur. He used you. James Harris === Subject: Re: JSH: Funding, real world, not fantasy > Its not even vague what Ullrich was doing. And, after I communicated > with his school--a private communication--he broke the rules by posting > about it on the newsgroup, and in response there were posters who did > then use racial slurs against me. He broke the rules? What rules are you talking about? === Subject: Re: JSH: Funding, real world, not fantasy === >Subject: Re: JSH: Funding, real world, not fantasy > Fokken Doos, keep your hands of my country, were proud of what we >> achieved in the last 10 years. Comments like these add to the few >> problems we still have. People like you! Bringing up the issue of >> South Africa and racism just shows how racist your thoughts >> really are. Prick. >> Even from half-way around the world, I was and am proud of South >> Africa (as a human being). Its because of you all (and other >> stories in the same vein) that I sometimes think were going >> to get out of the 21st century alive. >> However, many as the sins are that I would accuse Harris of, I >> have not seen him accuse any individual South African of racism, >> justly or otherwise. He did say he told a South African he was black. >> It looks to me like you just did what you just complained about, >> only with the name-plates of the positions reversed. >> Double-reverse racism? >> Jim Burns >Yup. I wasnt accusing South Africans of racism. I was giving >information relevant to context, like how it turns out that I ended up >mentioning my race on the newsgroup. >It was not an angry conversation, and I dont think there was much of a >stir on the newsgroup at the time. We just chatted about a few >things--that ended up being racially related--and went on our separate >ways. >However, David Ullrich probably pulled from that discussion that I am >what Americans typically call black, as I cant think of any other way >that he got the information, and he used that information later, when >he posted talking about the apropriateness of racial slurs, and >remember he was replying to me. >So he posted in reply to me that hed been angry at my talking of him >acting as my lapdog in an instance, and had thought the appropriate >reply would have been a racial slur, but he says he was talked out of >it. >The blatancy of the statement makes it indefensible, as most of you are >adults, and even a kid couldnt get away with, say, telling his father >that he thought to disparage him with some insult about his anatomy but >a school friend talked him out of it! >Its not even vague what Ullrich was doing. And, after I communicated >with his school--a private communication--he broke the rules by posting >about it on the newsgroup, and in response there were posters who did >then use racial slurs against me. >How dumb do those of you who defend Ullrich really believe everyone >else is? >Ullrich introduced race, in a context of anger, and talked of the >appropriateness of racial slurs. >Ullrich came whining on the newsgroup about my *private* complaint to >Oklahoma State University, and got a lot of sympathy as an outpouring >of hatred went against me, where some posters actually used racial >slurs. >Ullrichs supporters keep bringing this issue up, repeatedly making >posts saying that I tried to get him fired, or that I contact peoples >employers, or other statements of that effect, not giving the full >story, as they wage a campaign of disinformation. >In response Ive been posting the full story. >Now theres a problem I think with people who dont like the truth, but >believe that all that matters is what the majority presents as the >truth, and Ullrich has a lot of people with him, while Im basically by >myself. >So to you people, its perfectly fair that Ullrich introduced race, >used the newsgroup, talked of private communications with his school, >and did whatever--as long as hes part of the majority! >And he knows that, Im sure. Why else did he use you as he did? >He does have tenure at Oklahoma State University. His job was never >threatened. He couldnt have worried too much about sneakily >introducing race--as long as he didnt actually hurl a racial slur. >He used you. So you knew he had tenure and you knew his job was never in danger? Is that your story? So how does the call to the Attorney General fit into this scenario? How dumb do you think we are? One of these days youre going to pull a stunt like this on the wrong person. Every time you disappear I always wonder if youve finally fucked with someone who doesnt take lightly your interfering with their job. Consider yourself lucky that you just get called a nigger. >James Harris -- Mensanator Ace of Clubs === Subject: Re: JSH: Funding, real world, not fantasy === >Subject: Re: JSH: Funding, real world, not fantasy >He does have tenure at Oklahoma State University. His job was never >threatened. He couldnt have worried too much about sneakily >introducing race--as long as he didnt actually hurl a racial slur. >He used you. > So you knew he had tenure and you knew his job was never in > danger? Is that your story? So how does the call to the > Attorney General fit into this scenario? How dumb do you > think we are? > One of these days youre going to pull a stunt like this on > the wrong person. Every time you disappear I always wonder > if youve finally fucked with someone who doesnt take lightly > your interfering with their job. > Consider yourself lucky that you just get called a nigger. Go back to sleep, M. Ullrich never called Harris a nigger. You, however, are coming disgustingly close to threatening Harris. I would appreciate it if you didnt make Harris look good (in contrast to your incomparable self). I like my newsgroup politics nice and tidy. Jim Burns === Subject: Re: JSH: Funding, real world, not fantasy > Ullrich never called Harris a nigger. When did Jim Burns say that Ullrich called Harris a nigger? I missed that. > You, however, are coming disgustingly close to threatening > Harris. When did Jim Burns come close to threatening Harris? He was talking about what someone he referes to as the wrong person might do. > I would appreciate it if you didnt make Harris look good I cannot see how Jim Burns makes Harris look good. === Subject: Re: JSH: Funding, real world, not fantasy <41C5ED2E.A50C9F19@osu.edu> <6JidncokWvyG7VvcRVn-gg@whidbeytel.com> Discussion, linux) >> Ullrich never called Harris a nigger. > When did Jim Burns say that Ullrich called Harris a nigger? I missed that. >> You, however, are coming disgustingly close to threatening >> Harris. > When did Jim Burns come close to threatening Harris? He was talking about > what someone he referes to as the wrong person might do. >> I would appreciate it if you didnt make Harris look good > I cannot see how Jim Burns makes Harris look good. I think you need to check the program. Youre mixing up the characters. -- Jesse F. Hughes Usenet is demonstrably dangerous. It needs to be regulated. --James S. Harris, voice of reason and moderation === Subject: Re: JSH: Funding, real world, not fantasy === >Subject: Re: JSH: Funding, real world, not fantasy >Message-id: <41C5ED2E.A50C9F19@osu.edu> === >>Subject: Re: JSH: Funding, real world, not fantasy >>He does have tenure at Oklahoma State University. His job was never >>threatened. He couldnt have worried too much about sneakily >>introducing race--as long as he didnt actually hurl a racial slur. >>He used you. >> So you knew he had tenure and you knew his job was never in >> danger? Is that your story? So how does the call to the >> Attorney General fit into this scenario? How dumb do you >> think we are? >> One of these days youre going to pull a stunt like this on >> the wrong person. Every time you disappear I always wonder >> if youve finally fucked with someone who doesnt take lightly >> your interfering with their job. >> Consider yourself lucky that you just get called a nigger. > Go back to sleep, M. >Ullrich never called Harris a nigger. I never said he called Harris a nigger. If youll wake up and actually read whats been said, youll see the part where Harris claims that Ullrich supporters have called him a nigger. >You, however, are coming disgustingly close to threatening >Harris. How did I threaten him? I realize that a word to the wise is wasted on Harris, but warning him that invading someones personal space isnt a smart course of action is the right thing to do. >I would appreciate it if you didnt make Harris look >good (in contrast to your incomparable self). So you think right and wrong are relative? Sorry, but I believe that wrong is absolute and that NOTHING I say can ever make Harris look good. >I like my newsgroup politics nice and tidy. So that you never have to take a stand? So that as long as Harris never intrudes into _your_ life, hes just a harmless clown? >Jim Burns -- Mensanator Ace of Clubs === Subject: Re: JSH: Funding, real world, not fantasy Discussion, linux) >>I like my newsgroup politics nice and tidy. > So that you never have to take a stand? So that as long as Harris > never intrudes into _your_ life, hes just a harmless clown? Damn near harmless, perhaps? Or, in deference to Douglas Adams, mostly harmless? Harriss behavior in the OkState affair was reprehensible, but (1) not particularly effective in this case and (2) not repeated in any obvious way since. I dont think the JSH threat requires any stand from Jim Burns or you. Or me. -- Jesse F. Hughes All Chinese are Confucianists when successful, and Taoists when they are failures. -- Lin Yutang, /My Country and My People/ === Subject: Re: JSH: Funding, real world, not fantasy >I like my newsgroup politics nice and tidy. >>So that you never have to take a stand? So that as long as Harris >>never intrudes into _your_ life, hes just a harmless clown? > Damn near harmless, perhaps? > Or, in deference to Douglas Adams, mostly harmless? > Harriss behavior in the OkState affair was reprehensible, but (1) not > particularly effective in this case and (2) not repeated in any > obvious way since. Thats not entirely accurate. He tried the same stunt with me in February of this year. Or so he claimed. Rick === Subject: Re: JSH: Funding, real world, not fantasy <87d5x5q3ky.fsf@phiwumbda.org> Discussion, linux) >>I like my newsgroup politics nice and tidy. >So that you never have to take a stand? So that as long as Harris >never intrudes into _your_ life, hes just a harmless clown? >> Damn near harmless, perhaps? >> Or, in deference to Douglas Adams, mostly harmless? >> Harriss behavior in the OkState affair was reprehensible, but (1) not >> particularly effective in this case and (2) not repeated in any >> obvious way since. > Thats not entirely accurate. He tried the same stunt with me > in February of this year. Or so he claimed. Yes, another poster emailed me to remind me about that. Or so he claimed? Does that mean youre not sure whether he complained to Hamilton College? -- Jesse F. Hughes What you call reasonable is suspect since youve proven yourself to be an enemy of mathematics. -- James S. Harris defends the cause. === Subject: Re: JSH: Funding, real world, not fantasy >I like my newsgroup politics nice and tidy. >>So that you never have to take a stand? So that as long as Harris >>never intrudes into _your_ life, hes just a harmless clown? >Damn near harmless, perhaps? >Or, in deference to Douglas Adams, mostly harmless? >Harriss behavior in the OkState affair was reprehensible, but (1) not >particularly effective in this case and (2) not repeated in any >obvious way since. >>Thats not entirely accurate. He tried the same stunt with me >>in February of this year. Or so he claimed. > Yes, another poster emailed me to remind me about that. > Or so he claimed? Does that mean youre not sure whether he > complained to Hamilton College? Thats right. On or about February 10 of this year James posted, I hereby charge Rick Decker with academic fraud and note that his college is responsible for this rogue professor. Ive deliberately involved an official at his college to take away plausible deniability for his school in a phone call I made months ago. His college has been made aware of his behavior. I havent heard gales of laughter from the Deans office, so I cant say for sure whether James actually contacted Hamilton or was simply blowing smoke. In either case, I really like the title rogue professor. Id put it on my vita, but I cant figure where it belongs. Rick, Rogue Professor === Subject: Re: JSH: Funding, real world, not fantasy <87d5x5q3ky.fsf@phiwumbda.org> <87pt15iuvv.fsf@phiwumbda.org> Discussion, linux) > Rick, Rogue Professor You will always be Rick Decker of Hamilton College for me. But even that has a bit of roguishness about it. Like Robin Hood of Sherwood Forest, say. -- Jesse F. Hughes You shouldnt hate Mother Mathematics. -- James S. Harris === Subject: Re: JSH: Funding, real world, not fantasy === >Subject: Re: JSH: Funding, real world, not fantasy >Message-id: <87d5x5q3ky.fsf@phiwumbda.orgI like my newsgroup politics nice and tidy. >> So that you never have to take a stand? So that as long as Harris >> never intrudes into _your_ life, hes just a harmless clown? >Damn near harmless, perhaps? >Or, in deference to Douglas Adams, mostly harmless? >Harriss behavior in the OkState affair was reprehensible, but (1) not >particularly effective in this case and (2) not repeated in any >obvious way since. I was under the impression that at least one other person claims that Harris contacted their employer. And Harris still claims that he was within his rights in doing what he did. If you try to murder someone and fail to pull it off, you still go to jail, dont you? > I dont think the JSH threat requires any stand >from Jim Burns or you. Or me. Yeah, what do I care, I dont even put my name on these posts. Let Harris fuck with someone elses life. No skin off my nose. >-- >Jesse F. Hughes >All Chinese are Confucianists when successful, and Taoists when they >are failures. > -- Lin Yutang, /My Country and My People/ -- Mensanator Ace of Clubs === Subject: Re: JSH: Funding, real world, not fantasy === >>Subject: Re: JSH: Funding, real world, not fantasy >>Message-id: <87d5x5q3ky.fsf@phiwumbda.org>I like my newsgroup politics nice and tidy. > So that you never have to take a stand? So that as long as Harris > never intrudes into _your_ life, hes just a harmless clown? >>Damn near harmless, perhaps? >>Or, in deference to Douglas Adams, mostly harmless? >>Harriss behavior in the OkState affair was reprehensible, but (1) not >>particularly effective in this case and (2) not repeated in any >>obvious way since. >I was under the impression that at least one other person claims that >Harris contacted their employer. Thats correct. >And Harris still claims that he was >within his rights in doing what he did. Of course he was within his rights! >If you try to murder someone and >fail to pull it off, you still go to jail, dont you? What planet are you from? Murder is illegal. Making bogus complaints is not. >> I dont think the JSH threat requires any stand >>from Jim Burns or you. Or me. >Yeah, what do I care, I dont even put my name on these posts. Let Harris >fuck with someone elses life. No skin off my nose. >>-- >>Jesse F. Hughes >>All Chinese are Confucianists when successful, and Taoists when they >>are failures. >> -- Lin Yutang, /My Country and My People/ ************************ David C. Ullrich === Subject: Re: JSH: Funding, real world, not fantasy Discussion, linux) === >>Subject: Re: JSH: Funding, real world, not fantasy >>Message-id: <87d5x5q3ky.fsf@phiwumbda.org>I like my newsgroup politics nice and tidy. > So that you never have to take a stand? So that as long as Harris > never intrudes into _your_ life, hes just a harmless clown? >>Damn near harmless, perhaps? >>Or, in deference to Douglas Adams, mostly harmless? >>Harriss behavior in the OkState affair was reprehensible, but (1) not >>particularly effective in this case and (2) not repeated in any >>obvious way since. > I was under the impression that at least one other person claims that > Harris contacted their employer. And Harris still claims that he was > within his rights in doing what he did. Id say he was within his rights as well, depending on what you mean there. Are you suggesting he broke some law or something? > If you try to murder someone and fail to pull it off, you still go > to jail, dont you? >> I dont think the JSH threat requires any stand >>from Jim Burns or you. Or me. > Yeah, what do I care, I dont even put my name on these posts. Let Harris > fuck with someone elses life. No skin off my nose. Very dramatic. -- One these mornings gonna wake | Aint nobodys doggone business how up crazy, | my baby treats me, Gonna grab my gun, kill my baby. | Nobodys business but mine. Nobodys business by mine. | -- Mississippi John Hurt === Subject: Re: JSH: Funding, real world, not fantasy === >Subject: Re: JSH: Funding, real world, not fantasy >Message-id: <87mzw9iusb.fsf@phiwumbda.org> === >Subject: Re: JSH: Funding, real world, not fantasy >Message-id: <87d5x5q3ky.fsf@phiwumbda.orgI like my newsgroup politics nice and tidy. >> So that you never have to take a stand? So that as long as Harris >> never intrudes into _your_ life, hes just a harmless clown? >Damn near harmless, perhaps? >Or, in deference to Douglas Adams, mostly harmless? >Harriss behavior in the OkState affair was reprehensible, but (1) not >particularly effective in this case and (2) not repeated in any >obvious way since. >> I was under the impression that at least one other person claims that >> Harris contacted their employer. And Harris still claims that he was >> within his rights in doing what he did. >Id say he was within his rights as well, That explains a lot. >depending on what you mean >there. Are you suggesting he broke some law or something? Arent there laws about making false and frivolous charges against someone? >> If you try to murder someone and fail to pull it off, you still go >> to jail, dont you? > I dont think the JSH threat requires any stand >from Jim Burns or you. Or me. >> Yeah, what do I care, I dont even put my name on these posts. Let Harris >> fuck with someone elses life. No skin off my nose. >Very dramatic. >-- >One these mornings gonna wake | Aint nobodys doggone business how > up crazy, | my baby treats me, >Gonna grab my gun, kill my baby. | Nobodys business but mine. >Nobodys business by mine. | -- Mississippi John Hurt -- Mensanator Ace of Clubs === Subject: Re: JSH: Funding, real world, not fantasy Discussion, linux) >>Id say he was within his rights as well, > That explains a lot. >>depending on what you mean >>there. Are you suggesting he broke some law or something? > Arent there laws about making false and frivolous charges against > someone? What does the word charges mean here? Id guess that JSHs complaint to Oklahoma State wouldnt be illegal. Id guess that even his complaint to the Attorney General is likely not illegal, but who knows? Were not sure what it contains. But its hard to prove that JSH was knowingly lying in his complaints. This is a difficult fact to prove in a situation which allows for different interpretations. JSH behaved badly -- very badly -- throughout the episode, but Id be surprised if he broke the law in any obvious way. -- This confused and outraged many Matrix fans, whod already spent hours on the web explaining that man and computers could never really live in such a state of harmony and mutual benefit. -- http://www.pointlesswasteoftime.com === Subject: Re: JSH: Funding, real world, not fantasy > I was under the impression that at least one other person claims that > Harris contacted their employer. Actually it indeed happened twice. And one occurrence was successful. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: JSH: Funding, real world, not fantasy Discussion, linux) > > I was under the impression that at least one other person claims that > > Harris contacted their employer. > Actually it indeed happened twice. And one occurrence was > successful. Successful? Come on, details! Evidently, I dont know so much about these matters. It apparently happened three times. (1) Ullrich (2) Rick (who is apparently not positive that James did anything) (3) Your successful time (which must not be Rick) -- Not all features that are found on the Security tab are designed to help make your documents and files more secure. --Microsoft on Office security features (after it was pointed out by a third party that a certain password setting is easily bypassed.) === Subject: Re: JSH: Funding, real world, not fantasy > > I was under the impression that at least one other person claims that > > Harris contacted their employer. > > Actually it indeed happened twice. And one occurrence was > successful. > Successful? Come on, details! > Evidently, I dont know so much about these matters. It apparently > happened three times. > (1) Ullrich > (2) Rick (who is apparently not positive that James did anything) > (3) Your successful time (which must not be Rick) Michael Varney, around 2000. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: JSH: Funding, real world, not fantasy [Mensanator] > I was under the impression that at least one other person claims that > Harris contacted their employer. [Dik T. Winter] >> Actually it indeed happened twice. And one occurrence was >> successful. [Jesse F. Hughes] > Successful? Come on, details! > Evidently, I dont know so much about these matters. It apparently > happened three times. > (1) Ullrich > (2) Rick (who is apparently not positive that James did anything) > (3) Your successful time (which must not be Rick) Be truthful now: have you personally seen Wiles cash a paycheck since JSH announced that his proof is most easily seen to be false by noting that the entire approach is logically fallacious ? === Subject: Re: JSH: Funding, real world, not fantasy <41c24907$1_2@newsfeed.slurp.net> what we achieved in the last 10 years. Comments like these add > to the few problems we still have. People like you! Bringing > up the issue of South Africa and racism just shows how racist > your thoughts really are. Prick. > Even from half-way around the world, I was and am proud of South > Africa (as a human being). Its because of you all (and other > stories in the same vein) that I sometimes think were going > to get out of the 21st century alive. > However, many as the sins are that I would accuse Harris of, I > have not seen him accuse any individual South African of racism, > justly or otherwise. He did say he told a South African he was black. > It looks to me like you just did what you just complained about, > only with the name-plates of the positions reversed. > Double-reverse racism? > Jim Burns > Yup. I wasnt accusing South Africans of racism. I was giving > information relevant to context, like how it turns out that I > ended up mentioning my race on the newsgroup. > It was not an angry conversation, and I dont think there was > much of a stir on the newsgroup at the time. We just chatted > about a few things--that ended up being racially related--and went > on our separate ways. > However, David Ullrich [snip Harris-crap] I dont need it explained to me. I saw it, before you deleted various parts of the story. [un-snip Harris-slap] : Even writing as an American white, I think I can say that its : a tricky situation for American blacks (and, presumably, South : African blacks). : : As a group, they remember a time when solidarity was close to : the only weapon they had. It would be difficult to give that up : by refusing to back an individuals complaint, even if they : realize that individual is abusing that solidarity, playing the : race card for non-race reasons (like trying to get a critic to : go away). : : I think thats a big mistake. Recognition of the legitimacy of : their complaints was slowly won, at great cost, but it can be : quickly piddled away again if they dont police their own ranks. : But, then, its not my decision, is it? Just to make sure you get the point, Harris: when you accused David Ullrich of racism in order to get him to stop criticizing your (alleged) mathematics, you were pissing on Martin Luther King Jrs grave. Just imagine whatever you would say to someone else who would do that, double it, and apply it to yourself. TIA. Jim Burns === Subject: Re: JSH: Funding, real world, not fantasy Discussion, linux) >> But, why pick a racial slur? >> Obviously David Ullrich knew that a racial slur could be applied to me, >> as in another post some time before, in a discussion with a South >> African, I pointed out that I was black. So he probably was thinking >> of the word nigger. > Im a South African you insensitive clod!! Not all non-black South > Africans are racists, fucking idiot. BTW, we hardly know the word > n*gg*r. I think theres pronoun confusion here. The he in JSHs last sentence refers to David Ullrich, not the South African (whoever he was -- I dont know what conversation James is talking about). -- Jesse F. Hughes Would you please stop talking and start talking? -- Vincent Price as the Saint === Subject: Re: JSH: Funding, real world, not fantasy >But, why pick a racial slur? >Obviously David Ullrich knew that a racial slur could be applied to me, >as in another post some time before, in a discussion with a South >African, I pointed out that I was black. So he probably was thinking >of the word nigger. >>Im a South African you insensitive clod!! Not all non-black South >>Africans are racists, fucking idiot. BTW, we hardly know the word >>n*gg*r. > I think theres pronoun confusion here. The he in JSHs last > sentence refers to David Ullrich, not the South African (whoever he > was -- I dont know what conversation James is talking about). In which case, my sincerest appologies. Kinda a touchy feely subject these days ;) kalix === Subject: Re: JSH: Funding, real world, not fantasy [JSH] ... > So, according to Tim Peters, David Ullrich justifiably introduced race, Youve misrepresented my position here, and badly. Waste your own time figuring out how (hint: its obvious). > in a context where he noted he was angry, to try and explain to me how > NOT to talk to people! > But, why pick a racial slur? > Obviously David Ullrich knew that a racial slur could be applied to me, > as in another post some time before, in a discussion with a South > African, I pointed out that I was black. So he probably was thinking > of the word nigger. I dont know. Its plausible, but Id expect David to be more imaginative than that. > Now then, his claim is that he wanted to teach me a lesson, and now in > context his full claim then is that he thought that using the racial > slur nigger would teach me a lesson. Youre speculating. I dont know what he might have said, and neither do you. > How is that better? How is that better than what? ... > However, why does race matter? And why is it so important to teach me > a lesson, when race hadnt been the subject at hand? You hurt people with your ceaseless insults, accusations, disrespect, and even threats. People have tried to explain that to you more times than I could keep track of. Perhaps he thought that a stupid racial insult would make a point to you about your stupid insults that all attempts at rational explanation had failed to get across to you. Race doesnt matter at all. If you were a 500 pound slob and sensitive about that, then a stupid insult about your bulk would have been the same kind of thing. Accusing an academic of incompetence in their field, and of lying about work in their field, can be deeply offensive, and you do that routinely with seeming joy at the thought you might be causing pain. Its despicable behavior. But he didnt reply in kind to you, despite that youre still wishing he would. Tough luck for you. > After all, Id said that David Ullrich had *acted* as my lapdog in an > instance, which is a far cry from a demeaning racial insult meant to > indicate that someone is some degraded thing. You forget that I read your messages from that time. Your abusiveness toward David was prolonged, and ugly even to observe. Your lapdog insult appeared much more to be the last straw than something unbearable on its own. Poor James, typed one harmless word, and suffered mass persecution as a result? Dream on -- youre just reaping what you sowed. Oh well. You cant let it die, but I dont have to play along. You can easily enough keep this alive for another decade on your own. [snipped yet another repetition of the same rant] === Subject: Re: JSH: Funding, real world, not fantasy <871xdp4drl.fsf@phiwumbda.org> <87k6rg6f6x.fsf@phiwumbda.org> posting-account=XHGPzAwAAACBzDwz8l_9KYOmofDRUylj > I want to be a lapdog master. Are there any courses I can take? > First, you must find a master who makes you his lapdog. Then, when > the time is ready, you must defeat your master and gather lapdogs of > your own. Typically, this involves considering a racial epithet and > then thinking better of it. > How does one know, when one is a lapdog master. Are there official > lists. For all I know I might not even have made it as far as > lapdog yet. > Never mind. You are not lapdog master material. === Subject: Re: JSH: Funding, real world, not fantasy [Arturo Magidin] > ... > complaint. A bit hard, given the pruning that has been done. It seems > to me that James had spent about a month talking himself into calling > OSU, originally on incompetence and ethics grounds (David had said > he didnt know how to prove some algebra thing or other, and James > took it as an admission of incompetence or as lying, hence the > ethics claim). Then he argued that his complaint would be because > David had claimed that racial slurs are appropriate, when they are > never appropriate. Finally, he admitted that his complaint had been > an attempt to get him to stop posting, and that the claim of racism > was pretextual, not germane. > The last pointer I have to an admission that this was the case > occurred in October 2002, message > though it is gone from Google. I tried finding it on mathforum, but > couldnt. The subject of the thread was Current discussion on short > FLT Proof in case anyone who knows how to search mathforum better > than I do cares to look for it. Is this it? http://mathforum.org/discuss/sci.math/a/m/449434/453184 (I couldnt do anything with Diks djonru4qop3hrnqhnclmhsc94f05shojrj@4ax.com reference -- perhaps that resolves for him on a local news server.) Anyway, I dont really see James admit to anything there. Instead he appears to be giving David a lesson in appropriate posting behavior: ... > Youre a disgrace to professors in general. > I never tried to get you fired. I never tried to get you to stop > posting. > I TRIED TO GET YOU TO QUIT TRYING TO TALK TO ME!!! > Youre a fucking newsgroup stalker who has no morals who keeps getting > these fucking idiots to defend your immoral ass and Im sick of > it!!!!! > LEAVE ME THE FUCK ALONE YOU PIECE OF SHIT!!!!!!!! Interstingly enough, the number of exclamation points at the ends of the last three sentences is a segment of the Fibonacci sequence -- James does deep math even when seemingly just blowing a gasket . === Subject: Re: JSH: Funding, real world, not fantasy [...] >> I never tried to get you fired. I never tried to get you to stop >> posting. >> I TRIED TO GET YOU TO QUIT TRYING TO TALK TO ME!!! >> Youre a fucking newsgroup stalker[...] He very definitely has a point here. I know it is a rather dreadful condition to have to teach math at places like Oklahoma State - but this doesnt excuse responding to every single message from JSH. Just ignore Harris and he will disappear. === Subject: Re: JSH: Funding, real world, not fantasy >[...] > I never tried to get you fired. I never tried to get you to stop > posting. > I TRIED TO GET YOU TO QUIT TRYING TO TALK TO ME!!! > Youre a fucking newsgroup stalker[...] >He very definitely has a point here. I know it is a rather dreadful >condition to have to teach math at places like Oklahoma State Huh? Have you ever taught math at Oklahoma State? >- but >this doesnt excuse responding to every single message from JSH. Huh? excuse what, exactly? I dont have the right to reply to the posts I feel like replying to? You think it would be a good thing if he got the idea that making bogus complaints to peoples employers about racism was an effective way to get people to stop replying to his posts? >Just ignore Harris and he will disappear. ************************ David C. Ullrich === Subject: Re: JSH: Funding, real world, not fantasy > Just ignore Harris and he will disappear. Yes, but some of us are addicts.... It makes life hard, but it is not easy to quite. === Subject: Re: JSH: Funding, real world, not fantasy ... > (I couldnt do anything with Diks > djonru4qop3hrnqhnclmhsc94f05shojrj@4ax.com > reference -- perhaps that resolves for him on a local news server.) Although I have not yet found a way to see the complete message in or something like that.) -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: JSH: Funding, real world, not fantasy <41c24907$1_2@newsfeed.slurp.net> posting-account=jj3O3QwAAABZLagqq9jnjQLaOd53yftT > [Arturo Magidin] > The last pointer I have to an admission that this was the case > occurred in October 2002, message > though it is gone from Google. I tried finding it on mathforum, but > couldnt. The subject of the thread was Current discussion on short > FLT Proof in case anyone who knows how to search mathforum better > than I do cares to look for it. > Is this it? > http://mathforum.org/discuss/sci.math/a/m/449434/453184 > (I couldnt do anything with Diks > djonru4qop3hrnqhnclmhsc94f05shojrj@4ax.com > reference -- perhaps that resolves for him on a local news server.) > Anyway, I dont really see James admit to anything there. I never tried to get you fired. I never tried to get you to stop posting. I TRIED TO GET YOU TO QUIT TRYING TO TALK TO ME!!! (I believe he had said something along these lines before, because around this time I had already said something about his express purpose; but I have been unable to substantiate my memory on this by finding his posts, possibly since so many of them have been removed) Note what he is saying: contrary to claims that he did so because he felt this behavior was inappropriate for a professor at a public university, or because he felt a sense of indignation, or because he felt insulted, he is saying that the reason he made the complaint was as an attempt to get David to stop replying to his posts; he had hoped that Davids superiors would suggest, pressure, or order him to stop replying. If he did not realize that his actions were a possible threat to Davids job, then he was being negligently careless; the fact that he used a very serious subject (racial discrimination and hate speech) as a ->pretext<- to get someones actions in a public forum curtailed is what I find reprehensible. Even if the activity in question had actually taken place (which it did not, at least not the way James claimed it did at the time or since), using it as a ->pretext<- seems to me morally reprehensible. It is a serious enough issue that it should be pursued on its merits, not as a club to wield against someone you might not care to listen to. Arturo Magidin, sans .sig === Subject: Re: JSH: Funding, real world, not fantasy [Arturo Magidin] > The last pointer I have to an admission that this was the case > occurred in October 2002, message > though it is gone from Google. I tried finding it on mathforum, > but couldnt. The subject of the thread was Current discussion on > short FLT Proof in case anyone who knows how to search mathforum > better than I do cares to look for it. [Tim Peters] >> Is this it? >> http://mathforum.org/discuss/sci.math/a/m/449434/453184 >> (I couldnt do anything with Diks >> djonru4qop3hrnqhnclmhsc94f05shojrj@4ax.com >> reference -- perhaps that resolves for him on a local news server.) >> Anyway, I dont really see James admit to anything there. [Arturo] > I never tried to get you fired. I never tried to get you to stop > posting. > I TRIED TO GET YOU TO QUIT TRYING TO TALK TO ME!!! > (I believe he had said something along these lines before, because > around this time I had already said something about his express > purpose; but I have been unable to substantiate my memory on this by > finding his posts, possibly since so many of them have been removed) > Note what he is saying: contrary to claims that he did so because he > felt this behavior was inappropriate for a professor at a public > university, or because he felt a sense of indignation, or because he > felt insulted, he is saying that the reason he made the complaint was > as an attempt to get David to stop replying to his posts; he had hoped > that Davids superiors would suggest, pressure, or order him to stop > replying. It could be consistent to hold all of these simultaneously: 1. James wanted David to stop replying. 3. James thought the comment was especially inappropriate given Davids position at a public institution. Putting an ALL CAPS emphasis on #1 doesnt really preclude #2 and #3. When a person talks about their motivations, and even when theyre trying to be truthful, what they say is usually just part of the story -- even if they go on for pages. If you get them to do it twice, theyll rarely say exactly the same things either. Motivations are usually complex. Its convenient for James that his original post vanished from most archives, and obviously self-serving to hold now that his only motivation was fighting the evils of racism. Its still possible that there was an element of the latter at the start, despite that he only mentioned #1 above. Its even possible that James claimed that to be the case so often later that now he really believes it was always so. Who knows? Its not even clear that James does. It appears to me that he truly wanted #1, and for a long time, and then tried to milk Davids obscure remark for about a million times what it was worth. Hes still trying, despite that it doesnt work. Remind you of any other JSH behaviors youve seen ? > If he did not realize that his actions were a possible threat > to Davids job, then he was being negligently careless; I expect that he hoped they were, despite his disclaimer above (I didnt succeed, therefore thats not what I wanted <0.5 wink>). Hes certainly ranted often enough later that David shouldnt receive public funds, and posted fantasies about mathematicians who criticize his work getting fired and disgraced (even jailed ...), so, overall, I simply dont believe his I never tried to get you fired claim above. > the fact that he used a very serious subject (racial discrimination and > hate speech) as a ->pretext<- to get someones actions in a public forum > curtailed is what I find reprehensible. As above, I cant conclude it was entirely pretext at the time. Occams Razor suggests it was, but people are complicated. > Even if the activity in question had actually taken place (which it did > not, at least not the way James claimed it did at the time or since), > using it as a ->pretext<- seems to me morally reprehensible. It is a > serious enough issue that it should be pursued on its merits, not as a > club to wield against someone you might not care to listen to. It requires a determined imagination to find racism in Davids remark, and by all accounts JSH got nowhere trying to convince Davids employer or the state attorney general that the remark was actionable in any way. Score one for sanity. But what does it matter now, given that it failed? Ive seen the claim that its important to keep rehashing this because it reveals something important about JSHs character. I have a hard time believing that this piece of history is necessary toward that end, though. I saw my first JSH post several months ago -- had never heard of him before then. Going from this guy is confused to and seems invincibly ignorant, manipulative, hostile and unstable didnt take a week. Its not like he did something dubious once years ago then learned to project a convincing illusion of saintliness -- to the contrary, having looked up the history, he hasnt changed his posting behaviors in positive ways at all. If someone here thought of him as morally beyond reproach before the trumped-up racism claim, and thats what opened their eyes, then Ill stand corrected on this point. === Subject: Re: JSH: Funding, real world, not fantasy >[Arturo Magidin] >> [...] >It could be consistent to hold all of these simultaneously: >1. James wanted David to stop replying. >3. James thought the comment was especially inappropriate given > Davids position at a public institution. >[...] It appears to me that he truly wanted #1, and for a >long time, and then tried to milk Davids obscure remark for about a million >times what it was worth. Hes still trying, despite that it doesnt work. >Remind you of any other JSH behaviors youve seen ? Giggle. >> If he did not realize that his actions were a possible threat >> to Davids job, then he was being negligently careless; >[...] >It requires a determined imagination to find racism in Davids remark, and >by all accounts JSH got nowhere trying to convince Davids employer or the >state attorney general that the remark was actionable in any way. Score one >for sanity. Indeed. >But what does it matter now, given that it failed? Ive seen the claim that >its important to keep rehashing this because it reveals something important >about JSHs character. _My_ view is not that its important to keep rehashing this. But I do, reasonably or not, feel its important to make sure he doesnt get the idea that his behavior has succeeded in getting me to shut up. Important because that sanity we celebrate above is not universal in a world where people get in trouble for using the word niggardly. ************************ David C. Ullrich === Subject: Re: JSH: Funding, real world, not fantasy <41c24907$1_2@newsfeed.slurp.net> posting-account=Q2zO6wwAAABSLuGzZIjG0efOtB9n8fUY > [Arturo Magidin] not, at least not the way James claimed it did at the time or since), > using it as a ->pretext<- seems to me morally reprehensible. It is a > serious enough issue that it should be pursued on its merits, not as a > club to wield against someone you might not care to listen to. > It requires a determined imagination to find racism in Davids remark, and > by all accounts JSH got nowhere trying to convince Davids employer or the > state attorney general that the remark was actionable in any way. Score one > for sanity. I complained. I have a right to complain and in fact the newsgroup wouldnt have known about the complaint if David Ullrich hadnt come back on the newsgroup to complain himself. I acted well within my rights as a citizen. Now some of you may not believe that a citizen in this country should ever voice a complaint or you may believe that Ullrichs introduction of racial slurs in to the discusion didnt merit a complaint. But it was my decision. Now some of you may go on and on as if the discussion matters, but it doesnt change my rights, and I can assure you that I have no problem with registering complaints when people who work for taxpayers step over the line. I dont care what world you think you live in, but if youre representing a government agency in America, and I catch you stepping over the line, then Im going to push you back, or at least try. It was part of my training as an Army officer. > But what does it matter now, given that it failed? Ive seen the claim that > its important to keep rehashing this because it reveals something important > about JSHs character. I have a hard time believing that this piece of It amazes me how often some of you attempt to rewrite history. Posters keep bringing it up, accusing me of various things, and at times I will give the full story. The full story is that David Ullrich brought up racial slurs. David Ullrich replied to me talking about racial slurs more than a year after a comment when I said hed acted as my lapdog in an instance, and more than a year after Id apologized. All of that gets lost in posts like yours which end up being rants against me, with little real detail, or any actual facts, and then Im supposed to be the bad guy? I was an Army officer. I dont know what makes you people think that you can blabber on Usenet and change anything. David Ullrich needed correction. I gave the correction. > history is necessary toward that end, though. I saw my first JSH post > several months ago -- had never heard of him before then. Going from this > guy is confused to and seems invincibly ignorant, manipulative, hostile > and unstable didnt take a week. Its not like he did something dubious > once years ago then learned to project a convincing illusion of > saintliness -- to the contrary, having looked up the history, he hasnt > changed his posting behaviors in positive ways at all. If someone here > thought of him as morally beyond reproach before the trumped-up racism > claim, and thats what opened their eyes, then Ill stand corrected on this > point. LOL. I wonder if some of you even take yourselves seriously. This is Usenet. I mainly use this forum to air out various ideas. There are posters like David Ullrich who obsessively reply to my posts, even though I mostly ignore them. You wish to join that club? Ok. But dont pretend to think that others on the newsgroup dont realize what you are. After all, Ive been posting for years here. People like you have come and gone, over, and over, and over again. Its still my newsgroup. James Harris === Subject: Re: JSH: Funding, real world, not fantasy > I complained. I have a right to complain and in fact the newsgroup > wouldnt have known about the complaint if David Ullrich hadnt come > back on the newsgroup to complain himself. > I acted well within my rights as a citizen. I remember a report about a court case in Germany, where the judge said (in a rough translation): The accused behaved like a f***ing a**hole. Unfortunately, there is no law that forbids him to behave like a f***ing a**hole. === Subject: Re: JSH: Funding, real world, not fantasy >> [Arturo Magidin] >[...] >I complained. I have a right to complain and in fact the newsgroup >wouldnt have known about the complaint if David Ullrich hadnt come >back on the newsgroup to complain himself. >I acted well within my rights as a citizen. Whoops. Hoist by your own petard again - you want to be careful about that! Hint: Nobody has ever disputed that making that complaint was within your rights as a citizen. It was a despicable thing to do regardless. You seem to be arguing that the fact that it was withing your rights means its ok, but this is grossly inconsistent with the idea that you made the complaint in the first place! Whatever I said, I was within my rights as a citizen saying it. >Now some of you may not believe that a citizen in this country should >ever voice a complaint or you may believe that Ullrichs introduction >of racial slurs in to the discusion didnt merit a complaint. >But it was my decision. >Now some of you may go on and on as if the discussion matters, but it >doesnt change my rights, and I can assure you that I have no problem >with registering complaints when people who work for taxpayers step >over the line. The fact that I work for taxpayers does not change my rights as a citizen. >I dont care what world you think you live in, but if youre >representing a government agency in America, and I catch you stepping >over the line, then Im going to push you back, or at least try. And Im not representing a government agency here. >It was part of my training as an Army officer. >> [...] >David Ullrich needed correction. I gave the correction. You did, eh? Your attempts at giving correction seem to be about as effective as your attempts at proving theorems. ************************ David C. Ullrich === Subject: Re: JSH: Funding, real world, not fantasy Discussion, linux) > Hint: Nobody has ever disputed that making that complaint was > within your rights as a citizen. Well, lately Mensanator has disputed that. I think. -- Jesse F. Hughes But nothings being Dr. Ullrich is a particular case of somethings being such that nothing is it: (Ex)~(Ey)(y = x) -- John Correy on the failings of first order logic === Subject: Re: JSH: Funding, real world, not fantasy !3KEIp?*w`|bL5qr,H)LFO6Q=qx~iH4DN;i;/yuIsqbLLCh/!U#X[S~( 5eZ41to5f%E@ELIi $t^ VcLWP@J5p^rst0+(Ô>Er0=^1{]M9!p?&:z]|;&=NP3AhB!B_bi^]Pfkw > I complained. I have a right to complain and in fact the newsgroup > wouldnt have known about the complaint if David Ullrich hadnt come > back on the newsgroup to complain himself. It wasnt Ullrich that told us that you have contacted the Oklahoma State Attorney about this issue. -- David Kastrup, Kriemhildstr. 15, 44793 Bochum === Subject: Re: JSH: Funding, real world, not fantasy > I was an Army officer. And this is interesting? I do not give a crap what you were in the army. It means nothing here. === Subject: Re: JSH: Funding, real world, not fantasy > Its still my newsgroup. > James Harris I did not know that. I suspect you believe it, though. === Subject: Re: JSH: Funding, real world, not fantasy [JSH] ... > I complained. I think everyone knew that already. > I have a right to complain Yes. It doesnt make it a sensible or honorable thing to do, but you have the right. > and in fact the newsgroup wouldnt have known about the complaint if > David Ullrich hadnt come back on the newsgroup to complain himself. Thats because the complaint had no merit and so failed (twice, right? when it failed to interest anyone at the University, you went on to complain to the Oklahoma attorney general too?). If it had succeeded, I bet sci.math would have heard about it with or without David exercising his rights. > I acted well within my rights as a citizen. So did David, of course. > Now some of you may not believe that a citizen in this country should > ever voice a complaint or you may believe that Ullrichs introduction > of racial slurs in to the discusion didnt merit a complaint. I dont believe Ullrich introduced racial slurs. You keep claiming it, but I actually read his message, and the messages leading up to it. So no, I dont believe it merited a complaint either. Correct me if Im wrong, but the university and state officials you contacted also found no merit in your complaint. > But it was my decision. I really didnt think it was Davids decision -- unless you were just acting as his lapdog . > Now some of you may go on and on as if the discussion matters, but it > doesnt change my rights, and I can assure you that I have no problem > with registering complaints when people who work for taxpayers step > over the line. > I dont care what world you think you live in, but if youre > representing a government agency in America, and I catch you stepping > over the line, then Im going to push you back, or at least try. > It was part of my training as an Army officer. What was? Complaining about professors replying to you on Usenet? Its unclear. [Tim, oddly snipped by JSH] >> But what does it matter now, given that it failed? Ive seen the >> claim that its important to keep rehashing this because it reveals >> something important about JSHs character. I have a hard time >> believing that this piece of > It amazes me how often some of you attempt to rewrite history. What, it didnt fail? > Posters keep bringing it up, accusing me of various things, and at > times I will give the full story. > The full story is that David Ullrich brought up racial slurs. That again. No, he didnt. He *mentioned* racial slurs. Your version of the full story is a transparently self-serving gross caricature. [another repetition of the self-serving gross caricature snipped] >> history is necessary toward that end, though. I saw my first JSH >> post several months ago -- had never heard of him before then. Going >> from this guy is confused to and seems invincibly ignorant, >> manipulative, hostile and unstable didnt take a week. Its not like >> he did something dubious once years ago then learned to project a >> convincing illusion of saintliness -- to the contrary, having looked up >> the history, he hasnt changed his posting behaviors in positive ways at >> all. If someone here thought of him as morally beyond reproach before >> the trumped-up racism claim, and thats what opened their eyes, then Ill >> stand corrected on this point. > LOL. I wonder if some of you even take yourselves seriously. > This is Usenet. I mainly use this forum to air out various ideas. > There are posters like David Ullrich who obsessively reply to my posts, > even though I mostly ignore them. Thats a shame too, because it does real damage to your occassional claim to be interested in truth. David always strives to be accurate in his mathematical writing, is a highly competent mathematician, and has given you innumerable valid corrections to your work. If you paid attention to his criticims (instead of, say, ignoring them and calling him a liar by reßex), your work could improve rapidly. > You wish to join that club? Nope -- I dont see any point at all in talking math with you. > Ok. But dont pretend to think that others on the newsgroup dont > realize what you are. My reputation stands on my work, most of which isnt apparent here. Sorry, but Im not worried about it. > After all, Ive been posting for years here. > People like you have come and gone, over, and over, and over again. > Its still my newsgroup. I was posting here long before you first showed up, although I was absent during the years you were forging your reputation here. So if owning the newsgroup is a matter of seniority, its my newsgroup, all mine. Well, mine and Dik Winters. And Torkel Franzens. And ... well, there are lots of people who have been posting here longer than you. Still, its my newsgroup, but its OK by me if you post here. Just dont go claiming its your newsgroup -- that would really piss me off. Id be so angry Id probably blurt out something Id regret in court later. Nice try . === Subject: Re: JSH: Funding, real world, not fantasy > (I couldnt do anything with Diks > djonru4qop3hrnqhnclmhsc94f05shojrj@4ax.com > reference -- perhaps that resolves for him on a local news server.) string in Message ID... Tomasso. === Subject: Re: JSH: Funding, real world, not fantasy [Tim Peters] >> (I couldnt do anything with Diks >> djonru4qop3hrnqhnclmhsc94f05shojrj@4ax.com >> reference -- perhaps that resolves for him on a local news server.) [Tomasso vs noise] > string in Message ID... Then thats a reply to http://mathforum.org/discuss/sci.math/a/m/449434/453184 but looks like David skipped quoting the abuse at the originals end (which is the part I expect Arturo had in mind). === Subject: Re: JSH: Funding, real world, not fantasy ... > [Tomasso vs noise] > string in Message ID... > Then thats a reply to > http://mathforum.org/discuss/sci.math/a/m/449434/453184 > but looks like David skipped quoting the abuse at the originals end (which > is the part I expect Arturo had in mind). I have not yet found ways to let it show). -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: JSH: Funding, real world, not fantasy ... > The last pointer I have to an admission that this was the case > occurred in October 2002, message > though it is gone from Google. djonru4qop3hrnqhnclmhsc94f05shojrj@4ax.com -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: JSH: Funding, real world, not fantasy [Tim Peters] >> [snipped another repetition of JSHs standard Ullrich rant] >> ... >> [Will Twentyman] > facts for ourselves. You have been proven to be less than credible > about matters of (recent) history. [Tim] >> Of course theres no slur to be found. The incident referred to >> was in early October of 1999. You can find it easily. David >> Ullrich was truly pissed at JSH for calling him a liar repeatedly, >> and a lapdog at one point. JSH even apologized for that. As >> David has explained endlessly ever since, he thought that delivering >> some sort of racial slur (thats as specific as it ever got) would >> be an object lesson in *why* people shouldnt talk about other >> people the way JSH did. But he didnt do so. He said he thought it >> would have been appropriate to do so, and thats the extent of it. [David Kastrup] > You are already falling victim to JSHs propaganda. It seems to me that when I was younger, people generally showed more skill in applying Occams Razor . > Here is the sentence: But I do recall that the game you were playing > was such that it seemed to me a perfectly appropriate reply would be > some sort of racial slur - someone talked me out of that. Note that > Ullrich _never_ claimed that a racial slur was appropriate in any way, > he said that a racial slur seemed to fit with what JSH was dealing out: > and this exactly because it was inappropriate to start with. As you just quoted, some sort of racial slur seemed to me a perfectly appropriate reply. Unless you attach surprising meaning to the difference between a and some sort of here, Ullrich _never_ claimed that a racial slur was appropriate in any way just doesnt jibe with the quote calling some sort of racial slur a perfectly appropriate reply. I understand and appreciate the different contexts in which appropriate can be applied here, and I *believe* I understand what David meant at the time: that responding to JSHs baseless hurtful insults with some sort of racial slur would be a reply-in-kind that perhaps JSH could understand -- not specifically to hurt him, but as a way to get him to understand how his hurtful words sometimes made others feel. Thats arguably appropriate so far as it goes. I happen to believe its always wrong to use such speech in public, and from that more-distant view it would have been inappropriate to my eyes had he done so. Since he didnt so, I figure to his eyes too. > And even in this context, he let himself easily be convinced otherwise. And I accept that he decided against it on his own (as he says). > And it did not quite seem like he ever actually contemplated putting > his impression ever into action: sounds more like he was told you > should be ashamed to even think of it. >> I dont agree it would have been appropriate, > Agree with who? How do you make from the above that Ullrich would > claim that racial slurs are an appropriate thing? I dont want to repeat the perfectly appropriate quote again. >> but theres nothing objectionable about discussing its >> appropriateness. >> Well, except, apparently, to JSH. Of course theres no shortage of >> people who have slung actual racial insults at JSH. > There is no shortage of racial insults JSH himself has ßung at > others. Or of insults of other kinds. But I dont expect civil behavior from JSH. === Subject: Re: JSH: Funding, real world, not fantasy >[Tim Peters] > [snipped another repetition of JSHs standard Ullrich rant] > ... > [Will Twentyman] >> facts for ourselves. You have been proven to be less than credible >> about matters of (recent) history. >[Tim] > Of course theres no slur to be found. The incident referred to > was in early October of 1999. You can find it easily. David > Ullrich was truly pissed at JSH for calling him a liar repeatedly, > and a lapdog at one point. JSH even apologized for that. As > David has explained endlessly ever since, he thought that delivering > some sort of racial slur (thats as specific as it ever got) would > be an object lesson in *why* people shouldnt talk about other > people the way JSH did. But he didnt do so. He said he thought it > would have been appropriate to do so, and thats the extent of it. >[David Kastrup] >> You are already falling victim to JSHs propaganda. >It seems to me that when I was younger, people generally showed more skill >in applying Occams Razor . >> Here is the sentence: But I do recall that the game you were playing >> was such that it seemed to me a perfectly appropriate reply would be >> some sort of racial slur - someone talked me out of that. Note that >> Ullrich _never_ claimed that a racial slur was appropriate in any way, >> he said that a racial slur seemed to fit with what JSH was dealing out: >> and this exactly because it was inappropriate to start with. >As you just quoted, some sort of racial slur seemed to me a perfectly >appropriate reply. Unless you attach surprising meaning to the difference >between a and some sort of here, Ullrich _never_ claimed that a racial >slur was appropriate in any way just doesnt jibe with the quote calling >some sort of racial slur a perfectly appropriate reply. >I understand and appreciate the different contexts in which appropriate >can be applied here, and I *believe* I understand what David meant at the >time: that responding to JSHs baseless hurtful insults with some sort of >racial slur would be a reply-in-kind that perhaps JSH could understand -- >not specifically to hurt him, but as a way to get him to understand how his >hurtful words sometimes made others feel. Thats arguably appropriate so >far as it goes. I happen to believe its always wrong to use such speech in >public, and from that more-distant view it would have been inappropriate to >my eyes had he done so. Since he didnt so, I figure to his eyes too. Congratulations, you got it. Of course, some might say that you dont really deserve a lot of smartness points for having figured out something that Ive explicitly stated several times. But considering the difficulty some others (well, one other) seems to have here... ************************ David C. Ullrich === Subject: Re: JSH: Funding, real world, not fantasy [Tim Peters] ... >> I understand and appreciate the different contexts in which appropriate >> can be applied here, and I *believe* I understand what David meant at the >> time: that responding to JSHs baseless hurtful insults with some sort >> of racial slur would be a reply-in-kind that perhaps JSH could >> understand -- not specifically to hurt him, but as a way to get him to >> understand how his hurtful words sometimes made others feel. Thats >> arguably appropriate so far as it goes. I happen to believe its always >> wrong to use such speech in public, and from that more-distant view it >> would have been inappropriate to my eyes had he done so. Since he didnt >> [do] so, I figure to his eyes too. [David C. Ullrich] > Congratulations, you got it. Yet for some reason I dont feel like celebrating <0.9 wink>. > Of course, some might say that you dont really deserve a lot of > smartness points for having figured out something that Ive explicitly > stated several times. Nope, no smartness points at all. I would claim minimal points for reading comprehension and archive searching skills, but then Im afraid Id have to accept demerits too for actually spending the time to find and read all that stuff <0.9 wink>. > But considering the difficulty some others (well, one other) seems to > have here... Yup, another repetition sure does seem pointless. While I dont think your original post was entirely prudent, on an offensiveness scale from 1 to 10 I rate it near 0. I would have apologized for it anyway -- but thats easy to say given that I havent been subjected to endless abuse from JSH myself. In all, I admire your restraint. just-another-fucking-idiot-defending-your-immoral-ass-ly yrs - tim === Subject: Re: JSH: Funding, real world, not fantasy >[Tim Peters] > [snipped another repetition of JSHs standard Ullrich rant] ... [Will Twentyman] >> facts for ourselves. You have been proven to be less than credible >> about matters of (recent) history. >[Tim] Of course theres no slur to be found. The incident referred to > was in early October of 1999. You can find it easily. David > Ullrich was truly pissed at JSH for calling him a liar repeatedly, > and a lapdog at one point. JSH even apologized for that. As > David has explained endlessly ever since, he thought that delivering > some sort of racial slur (thats as specific as it ever got) would > be an object lesson in *why* people shouldnt talk about other > people the way JSH did. But he didnt do so. He said he thought it > would have been appropriate to do so, and thats the extent of it. >[David Kastrup] >> You are already falling victim to JSHs propaganda. >It seems to me that when I was younger, people generally showed more skill >in applying Occams Razor . >> Here is the sentence: But I do recall that the game you were playing >> was such that it seemed to me a perfectly appropriate reply would be >> some sort of racial slur - someone talked me out of that. Note that >> Ullrich _never_ claimed that a racial slur was appropriate in any way, >> he said that a racial slur seemed to fit with what JSH was dealing out: >> and this exactly because it was inappropriate to start with. >As you just quoted, some sort of racial slur seemed to me a perfectly >appropriate reply. Unless you attach surprising meaning to the difference >between a and some sort of here, Ullrich _never_ claimed that a racial >slur was appropriate in any way just doesnt jibe with the quote calling >some sort of racial slur a perfectly appropriate reply. >I understand and appreciate the different contexts in which appropriate >can be applied here, and I *believe* I understand what David meant at the >time: that responding to JSHs baseless hurtful insults with some sort of >racial slur would be a reply-in-kind that perhaps JSH could understand -- >not specifically to hurt him, but as a way to get him to understand how his >hurtful words sometimes made others feel. Thats arguably appropriate so >far as it goes. I happen to believe its always wrong to use such speech in >public, and from that more-distant view it would have been inappropriate to >my eyes had he done so. Since he didnt so, I figure to his eyes too. > Congratulations, you got it. > Of course, some might say that you dont really deserve a lot of > smartness points for having figured out something that Ive explicitly > stated several times. But considering the difficulty some others > (well, one other) seems to have here... David, you are the one who evidently brought race into the conversation ... in a sly, backhanded way. You should apologize and move on. JSH is right on this one. === Subject: Re: JSH: Funding, real world, not fantasy <41c24907$1_2@newsfeed.slurp.net> posting-account=Q2zO6wwAAABSLuGzZIjG0efOtB9n8fUY > [snipped another repetition of JSHs standard Ullrich rant] > ... > [Will Twentyman] the >> facts for ourselves. You have been proven to be less than credible about >> matters of (recent) history. > Of course theres no slur to be found. The incident referred to > was in early October of 1999. You can find it easily. David > Ullrich was truly pissed at JSH for calling him a liar repeatedly, > and a lapdog at one point. JSH even apologized for that. As > David has explained endlessly ever since, he thought that delivering > some sort of racial slur (thats as specific as it ever got) would > be an object lesson in *why* people shouldnt talk about other > people the way JSH did. But he didnt do so. He said he thought it > would have been appropriate to do so, and thats the extent of it. Notice the twisting and rationalization here. Supposedly I am to blame for David Ullrich talking about a racial slur being the appropriate reply. And remember, Ullrich made his comments MORE THAN A YEAR after I said hed acted as my lapdog in an instance, and more than a year after Id apologized for those comments, as I noticed afterwards that his posts were...strange. I thought I was being nice by apologizing then, but with people like Ullrich, thats not enough. > You are already falling victim to JSHs propaganda. Here is the > sentence: But I do recall that the game you were playing was such > that it seemed to me a perfectly appropriate reply would be some sort > of racial slur - someone talked me out of that. Note that Ullrich Notice that this poster has removed the part where Ullrich speaks of being angry. > _never_ claimed that a racial slur was appropriate in any way, he said > that a racial slur seemed to fit with what JSH was dealing out: and > this exactly because it was inappropriate to start with. And even in > this context, he let himself easily be convinced otherwise. The fact is that Ullrich is TELLING me in a reply that he thought it appropriate to use some racial slur in reply to me on the newsgroup. Thats a public post as Usenet is quite public. Like, lets say he wanted to call me a chink, or a jew-bastard. His own words are that hes thinking this is an appropriate reply but was talked out of it, but he wishes to share this information WITH THE NEWSGROUP, in reply to me, as posts here are quite public. > And it did not quite seem like he ever actually contemplated putting > his impression ever into action: sounds more like he was told you > should be ashamed to even think of it. But if that were the case, why would he publicize it? Lets say you talk to a friend about fucking a goat, saying you were thinking it would be an appropriate way to let out your sexual frustrations. Your friend tells you that its a bad idea. You come on Usenet, and point out that you thought it a great idea to fuck a goat, but were talked out of it!!! It makes no sense. Ullrich clearly wanted to use the power of racial slurs without having to suffer the consequences. If he came out and poster that I was a nigger or something like that, theres no way he could escape the consequences, so instead he just talked about WANTING to post a racial slur. Its not even vague. > I dont agree it would have been appropriate, > Agree with who? How do you make from the above that Ullrich would > claim that racial slurs are an appropriate thing? Because thats what he said. > but theres nothing objectionable about discussing its > appropriateness. > Well, except, apparently, to JSH. Of course theres no shortage of > people who have slung actual racial insults at JSH. Actually, the racial insults came *after* Ullrich came on the newsgroup talking about my private communication with his school (yet another ethics violation), and then there were posters who just started slinging the word nigger around. And remember, David Ullrich is the one who brought up racial slurs!!! Hes the one who defended his comments. Hes the one who publicized my complaint on the newsgroup. Hes the one lapping up the attention, probably feeling quite proud of himself...at least for a while. > There is no shortage of racial insults JSH himself has ßung at > others. Name one. > -- > David Kastrup, Kriemhildstr. 15, 44793 Bochum Oh yeah, David Kastrup is one of the people who likes to keep bringing this topic up. And remember, I didnt start this, as yet again some poster put up something that shorted the story. Facts: David Ullrich introduced the subject of racial slurs. David Ullrich was reacting more than a year after I said hed acted as my lapdog in an instance. David Ullrich is the one who came on the newsgroup to publicize my complaint. One of the odder posts from Ullrich came a little bit after his post talking about the appropriateness of a racial slur when he was defending his statement, and he argued about why a racial slur could be an appropriate reply. His example was of someone breaking into his house to rape his daughter. I assume he does in fact have a daughter. Why did he assume that a racial slur would apply in such a case? And for the record, I dont say you hurl a racial slur at someone breaking into your house to rape your daughter. You shoot the fucker. Shoot first. Talk later. James Harris === Subject: Re: JSH: Funding, real world, not fantasy >> [snipped another repetition of JSHs standard Ullrich rant] >> ... >> [Will Twentyman] >the > facts for ourselves. You have been proven to be less than >credible about > matters of (recent) history. >> Of course theres no slur to be found. The incident referred to >> was in early October of 1999. You can find it easily. David >> Ullrich was truly pissed at JSH for calling him a liar repeatedly, >> and a lapdog at one point. JSH even apologized for that. As >> David has explained endlessly ever since, he thought that >delivering >> some sort of racial slur (thats as specific as it ever got) >would >> be an object lesson in *why* people shouldnt talk about other >> people the way JSH did. But he didnt do so. He said he thought >> would have been appropriate to do so, and thats the extent of it. >Notice the twisting and rationalization here. Supposedly I am to blame >for David Ullrich talking about a racial slur being the appropriate >reply. >And remember, Ullrich made his comments MORE THAN A YEAR after I said >hed acted as my lapdog in an instance, and more than a year after Id >apologized for those comments, as I noticed afterwards that his posts >were...strange. >I thought I was being nice by apologizing then, but with people like >Ullrich, thats not enough. >> You are already falling victim to JSHs propaganda. Here is the >> sentence: But I do recall that the game you were playing was such >> that it seemed to me a perfectly appropriate reply would be some sort >> of racial slur - someone talked me out of that. Note that Ullrich >Notice that this poster has removed the part where Ullrich speaks of >being angry. >> _never_ claimed that a racial slur was appropriate in any way, he >said >> that a racial slur seemed to fit with what JSH was dealing out: and >> this exactly because it was inappropriate to start with. And even in >> this context, he let himself easily be convinced otherwise. >The fact is that Ullrich is TELLING me in a reply that he thought it >appropriate to use some racial slur in reply to me on the newsgroup. >Thats a public post as Usenet is quite public. >Like, lets say he wanted to call me a chink, or a jew-bastard. >His own words are that hes thinking this is an appropriate reply but >was talked out of it, but he wishes to share this information WITH THE >NEWSGROUP, in reply to me, as posts here are quite public. >> And it did not quite seem like he ever actually contemplated putting >> his impression ever into action: sounds more like he was told you >> should be ashamed to even think of it. >But if that were the case, why would he publicize it? >Lets say you talk to a friend about fucking a goat, saying you were >thinking it would be an appropriate way to let out your sexual >frustrations. >Your friend tells you that its a bad idea. >You come on Usenet, and point out that you thought it a great idea to >fuck a goat, but were talked out of it!!! >It makes no sense. Ullrich clearly wanted to use the power of racial >slurs without having to suffer the consequences. >If he came out and poster that I was a nigger or something like that, >theres no way he could escape the consequences, so instead he just >talked about WANTING to post a racial slur. >Its not even vague. >> I dont agree it would have been appropriate, >> Agree with who? How do you make from the above that Ullrich would >> claim that racial slurs are an appropriate thing? >Because thats what he said. >> but theres nothing objectionable about discussing its >> appropriateness. >> Well, except, apparently, to JSH. Of course theres no shortage of >> people who have slung actual racial insults at JSH. >Actually, the racial insults came *after* Ullrich came on the newsgroup >talking about my private communication with his school (yet another >ethics violation), and then there were posters who just started >slinging the word nigger around. >And remember, David Ullrich is the one who brought up racial slurs!!! >Hes the one who defended his comments. >Hes the one who publicized my complaint on the newsgroup. >Hes the one lapping up the attention, probably feeling quite proud of >himself...at least for a while. >> There is no shortage of racial insults JSH himself has ßung at >> others. >Name one. >> -- >> David Kastrup, Kriemhildstr. 15, 44793 Bochum >Oh yeah, David Kastrup is one of the people who likes to keep bringing >this topic up. And remember, I didnt start this, as yet again some >poster put up something that shorted the story. >Facts: David Ullrich introduced the subject of racial slurs. David >Ullrich was reacting more than a year after I said hed acted as my >lapdog in an instance. David Ullrich is the one who came on the >newsgroup to publicize my complaint. >One of the odder posts from Ullrich came a little bit after his post >talking about the appropriateness of a racial slur when he was >defending his statement, and he argued about why a racial slur could be >an appropriate reply. >His example was of someone breaking into his house to rape his >daughter. >I assume he does in fact have a daughter. >Why did he assume that a racial slur would apply in such a case? >And for the record, I dont say you hurl a racial slur at someone >breaking into your house to rape your daughter. >You shoot the fucker. Shoot first. Talk later. >James Harris Undeniably the nut makes a certain amount of sense here. A greater mystery is why the other nut (Ullrich) cant leave the poor guy alone. === Subject: Re: JSH: Funding, real world, not fantasy !3KEIp?*w`|bL5qr,H)LFO6Q=qx~iH4DN;i;/yuIsqbLLCh/!U#X[S~( 5eZ41to5f%E@ELIi $t^ VcLWP@J5p^rst0+(Ô>Er0=^1{]M9!p?&:z]|;&=NP3AhB!B_bi^]Pfkw >> There is no shortage of racial insults JSH himself has ßung at >> others. > Name one. I quote two in -- David Kastrup, Kriemhildstr. 15, 44793 Bochum === Subject: Re: JSH: Funding, real world, not fantasy Discussion, linux) James, speaking of distractions... I notice that youre not posting on factoring any more and youve deleted at least one of your posts from sci.crypt. I know that the issue may be sensitive, but just between pals... You can tell me... Your method works so well that youre trying to avoid the topic and erase traces just in the interest of preserving international commerce, right? Is this on your own initiative, or did MJ-12 ask you to take these steps? -- And yes, I will be darkening the doors of some of you, sooner than you think, even if it is going to be a couple of years, and when you look in my eyes on that last day of work at your school, then maybe youll understand mathematics. -- James S. Harris on Judgment Day === Subject: Re: JSH: Funding, real world, not fantasy === >Subject: Re: JSH: Funding, real world, not fantasy >Message-id: <87sm643rcf.fsf@phiwumbda.orgJames, speaking of distractions... >I notice that youre not posting on factoring any more and youve >deleted at least one of your posts from sci.crypt. >I know that the issue may be sensitive, but just between pals... You >can tell me... >Your method works so well that youre trying to avoid the topic and >erase traces just in the interest of preserving international >commerce, right? Is this on your own initiative, or did MJ-12 ask you >to take these steps? Gosh, do you think so? Hes obviously still alive, so maybe they just paid him off to stop development of his baby idea? So maybe I could make some quick holiday cash by merely _suggesting_ a novel approach to factoring? That would be great. I wouldnt have to actually make it work, just scare them into thinking BUT WHAT IF IT WORKS? Such as factoring by the Collatz Conjecture. In the regular 3x+1 system there are no known non-trivial loops. When generalizing that to 3x+C, the conjecture fails whenever C is not a power of 3. That failure is related to the factors of C, so if I started with 3x+RSA640 I could make the factors of RSA640 pop out of the appropriate Collatz sequence. I dont want to say any more at this time. Ill be waiting for a phone call. So, if you never hear me speak of this again... >-- >And yes, I will be darkening the doors of some of you, sooner than you >think, even if it is going to be a couple of years, and when you look >in my eyes on that last day of work at your school, then maybe youll >understand mathematics. -- James S. Harris on Judgment Day -- Mensanator Ace of Clubs === Subject: Re: JSH: Funding, real world, not fantasy [Tim Peters] > [snipped another repetition of JSHs standard Ullrich rant] > ... > [Will Twentyman] >> facts for ourselves. You have been proven to be less than >> credible about matters of (recent) history. [Tim] > Of course theres no slur to be found. The incident referred to > was in early October of 1999. You can find it easily. David > Ullrich was truly pissed at JSH for calling him a liar repeatedly, > and a lapdog at one point. JSH even apologized for that. As > David has explained endlessly ever since, he thought that delivering > some sort of racial slur (thats as specific as it ever got) > would be an object lesson in *why* people shouldnt talk about other > people the way JSH did. But he didnt do so. He said he thought > it would have been appropriate to do so, and thats the extent of it. [JSH] > Notice the twisting and rationalization here. Specifically where? I pointed to the precise message in question, and stand by my summary as accurate. > Supposedly I am to blame for David Ullrich talking about a racial > slur being the appropriate reply. No, but you are to blame for your bad behavior in response to Davids message. Youre also responsible for keeping this going for years. > And remember, Ullrich made his comments MORE THAN A YEAR after I said > hed acted as my lapdog in an instance, and more than a year after Id > apologized for those comments, as I noticed afterwards that his posts > were...strange. > I thought I was being nice by apologizing then, I dont know your motives, but David was clearly appreciative of the apology at the time. > but with people like Ullrich, thats not enough. He accepted your apology, and quite graciously: Its your subsequent bad behavior that kept you in low esteem. [David Kastrup] >> You are already falling victim to JSHs propaganda. Here is the >> sentence: But I do recall that the game you were playing was such >> that it seemed to me a perfectly appropriate reply would be some sort >> of racial slur - someone talked me out of that. Note that Ullrich [JSH] > Notice that this poster has removed the part where Ullrich speaks of > being angry. He didnt remove anything. Boy was I mad about that is a sentence from the original message linked to above that nobody bothered quoting in this thread. What of it? He _was_ angry. Thats why you apologized to begin with (which, as far as I can tell, was your last honorable action in this affair). [David Kastrup] >> _never_ claimed that a racial slur was appropriate in any way, he >> said that a racial slur seemed to fit with what JSH was dealing out: and >> this exactly because it was inappropriate to start with. And even in >> this context, he let himself easily be convinced otherwise. [JSH] > The fact is that Ullrich is TELLING me in a reply that he thought it > appropriate to use some racial slur in reply to me on the newsgroup. In response to the things you were calling him a year earlier, he showed laudable restraint in not doing so. > Thats a public post as Usenet is quite public. > Like, lets say he wanted to call me a chink, or a jew-bastard. So you apparently believe its OK for you to spout racial epithets. I find them offensive regardless of context. > His own words are that hes thinking this is an appropriate reply but > was talked out of it, but he wishes to share this information WITH THE > NEWSGROUP, in reply to me, as posts here are quite public. I read his reply. Your paranoid tendencies dont help you in social interactions. If you were able to read it as a reply to you, in context, it would have been clear. [David Kastrup] >> And it did not quite seem like he ever actually contemplated putting >> his impression ever into action: sounds more like he was told you >> should be ashamed to even think of it. [JSH] > But if that were the case, why would he publicize it? Apparently because you made a point of publicizing how you hurt his feelings a year earlier, as part of a goofy speculation that Ullrich was posting under the name Wilma in an attempt to sucker you. Of course you see no connection between the abusive things you say and the responses you get. > Lets say you talk to a friend about fucking a goat, saying you were > thinking it would be an appropriate way to let out your sexual > frustrations. > Your friend tells you that its a bad idea. > You come on Usenet, and point out that you thought it a great idea to > fuck a goat, but were talked out of it!!! > It makes no sense. Ullrich clearly wanted to use the power of racial > slurs without having to suffer the consequences. He quite clearly did not. If you honestly believe this, hire a lawyer and sue him. Your own motives are also clear, which is why Im sure you wont. [snipped the rest -- just another repeition of the same rant] === Subject: Re: JSH: Funding, real world, not fantasy !3KEIp?*w`|bL5qr,H)LFO6Q=qx~iH4DN;i;/yuIsqbLLCh/!U#X[S~( 5eZ41to5f%E@ELIi $t^ VcLWP@J5p^rst0+(Ô>Er0=^1{]M9!p?&:z]|;&=NP3AhB!B_bi^]Pfkw > [Tim Peters] >> It makes no sense. Ullrich clearly wanted to use the power of >> racial slurs without having to suffer the consequences. > He quite clearly did not. If you honestly believe this, hire a > lawyer and sue him. Your own motives are also clear, which is why > Im sure you wont. He indeed contacted the Oklahama State Attorney and made a big Brouhaha from that until he was told that there was nothing there to prosecute. So he clearly managed to immerse himself sufficiently in that delusion to actually try something absurd like that: thats one thing you cant accuse him of. -- David Kastrup, Kriemhildstr. 15, 44793 Bochum === Subject: Re: Funding, real world, not fantasy > David Ullrich gets a paycheck from Oklahoma State University, right? > Hes tax payer supported. And only those who agree with James Harris should be tax payer supported... right... I was just thinkng making a racial slur........ but nope..... not today..... === Subject: JSH: Subject of race posting-account=Q2zO6wwAAABSLuGzZIjG0efOtB9n8fUY It has long fascinated me how easily posters on the sci.math newsgroup lie about, well, just about anything, and back when this whole Ullrich mess popped up, there were posters chiding me for bringing up my race! Apparently they decided that Id mentioned I was black in order to manipulate or something. Actually I ended up in this interesting discussion with this person from South Africa, where I went on about my theory that all people are basically mutts. At some point, it seemed pertinent in the discussion that I was what Americans typically call black. So thats how my race got known to the newsgroup, and thats apparently how David Ullrich picked up that Im black. What makes this story weirder, besides the eagerness with which posters routinely lie on this newsgroup, is that another poster decided to make a big deal later when I called him a mongrel. Well, to me, all people are mutts. And that goes to the reality that with the human species there just isnt any such thing as purebreeding (to see how wacky this newsgroup is, dig into the archives and read the discussions about THAT). Now, those happy friendly dogs are mutts, and the nasty, snarly ones are mongrels, the way I understand it. So to me, calling someone a mongrel, was just in keeping with the mutt philosophy, but in an insulting way! Next thing you know, Im being called racist by this poster who sees the term mongrel as a racial insult! But theres a problem with that view. Some people believe that there IS such a thing as a purebreed human. And that inter-breeding between one of these pure humans and others is a crime against humanity (odd, but true). They call it miscegenation. So, if you believe that there are purebreeds, and that you can breed with a lesser human to produce a human mutt that way, then mongrel might be an applicable racial epithet in your world. I just dont see it that way, though I can understand that someone brought up in a society that DOES see it that way, could get outraged if they see a favorite racial epithet in their world, thrown out, albeit not as a racial slur, on a public forum like this one. Apparently in Latin American countries--assuming posters discussing this issue have been at least somewhat truthful--theres this whole world wrapped around the breeding issue where mongrel is a racial slur. I say, its better not to introduce the topic of race in anger at all, as its just so messy. I had a nice discussion with that South African. It made me feel kind of good about humanity, you know? But David Ullrich pulled one thing out of it, and thought it useful to hurl race back into the discussion on the newsgroup in the context of anger, mentioning that he was angry in his very post. And look at the mess he made. Sure, posters can try to blame me because they lie. If you wish, you can believe people who lie. Thats your perogative. But that doesnt change the truth. James Harris === Subject: Re: JSH: Subject of race > Let it die. OK. Your move. Amazing! -- Min I blame the jelly === Subject: Re: Subject of race > It has long fascinated me how easily posters on the sci.math newsgroup > lie about, well, just about anything, and back when this whole Ullrich > mess popped up, there were posters chiding me for bringing up my race! Why did you bring up your race? > Actually I ended up in this interesting discussion with this person > from South Africa, where I went on about my theory that all people are > basically mutts. Why did you bring up your theory that all people are basically mutts? > At some point, it seemed pertinent in the discussion that I was what > Americans typically call black. At some point, to you, it seemed pertinent in the discussion that you were what Americans typically call black? Why? > So thats how my race got known to the newsgroup, and thats apparently > how David Ullrich picked up that Im black. And why should anyone here care how David Ullrich picked up that youre black? > What makes this story weirder, besides the eagerness with which posters > routinely lie on this newsgroup, is that another poster decided to make > a big deal later when I called him a mongrel. Are you surprised that some people object to being called a mongrel? > Next thing you know, Im being called racist by this poster who sees > the term mongrel as a racial insult! Well, if it makes you feel any better, I do not consider Ômongrel to be a racial insult. But why did you call him a mongrel? > I say, its better not to introduce the topic of race in anger at all, > as its just so messy. Its better not to introduce the topic of mongrels either, perhaps. > And look at the mess he made. Tsk tsk tsk... Here is a thought... Go blow a dead bear, James.... === Subject: Re: Subject of race > It has long fascinated me how easily posters on the sci.math newsgroup > lie about, well, just about anything, and back when this whole Ullrich > mess popped up, there were posters chiding me for bringing up my race! > Why did you bring up your race? Does he belong to a *race*? Yuck! Dirk Vdm === Subject: Re: Subject of race !3KEIp?*w`|bL5qr,H)LFO6Q=qx~iH4DN;i;/yuIsqbLLCh/!U#X[S~( 5eZ41to5f%E@ELIi $t^ VcLWP@J5p^rst0+(Ô>Er0=^1{]M9!p?&:z]|;&=NP3AhB!B_bi^]Pfkw >> It has long fascinated me how easily posters on the sci.math >> newsgroup lie about, well, just about anything, and back when >> this whole Ullrich mess popped up, there were posters chiding me >> for bringing up my race! >> Why did you bring up your race? > Does he belong to a *race*? > Yuck! Hey, you cant hold them responsible. Anyway, on the topic of race Ill offer the following gem: . -- David Kastrup, Kriemhildstr. 15, 44793 Bochum === Subject: Re: Subject of race === >Subject: Re: Subject of race >Message-id: newsgroup lie about, well, just about anything, and back when > this whole Ullrich mess popped up, there were posters chiding me > for bringing up my race! > Why did you bring up your race? >> Does he belong to a *race*? >> Yuck! >Hey, you cant hold them responsible. Anyway, on the topic of race >Ill offer the following gem: >. That was awful. >-- >David Kastrup, Kriemhildstr. 15, 44793 Bochum -- Mensanator Ace of Clubs === Subject: Re: Subject of race >> It has long fascinated me how easily posters on the sci.math >> newsgroup lie about, well, just about anything, and back when >> this whole Ullrich mess popped up, there were posters chiding me >> for bringing up my race! >> Why did you bring up your race? > Does he belong to a *race*? > Yuck! > Hey, you cant hold them responsible. Anyway, on the topic of race > Ill offer the following gem: > . Slow and steady. Dirk Vdm === Subject: Re: Subject of race > Slow and steady. In -Galaxy Magazine- in days gone by there would be an outrageous pun Here is a typical sample: By the year 2483, mankind had finally developed a sense of history. Many buildings and other historical structures were restored to their former glory. The Palace of Atlantis was moved to dry ground. The limestone casing and gold cap were put back on the Pyramid of Cheops. The Parthenon was completely rebuilt. The Great Wall of China was repaired and cleansed of all posters and graffiti. The Statue of Liberty was patched, strengthened, and reopened. Most were made into elaborate museums of their former usages, often going into great detail about features not normally easily visible. One day, at the Parthenon, a volunteer docent noticed that one member of her group was missing. She looked in all directions, but couldnt see him anywhere in their current section, the one about its architecture. Luckily, brave Ferdinand Feghoot was among the group, and boldly set out to look for his missing colleague. He quickly found him, in a dark corner, hidden by a display about bas-reliefs that were originally just below the roof, too high up on the outside wall to see well. The docent was much relieved to have her missing charge returned, and worried that she was getting incompetent due to her advanced age of nearly 200. Ferdinand reassured her, saying... You just couldnt see the tourist for the frieze! For more of the same see: http://www.speakeasy.org/~davearonson/personal/old/ feghoot.html Bob Kolker === Subject: Re: Subject of race > Slow and steady. > In -Galaxy Magazine- in days gone by there would be an outrageous pun > Here is a typical sample: > By the year 2483, mankind had finally developed a sense of history. Many > buildings and other historical structures were restored to their former > glory. The Palace of Atlantis was moved to dry ground. The limestone > casing and gold cap were put back on the Pyramid of Cheops. The > Parthenon was completely rebuilt. The Great Wall of China was repaired > and cleansed of all posters and graffiti. The Statue of Liberty was > patched, strengthened, and reopened. Most were made into elaborate > museums of their former usages, often going into great detail about > features not normally easily visible. > One day, at the Parthenon, a volunteer docent noticed that one member of > her group was missing. She looked in all directions, but couldnt see > him anywhere in their current section, the one about its architecture. > Luckily, brave Ferdinand Feghoot was among the group, and boldly set out > to look for his missing colleague. He quickly found him, in a dark > corner, hidden by a display about bas-reliefs that were originally just > below the roof, too high up on the outside wall to see well. > The docent was much relieved to have her missing charge returned, and > worried that she was getting incompetent due to her advanced age of > nearly 200. Ferdinand reassured her, saying... > You just couldnt see the tourist for the frieze! > For more of the same see: > http://www.speakeasy.org/~davearonson/personal/old/ feghoot.html And to continue this rather off-topic thread: http://www.photogs.com/bwworld/winogrand-hondajoke.html Dont look at the bottom line before you reach it ;-) Dirk Vdm === Subject: Re: JSH: Subject of race > It has long fascinated me how easily posters on the sci.math newsgroup > lie about, well, just about anything, and back when this whole Ullrich > mess popped up, there were posters chiding me for bringing up my race! Let it die. === Subject: self study on topology I was wondering if any of you knew of a good book for self study on general (not algebraic) topology? MN === Subject: Re: self study on topology >I was wondering if any of you knew of a good book for self study on >general (not algebraic) topology? My (admittedly not very expert) suggestion is that you buy all four of these Dover books: Stephen Willard, General Topology (ISBN: 0486434796) Theodore W. Gamelin & Robert Everist Greene, Introduction to Topology: Second Edition (ISBN: 0486406806) George McCarty, Topology: An Introduction with Application to Topological Groups (ISBN: 0486656330) Lynn Arthur Steen & J. Arthur Seebach, Jr., Counterexamples in Topology (ISBN: 048668735X) One of them is bound to meet your needs (Steen & Seebach being a useful supplement to any of the others), none of then is bad, and you wont have wasted your money even if you find you need another book (Munkres, Kelley, Armstrong, Janich?) as well. -- Angus Rodgers Contains mild peril === Subject: Re: self study on topology <2hias0driiqlk3r80kfv98jfkcpvdj37t5@4ax.com> posting-account=_-j7cgwAAADnQK9-r68QgRsgfV-jhA3A >I was wondering if any of you knew of a good book for self study on >general (not algebraic) topology? > My (admittedly not very expert) suggestion is that you buy all four > of these Dover books: > Stephen Willard, General Topology (ISBN: 0486434796) Is this the Dover edition? I ask, Willard is a great book, and Dover has recently published a very inexpensive edition. Ôcid Ôooh === Subject: Re: self study on topology >I was wondering if any of you knew of a good book for self study on general >(not algebraic) topology? I consider Kelley to be rather good. Remember that you do not have to be able to do ALL the exercises. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: self study on topology > I consider Kelley to be rather good. Remember that you > do not have to be able to do ALL the exercises. j.L.Kelleys book is good but I am not so sure it is fit for -self- study. The studier would have to be pretty solid mathematically to assimilate the material properly. I did my first year graduate course in topology at UC Berkeley using Kelley. Bob Kolker === Subject: Re: self study on topology > I was wondering if any of you knew of a good book for self study on general > (not algebraic) topology? As far as topological self-study is concerned, you are a doughnut ;-) === Subject: Re: self study on topology In message , Gib Bogle >> I was wondering if any of you knew of a good book for self study on general >> (not algebraic) topology? >As far as topological self-study is concerned, you are a doughnut ;-) Only if hes got a blocked nose, or a cleft palate. -- David Hartley === Subject: Re: self study on topology >> I was wondering if any of you knew of a good book for self study on general >> (not algebraic) topology? >As far as topological self-study is concerned, you are a doughnut ;-) Thats hardly a safe assumption, in this day of multiple piercings. Its probably (but not absolutely) safe to assume mjn has an abelian fundamental group, though--but now weve moved on to algebraic topology, havent we? Oh, well. Lee Rudolph === Subject: Re: self study on topology >As far as topological self-study is concerned, you are a doughnut ;-) > Thats hardly a safe assumption, in this day of multiple piercings. > Its probably (but not absolutely) safe to assume mjn has an > abelian fundamental group, though--but now weve moved on to > algebraic topology, havent we? Oh, well. Lets keep it clean guys. === Subject: Re: self study on topology >I was wondering if any of you knew of a good book for self study on general >(not algebraic) topology? Moore, Theral O. Elementary General Topology. Munkres, James R. Topology. -- Stephen J. Herschkorn sjherschko@netscape.net === Subject: Re: self study on topology > I was wondering if any of you knew of a good book for self study on general > (not algebraic) topology? There is a book on set point topology in the Schaums Outline Series. Lots of worked out example and lots of exercises. Best of all, it is inexpernsive. You can probably get a used one for ten dollars or less. Bob Kolker === Subject: Re: looking for a certain kind of instructional toy posting-account=Sny74g0AAADy66iGh6ZMdSlIFta_KAXh A large number of the graph editing/viewing tools available do something like this... allow you to pick up a node and move it, without disconnecting its arcs i.e. yEd http://www.yworks.com/en/products_yed_about.htm Various diagramming tools, like Dia or MS Word drawings allow drawing with connectors between shapes, but its a mess in that lines anchor to a point on the shape, rather than shift to the best point as the shape moves. But if youre using dots, tiny filled circles as the shapes (fill color same as line color), this problem might be ignorable. Some java applets/programs... http://javaboutique.webdeveloper.com/Graph/ Touchgraph The things out there seem much more complicated than what you want; however. === Subject: Convergence of Fourier Series question posting-account=7F2l2A0AAADa4fqB0iS_pTUYO3MGXdr5 If f and g are 2pi-periodic L2 functions, then how can I prove that the fourier series of their convolution f * g converges absolutely? Ways Ive tried: Are there any growth results about L2 functions? Then I may use the convolution theorem. Alternatively, can I prove that the convolution is Holder continuous or B.V.? Then I could also prove that the series converges. But how do I know it converges absolutely? Any help would be appreciated. === Subject: Re: Convergence of Fourier Series question posting-account=ZeRDXwsAAACLpj2mpKc97NFPxBaFxAzp Hint: the Fourier series of the convolution is the ___ of the Fourier series of f and of g. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Convergence of Fourier Series question > If f and g are 2pi-periodic L2 functions, then how can I prove that the > fourier series of their convolution f * g converges absolutely? > Ways Ive tried: > Are there any growth results about L2 functions? Then I may use the > convolution theorem. > Alternatively, can I prove that the convolution is Holder continuous or > B.V.? Then I could also prove that the series converges. > But how do I know it converges absolutely? > Any help would be appreciated. It is easier than you think. The Fourier series of f*g is FG, where F and G are the Fourier series of f and g. F and G are sequences in l_2, therefore FG is a sequence in l_1 ........ === Subject: Re: Convergence of Fourier Series question posting-account=7F2l2A0AAADa4fqB0iS_pTUYO3MGXdr5 question. Sometimes asking questions does that. I used Parsevals identity and the fact that the fourier coefficients of f*g are ab. === Subject: Re: Amazing story - Roulette Scanning <41b494ea$19$fuzhry+tra$mr2ice@news.patriot.net> posting-account=JUztfAwAAADv1PUBBOcJTiECyhwXix6x > Look, before anyone says it again, the system is NOT chaotic. The > system is deterministic, I take it, then, you are unaquainted with the catch-phrase deterministic chaos? > with all initial parameters measured to within > resonable accuracy one can, at the very, least get a statistical > advantage. It is a characteristic of chaotic systems that, even with measurements within reasonable accuracy, ones predictions decay to statistically challenged in an unreasonably short time. > In the work of Farmer, Packard et al. they measured the > initial velocity of the wheel by determing frequency, likewise for the > pea. The randomness in the work of Farmer and Packard (the reason why > they had to selected quadrants) is because they were never able to make > resonable measurement of the relative inital position of the pea to the > wheel, thus resulting in random bounces off the dividers. The bounces will always be random from the point of view of the experimenter. Thats what error bars are for. The question is, how random, and how badly do the random errors propagate? > In the work of the chaos cabal at UCSC the major problems were > associated with computational power (particularily under the constraint > of not getting caught by casino security), as well as pure and simple > human reaction time, as pointed out earlier. > As far as when bets are closed it depends on the location of the > casino, the governing body determines this. > If this problem was chaotic i think Farmer Packard etc would have > figured that out and quit, or atleast some of their later collaborators > would have figured it out and poked a bit of fun at them over it. Probably the chaotic not-chaotic slogan is simply inadequate, as are all slogans. All deterministic systems can be evolved for some interval with useful but declining accuracy, the accuracy depending on many factors, including those inherent in the simultation (accuracy of measurments, significant digits, fineness of grid) and those inherent in the evolution of the system. Some better language and analysis is needed to quantify how chaotic, how fast. Like after three glompfzals, our predictions are essentially no better than picking a random point in the phase space. It is left to the reader to develop the glompfzal. CRs) If a slogan were adequate, it would have been the theorem. === Subject: mathematicians utter contempt for common sense Ill show this sig to a few hundred newsgroups, see if the laughter wakes any of you from decades of dreaming. Herc -- YOU CANT PROVE ME..............T |- G <=> ~phi(G) If you prove its true then it has a proof, which makes it false. If you dont prove it, then its true. 10,000 people in sci.math ALL believe that it means mathematics will always be incomplete. === Subject: Re: mathematicians utter contempt for common sense |YOU CANT PROVE ME..............T |- G <=> ~phi(G) There is an important qualifier youre leaving out: prove *in the formal system T*. |If you prove its true *in system T* |then it has a proof, which makes it false. AND shows that the system T cant both have all of its axioms correct and all of its rules of inference valid. Hence the proof in system T does not deserve to be called simply a proof. |If you dont prove it, *in system T* | then its true. |10,000 people in sci.math ALL believe that it means mathematics will always |be incomplete. No. Almost all of them believe only that it means each formal system for mathematics is incomplete. I dont know what it would mean to say that mathematics itself (mother mathematics as James Harris has been known to say) is incomplete. Keith Ramsay === Subject: Re: mathematicians utter contempt for common sense > |YOU CANT PROVE ME..............T |- G <=> ~phi(G) > There is an important qualifier youre leaving out: prove *in the formal > system T*. [...] In Hofstadters Godel Escher Bach ... , he explains his MU-puzzle: -- is MU a theorem in the formal system? I cant find my copy of the book. I was able to find a recent (2001) book review that explains the problem here: Of course, nothing here beats the book itself; I think Hofstadter does a very good job of explaining formal systems, theoremhood in formal systems, and much more. David Bernier [my answer: * ] . . . . . . . . . . . . . . . no . . . . . . . . . . . . . . Hint: check that any theorem in the MIU-system has a number of ÔI symbols congruent to +/- 1 (mod 3) [ lifted from some USENET post ] === Subject: Re: mathematicians utter contempt for common sense > |YOU CANT PROVE ME..............T |- G <=> ~phi(G) > There is an important qualifier youre leaving out: prove *in the formal > system T*. > |If you prove its true > *in system T* > |then it has a proof, which makes it false. > AND shows that the system T cant both have all of its axioms correct > and all of its rules of inference valid. Hence the proof in system T does > not deserve to be called simply a proof. > |If you dont prove it, > *in system T* > | then its true. > |10,000 people in sci.math ALL believe that it means mathematics will always > |be incomplete. > No. Almost all of them believe only that it means each formal system > for mathematics is incomplete. I dont know what it would mean to say > that mathematics itself (mother mathematics as James Harris has > been known to say) is incomplete. That is a scattered cover up to substantiate the claim as an oxymoronic PROOF. No statements practically used in mathamatics have their formula considered IN A SYSTEM. the hypotenuse is the sum of the squares of the other two sides.... theres no IN THIS SYTEM! For every statement this has no proof in system S, there is an equivalent statement this has no proof in any system whatsoever. And your PROOF of the truth of this macro godel statement cannot be applied. What you are all ignoring is that theorem provers come in 2 ßavors: Belief Revision Truth Maintenance In Belief Revision you can assume anything is true, like a godel statement until it is disproven, which it isnt. This the DOMAIN that Godels proof holds water, no generic claims about his pardoxical statements hold throughout. In Truth Maintenance you take unforgiving responsibility when you claim a statement is true. T |- Af, f <-> phi(f) All true statements must be proven. SIMPLE NO? T |- G <=> ~phi(G) this is just G=~G in disguise. This is an invalid formula in Truth Maintenance Theorem Provers. A true statement is a subset of the formula sequence that is its proof. ------------------------------------------------------------- ------- G -> ~proof(G) [1] G C P .....P= !proof(G) where G -> proof(G) [contradicts 2] Why on Earth would you define truth as possibly unproven? Herc === Subject: Re: mathematicians utter contempt for common sense posting-account=_-j7cgwAAADnQK9-r68QgRsgfV-jhA3A > Ill show this sig to a few hundred newsgroups, see if the laughter wakes any of you from decades of dreaming. > Herc > -- > YOU CANT PROVE ME..............T |- G <=> ~phi(G) > If you prove its true then it has a proof, which makes it false. > If you dont prove it, then its true. > 10,000 people in sci.math ALL believe that it means mathematics will always be incomplete. Mathematics is an activity. It cant be incomplete in any *pejorative* sense. Some fields, however, are incomplete in a technical sense -- for example, there are sentences true in the standard model of the naturals that cant be proven in PA. In particular, this is because there exist *other* models of the naturals where the sentence is false. This is a *good* thing. It means that the field of number theory is much *righer* than Hilbert imagined. Ôcid Ôooh === Subject: Re: mathematicians utter contempt for common sense posting-account=EyMaYgwAAADfNipxC0VCUnoeEOLCO7Ww > Ill show this sig to a few hundred newsgroups, see if the laughter > wakes any of you from decades of dreaming. > Herc > -- > YOU CANT PROVE ME..............T |- G <=> ~phi(G) > If you prove its true then it has a proof, which makes it false. > If you dont prove it, then its true. > 10,000 people in sci.math ALL believe that it means mathematics will > always be incomplete. > Mathematics is an activity. It cant be incomplete in any *pejorative* > sense. Some fields, however, are incomplete in a technical sense -- > for example, there are sentences true in the standard model of the > naturals that cant be proven in PA. In particular, this is because > there exist *other* models of the naturals where the sentence is false. > This is a *good* thing. It means that the field of number theory is > much *righer* than Hilbert imagined. Unfortunately Hilbert didnt imagine that Number Theory was right. Since he on many occasions called mathematics nothing but the Den of Thieves of physicicts, and number theory in particular, nonsense on a sheet of paper. The only thing that appartently suprised him about model theory, was that Goedel was righter than Cantor. Since Goedels Theorems arent models, whereas Cantors are. > Ôcid Ôooh === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics >> A second example might be your statement to Lester that: The >> Ôcalculations, as you call them, _are_ the explanations. This >> assumed link between arbitrary calculations and reality is pretty >> magical sounding to me. But Im sure that Lester will explain that >> to you. > It isnt magic when it leads to good technology. Technology is solid > and sound reason for using a theory. That is why quantum field theory > is a winner. It is behind most of our best technology. > And theories do not -explain- anything. Which begs the question - is there anything that explains anything? Whats *is* an explanation? They predict. They also function > as good intuition pumps for making more good theories and promoting > engineering and applications. We cannot know the Real Reality (i.e. > the reality beyond the appearences). Appearances are real realities. To call them appearances instead of real realities might be caused by..[explanation] > The only things we really -know- (as opposed to guess at or infer or > hypothesize) is direct experience. But guessing is very much part of direct experience since [expectancy]->[confirmation yes/no] cycling is what direct experience is all about. === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics glhansen@steel.ucs.indiana.edu (Gregory L. Hansen) in >>glhansen@steel.ucs.indiana.edu (Gregory L. Hansen) in >>glhansen@steel.ucs.indiana.edu (Gregory L. Hansen) in >[...] >Did you think F=ma is any more explanatory? >>Oh, hell, yes. F, m, and a are explained in terms of one another. QM >>merely asserts there is some explanation but cant say what it is. >The potential in quantum mechanics has the same role as the index of >refraction in optics. And, in a sense, the same role as force in >classical mechanics. A wave packet will tend to be drawn toward low spots >of the potential and pushed away from high spots. Electrons are bound to >atoms because of the attractive force between the two; an atom can >transition to a higher energy state when, e.g., another atom bumps into it >and pushes the peices around. >>Yes, yes, this is all very interesting. I always imagined there was >>some reason electrons didnt go marching down Main Street in unison on >>New Years Day. QM just doesnt explain what all this anthropomorphism >>really amount to. >If you like F=ma, then I dont know why youd have a problem with a >wavefunction attracted to lows and repelled from highs in the potential. >Do you know how force and potential energy are related? I assume you know how they are related. Do you know why they are related? >And did you, by any chance, notice that force in classical mechanics isnt >itself explained, but simply defined as that which causes an acceleration? Well, force causes acceleration; it doesnt cause an acceleration unless mediated by mass. What kind of explanation do you expect for force? What kind of explanation for force or mass or even acceleration is possible? I dont say no better explanation for force etc. is possible. I do say that Newton explained what he could of force pretty effectively. Mechanics engages in a mechanical reduction of causes by explaining factors in terms of one another. >[...] >What makes you think mechanics or science are more than self-consistent >plausibilities? >>Well, the point of my observation was the standard of plausibility >>and not self consistency. If all science is based on is plausibility, >>it, like Euclidean geometry, rests on a rather sandy foundation. >Get used to it. As Poincare said, science doesnt tell you what things >are. It organizes relationships between them, and any theory is a true >theory to the extent that if faithfully describes those relationships >within the theorys valid regime of application. Read Science and >Hypothesis by Poincare, which is usefully close to modern views on the >philosophy of science despite being a hundred years old. >>No, no. Science tells us what things are. Thats why we keep it >>around. Its mysticism that doesnt tell us what things are but >>maintains it needs to be kept around as a substitute for science. >Science has grown out of that viewpoint after a few theories that say what >things are have fallen away. None of the macro cause and effect theories Im familiar with have fallen away. They have merely been supplanted at the micro level by QM postulates which turn out to be true but of ambiguous origin in the sense that they dont explain what they explain or fail to explain. If classical mechanics had taken a similar route, we would still be doing classical mechanics supplemented by arbitrary postulates of dubious orign and ambiguous mechanical significance. >But to claim to know what things REALLY are seems far more akin to >claiming knowledge about spirits and other unmeasurables to me. Not necessarily although I have to admit that such a conclusion certainly mirrors contemporary thinking. Personally I consider that if one can show that alternatives of a specific empirical theory are inherently self contradictory truth of the theory itself is necessary. Conversely, showing self contradiction within an empirical theory shows the theory to be false regardless of what experiments fail to contradict, which is the approach Ive taken with special relativity. >[...] >>Youre talking empiricism not knowledge. Precisely whats wrong with >>positivism. A thousand years of observations do not an idea make. >Science is an empirical practice. A theory is good if and only if it >stands up to empirical scrutiny. If it cant, the theory is ßawed. And >if you cant measure every part of every phenomenon with infinite >precision from the beginning to the end of time, then you might never know >you have a ßawed theory. >>And my point is empiricists never empirically know anything. >You cant have missed the existence of modern technology, so I think you >must be using a personal, restrictive definition of what it means to know >something. I think youll find development of modern technology is largely a reßection of classical mechanics with the enhancement of quantum theories. I dont know many machines that inherently rely on quantum ambiguity. We certainly have things like tunneling diodes that rely on quantum suppositions. But those suppositions themselves are not based on any mechanical understanding of the forces at work. They are just suppositions that turn out to reßect poorly understood mechanisms. >[...] >>Well, since you chose not comment on my discussion of contraction >>hypotheses, I cant comment on Lorentz except to say that MM can be >>performed successfully with radiation polarized normal to the plane of >>rotation and the absolute motion of the earth through space detected. >Okay, Ill comment on it. The Lorentz transforms form a group, which >means if you think you find a contradiction in them, you owe it to >yourself to figure out why youre wrong. >In your particular example, the length of an object is defined by the >hollow cube, is moving around in there, that doesnt make a bit of >difference as long as you know what you want to call the front and what >you want to call the back. The gas molecule might itself have a different >length contraction than the block as a whole, but if its between the >front and back in any frame, it will be between the front and back in all >frames. The object itself isnt even necessary. Pick any two points. >>how do we average all these different frames of reference since any >>average of vs would be linear but the effect is non linear? >If you want to calculate a length from the frame of each individual >observer is not oberving simultaneously from all those different reference >frames. The observer observes from his own rest frame. OK. Back to the observer paradox. I guess weve regressed to ground zero for relativistic explanations because I dont need an observer to explain and justify my geometric conclusions but relativity does. >>Einsteins geometric contraction hypothesis applies to a body moving >>at any particular velocity. Different vs, different contraction >>factors. So, which geometry applies to the group of interstitial >>bodies that constitute the body as a whole that Einstein uses to >>explain frequency dilation at v when there are numerous different vs? >>Surely, youre not going to say net v for the body as whole because >>there is no body as a whole; there are only aggregates of interstitial >>frames of reference with vs of their own. And vs average linearly >>whereas frequency dilation factors are non linear. >Einsteins geometric contraction hypothesis relates a length measured in >one frame to a length measured in another frame. When you, Lester, >measure (taking an example from in front of me) the diameter of a >Vanilla Pepsi can, do you need to measure the speeds of each individual >atom within the can? Review the derivation of length contraction and the >definition of length that is used. I dont need to measure anything in my spatial geometry because the problem is logic and not geometry. You, on the other hand, need to resort to observers and personalized measurement because the spatial geometry in relativity contradiction hypotheses is self contradictory on its own terms. >A pre-The Matrix twist on Descartes question, from a philosophy class, >is how do you know youre not a brain in a jar with memories and sensory >data given you by an interactive computer program, and all your >experiences lead you to conclude the wrong laws of nature? >>Probably the same way you can know that youre not standing on your >>head: logical inference. Science should try it some time. >How is your logical inference different from the way you want things to >be? >>It doesnt. Its just different from empirical observation. Empirical >>observation isnt knowledge. Logical inference is. It may be right or >>wrong knowledge, but its the only form of knowledge there is. >Logical inference without data is fantasy. If youre not beholden to >empirical observation, you can build any kind of abstract world that you >like. I never suggested inference without data. Empirical observations are the data. Logical inference is what we make of the data interrelated. >Logic doesnt tell you what your premises have to be, which is why its >always bugged me when Vulcans in Star Trek go running around saying >Thats illogical. Its pragmatic to suppose that youre not a brain in >a jar being fed false experiences, but you cant prove it from a priori >considerations. >>Well, you are a brain in a jar, the skull, being fed experiences by >>the senses, and its up to the brain in the jar to decipher truth from >>falsity through logical inference. I dont know what a priori >>considerations are and neither does anyone else except to say that >>theyre assumptions, neither true nor false. >A priori means knowable without reference to particular facts or >experience. Your logical inference is something that is done with >postulates. Where do those postulates come from? As far as I can tell, >you want postulates that do not appeal to any particular facts or >experiences, and yet say something useful about particular facts or >exeriences. Good luck. Goodness has nothing to do with it. Nor do postulates. What you do need is mechanically irreducible and unregressable truth, by which I mean some empirical observation which is irreducible because alternatives are self contradictory. Logical inference is then done with that mechanism on other reducible empirical observations to determine their relations to one another. >[...] >I think you must have meant an explanation with elements that nobody >thinks to ask the explanation of. >>No, I mean an explanation with elements that nobody needs to ask the >>explanation of because the explanation is evident in the explanation >>without interpretation or the divine intercession of an interpreter. >The explanation is evident in the explanation? Go right ahead, but I >urge you again to be careful of unstated assumptions without which the >explanation would not be so evident. Well, you just start with the empirical observation [not] and work up from there. T:[not][not not] is a tautology and tautologies are always true because they include all possibilities and exclude no possibilities. Then we find that the empirical observation [not] is itself always true because its logical regression [not not] is self contradictory. Which implies that [not] is the logic mechanism were looking for because it is irreducible and unregressable. >interpretation of quantum fields. Theres another view advanced by a >a basic result in ßuid mechanics, for instance, that two vortices will >attract or repel each other, according to the relative directions of their >spin axes, analogously to a Coulomb force. He likes to think of a ßuid >thats ultimately particulate, but ßuid mechanics is typically done in >the continuum limit and I see no logical problem with assuming the ßuid >is itself a continuum. I agree completely and Ill even give it a name: the ether. >and necessary, youre fooling yourself. First, because you know from >priori knowledge. Even if there were no concrete examples there will >always be possibilities that just havent occured to you yet, or the >possibility that there are possibilities that havent occured to you yet. There are always possibilities that just havent occurred to me yet or to you or to others. Quantum theory is filled with them and their symmetries and with quantum theorists hunting for them. I take nothing except basic truth T:[not][not not] as self evident and that only because the term self evident means evident of itself in that alternatives are inherently self contradictory. Maybe there are other definitions for self evidence, but that is the one I use. You seem to think Im whistling in the dark regarding the existence of of the mechanical origin of Plancks constant, Im enclosing a copy: > Plancks Constant >Previously in the thread Angular Momentum in Rotating Bodies, I >presented an analytical framework for the interpretation of dr/dt in >circular rotation of a point mass m at velocity v and radius r. No one >I know of agrees with my interpretation of dr/dt. However, in the >interests of further establishing this general framework, I would like >to pursue general developement of the idea which culminates in the >analytical definition of Plancks constant. >We begin by noting that in cases of circular rotation at constant >angular velocity we have a centripetally directed dr/dt acting on >point mass m of a magnitude equal to tangential velocity v. This is >what causes the rotation of v and produces r as a consequence of >rotation. >We then integrate dr/dt along r which produces 1/2 mvr/2pi with units >of measure equal to rr/t. Now, I have been cautioned on several >occasions not to suggest that this quantity represents angular >momentum in conventional terms and I agree. Perhaps we should simply >call it rotational momentum to prevent confusion. >What we notice immediately however is that it bears the same form as >the quantity mvr corresponding to Plancks constant. However, we have >to straighten certain things out in this connection. >In conventional macro angular rotation such as ßywheels we have a >centripetal dr/dt and tangential v which are equal to each other. They >are effectively bound up through tensile forces internal to the body >undergoing rotation. In celestial angular mechanics on the other hand >we have a wide variety of potential dr/dts and tangential orbital >velocities operating in various combinations. >different situation. The tangential velocity of rotation v is constant >under all circumstances. In other words, v = c. Thus dr/dt operates >mass. >second) times an analytical masslet, m0 (kg-sec) and interpret the >quantity mvr as a multiple of nm0vr. Further we can interpret r as a >function of c/n such that Plancks constant = m0cc. In other words, m0 >is roughly on the order of 10^-50 kg-sec in magnitude and Plancks >constant corresponds to the multiple of m0 and the square of the >velocity of light. >We notice several things about rotational momentum. In linear motion >at constant velocity rotational momentum is zero because dr/dt and mvr >are both zero. And in circular rotation at a constant angular velocity >rotational momentum is constant because mvr is constant. This >represents the analytical distinction between circular and linear >motion. >Further we notice that dr/dt can be of any magnitude. It is not bound >by the constancy of the velocity of light as an upper limit because it >doesnt go anywhere. It only produces rotation in relation to actual >tangential motion v = c. >mass and radius of rotation are inversely proportional, that is that >remove DEL in address for email Linear versus Analytical Mechanics One of the really unfortunate aspects of Newtons choice of a linear frame of reference for the analysis of mechanics is that r is poorly defined and t is not defined at all. In other words, r is only defined in direction and t is not defined by any consideration pertinent to the analytical frame of reference. And this had a pernicious impact on the subsequent development of angular mechanics as well as relativistic considerations and quantum mechanics in the twentieth century. The problem is that r and t and their combinations are all we have to work with. Taken to the second level of compounding we have six combinations: r, 1/t, r/t, r/tt, rr/t, and rr/tt. However, in the linear analytical frame of reference the next to last combination rr/t was overlooked because there is no apparent application for it in linear mechanical contexts. On the other hand, in angular frames of reference we have applications for all combinations and all the elements are well defined. The radius of rotation is well defined in terms of direction and magnitude and time is well defined in analytical terms as whatever time is needed for 2pi radians of rotation. The rr/t combination is also well defined in angular terms. However, in extrapolating the idea of rr/t from linear to angular contexts in classical mechanics, whoever devised the analytical approach made the mistake of trying to emulate linear mechanics in the sense of explaining rotation as a linear progression of r instead of a simple radial v in combination with tangential v. This is more akin to an anachronistic pre Newtonian view of mechanics. Kepler thought that some force of angels was needed to keep planets in orbit around the sun and regarded that force as tangential in direction. Newton on the other hand recognized that the only force needed was centripetal in nature and not tangential. But whoever devised the analytical considerations underlying angular mechanics apparently never considered the Newtonian perspective and presumably relied on the pre Newtonian rationale. Thus we wind up with a conceptual schism among the various realms of angular mechanics. On the one hand we have orbital angular mechanics, the macro realm of ordinary angular mechanics, and the micro realm of quantum effects. And unfortunately there is no conceptual integration among them. We are convinced that all represent mechanical realms but we have no basis for comprehending each in terms of the others. Orbital angular mechanics represents the realm of remote interactions dealt with in terms of inverse square centripetal forces and tangential orbital velocities. Whereas the macro realm of ordinary angular mechanics deals with linear analogs such as moments of inertia instead of mass, torque instead of force, and angular acceleration and velocity instead of their linear analogs. The micro realm of angular mechanics on the other hand is dealt with on the merely descriptive basis of formalisms. This is the realm of quantum mechanics - QM - or as I prefer to call it quantum magic where things dont seem to happen for any definite mechanical reason at all. However with the redefinition of macro angular momentum and Plancks constant in circular rotation we are at last in a position to understand the mechanical differences among the realms in conceptual terms. The micro realm of quantum effects is one of constant tangential velocity of rotation v = c and a variable radial dr/dt. The macro realm of ordinary angular mechanics on the other hand is one in which the tangential velocity of rotation is variable but tangential v = radial dr/dt and both are kept in strict synchronization by internal tensile forces. And finally orbital angular mechanics is defined by various combinations of tangential v and radial dr/dt. This is normally thought of in celestial terms but in point of fact applies equally to the atomic realm as well. === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics >> A second example might be your statement to Lester that: The >> Ôcalculations, as you call them, _are_ the explanations. This >> assumed link between arbitrary calculations and reality is pretty >> magical sounding to me. But Im sure that Lester will explain that to >> you. > It isnt magic when it leads to good technology. Damn, Bob. Please read for comprehension and note the context. I never said nor implied otherwise. > Technology is solid and > sound reason for using a theory. That is why quantum field theory is a > winner. It is behind most of our best technology. You talk about QM as if it were explained by a monolithic single theory and all aspects of that single theory have been empirically proven. > And theories do not -explain- anything. They predict. And are useful *only* to the extent they predict. Please explain this to Wolf. > They also function > as good intuition pumps for making more good theories and promoting > engineering and applications. We cannot know the Real Reality (i.e. the > reality beyond the appearences). The only things we really -know- (as > opposed to guess at or infer or hypothesize) is direct experience. Please explain this to Wolf et al. -- Dont you see that the whole aim of Newspeak is to narrow the range of thought? In the end we shall make thoughtcrime literally impossible, because there will be no words in which to express it. -- George Orwell as Syme in 1984t === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics >> Well, one good example is available in my reply to your reply to Stlbl >> above: your assertion that any unfalsified theory was evidence. > I never said or implied that. I never said you did, Bob. There is something wrong with your reader. I was replying to Wolf. > We can never know when a theory is true. > We can only know when it is falsified. A non-falsified theory with a > good record of predictions (many kinds of things predicted or related) > is sufficient reason for staying with the theory. If the theory leads to > good technology that is even more reason for staying with the theory. We > stay with a theory because it is productive and useful, not because it > is true. Agreed. -- Dont you see that the whole aim of Newspeak is to narrow the range of thought? In the end we shall make thoughtcrime literally impossible, because there will be no words in which to express it. -- George Orwell as Syme in 1984t === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics >The calculations, as you call them, _are_ the explanations. I once had a Physics Prof announce that In Physics meaning has no meaning, the only thing that matters is whether we can manipulate the formalisms. Im not sure what this contributes to the thread, but its an interesting quote. Dark skies, tom -- We have discovered a therapy ( NOT a cure ) for the common cold. Play tuba for an hour. === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics >>The calculations, as you call them, _are_ the explanations. > I once had a Physics Prof announce that In Physics meaning > has no meaning, the only thing that matters is whether we can > manipulate the formalisms. > Im not sure what this contributes to the thread, but its > an interesting quote. > Dark skies, > tom He was right. But of course the really odd thing is that those manipulated formalisms somehow refer to the real world.... === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics >The calculations, as you call them, _are_ the explanations. >> I once had a Physics Prof announce that In Physics meaning >> has no meaning, the only thing that matters is whether we can >> manipulate the formalisms. >> Im not sure what this contributes to the thread, but its >> an interesting quote. >> Dark skies, >> tom >He was right. >But of course the really odd thing is that those manipulated formalisms >somehow refer to the real world.... Unfortunately, QM doesnt explain the somehow, which is what a mechanics is supposed to do. And I daresay there are a multitude of formalisms that somehow dont apply for reasons QM is too busy providing intuition pumps to supply. === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics >> Unfortunately, QM doesnt explain the somehow, which is what a >> mechanics is supposed to do. >Tell me. How does a Lagrangian formulation of mechanics explain >anything? What it does is imply some laws which when applied produce >good predictions. What makes you think there are entities behind the >appearences that behave mechanically? What makes you think there arent. By, George, I do believe youve just confessed that QM isnt mechanics. > What evidence do you have. What evidence do you have that there is no mechanics? All QM has at presence are educated speculations, some of which turn out to be correct and many of which turn out to be incorrect, and no mechanics to explain why any of their guesses are correct. >Classical physics which was solidly mechanics is an empirical failure Well, not exactly. Quantum theorists just took advantage of emprical failures of classical mechanics to suggest there is no mechanics and informed intuition or educated guesses were superior. >which is why we have quantum theory and relativity. The truly mechanical >theories such as statistical mechanics are heuristics, not fundemental >models of reality. QM works. Relativity works. What more do you want? Mechanics. Something that shows how they work. === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics >> Unfortunately, QM doesnt explain the somehow, which is what a >> mechanics is supposed to do. > Tell me. How does a Lagrangian formulation of mechanics explain > anything? What it does is imply some laws which when applied produce > good predictions. What makes you think there are entities behind the > appearences that behave mechanically? What evidence do you have. > Classical physics which was solidly mechanics is an empirical failure > which is why we have quantum theory and relativity. The truly mechanical > theories such as statistical mechanics are heuristics, not fundemental > models of reality. QM works. Relativity works. What more do you want? > Bob Kolker Lester want to be recognised as the one who explains the _reasons why_ everything is the way it is. But just why mecvhanism should be the reasons why, he cant say; nor why the mechnaism of differences between doifferences is the fundamental mechanism. IOW, Lester cant accept that things are simply what they are, and the best we can do is describe how things happen. IOW, he cant accept what I call the Fundamnetal Ignorance Theorem (first expressed by Bertrand Russell): When we know that we say is true, we dont know what it means. When we know what mean, we dont know if its true. Now, I wonder how Lester will blast me for that piece of heresy. :-) === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics : Lester want to be recognised as the one who explains the _reasons why_ : everything is the way it is. But just why mecvhanism should be the : reasons why, he cant say; nor why the mechnaism of differences between : doifferences is the fundamental mechanism. The following is from the preface for the second edition of Newtons Principia: I can hear some people disagreeing with this conclusion and muttering something or other about occult qualities. They are always prattling on and on to the effect that gravity is something occult, and that occult causes are to be banished completely from philosophy. But it is easy to answer them: occult causes are not those causes whose existence is very clearly demonstrated by observations, but only those whose existence is occult, imagined, and not yet proved. Therefore gravity is not an occult cause of celestial motions, since it has been shown from phenomena that this force really exists. Rather, occult causes are the refuge of those who assign the governing of these motions to some sort of vortices of a certain matter utterly fictitious and completely imperceptible to the senses. But will gravity be called an occult cause and be cast out of natural philosophy on the grounds that the cause of gravity itself is occult and not yet found? Let those who so believe take care lest they believe in an absurdity that, in the end may overthrow the foundations of all philosophy. For causes generally proceed in a continuous chain from compound to more simple; when you reach the simplest cause, you will not be able to proceed any further. Therefore no mechanical explanation can be given for the simplest cause; for if it could, the cause would not yet be the simplest. Will you accordingly call these simplest causes occult, and banish them? It was written by Roger Cotes in 1713. Stephen === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics >: Lester want to be recognised as the one who explains the _reasons why_ >: everything is the way it is. But just why mecvhanism should be the >: reasons why, he cant say; nor why the mechnaism of differences between >: doifferences is the fundamental mechanism. >The following is from the preface for the second edition of Newtons >Principia: > I can hear some people disagreeing with this conclusion and > muttering something or other about occult qualities. They are always > prattling on and on to the effect that gravity is something occult, and > that occult causes are to be banished completely from philosophy. But > it is easy to answer them: occult causes are not those causes whose > existence is very clearly demonstrated by observations, but only those > whose existence is occult, imagined, and not yet proved. Therefore > gravity is not an occult cause of celestial motions, since it has been > shown from phenomena that this force really exists. Rather, occult > causes are the refuge of those who assign the governing of these motions > to some sort of vortices of a certain matter utterly fictitious and > completely imperceptible to the senses. > But will gravity be called an occult cause and be cast out of natural > philosophy on the grounds that the cause of gravity itself is occult > and not yet found? Let those who so believe take care lest they believe > in an absurdity that, in the end may overthrow the foundations of > all philosophy. For causes generally proceed in a continuous chain > from compound to more simple; when you reach the simplest cause, you will > not be able to proceed any further. Therefore no mechanical explanation > can be given for the simplest cause; for if it could, the cause would > not yet be the simplest. Will you accordingly call these simplest > causes occult, and banish them? >It was written by Roger Cotes in 1713. With which I agree and maintain that if quantum observations are in fact the simplest cause, the reason why has yet to be shown, nor has the reason they are not the simplest cause because quantum theory doesnt deal in causes for quantum observations. Quantum theory as I understand it maintains there are no causes. === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics > Unfortunately, QM doesnt explain the somehow, which is what a > mechanics is supposed to do. >> Tell me. How does a Lagrangian formulation of mechanics explain >> anything? What it does is imply some laws which when applied produce >> good predictions. What makes you think there are entities behind the >> appearences that behave mechanically? What evidence do you have. >> Classical physics which was solidly mechanics is an empirical failure >> which is why we have quantum theory and relativity. The truly >> mechanical theories such as statistical mechanics are heuristics, not >> fundemental models of reality. QM works. Relativity works. What more >> do you want? >> Bob Kolker > Lester want to be recognised as the one who explains the _reasons why_ > everything is the way it is. But just why mecvhanism should be the > reasons why, he cant say; nor why the mechnaism of differences between > doifferences is the fundamental mechanism. > IOW, Lester cant accept that things are simply what they are, and the > best we can do is describe how things happen. IOW, he cant accept what > I call the Fundamnetal Ignorance Theorem (first expressed by Bertrand > Russell): When we know that we say is true, we dont know what it means. > When we know what mean, we dont know if its true. To me, Fundamental Ignorance is that willed ignorance that you display when you argue *against* explaining the _reasons why_ things are the way they are. An excellent reply for a novice hoping for entry into the priesthood of Scientific Faith. BTW, I prefer to judge Lester by his own words and not by your revisionist interpretations of them. -- Dont you see that the whole aim of Newspeak is to narrow the range of thought? In the end we shall make thoughtcrime literally impossible, because there will be no words in which to express it. -- George Orwell as Syme in 1984t === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics [...] > To me, Fundamental Ignorance is that willed ignorance that you display > when you argue *against* explaining the _reasons why_ things are the way > they are. An excellent reply for a novice hoping for entry into the > priesthood of Scientific Faith. I dont understand the point of your comment. Are you claiming that I am trying to enter the Pristehood? Whatever gave you that idea? Are you implying that I am a novice? Since I dont know what you mean by novice, I have no idea what imnplication might mean, but Im pretty sure its not intended to be complimentary. Are you claiming that I refuse to explain the reasons-why? That depends on what reasons-why are being offered, or more precisely, on what the speaker intends with why. I do detect something rather more than annoyance in your remarks. Whats your game? Why do my remarks offend you? Are you suggesting that I refuse to accept that we can ever know why there is something rather than nothing? In the narrow sense of How did the Something within we exist come about? a partial answer can be given. Currently, it starts with a big bang, but since the maths around that singularity are rather, er singular, even the physicists are careful to hedge their bets by pointing out that this the best they can sofar. The story of what happened after the bang is somewhat better grounded. In the wider sense of Howcome did it get started at all? there is no scientific answer (though there are plenty of more or less plausible and entertaining sci-fi speculations.) Profound ignorance is what we must admit at this point. In the rather different sense of Is there some reason or purpose for it all? there is no answer, there are only statements of belief. Youre welcome to guess what my statement of belief might be. :-) > BTW, I prefer to judge Lester by his own words and not by your > revisionist interpretations of them. > Well, any judgement you make will be your revisionist interpretation, is all. I dont see that it makes any difference. Oh, that phrase willed ignorance belongs to theology, at least as far as my admittedly limited reading in that field indicates. Are you trying to bring in some theological version of the reasons-why? I can see that if you commit to theological reasons, you would be annoyed at any remark that implies that such reasons-why arent reasons at all. === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics > [...] >> To me, Fundamental Ignorance is that willed ignorance that you display >> when you argue *against* explaining the _reasons why_ things are the >> way they are. An excellent reply for a novice hoping for entry into >> the priesthood of Scientific Faith. > I dont understand the point of your comment. Are you claiming that I am > trying to enter the Pristehood? Whatever gave you that idea? Are you > implying that I am a novice? Since I dont know what you mean by > novice, I have no idea what imnplication might mean, but Im pretty > sure its not intended to be complimentary. Are you claiming that I > refuse to explain the reasons-why? That depends on what reasons-why are > being offered, or more precisely, on what the speaker intends with > why. I do detect something rather more than annoyance in your remarks. > Whats your game? You must be severely challenged in the interpretation of metaphor. I have no Ôgame. >Why do my remarks offend you? Well, now. Arent you the paragon of innocence. > Are you suggesting that I refuse to accept that we can ever know why > there is something rather than nothing? In the narrow sense of How did > the Something within we exist come about? a partial answer can be > given. Currently, it starts with a big bang, but since the maths around > that singularity are rather, er singular, even the physicists are > careful to hedge their bets by pointing out that this the best they can > sofar. The story of what happened after the bang is somewhat better > grounded. > In the wider sense of Howcome did it get started at all? there is no > scientific answer (though there are plenty of more or less plausible and > entertaining sci-fi speculations.) Profound ignorance is what we must > admit at this point. If you did in fact admit profound ignorance, rather than defend the more or less plausible and entertaining sci-fi speculations as truth, then we would have nothing to discuss. > In the rather different sense of Is there some reason or purpose for it > all? there is no answer, there are only statements of belief. Youre > welcome to guess what my statement of belief might be. :-) I have no choice but to infer your beliefs from your posts. >> BTW, I prefer to judge Lester by his own words and not by your >> revisionist interpretations of them. >> > Well, any judgement you make will be your revisionist interpretation, is > all. I dont see that it makes any difference. > Oh, that phrase willed ignorance belongs to theology, at least as far > as my admittedly limited reading in that field indicates. Your admittedly limited reading in that field leads you to serious mistakes. The statement has nothing to do with theology. > Are you trying > to bring in some theological version of the reasons-why? I can see that > if you commit to theological reasons, you would be annoyed at any remark > that implies that such reasons-why arent reasons at all. LOL. Sorry, Wolf, but you simply lack the rhetorical skill to tar me with that brush. I have not offered any theological arguments in my observations about your beliefs concerning science. I have argued only for the Scientific Method in the search for scientific evidence. -- Dont you see that the whole aim of Newspeak is to narrow the range of thought? In the end we shall make thoughtcrime literally impossible, because there will be no words in which to express it. -- George Orwell as Syme in 1984t === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics [...] >> Oh, that phrase willed ignorance belongs to theology, at least as >> far as my admittedly limited reading in that field indicates. > Your admittedly limited reading in that field leads you to serious > mistakes. The statement has nothing to do with theology. Sorry, but Ive never before encountered that phrase in discussions about scientific evidence for or against some claim, only in theological contexts, where it is considered a sin. Since you imply that my comments constitute some sort of heresy against the Scientific Faith, my inference isnt as far wrong as you may wish to claim. >> Are you trying to bring in some theological version of the >> reasons-why? I can see that if you commit to theological reasons, you >> would be annoyed at any remark that implies that such reasons-why >> arent reasons at all. > LOL. Sorry, Wolf, but you simply lack the rhetorical skill to tar me > with that brush. I have not offered any theological arguments in my > observations about your beliefs concerning science. I have argued only > for the Scientific Method in the search for scientific evidence. Sofar, you havent once said anything that touches on my beliefs, only on my comments, from which you claim to be able to infer my beliefs. Since you capitalise Scientific Method, am I correct in inferring that you believe it is a path to Truth? If not, what do you intend by capitalising the phrase? In any case, Im not at all clear just what you object to and why. It seems to have something to do with the origin of life, but you havent as far as I can make out made your objections clear. On the one hand you claim that the Scietific Method leads to truth (or Truth, I dunno), OTOH, you object to maybe-explanations of the o-o-l on the grounds that theyre not proven, or not evidence, or something. But these maybe-explanations are attempts to account for the facts as known. That they arent any better than maybe-explanations is just the way it is. For now, anyway. Maybe for the foreseeable future. I dunno. But Im pretty sure that evcentually some scientific account will be available. (There, Ive actually _stated_ a belief - you neednt infer it. Saved you a lot of work, no doubt.) Oh, re your LOLs -- great rhetorical skills there. You must have laboured long and hard to come up with such witty ripostes. === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics > [...] > Oh, that phrase willed ignorance belongs to theology, at least as > far as my admittedly limited reading in that field indicates. >> Your admittedly limited reading in that field leads you to serious >> mistakes. The statement has nothing to do with theology. > Sorry, but Ive never before encountered that phrase in discussions > about scientific evidence for or against some claim, only in theological > contexts, where it is considered a sin. Ive never seen it in either context. I simply stuck two words together to mean a type of ignorance that is not accidental, but rather willed, usually done to avoid looking at facts. If you examine previous posts you will see that I invented the phrase as a mockery of your intended insult of Lester where you said: [Lester] cant accept what I call the Fundamnetal Ignorance Theorem (first expressed by Bertrand Russell): When we know that [what] we say is true, we dont know what it means. When we know what [it] mean[s], we dont know if its true. I think my phrase is as valid as yours, and much more descriptive of your replies. You seem determined to lead this discussion away from science and into religion. However, if you accept the definition of sin as Ômissing the mark, then I suppose you could say that Ôwilled ignorance is shooting your arrow in a direction guaranteed to miss the mark. > Since you imply that my comments > constitute some sort of heresy against the Scientific Faith, my > inference isnt as far wrong as you may wish to claim. No, on the contrary. Your comments are not Ôheresy against the Scientific Faith, but rather the ingratiating repetitions of a toady hoping to become a high priest of that faith. I personally believe that properly done science should require no faith. > Are you trying to bring in some theological version of the > reasons-why? I can see that if you commit to theological reasons, you > would be annoyed at any remark that implies that such reasons-why > arent reasons at all. >> LOL. Sorry, Wolf, but you simply lack the rhetorical skill to tar me >> with that brush. I have not offered any theological arguments in my >> observations about your beliefs concerning science. I have argued >> only for the Scientific Method in the search for scientific evidence. > Sofar, you havent once said anything that touches on my beliefs, only > on my comments, Which leads unavoidably to the conclusion that your comments have all been lies. > from which you claim to be able to infer my beliefs. Yes, I made the apparently erroneous assumption that your comments arose from your beliefs. Would it be safe to continue in the now corrected assumption that everything you post henceforth is also a lie. > Since you capitalise Scientific Method, am I correct in inferring that > you believe it is a path to Truth? Not Universal Truth. But certainly the accepted method for discovering scientific truth. > If not, what do you intend by capitalising the phrase? What did you intend by capitalizing the phrase Fundamnetal Ignorance Theorem? > In any case, Im not at all clear just what you object to and why. I am aware of your disability. Remember? I called it Ôwilled ignorance. It does indeed have serious consequences. > It > seems to have something to do with the origin of life, but you havent > as far as I can make out made your objections clear. Not even warm. > On the one hand you > claim that the Scietific Method leads to truth (or Truth, I dunno), > OTOH, you object to maybe-explanations of the o-o-l on the grounds that > theyre not proven, or not evidence, or something. But these > maybe-explanations are attempts to account for the facts as known. ÔMaybe-explanations are speculation, which is a valid word and quite proper in the context. And speculation does not in any way account for Ôthe facts as known. Which is what this whole stupid thread is about and why I accuse you of Ôwilled ignorance. > That > they arent any better than maybe-explanations is just the way it is. > For now, anyway. Maybe for the foreseeable future. I dunno. But Im > pretty sure that evcentually some scientific account will be available. > (There, Ive actually _stated_ a belief - you neednt infer it. Saved > you a lot of work, no doubt.) account will be available. Now if you would just quit referring to such speculation as fact in the future, then possibly we can drop this stupid thread. > Oh, re your LOLs -- great rhetorical skills there. You must have > laboured long and hard to come up with such witty ripostes. Not at all. Laughing out loud was indeed my response to many of your statements. It was not a rhetorical device. -- Dont you see that the whole aim of Newspeak is to narrow the range of thought? In the end we shall make thoughtcrime literally impossible, because there will be no words in which to express it. -- George Orwell as Syme in 1984t === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics >> [...] [re: wiklled ignorance:] > Ive never seen it in either context. I simply stuck two words together > to mean a type of ignorance that is not accidental, but rather willed, > usually done to avoid looking at facts. OK. > If you examine previous posts > you will see that I invented the phrase as a mockery of your intended > insult of Lester where you said: > [Lester] cant accept what I call the Fundamnetal Ignorance Theorem > (first expressed by Bertrand Russell): > When we know that [what] we say is true, we dont know what it means. > When we know what [it] mean[s], we dont know if its true. > I think my phrase is as valid as yours, and much more descriptive of > your replies. Only becaues you operate with what IMO are incorrect notions of beliefs and lies. (Ive snipped that part of your post.) As explicitly as I can say it: The contrary of a belief statement is not a lie. [...] > No, on the contrary. Your comments are not Ôheresy against the > Scientific Faith, but rather the ingratiating repetitions of a toady > hoping to become a high priest of that faith. I personally believe that > properly done science should require no faith. Me, a toady? Oh, Albert, Albert, how low you have fallen. If anything, youre the toady, with your reiterated references to a Scientific Method, in capitals, yet! [...] >> Sofar, you havent once said anything that touches on my beliefs, only >> on my comments, > Which leads unavoidably to the conclusion that your comments have all > been lies. Only by your defintion, which I find odd, to say the least. The usual claim is that belief statements are not truthfunctions. Hnece their relationship to lies is, um unclear, to put it mildly. I try to avoid belief statements, though I know thats difficult. If you are claiming that I assert as truths statements I dont beleive in, I have two comments on that. A) What does belief have to do with truth? B) I offer commentys as more or less probbaly true - and I assume that the careful reader will be able to asses probbale truths. Your unpleasant attacks started when I offreed _possible_ scenarios for the origin of loifge. I didnt claim they were true. I didnt claim they were proven. I didnt claim I believed them. All these things you read into my comments because of your quaint notion that in discussions one only utters statments that one believes (whatver you mean by that - Ive found it difficult to figure what people mean when they use that word.) >> from which you claim to be able to infer my beliefs. > Yes, I made the apparently erroneous assumption that your comments arose > from your beliefs. Would it be safe to continue in the now corrected > assumption that everything you post henceforth is also a lie. No, because I dont claim knowlege of truth or Truth, just tentative attempts. >> Since you capitalise Scientific Method, am I correct in inferring that >> you believe it is a path to Truth? > Not Universal Truth. But certainly the accepted method for discovering > scientific truth. Which is not a very great truth, but is the best we can do (I dont believe in Universal Truth, just in local and limited truths, of varying imnportance. The truths in personal relationships are very important. Thats naother beleif statement, in case you missed it.) >> If not, what do you intend by capitalising the phrase? > What did you intend by capitalizing the phrase Fundamnetal Ignorance > Theorem? Irony. Some ironies point the way to a truth (small t.) >> In any case, Im not at all clear just what you object to and why. > I am aware of your disability. Remember? I called it Ôwilled > ignorance. It does indeed have serious consequences. >> It seems to have something to do with the origin of life, but you >> havent as far as I can make out made your objections clear. > Not even warm. >> On the one hand you claim that the Scietific Method leads to truth (or >> Truth, I dunno), OTOH, you object to maybe-explanations of the o-o-l >> on the grounds that theyre not proven, or not evidence, or something. >> But these maybe-explanations are attempts to account for the facts as >> known. > ÔMaybe-explanations are speculation, which is a valid word and quite > proper in the context. And speculation does not in any way account for > Ôthe facts as known. Which is what this whole stupid thread is about > and why I accuse you of Ôwilled ignorance. Ok, now that you;ve made yourself clear, kindly point me to what I am deliberately ignorant of. >> That they arent any better than maybe-explanations is just the way it >> is. For now, anyway. Maybe for the foreseeable future. I dunno. But >> Im pretty sure that evcentually some scientific account will be >> available. (There, Ive actually _stated_ a belief - you neednt infer >> it. Saved you a lot of work, no doubt.) > will be available. Now if you would just quit referring to such > speculation as fact in the future, then possibly we can drop this stupid > thread. I never did - thats what you read into my comments. >> Oh, re your LOLs -- great rhetorical skills there. You must have >> laboured long and hard to come up with such witty ripostes. > Not at all. Laughing out loud was indeed my response to many of your > statements. It was not a rhetorical device. Chuckle. === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics > Unfortunately, QM doesnt explain the somehow, which is what a > mechanics is supposed to do. >> Tell me. How does a Lagrangian formulation of mechanics explain >> anything? What it does is imply some laws which when applied produce >> good predictions. What makes you think there are entities behind the >> appearences that behave mechanically? What evidence do you have. >> Classical physics which was solidly mechanics is an empirical failure >> which is why we have quantum theory and relativity. The truly mechanical >> theories such as statistical mechanics are heuristics, not fundemental >> models of reality. QM works. Relativity works. What more do you want? >> Bob Kolker >Lester want to be recognised as the one who explains the _reasons why_ >everything is the way it is. But just why mecvhanism should be the >reasons why, he cant say; nor why the mechnaism of differences between >doifferences is the fundamental mechanism. Wolfs reading comprehension is rather poor not to mention his rather comical editing skills. Probably stream of consciousness appraisals of what he wants to imagine hes read. >IOW, Lester cant accept that things are simply what they are, Once more Wolf universalizes a personal observation. What bothers Wolf is that I cant accept that things simply are what he believes they are because Im not particularly partial to beliefs in any form as a substitute for science. > and the >best we can do is describe how things happen. IOW, he cant accept what >I call the Fundamnetal Ignorance Theorem (first expressed by Bertrand >Russell): When we know that we say is true, we dont know what it means. >When we know what mean, we dont know if its true. Yes, well, I daresay when we dont understand what you mean, all we have to do is reread this particular comment. >Now, I wonder how Lester will blast me for that piece of heresy. :-) Heresy, what heresy? Just a rather confused description of your beliefs as far as I can tell. === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics >>IOW, Lester cant accept that things are simply what they are, > Once more Wolf universalizes a personal observation. What bothers > Wolf is that I cant accept that things simply are what he believes > they are because Im not particularly partial to beliefs in any form > as a substitute for science. Its nice to know that you know what I believe what things are, because I dont. Enlighten me. === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics >IOW, Lester cant accept that things are simply what they are, >> Once more Wolf universalizes a personal observation. What bothers >> Wolf is that I cant accept that things simply are what he believes >> they are because Im not particularly partial to beliefs in any form >> as a substitute for science. >Its nice to know that you know what I believe what things are, because >I dont. Enlighten me. All you have to do is read your own posts, Wolf. Youre pretty long on observation and pretty short on explanations. === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics > The calculations, as you call them, _are_ the explanations. >> I once had a Physics Prof announce that In Physics meaning has no >> meaning, the only thing that matters is whether we can manipulate the >> formalisms. >> Im not sure what this contributes to the thread, but its >> an interesting quote. >> Dark skies, >> tom > He was right. > But of course the really odd thing is that those manipulated formalisms > somehow refer to the real world.... Somehow? LOL. Well, sometimes they do and sometimes they dont. That area between mathematics and the real world that you refer to as Ôsomehow I assume defines where your faith comes into play. -- Dont you see that the whole aim of Newspeak is to narrow the range of thought? In the end we shall make thoughtcrime literally impossible, because there will be no words in which to express it. -- George Orwell as Syme in 1984t === Subject: Re: Science, Philosophy, Mysticism, Art, Mathematics, and Physics >> The calculations, as you call them, _are_ the explanations. > I once had a Physics Prof announce that In Physics meaning has no > meaning, the only thing that matters is whether we can manipulate the > formalisms. > Im not sure what this contributes to the thread, but its > an interesting quote. > Dark skies, > tom >> He was right. >> But of course the really odd thing is that those manipulated >> formalisms somehow refer to the real world.... > Somehow? LOL. Well, sometimes they do and sometimes they dont. That > area between mathematics and the real world that you refer to as > Ôsomehow I assume defines where your faith comes into play. To quote you: Damn, Albert, read for comprehension. Somehow does not deny sometimes they do and sometimes they dont. The issue is, why do they refer to the real world at all, not what proportion does so. Though it is odd, isnt it, that so much math that began as pure manipulation of the formalisms turned out and still turns out to be applicable to the real world. I guess I must be on your bad-guy list, since you react with foaming mouth and irrelevant comments to just about everything I say - even when I make a point that doesnt disagree with you. === Subject: Einsteins Equations are Holographic tHooft and Susskind building on Bekenstein and Hawking conjectured that the dimensionless information content in a volume of space is the area of its boundary divided by 4Planck area. Whether those are c-bits or qubits is left unclear. In Cartans forms, which are automatically Diff(4) invariant, and which permit integrals on curved manifolds, circumventing some of the gravity nonlocality problem, the Levi-Civita connection field is a 1-form and the curvature is a 2-form. Einsteins field equation, including the dark energy local field correction, is Guv + /zpfguv = 8pi(G/c^4)Tuv The dimensions of the marble geometrodynamic LHS are 1/Area consistent with the Cartan curvature 2-form with INVARIANT Hodge DeRham integrals over 2D coform AREAS. This is automatically HOLOGRAPHIC since VOLUMES are replaced by AREAS! This is because 8pi(G/c^4) has dimension [Length/Energy] = (String Tension)^-1. Note that non-Perturbative background-independent Quantum Loop Gravity also rests fundamentally on the quantum area operator as does my own macro-quantum coherent More is Different emergence derivation of Einsteins local GR from the rigid Goldstone phase of the Higgs Vacuum Order Parameter in the Inßationary Phase Transition of the Big Bang from the unstable ßat false micro-quantum vacuum to the stable curved macro-quantum coherent holographic vacuum with lower zero point energy density (small Cosmological Constant) and lower entropy (smaller phase space volume). That is, Cartans tetrads eu^a come from the Bohm elasticity giant pilot wave constraint eu^a,a = Kronecker Deltau^a,a + (Area Quantum)(Goldstone Phase),u ,a is ordinary partial derivative When the rigid Goldstone Phase = 0 eu^a = Kronecker Deltau^a guv(Curved LNIF) = eu^a(Minkowski)abev^b = (Minkowski)uv = PRE-INFLATION FALSE VACUUM in that limit. In general guv(LNIF) = [Minkowski (LIF)]uv + (1/2)(Eu,v + Ev,u) Eu = (Quantum of Area)(Goldstone Phase),u This is not perturbation theory and guv is a dynamical field. Note also that the Vilenken unstable ßat DARK ENERGY vacuum domain wall solution is a finite spacetime blob Lorentzian instanton inside of which there is zero conformal curvature with a non-trivial {LC} connection field. Hovering LNIF observers at a fixed distance z from the wall (x-y plane) must fire their rocket motors away from the wall that is effectively an anti-gravity field in Newtons sense. Timelike LIF geodesics appear as hyperbolic constant accelerating Rindler motion to these stationary hovering non-geodesic LNIF observers using non-gravity force (ejected propellant) to keep off the geodesics that recede from the wall in the walls brief violent history. This is Curvature without curvature a nonlocal GR analog to the Bohm-Aharonov effect of Magnetism without magnetism. The gravity energy is also nonlocal and this is another example of the disembodied footprint of micro-quantum nonlocality in the local macro-quantum Einstein field equations. There is no such thing as the classical world there is only the macro-quantum world created in the More is different Inßationary Big Bang. The conformally curved vacuum region outside the finite spacetime blob of the Vilenken-Taub Curvature without curvature solution is like the magnetic ßux inside the long thin solenoid in the Bohm-Aharonov electron beam experiment. The need for LNIF non-geodesic observers to fire their rockets away from the wall to stay at a fixed distance z from the wall is like the fringe shift in the Bohm-Aharonov experiment. However, here EVERY POINT in the BLOB is like the coming together of the two paths for the alternative histories of the electron in the Bohm-Aharonov analog. This is familiar in GR where the universe recedes equally from every vantage point with no preferred center like an infinite homogeneous rubber sheet stretching isotropically from every point. === Subject: Re: Einsteins Equations are Holographic posting-account=sASPfg0AAAB32ck2Ys0CgbD_dk7GKPYH Well, the digital philosophy crowd shouldnt think there really is such a thing as a qubit, since they dont allow those funny parallel universes in the CA models. Hmmm. === Subject: Ways of summing to S = binomial coef? Numerically, fooling around, I discover that the number of ways of producing a sum S by summing N range=0..S integers is #ways = S+N-1 choose N-1 Eg., S=4 N=1 #=1 S=4 N=2 #=5 S=4 N=3 #=15 S=4 N=4 #=35 S=4 N=5 #=70 (also works up into the zillions, numerically S=20 N=21 #=137846528820) Is there an obvious reason that it comes out a simple binary coefficient? -- Ron Hardin rhhardin@mindspring.com On the internet, nobody knows youre a jerk. === Subject: Re: Ways of summing to S = binomial coef? > Numerically, fooling around, I discover that the number of ways > of producing a sum S by summing N range=0..S integers is > #ways = S+N-1 choose N-1 > Eg., S=4 N=1 #=1 > S=4 N=2 #=5 > S=4 N=3 #=15 > S=4 N=4 #=35 > S=4 N=5 #=70 > (also works up into the zillions, numerically > S=20 N=21 #=137846528820) > Is there an obvious reason that it comes out a simple binary coefficient? You can represent such a sum by a sequence of S stars separated by N-1 slashes, for example 7 = 2+3+0+2 may be represented as **/***//** Hence the number of sums equals the number of sequences which may be formed with S stars and N-1 slashes. This number is clearly S+N-1 choose N-1. Jos.8e H. Nieto === Subject: Re: Ways of summing to S = binomial coef? > Numerically, fooling around, I discover that the number of ways > of producing a sum S by summing N range=0..S integers is > #ways = S+N-1 choose N-1 > Eg., S=4 N=1 #=1 > S=4 N=2 #=5 > S=4 N=3 #=15 > S=4 N=4 #=35 > S=4 N=5 #=70 > (also works up into the zillions, numerically > S=20 N=21 #=137846528820) > Is there an obvious reason that it comes out a simple binary coefficient? Oh I see, you can do it as a partitioning. -- Ron Hardin rhhardin@mindspring.com On the internet, nobody knows youre a jerk. === Subject: Virtual Reality Telerobotic System posting-account=PzzHLg0AAAB8BE5nGf58ZT1EVzm80ILK This paper describes a telerobotic system operated through a virtual reality (VR) interface. A least squares method is used to find the transformation mapping, from the virtual to real environments. Results revealed an average transformation error of 3mm. The system was tested for the task of planning minimum time shaking trajectories to discharge the contents of a suspicious package onto a workstation platform. Performance times to carry out the task directly through the VR interface showed rapid learning, reaching standard time (288 seconds) within 7 to 8 trials - exhibiting a learning rate of 0.79. Please visit: or download: Kartoun Uri. http://www.compactech.com/kartoun/ === Subject: Cooperative Human-Robot Learning System using a Virtual Reality Telerobotic Interface posting-account=PzzHLg0AAAB8BE5nGf58ZT1EVzm80ILK A cooperative human-robot learning system for remote robotic operations using a virtual reality (VR) interface is presented. The paper describes the overall system architecture, and the VR telerobotic system interface. Initial tests using on-line control through the VR interface for the task of shaking out the contents of a plastic bag are presented. The system employs several state-action policies. System states are defined by: type of bag, status of robot, and environment. Actions are defined by initial grasping point, lift and shake trajectory. A policy is a set of state-action pairs to perform a robotic task. The system starts with knowledge of the individual operators of the robot arm, such as opening and closing the gripper, but it has no policy for deciding when these operators are not appropriate, nor does it have knowledge about the special properties of the bags. An optimal policy is defined as the best action for a given state that is learned from experience and human guidance. A policy is found to be beneficial if a bag was grabbed successfully and all its contents extracted. Please download and give opinions and suggestions please: Kartoun Uri - kartoun@yahoo.com http://www.compactech.com/kartoun/ === Subject: The Universes Next Door PS The NASA Pioneer 10&!! Anomaly a_g = cH ~ 10^-7 cm/sec^2 directed back to Sun is more evidence for the local macro-quantum Higgs order parameter, this time with S^2 symmetry forming a dark energy hedgehog topological defect starting at 20AU from Sun. ending we do not know where yet. The Galactic Halo holding our solar system in the Galaxy is also a dark energy exotic vacuum blob that is more stable than Vilenkens thin vacuum domain wall. Preliminaries on the nonlocality of gravity energy from Penrose Road to Reality. Note that Shipovs oriented point in his torsion theory extension of 1916 GR has a non-trivial topology configuration space with a spinor structure as shown in detail by Roger Penrose. The Cartan p-form is a density unlike the graded Grassmann algebra analog to it. A p-form in a N > p space is a N - p dimensional hyper plane element that is dual to the p mult-vector field. The multi-vector from Grassmannian wedge products is not a density for integration. trajectories and the dual p forms as the pilot qubit wave fronts. The p-form is the intersection of p 1-form covectors (N-1 dim hyperplane elements) Fig 12.10 p.228 Penrose. See Fig 12.7 & 12.8 & 12.9 p. 226 on covectors as generalized contours but with a twist obstruction p. 225 The p-form is what we integrate over a p-dim submanifold of the N-dim manifold. The topology is generally mutiply connected with Betti numbers and other global topological measures. Curvature is a 2-form integrated over 2-dim sub-manifolds of spacetime. Diff(4) is automatic for these global integrals and they are, therefore, independent of the arbitrary choice of overlapping local coordinate patches or charts whose atlas covers the entire manifold. The overlap transition functions between them are precisely Einsteins general coordinate transformations (GCT) and GCT symmetry means completely arbitrary LOCAL choices of coordinate charts exactly like the completely arbitrary choice of phases in SU(n) local gauge theories! There is no rule that we MUST choose the largest possible local charts for example. However, each choice of a local coordinate chart specifies a possible distribution of local observers some (LIF) on intrinsic geodesics of the metric space others (LNIF) not. That is, there is a well conceived physical measurement scheme associated with EVERY GCT subject to local causality light cone constraints and negligible quantum gravity uncertainty in the light cone localizations. Every GCT transition function is a switch from one configuration of local observers to another all inside a small enough spacetime blob all exchange light signals. One of the beauties of this ... is that it automatically deals with any changes of variable that we may choose to invoke. The p-forms are INVARIANT under GCT and so are their GLOBAL INTEGRALS. There is an analog to the Cauchy integral residue theorem sum over poles with the Betti-numbered wormhole handles analogous to the poles in evaluating the integrals. For our problem we are talking about the hologram closed 2-surfaces enclosing volumes. The parameters x^u or x^u could be taken to be one of the coordinates in a coordinate patch in this ambient space, where we are happy to change to a different coordinate when we pass to another coordinate patch. p. 230 This eliminates the explicit mention of awkward quantities known as ÔJacobians p. 235 *None of this point set topology manifold structure closely tied to local causal measurement theory is in Hal Puthoffs too simple PV theory without a consistent measurement theory. Splitting universes require a non-Hausdorf manifold. Fig 12.5 p. 223 A Hausdorff space forbids the splitting and fusion of alternative world timelines in a PK Dickian multi-verse of parallel universes next door. A non-Hausdorff space means we can pass to a universe next door where Phillip Roths The Conspiracy Against America and P.K. Dicks The Man in the High Castle are actual realities down to the last comma! tHooft and Susskind building on Bekenstein and Hawking conjectured that the dimensionless information content in a volume of space is the area of its boundary divided by 4Planck area. Whether those are c-bits or qubits is left unclear. In Cartans forms, which are automatically Diff(4) invariant, and which permit integrals on curved manifolds, circumventing some of the gravity nonlocality problem, the Levi-Civita connection field is a 1-form and the curvature is a 2-form. Einsteins field equation, including the dark energy local field correction, is Guv + /zpfguv = 8pi(G/c^4)Tuv The dimensions of the marble geometrodynamic LHS are 1/Area consistent with the Cartan curvature 2-form with INVARIANT Hodge DeRham integrals over 2D coform AREAS. This is automatically HOLOGRAPHIC since VOLUMES are replaced by AREAS! This is because 8pi(G/c^4) has dimension [Length/Energy] = (String Tension)^-1. Note that non-Perturbative background-independent Quantum Loop Gravity also rests fundamentally on the quantum area operator as does my own macro-quantum coherent More is Different emergence derivation of Einsteins local GR from the rigid Goldstone phase of the Higgs Vacuum Order Parameter in the Inßationary Phase Transition of the Big Bang from the unstable ßat false micro-quantum vacuum to the stable curved macro-quantum coherent holographic vacuum with lower zero point energy density (small Cosmological Constant) and lower entropy (smaller phase space volume). That is, Cartans tetrads eu^a come from the Bohm elasticity giant pilot wave constraint eu^a,a = Kronecker Deltau^a,a + (Area Quantum)(Goldstone Phase),u ,a is ordinary partial derivative When the rigid Goldstone Phase = 0 eu^a = Kronecker Deltau^a guv(Curved LNIF) = eu^a(Minkowski)abev^b = (Minkowski)uv = PRE-INFLATION FALSE VACUUM in that limit. In general guv(LNIF) = [Minkowski (LIF)]uv + (1/2)(Eu,v + Ev,u) Eu = (Quantum of Area)(Goldstone Phase),u This is not perturbation theory and guv is a dynamical field. Note also that the Vilenken unstable ßat DARK ENERGY vacuum domain wall solution is a finite spacetime blob Lorentzian instanton inside of which there is zero conformal curvature with a non-trivial {LC} connection field. Hovering LNIF observers at a fixed distance z from the wall (x-y plane) must fire their rocket motors away from the wall that is effectively an anti-gravity field in Newtons sense. Timelike LIF geodesics appear as hyperbolic constant accelerating Rindler motion to these stationary hovering non-geodesic LNIF observers using non-gravity force (ejected propellant) to keep off the geodesics that recede from the wall in the walls brief violent history. This is Curvature without curvature a nonlocal GR analog to the Bohm-Aharonov effect of Magnetism without magnetism. The gravity energy is also nonlocal and this is another example of the disembodied footprint of micro-quantum nonlocality in the local macro-quantum Einstein field equations. There is no such thing as the classical world there is only the macro-quantum world created in the More is different Inßationary Big Bang. The conformally curved vacuum region outside the finite spacetime blob of the Vilenken-Taub Curvature without curvature solution is like the magnetic ßux inside the long thin solenoid in the Bohm-Aharonov electron beam experiment. The need for LNIF non-geodesic observers to fire their rockets away from the wall to stay at a fixed distance z from the wall is like the fringe shift in the Bohm-Aharonov experiment. However, here EVERY POINT in the BLOB is like the coming together of the two paths for the alternative histories of the electron in the Bohm-Aharonov analog. This is familiar in GR where the universe recedes equally from every vantage point with no preferred center like an infinite homogeneous rubber sheet stretching isotropically from every point. === Subject: Re: The Universes Next Door >PS The NASA Pioneer 10&!! Anomaly a_g = cH ~ 10^-7 cm/sec^2 directed >back to Sun is more evidence for the local macro-quantum Higgs order >parameter, this time with S^2 symmetry forming a dark energy hedgehog >topological defect starting at 20AU from Sun. ending we do not know >where yet. The Galactic Halo holding our solar system in the Galaxy is >also a dark energy exotic vacuum blob that is more stable than >Vilenkens thin vacuum domain wall. >Preliminaries on the nonlocality of gravity energy from Penrose Road to >Reality. >Note that Shipovs oriented point in his torsion theory extension of >1916 GR has a non-trivial topology configuration space with a spinor >structure as shown in detail by Roger Penrose. >The Cartan p-form is a density unlike the graded Grassmann algebra >analog to it. A p-form in a N > p space is a N - p dimensional hyper >plane element that is dual to the p mult-vector field. The multi-vector >from Grassmannian wedge products is not a density for integration. >trajectories and the dual p forms as the pilot qubit wave fronts. >The p-form is the intersection of p 1-form covectors (N-1 dim hyperplane >elements) Fig 12.10 p.228 Penrose. See Fig 12.7 & 12.8 & 12.9 p. 226 on >covectors as generalized contours but with a twist obstruction p. 225 >The p-form is what we integrate over a p-dim submanifold of the N-dim >manifold. The topology is generally mutiply connected with Betti numbers >and other global topological measures. >Curvature is a 2-form integrated over 2-dim sub-manifolds of spacetime. >Diff(4) is automatic for these global integrals and they are, therefore, >independent of the arbitrary choice of overlapping local coordinate >patches or charts whose atlas covers the entire manifold. The overlap >transition functions between them are precisely Einsteins general >coordinate transformations (GCT) and GCT symmetry means completely >arbitrary LOCAL choices of coordinate charts exactly like the completely >arbitrary choice of phases in SU(n) local gauge theories! There is no >rule that we MUST choose the largest possible local charts for example. >However, each choice of a local coordinate chart specifies a possible >distribution of local observers some (LIF) on intrinsic geodesics of the >metric space others (LNIF) not. That is, there is a well conceived >physical measurement scheme associated with EVERY GCT subject to local >causality light cone constraints and negligible quantum gravity >uncertainty in the light cone localizations. >Every GCT transition function is a switch from one configuration of >local observers to another all inside a small enough spacetime blob >all exchange light signals. >One of the beauties of this ... is that it automatically deals with any >changes of variable that we may choose to invoke. >The p-forms are INVARIANT under GCT and so are their GLOBAL INTEGRALS. >There is an analog to the Cauchy integral residue theorem sum over poles >with the Betti-numbered wormhole handles analogous to the poles in >evaluating the integrals. For our problem we are talking about the >hologram closed 2-surfaces enclosing volumes. >The parameters x^u or x^u could be taken to be one of the coordinates >in a coordinate patch in this ambient space, where we are happy to >change to a different coordinate when we pass to another coordinate >patch. p. 230 >This eliminates the explicit mention of awkward quantities known as >Jacobians p. 235 >*None of this point set topology manifold structure closely tied to >local causal measurement theory is in Hal Puthoffs too simple PV theory >without a consistent measurement theory. >Splitting universes require a non-Hausdorf manifold. Fig 12.5 p. 223 >A Hausdorff space forbids the splitting and fusion of alternative world >timelines in a PK Dickian multi-verse of parallel universes next door. A >non-Hausdorff space means we can pass to a universe next door where >Phillip Roths The Conspiracy Against America and P.K. Dicks The Man >in the High Castle are actual realities down to the last comma! >tHooft and Susskind building on Bekenstein and Hawking conjectured that >the dimensionless information content in a volume of space is the area >of its boundary divided by 4Planck area. Whether those are c-bits or >qubits is left unclear. >In Cartans forms, which are automatically Diff(4) invariant, and which >permit integrals on curved manifolds, circumventing some of the gravity >nonlocality problem, the Levi-Civita connection field is a 1-form and >the curvature is a 2-form. >Einsteins field equation, including the dark energy local field >correction, is >Guv + /zpfguv = 8pi(G/c^4)Tuv >The dimensions of the marble geometrodynamic LHS are 1/Area consistent >with the Cartan curvature 2-form with INVARIANT Hodge DeRham integrals >over 2D coform AREAS. This is automatically HOLOGRAPHIC since VOLUMES >are replaced by AREAS! >This is because 8pi(G/c^4) has dimension [Length/Energy] = (String >Tension)^-1. >Note that non-Perturbative background-independent Quantum Loop Gravity >also rests fundamentally on the quantum area operator as does my own >macro-quantum coherent More is Different emergence derivation of >Einsteins local GR from the rigid Goldstone phase of the Higgs Vacuum >Order Parameter in the Inßationary Phase Transition of the Big Bang >from the unstable ßat false micro-quantum vacuum to the stable curved >macro-quantum coherent holographic vacuum with lower zero point energy >density (small Cosmological Constant) and lower entropy (smaller phase >space volume). >That is, Cartans tetrads eu^a come from the Bohm elasticity giant pilot >wave constraint >eu^a,a = Kronecker Deltau^a,a + (Area Quantum)(Goldstone Phase),u >,a is ordinary partial derivative >When the rigid Goldstone Phase = 0 >eu^a = Kronecker Deltau^a >guv(Curved LNIF) = eu^a(Minkowski)abev^b = (Minkowski)uv = PRE-INFLATION >FALSE VACUUM >in that limit. >In general >guv(LNIF) = [Minkowski (LIF)]uv + (1/2)(Eu,v + Ev,u) >Eu = (Quantum of Area)(Goldstone Phase),u >This is not perturbation theory and guv is a dynamical field. >Note also that the Vilenken unstable ßat DARK ENERGY vacuum domain wall >solution is a finite spacetime blob Lorentzian instanton inside of >which there is zero conformal curvature with a non-trivial {LC} >connection field. Hovering LNIF observers at a fixed distance z from the >wall (x-y plane) must fire their rocket motors away from the wall that >is effectively an anti-gravity field in Newtons sense. Timelike LIF >geodesics appear as hyperbolic constant accelerating Rindler motion to >these stationary hovering non-geodesic LNIF observers using non-gravity >force (ejected propellant) to keep off the geodesics that recede from >the wall in the walls brief violent history. >This is Curvature without curvature a nonlocal GR analog to the >Bohm-Aharonov effect of Magnetism without magnetism. The gravity >energy is also nonlocal and this is another example of the disembodied >footprint of micro-quantum nonlocality in the local macro-quantum >Einstein field equations. There is no such thing as the classical >world there is only the macro-quantum world created in the More is >different Inßationary Big Bang. >The conformally curved vacuum region outside the finite spacetime blob >of the Vilenken-Taub Curvature without curvature solution is like the >magnetic ßux inside the long thin solenoid in the Bohm-Aharonov >electron beam experiment. The need for LNIF non-geodesic observers to >fire their rockets away from the wall to stay at a fixed distance z from >the wall is like the fringe shift in the Bohm-Aharonov experiment. >However, here EVERY POINT in the BLOB is like the coming together of the >two paths for the alternative histories of the electron in the >Bohm-Aharonov analog. This is familiar in GR where the universe recedes >equally from every vantage point with no preferred center like an >infinite homogeneous rubber sheet stretching isotropically from every point. This approach to parallel universes is way to complicated and too hard to understand. Its really very simple, when you use, The Smart Universal Model. First you start with a very basic unified field structure for a relatively show this at my Website. This from this foundation or a starting building block ( or brick). You build structures that move from the physics level to the chemistry level...., stellar, galactic, universal to parallel universes. They must all ßow and fit in perfectly in the sizes of the micro-universe anf the universe in such a way that it remains relatively perpetual in motion, and grows ( or evolves) in time, with minimum galactic or universal collisions. I show the basic building blocks or foundations that allow this to occur with a easy clear understanding. I think it is important that parallel universes grow eternally without running into each other to allow beings to exist independently in their own world or universe. This removes the chaos and curruption state of people fighting over one square inch of land, like they do on this planet. I think each universe should have independent isolation fields which prevents not only prevents collisions of multi-parallel universes, but also allows beings to exist happily in their own world. There can be sharing zones within the parallel universes for those with common interests. The Smart Model is in my opinion the most accurate and allows for free will choices of beings in the universe. I think the current state of the universe is like a giant universal chemical interaction on the universal scale. the nearest parallel universe could be the H2 atom type universe right next door to us. What about the rest of the universe and how does it expand eternally. Well according to the Smart Model, The Conservation of Matter and Energy had to be updated in such a way to allow for the creation of more energy and matter within galaxies and universes. The galaxies spiral with arms opening and closing allowing for the Creation of new matter and energy. The creation of new anti-matter collisions. As the new energy is created it cools and slows down producing new matter which can be in the form of new solar systems and planets. The Smart Model is also involved in the discovery of stars that never burn out and provide light energy perpetually. In larger suns in can be observed that a Lithium energy field forms in the outer layers of the sun. There appears to be a constant fusion reaction between Lithium and Deuterium and vise versa. The Smart Model also seeks to make these type of fusion reactors ( theoretically) that provides clean fusion energy without radioactivity. For more information about the Smart Model go to my Website. Smarts Alt. Physics News Group http://pub39.bravenet.com/forum/show.php?usernum=3320272813& cpv=1 S. Enterprize (Science Journal) http://smart1234.s-enterprize.com/ === Subject: Re: The Universes Next Door > PS The NASA Pioneer 10&!! Anomaly a_g = cH ~ 10^-7 cm/sec^2 directed > back to Sun is more evidence for the local macro-quantum Higgs order > parameter, this time with S^2 symmetry forming a dark energy hedgehog > topological defect starting at 20AU from Sun. ending we do not know > where yet. The Galactic Halo holding our solar system in the Galaxy > is also a dark energy exotic vacuum blob that is more stable than > Vilenkens thin vacuum domain wall. > Preliminaries on the nonlocality of gravity energy from Penrose Road > to Reality. > Note that Shipovs oriented point in his torsion theory extension of > 1916 GR has a non-trivial topology configuration space with a spinor > structure as shown in detail by Roger Penrose. > The Cartan p-form is a density unlike the graded Grassmann algebra > analog to it. A p-form in a N > p space is a N - p dimensional hyper > plane element that is dual to the p mult-vector field. The > multi-vector from Grassmannian wedge products is not a density for > integration. > trajectories and the dual p forms as the pilot qubit wave fronts. > The p-form is the intersection of p 1-form covectors (N-1 dim > hyperplane elements) Fig 12.10 p.228 Penrose. See Fig 12.7 & 12.8 & > 12.9 p. 226 on covectors as generalized contours but with a twist > obstruction p. 225 > The p-form is what we integrate over a p-dim submanifold of the N-dim > manifold. The topology is generally mutiply connected with Betti > numbers and other global topological measures. > Curvature is a 2-form integrated over 2-dim sub-manifolds of > spacetime. Diff(4) is automatic for these global integrals and they > are, therefore, independent of the arbitrary choice of overlapping > local coordinate > patches or charts whose atlas covers the entire manifold. The overlap > transition functions between them are precisely Einsteins general > coordinate transformations (GCT) and GCT symmetry means completely > arbitrary LOCAL choices of coordinate charts exactly like the > completely arbitrary choice of phases in SU(n) local gauge theories! > There is no > rule that we MUST choose the largest possible local charts for > example. However, each choice of a local coordinate chart specifies a > possible distribution of local observers some (LIF) on intrinsic > geodesics of the metric space others (LNIF) not. That is, there is a > well conceived > physical measurement scheme associated with EVERY GCT subject to local > causality light cone constraints and negligible quantum gravity > uncertainty in the light cone localizations. > Every GCT transition function is a switch from one configuration of > local observers to another all inside a small enough spacetime blob > all exchange light signals. > One of the beauties of this ... is that it automatically deals with > any changes of variable that we may choose to invoke. > The p-forms are INVARIANT under GCT and so are their GLOBAL INTEGRALS. > There is an analog to the Cauchy integral residue theorem sum over > poles with the Betti-numbered wormhole handles analogous to the poles > in evaluating the integrals. For our problem we are talking about the > hologram closed 2-surfaces enclosing volumes. > The parameters x^u or x^u could be taken to be one of the > coordinates > in a coordinate patch in this ambient space, where we are happy to > change to a different coordinate when we pass to another coordinate > patch. p. 230 > This eliminates the explicit mention of awkward quantities known as > ÔJacobians p. 235 > *None of this point set topology manifold structure closely tied to > local causal measurement theory is in Hal Puthoffs too simple PV > theory without a consistent measurement theory. > Splitting universes require a non-Hausdorf manifold. Fig 12.5 p. 223 > A Hausdorff space forbids the splitting and fusion of alternative > world timelines in a PK Dickian multi-verse of parallel universes > next door. A non-Hausdorff space means we can pass to a universe next > door where > Phillip Roths The Conspiracy Against America and P.K. Dicks The > Man > in the High Castle are actual realities down to the last comma! > tHooft and Susskind building on Bekenstein and Hawking conjectured > that the dimensionless information content in a volume of space is > the area > of its boundary divided by 4Planck area. Whether those are c-bits or > qubits is left unclear. > In Cartans forms, which are automatically Diff(4) invariant, and > which permit integrals on curved manifolds, circumventing some of the > gravity nonlocality problem, the Levi-Civita connection field is a > 1-form and > the curvature is a 2-form. > Einsteins field equation, including the dark energy local field > correction, is > Guv + /zpfguv = 8pi(G/c^4)Tuv > The dimensions of the marble geometrodynamic LHS are 1/Area > consistent with the Cartan curvature 2-form with INVARIANT Hodge > DeRham integrals > over 2D coform AREAS. This is automatically HOLOGRAPHIC since VOLUMES > are replaced by AREAS! > This is because 8pi(G/c^4) has dimension [Length/Energy] = (String > Tension)^-1. > Note that non-Perturbative background-independent Quantum Loop Gravity > also rests fundamentally on the quantum area operator as does my own > macro-quantum coherent More is Different emergence derivation of > Einsteins local GR from the rigid Goldstone phase of the Higgs Vacuum > Order Parameter in the Inßationary Phase Transition of the Big Bang > from the unstable ßat false micro-quantum vacuum to the stable curved > macro-quantum coherent holographic vacuum with lower zero point energy > density (small Cosmological Constant) and lower entropy (smaller phase > space volume). > That is, Cartans tetrads eu^a come from the Bohm elasticity giant > pilot wave constraint > eu^a,a = Kronecker Deltau^a,a + (Area Quantum)(Goldstone Phase),u > ,a is ordinary partial derivative > When the rigid Goldstone Phase = 0 > eu^a = Kronecker Deltau^a > guv(Curved LNIF) = eu^a(Minkowski)abev^b = (Minkowski)uv = > PRE-INFLATION FALSE VACUUM > in that limit. > In general > guv(LNIF) = [Minkowski (LIF)]uv + (1/2)(Eu,v + Ev,u) > Eu = (Quantum of Area)(Goldstone Phase),u > This is not perturbation theory and guv is a dynamical field. > Note also that the Vilenken unstable ßat DARK ENERGY vacuum domain > wall solution is a finite spacetime blob Lorentzian instanton > inside of > which there is zero conformal curvature with a non-trivial {LC} > connection field. Hovering LNIF observers at a fixed distance z from > the wall (x-y plane) must fire their rocket motors away from the wall > that > is effectively an anti-gravity field in Newtons sense. Timelike LIF > geodesics appear as hyperbolic constant accelerating Rindler motion > to these stationary hovering non-geodesic LNIF observers using > non-gravity force (ejected propellant) to keep off the geodesics that > recede from > the wall in the walls brief violent history. > This is Curvature without curvature a nonlocal GR analog to the > Bohm-Aharonov effect of Magnetism without magnetism. The gravity > energy is also nonlocal and this is another example of the disembodied > footprint of micro-quantum nonlocality in the local macro-quantum > Einstein field equations. There is no such thing as the classical > world there is only the macro-quantum world created in the More is > different Inßationary Big Bang. > The conformally curved vacuum region outside the finite spacetime blob > of the Vilenken-Taub Curvature without curvature solution is like the > magnetic ßux inside the long thin solenoid in the Bohm-Aharonov > electron beam experiment. The need for LNIF non-geodesic observers to > fire their rockets away from the wall to stay at a fixed distance z > from the wall is like the fringe shift in the Bohm-Aharonov > experiment. > However, here EVERY POINT in the BLOB is like the coming together of > the two paths for the alternative histories of the electron in the > Bohm-Aharonov analog. This is familiar in GR where the universe > recedes equally from every vantage point with no preferred center > like an infinite homogeneous rubber sheet stretching isotropically > from every point. Heres a list of names, concepts and authors of fiction (in no particular order): Higgs (*) dark energy hedgehog Vilenkin (+/- Taub) (* - but only to Vilenkin) Shipov Penrose (*) Cartan (*) Grassman (*) Bohm (in connexion with hidden-variable theories) (and +/- Aharonov) (*) Betti Hal Puthoff (*) Dick multi-verse (or should that be Dicke? I do but jest here) tHooft and Susskind, [...] Bekenstein and Hawking (* - but not to Bekenstein) Goldstone phase (*) Lorentzian instanton (* - to Lorentz, and to instanton: but not to the combination) Hodge-Derham integrals I have appended an asterisk to those with which I am familiar - but as to their connexion? So, I wish to ask some questions: 1) was da hedgehog I nearly ran over las night charmed, as well as non-colo(u)red? 2) was dat hedgehog spinnin or isospinnin? 3) who dis Sar-fatty-man who so copulatin smart? 4) if dey am nex door, am dey universes? How many differen ones ya know, man? 5) is G-d a boson or a fermion? Spin statistiks _so_ importan in da church, ya kno! 6) ya write about da wall, man: you another brick in it, man? In utter confusion, John johnDOTmorrisonATtescoDOTnet -- The difference between intelligence and stupidity is that intelligence has its limits. - [Trad.] === Subject: Re: The Universes Next Door > PS The NASA Pioneer 10&!! Anomaly a_g = cH ~ 10^-7 cm/sec^2 directed > [remainder of long post snipped] Do you really have to crosspost to five NGs? Not that I cant see the humor of posting to both sci.military and sci.skeptic. -- Military intelligence is a contradiction in terms -- Groucho Marx === Subject: Techniques for averages? Say I have check 5 seperate URLs and check them at the following times, noting those that do not work at that time. 10:00A - #4. 10:05A - #3, #4 10:10A - all work 10:15A - all work 10:20A - #4 The results are as follows: #1 - good 100% of time between 10A - 10:20A #2 - good 100% #3 - good 80 % #4 - good 40% #5 - good 100% I check the links more than once because the state of the Internet is constantly changing. I need more than one sample to produce a good estimate of link success. What exactly is the above referred to as? Meaning, one check of a condition will produce extremely biased or inaccurate results vs. several checks producing more accurate or unbiased results. Is there a theory or field that this falls into? How do I determine on the first check that such a system will require more samples for a good estimate? Then, how do I determine which intervals each check should be executed at? The above example isnt specific to URL execution states. Other examples mght be cars trying to beat a train at a railroad crossing once/week, airplane crashes, creation of super novas. Brett === Subject: Re: Techniques for averages? posting-account=Glvc4AwAAADzVCZ73XnxpzMhXir6xVzs > Say I have check 5 seperate URLs and check them at the following times, > noting those that do not work at that time. > 10:00A - #4. > 10:05A - #3, #4 > 10:10A - all work > 10:15A - all work > 10:20A - #4 > The results are as follows: > #1 - good 100% of time between 10A - 10:20A > #2 - good 100% > #3 - good 80 % > #4 - good 40% > #5 - good 100% > I check the links more than once because the state of the Internet is > constantly changing. I need more than one sample to produce a good estimate > of link success. What exactly is the above referred to as? Meaning, one > check of a condition will produce extremely biased or inaccurate results vs. > several checks producing more accurate or unbiased results. Is there a > theory or field that this falls into? Estimation theory (a branch of statistics) covers a lot of ground, including this. There is a parameter p_i that you are trying to estimate = probability that a link is up. With any parameter estimation problem, you can ask such things as what is an unbiased estimator (for a success probability, its the obvious #successes/#trials). > How do I determine on the first check that such a system will require more > samples for a good estimate? For any estimator you can calculate the variance of that estimator -- how much spread around the real value. That tells you how tight an estimate it is. I think its going to decrease as sqrt(# trials) in this case. > Then, how do I determine which intervals each > check should be executed at? Without more assumptions about outage statistics, you cant answer that question. - Randy === Subject: Re: Existence of countable Hamel basis at 09:34 PM, anonymous@mathforum.org (Felix) said: >All normed spaces as vector spaces have basis,so called >Hamel basis. >Hamel bases in infinite dimensional Banach spaces >are uncountable.This follows from Baire category theorem. What if the >infinite dimensional space isnt complete? >Does it always contain countable Hamel basis? No. >The space d={(x_n):only finitely many x_n =/=0} has >e_n=(0,..,0,1,0,...0) as Hamel basis. Make a slight change; index the elements on an uncountable set. That is, instead of {x in R^I| all but finitely many X_i are zero} use {x in R^U, U uncountable| all but finitely many X_i are zero}. That gives you an example of an incomplete space with no countable Hamel basis. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolicited bulk E-mail subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not === Subject: Re: Why (or not) use single letter variable names? <41c07852$7$fuzhry+tra$mr2ice@news.patriot.net> <41c214ce$2$fuzhry+tra$mr2ice@news.patriot.net> at 01:08 PM, jmfbahciv@aol.com said: >Heh. Its been my experience that people like you created bigger and >more messes because of an inability to see a complete computing usage >picture. ;-) Really? Seeing a complete picture requires thought prior to coding, which was precisely my point. >Your thinking is IBMish, mine is DECish. DEC also did things like requirement analysis. I dont know whether that remains the case now that theyre Hewlett PacPaq. >You clearly do not understand the issues from the point of the very >beginning of a project to the point where the code is cycled into >maintenance mode while being merged into the next development cycle. Ive been involved in all phases, and not just with IBM hardware or software. >Not at all. I belong in the dont waste the coders time with >useless and long meetings and paperwork. Then its a good thing that I didnt suggest useless and long meetings and paperwork, isnt it. But I understand that if you cant rebut what the whole cloth. >This shows that you dont what youre talking about. There is never >time to do it right; Perhaps not where youre worked. >the code would never ship if that were the exit criteria of field test. Oddly enough, Ive been on projects where we had code and design reviews yet managed to ship ahead of schedule. >Not at all. You seem to think that code developers have to do all >the work involved with starting a project and finishing that >project. Sorry, Uri Geller, but youre wrong again. What I think is that iif the coders arent involved in the design then youre going to have problems. >About 5% of the manhours needed to do a project is coding; Water is wet. Your own figures should tell you why keyboard speed is not an important factor. >I know you know that. Indeed, but the above was the first sign I saw that *you* knew it. >This tells me that you know better; acceptable cost means that >there is a compromise between correct code and working with what >youve got running. That compromise is quite remote from optizing for coding speed or run time. >The coders Im talking about used mostly MACRO-10 which is an >assembler. Then its likely that your standards derived from the word size on the PDP-6, which just happens to be 36 bits. >yes, and all of a sudden FSVO all of a sudden that is truly bizarre, given that the subject of this thread is Why (or not) use single letter variable names? >and all of a sudden youre redefining long to be 2We were talking about variables that have enough characters to >traipse across a listing page. In your dreams. Had you said that by long you meant 40 characters, then I would not have defended bah-long variable names. >Oh, honey. Now youre in putdown mode to save face. No, Im in put-down mode because that was the mode that *you* chose to operate in. Had you politely disagreed then I would have phrased things differently. However, I see no reason to be polite to rude fools with delusion of adequacy. >Do you have any idea about how people read? Yes; poorly, in many cases. In your case, for instance. >Then you dont know your job well enough. Youre clutching at straws; you dont have the remotest concept of what I was developing or how well it turned it. You are, of course, wrong yet again. >Most variable names are surround by constructs of the language. So >that implies that a line of code will be the variable name length >minus 30 characters or more. It imples no such thing. Perhaps you dont understand what the word implies means. Ive seen plenty of code where the syntactiv overhead was far smaller than your 30 character value. >If the variable name lengths are greater than six, the lines of of >code become too long, produce wraparound, and are simply unreadable >without a straightedge to match the first character of the coding >line with the last character of the coding line. What are you smoking? Ive seen plenty of programs with 10-20 character names where the lines of code where not too long and were perfectly readable without a straightedge. As for wrap-around, that can make the program more readable rather than less, assuming that you indent appropriately. If youre talking about random wrap-around, then you have bigger issues than variable length. >The code becomes a spaghetti mess if more than one of these >long-length variables show up in one line of code. FSVO long considerably larger than your six characters. >We were talking about lengths that fully documented the purpose of >the variable. What do you mena we? I was talking about namesthat gave a brief reminder of the purpose of the variable. >I sure hope you get to this last part before you killfile >me...again. for hypocritical fools like you. *PLONK* -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolicited bulk E-mail subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not === Subject: Re: Why (or not) use single letter variable names? <41c07852$7$fuzhry+tra$mr2ice@news.patriot.net> <41c214ce$2$fuzhry+tra$mr2ice@news.patriot.net> <41c4b6bb$7$fuzhry+tra$mr2ice@news.patriot.net at 01:08 PM, jmfbahciv@aol.com said: >>Heh. Its been my experience that people like you created bigger and >>more messes because of an inability to see a complete computing usage >>picture. ;-) >Really? Seeing a complete picture requires thought prior to coding, >which was precisely my point. >>Your thinking is IBMish, mine is DECish. >DEC also did things like requirement analysis. Sure. DEC did a lot of other things that defined a project. Most of this prep stuff wasnt done by the developers. In the olden days, our inputs were from the field which was populated by salesmen (who listened to our customers) and field service people (who fixed stuff and listened to our customers). WE also sent developers to symposia to listen to our customers. I assure you we did not have our developers spend 95% of their time in meetings. > .. I dont know whether >that remains the case now that theyre Hewlett PacPaq. Nope. The buzz is that theyre laying off the people who know how to do the work. >>You clearly do not understand the issues from the point of the very >>beginning of a project to the point where the code is cycled into >>maintenance mode while being merged into the next development cycle. >Ive been involved in all phases, and not just with IBM hardware or >software. I you have been involved. The question is whether you noticed all the details that are involved with software production. You clearly havent. I also think it takes staying in one place for at least decade to learn all of the work that is involved in making a product. If a person works on many aspects of software, its very difficult to learn about all the manpower that goes into making something from idea to ship. >>Not at all. I belong in the dont waste the coders time with >>useless and long meetings and paperwork. >Then its a good thing that I didnt suggest useless and long meetings >and paperwork, isnt it. But I understand that if you cant rebut what >the whole cloth. It has occurred to me that you are defining coding as the phase of a project that consists of typing in the code. This is only a piece of coding; I agree that this task is about 5% of a coding job. >>This shows that you dont what youre talking about. There is never >>time to do it right; >Perhaps not where youre worked. TW, who was considered a bit god, became our expert in writing device drivers. After writing many drivers, he would have liked to have redone his first device driver. The same is true with doing the development, s/he figured out a better way to do it. >>the code would never ship if that were the exit criteria of field test. >Oddly enough, Ive been on projects where we had code and design >reviews yet managed to ship ahead of schedule. We usually didnt do the formal review option. Our OS approach was to do an ongoing code and design reviews. The other OS did the formal review format. I always thought that the difference was because they had more than a dozen developers and we only had 2, 3, or 4. >>Not at all. You seem to think that code developers have to do all >>the work involved with starting a project and finishing that >>project. >Sorry, Uri Geller, but youre wrong again. What I think is that iif >the coders arent involved in the design then youre going to have >problems. You have been using the word coding within a very, very, very narrow definition. I sure hope you get to this last part before you killfile >>me...again. >for hypocritical fools like you. >*PLONK* Ah, well. /BAH Subtract a hundred and four for e-mail. === Subject: Re: Why (or not) use single letter variable names? |>>A programmer who knows his biz will not have to read the purpose of |>>a variable every time he needs to reference it in his code. |>A programmer who knows his business will chose names that remind the |>reader of their purpose. | |sure. But if the reader of the code has to spend any more than |a nanosecond to read the variable, the readers time is completely |wasted, especially if the reader is a followup developer and/or |maintainer of that code. People who do real development for |a living want to be able to scan a page of code as fast as |one would scan a page of a novel without side-to-side eye |movement. Once a variable name gets greater than 6, perhaps 8, |characters, the coders eyeballs have start working harder. |Its a waste of brain energy and time. Ive been doing real development for a living for the past five years. A lot of our code was originally written in Fortran, and needed to compile on a system where the available Fortran compiler allegedly (it was before my time) required variables to be only 6 characters long. Since then, some code (including some C code) was written by people who had gotten in a habit of sticking to no more than 6 character variable names. I can assure you that this does not help us read this code any faster. Quite to the contrary; this slows us down quite a bit. Even if one remembers the meaning of a six letter name, the time it takes to read it is longer than if it were closer to comprehensible in the ordinary way. To me its something like reading French. I may know all the words, but its still much slower than reading in English, even if the English is introducing new terms and names and the French is not. One of the projects Ive worked on was started more recently, and the original developers tended to write names such as ConfigurationFileSelectionWidget. I do feel that they tended to go too far, but I still find that part of the code easier to read than code which refers to things like CFSLWG. What Shmuel Metz has been writing on this thread strikes me as generally sound. What you have been writing strikes me as very opinionated, as usual. cute to be able to have Greek letters for variable names, I was being more precise than it might have sounded. I was about to write that he thought it was a good idea, but I realized right away that this was not accurate; we are both simply amused by the idea. Certainly, however, we use variables named theta in routines doing certain geometrical calculations. Keith Ramsay === Subject: Re: Why (or not) use single letter variable names? >cute to be able to have Greek letters for variable names, I was being >more precise than it might have sounded. I was about to write that he >thought it was a good idea, but I realized right away that this was >not accurate; we are both simply amused by the idea. Why amused? If Unicode ever becomes the norm, I would consider it reasonable to extend the supported character sets for variables to other alphabets, especially[1] if the usage was restricted to single letter variable names. The basic question is which is more readable, and I often find the Greek letters to be clearer than their names. [1] Although the restriction might not be a good idea. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolicited bulk E-mail subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not === Subject: Re: Why (or not) use single letter variable names? |Why amused? If Unicode ever becomes the norm, I would consider it |reasonable to extend the supported character sets for variables to |other alphabets, especially[1] if the usage was restricted to single |letter variable names. The basic question is which is more readable, |and I often find the Greek letters to be clearer than their names. It seems a little premature, perhaps? I expect standardization gradually to make it safer to use fancier text. On sci.math for example, people generally ask that plain ASCII be used, since otherwise a lot of people would find it a pain to read, but it would seem a little perverse if we *never* got to the point where our messages contained formulas displayed in the usual way (for chalk-talk). I suppose this might occur by the creation of another group where some other format is used, and a gradual migration over to it. Keith Ramsay === Subject: Re: Why (or not) use single letter variable names? >>cute to be able to have Greek letters for variable names, I was being >>more precise than it might have sounded. I was about to write that he >>thought it was a good idea, but I realized right away that this was >>not accurate; we are both simply amused by the idea. >Why amused? If Unicode ever becomes the norm, I would consider it >reasonable to extend the supported character sets for variables to >other alphabets, especially[1] if the usage was restricted to single >letter variable names. The basic question is which is more readable, >and I often find the Greek letters to be clearer than their names. Often? I would say always. It might be somewhat more difficult to communicate orally, but is this always a problem? Mathematics is a written language, and there are not too many constants other than those expressed in decimal notation. I would not understand someone reading numbers in Chinese, but I would understand someone Chinese writing the same number down in numerals. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Why (or not) use single letter variable names? >|>>A programmer who knows his biz will not have to read the purpose of >|>>a variable every time he needs to reference it in his code. >|>A programmer who knows his business will chose names that remind the >|>reader of their purpose. >|sure. But if the reader of the code has to spend any more than >|a nanosecond to read the variable, the readers time is completely >|wasted, especially if the reader is a followup developer and/or >|maintainer of that code. People who do real development for >|a living want to be able to scan a page of code as fast as >|one would scan a page of a novel without side-to-side eye >|movement. Once a variable name gets greater than 6, perhaps 8, >|characters, the coders eyeballs have start working harder. >|Its a waste of brain energy and time. >Ive been doing real development for a living for the past five years. >A lot of our code was originally written in Fortran, and needed to >compile on a system where the available Fortran compiler allegedly >(it was before my time) required variables to be only 6 characters >long. Since then, some code (including some C code) was written >by people who had gotten in a habit of sticking to no more than >6 character variable names. I can assure you that this does not help >us read this code any faster. Quite to the contrary; this slows us down >quite a bit. Even if one remembers the meaning of a six letter name, >the time it takes to read it is longer than if it were closer to >comprehensible in the ordinary way. To me its something like reading >French. I may know all the words, but its still much slower than reading >in English, even if the English is introducing new terms and names >and the French is not. >One of the projects Ive worked on was started more recently, and the >original developers tended to write names such as >ConfigurationFileSelectionWidget. I do feel that they tended to go too >far, but I still find that part of the code easier to read than code which >refers to things like CFSLWG. You should take a look at how we encoded our meanings. For instance, we could see a random error message on the TTY screen and immediately know which usermode program caused it, open up the source, search for the prefix which wasnt an English word and find, not only where in the source the error occured by why it occurred. Our naming conventions (Note that naming conventions across a product is a key part of code design) were consistent for all software we shipped within an OS product line. Most of the conventions were used company wide. You, as a programmer, didnt have to keep all variable names memorized. All you had to know is the convention and you could knew the purpose of the variable. Take a look at the spellings of the kids who shorten their messages. Thats how we conveyed variable meanings. >What Shmuel Metz has been writing on this thread strikes me as >generally sound. What you have been writing strikes me as very >opinionated, as usual. You should note the difference between opinionated and years of experience. /BAH Subtract a hundred and four for e-mail. === Subject: Re: Why (or not) use single letter variable names? |There was guy who had a job to convert a profs IBM cards chocked |full of data into disk storage. The prof had his own definition |of what all the holes meant and packed his data as much as he |could on those cards. He had a lot of data. After a decade or |so, he wanted his cards converted to the disk. He lost his |definition and had problems recalling what different patterns |of holes meant. | |Long-term thinking is required here and we havent had much |practice in the computing biz because its so new. I found Stewart Brands _The Clock of the Long Now_ somewhat interesting. He has some discussion of this problem with changing formats of data. He puts it in the context of the question of how to maintain continuity over long periods of time. But its quite a hard problem, since not only are we not ready to maintain data over long periods of time, were often having trouble maintaining it over relatively short periods of time. My brother used to deal with radar data for meteorology. It was so very easy for data to fall through the cracks and become unreadable in just a few years. Keith Ramsay === Subject: Re: Why (or not) use single letter variable names? >|There was guy who had a job to convert a profs IBM cards chocked >|full of data into disk storage. The prof had his own definition >|of what all the holes meant and packed his data as much as he >|could on those cards. He had a lot of data. After a decade or >|so, he wanted his cards converted to the disk. He lost his >|definition and had problems recalling what d