mm-1069 === Subject: Re: Orthonormal basis of an infinite-dimensional Hilbert space >How do I prove that the basis is NOT countable if I take only FINITE >linear combinations of vectors from the basis? >*-----------------------* > www.GroupSrv.com >*-----------------------* The key concept here is Hamel basis. I try to remember how the proof runs. I guess something like this: depart from some finite set of independent vectors, which spans of course a finite-dimensinal subspace. No matter how large it is, by definition you can always find a next vector that is independent of all what you already have. You can imagine any countable i.e. unlimited step-by-step process; you can imagine any countable number of such processes: you will never be done. It is at this point in the reasoning that transfinite induction and the axiom of choice come in. This is in my opinion no proof, only a beginning. Library of Delft University) offers an excellent introduction to Schauder bases in Banach spaces, orhtonomal bases in Hilbert spaces, Hamel bases in general infinite-dimensional vector sapces. I hope that this will help. Johan E. Mebius Title The infinite-dimensional topology of function spaces / by van Mill Publisher Amsterdam : Elsevier, 2001 ISBN 0-444-50557-1 Descr. 630 blz. Series (North-Holland mathematical library ISSN:0924-6509 64) Document type monografie Classific. BRF / Functieruimten / Function spaces BWA / Algemene topologie / General topology Subject functieruimten topologie Shelf number TW - 57N20 Mill === Subject: Re: Why are reals uncountable yet algorithms countable (long)? (and the about the Q set)! Now, can I complicate and ask if the infinite limit |Nx|Nx.... is countable or not? Seratend. > Quick simple question, is |Nx|N isomorphic to |R? > Seratend. > Quick simple answer: no > Oh, okay, a little explanation. the product N x N is actually isomorphic > to N. I presume here we mean by isomorphism a bijection of sets. > The usual argument given is to start by looking at the following picture > (1,1) (1,2) (1,3) (1,4) ... > (2,1) (2,2) (2,3) (2,4) ... > (3,1) (3,2) (3,3) (3,4) ... > (4,1) (4,2) (4,3) (4,4) ... > . . . . > . . . . > . . . . > and then snake along > (1,1)->(1,2)->(2,1)->(3,1)->(2,2)->(1,3)->(1,4)->(2,3)... > This goes through the pairs that add up to 2, then the pairs that add up > to 3, then to 4, etc. This eventually works its way through every pair > of natural numbers. > If this looks a little iffy (which it might) one can note the following. > Given a natural number n>=2, there are finitely many pairs (a,b) in NxN > with a+b=n. One can write NxN=U_(n>=2) {(a,b)| a+b=n} which is the > countable union of finite sets, and thus must be countable. > -Ron === Subject: Re: Why are reals uncountable yet algorithms countable (long)? > |I know of no Mathematician who defines the reals in terms of decimal > |expansions. > Neither do I, and it seems to be with good reason. I remember once > a mathematician wondering aloud about the possibility of defining them > that way, perhaps in an introductory real analysis textbook, thinking > that students might find it agreeable. I've seen it, you define the real that way, but then you put them into unique 1-1 correspondance with a more traditional system and then define addition and mulitplication in the other system and by uniqueness of the 1-1 correspondance the definition of addition and multiplication is well-defined. The main reason this isn't done often is because it doesn't really save any effort, it serves mainly an ontological purpose to say what is a real number and say that for a fixed finite ordinal k (that isn't 0 or 1) a real number is an ordered pair of an integer and a member of a special subset of functions from the naturals into k. The common gradeschool definition. There really is no other purpose to that definition. === Subject: integral problem hi all, data: f(eta) and h(x,y) with eta = y/l(x) how can i int follow differential equation? f* (df/d(eta))*(@h/@y) = 0 @=partial and now? could anyone help me? === Subject: Re: Ring of continuous real functions === Subject: Re: Ring of continuous real functions >> 2) If p:C(X) -> R is a nonzero algebra homomorphism then there's >> an unique a in X such that p(f) = f(a) for each f in C(X). > Remember that homomorphisms are assumed to be linear, so a > non-zero one will be surjective. Remember? Oh yea, linear algebra gives 'algebra' a parochial meaning. Properly then isn't an 'algebra' just an inner product space? >The evaluation at a, E_a:X -> R, f -> f(a) is a homomorphism >ker E_a = { f in C(X) | f(a) = 0 } is a maximal ideal >When X is compact and I a maximal ideal, >then some a in X with I = ker E_a. > So you know this result? Good. This is the hard part. Ah, it was key part. >If p:C(X) -> R is a surjection, then as R is a field, ker p >is a maximal ideal. Hence some a with ker p = ker E_a. >Can I go from that to p = E_a? > Not directly. Recall that linear functionals with the same > kernel are scalar multiples of each other and evaluate at > the constant function 1 to find the scalar. Yes, easy show is p(1) = 1, the constant function 1 is mapped to 1. Thus p(a) = p(a1) = a.p(1) = a by linearity and p is surjection. Indeed, p(f(a)) = f(a) is the point I was lacking. > Alternatively, for given function f, consider g=f-f(a). Thus p(f) = p(f - f(a) + f(a)) = p(f - f(a)) + p(f(a)) = f(a) as f - f(a) in ker E_a = ker p Is C(X) customarily given a topology? The metric from the norm ||f|| = sup f(X) making C(X) a Banach space (with scalars R)? ---- === Subject: Re: Ring of continuous real functions Originator: grubb@lola > 2) If p:C(X) -> R is a nonzero algebra homomorphism then there's > an unique a in X such that p(f) = f(a) for each f in C(X). >> Remember that homomorphisms are assumed to be linear, so a >> non-zero one will be surjective. >Remember? Oh yea, linear algebra gives 'algebra' a parochial meaning. >Properly then isn't an 'algebra' just an inner product space? ??? No. Completely different things. Most inner product spaces don't have amultiplication. The 'inner product' of two vectors is a scalar for an inner product space. For algebras, the product of two vectors is another vector. >Is C(X) customarily given a topology? >The metric from the norm ||f|| = sup f(X) >making C(X) a Banach space (with scalars R)? Yes, although many books do things over C instead of R. --Dan Grubb === Subject: sums of Bessel functions I've got a problem with sums of modified bessel functions I_k(t) I need to have sth. like this sum_{k=0}^ infty ( a^k * I_k (t) ) I know that sum_{k= - infty}^ infty ( a^k * I_k (t) )=exp( t/2 (a+1/a) ) but I need sum that starts from k=0. Zbyszek. === Subject: numerical solution of ODEs by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iAKDtEF00791; I am trying to get familiar with basic strategies of consructing methods for numerical solution of Ordinary Differential Equations, and the state of the art in this field. I have read two volumes of 'Solution of Ordinary Differential Equations' by Hairer, Wanner so far. As I've understood, the basic strategy proposed there is in brief as follows. We choose some form of a method where coefficients are unknown (one of the most general forms is general linear methods, which include Runge-Kutta and multistep methods as particular cases). Then we are trying to find coefficients from satisfying a set of formal conditions (most popular are order conditions and various sorts of stabilities, like D,A or L- stability). Is there a radically different approach? Could you recommend any books on it? As an example, I've heard that Lie groups can be somehow applied numerically. I've also read a book by Hackbusch on numerical solution of integral equations. Since an ODE has an equivalent formulation as a Volterra integral equation of the second kind, a natural question is how successful can applying methods for solution of integral equations to differential equations be? Some of them are analogous, for example, a collocation method which exists for both integral and differential equations (and which is also an implicit Runge-Kutta method with an arbitrarily high order). Its drawback is that it leads to large dense matrices, but in integral equations it's facilitated by use of special solvers like a multi-grid method or representation in wavelet basis. Why not applying these techniques for ODEs? If they ARE applied, where can I read about it? === Subject: Re: numerical solution of ODEs >I am trying to get familiar with basic strategies of consructing > methods for numerical solution of Ordinary Differential Equations, > and the state of the art in this field. > I have read two volumes of 'Solution of Ordinary Differential > Equations' by Hairer, Wanner so far. As I've understood, the basic > strategy proposed there is in brief as follows. We choose some form > of a method where coefficients are unknown (one of the most general > forms is general linear methods, which include Runge-Kutta and > multistep methods as particular cases). Then we are trying to find > coefficients from satisfying a set of formal conditions (most popular > are order conditions and various sorts of stabilities, like D,A or L- > stability). > Is there a radically different approach? Could you recommend any > books on it? As an example, I've heard that Lie groups can be somehow > applied numerically. > I've also read a book by Hackbusch on numerical solution of integral > equations. Since an ODE has an equivalent formulation as a Volterra > integral equation of the second kind, a natural question is how > successful can applying methods for solution of integral equations to > differential equations be? Some of them are analogous, for example, a > collocation method which exists for both integral and differential > equations (and which is also an implicit Runge-Kutta method with an > arbitrarily high order). Its drawback is that it leads to large dense > matrices, but in integral equations it's facilitated by use of > special solvers like a multi-grid method or representation in wavelet > basis. Why not applying these techniques for ODEs? If they ARE > applied, where can I read about it? I suggest Lester Ford's book Differential Equations. John Lowry Flight Physics === Subject: existence of numerical methods using logic by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iAKDtFA00795; The question is about the principal existence of an algorithm for numerical solution of various problems with an arbitrary precision. Can mathematical logic help answering it? As an example, suppose we have an equation x^2-2=0. Suppose we have also axiomatized in the first order language all concepts needed to formulate this equation (the way like in Mizar project, www.mizar.org). Is now the statement 'the m-th decimal digit of the solution is n' decidable? I know logic only by tales of my friend, sorry if the question makes === Subject: Re: Cantor's diagonal proof wrong? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id iAKDtFq00799; >> > I can write Sum(n=1 oo | 3/(10^n)) and I can replace those words with >> > 1/3 in any equation, and not change the value, the meaning, or the >> > truth, of that equation. >> ... >> > So, for any concept which translates to a processes which never ends, >> > we know that the process can't actually exist, but it can still be >> > useful to talk, and think, as if it did. >> But in mathematics it is *not* thought that the actual process of adding >> infinitely many numbers together does exist. >Yes, and I have no issue with infinite series. I never said I did. I just >said the infinite processes doesn't actually exist because it doesn't and >can't complete (and that confused some people as to what my point was >probably because they haven't read all my posts in this rather out of >control thread). We simply use the logic of limits to determine, and >define, what numbers each series is equivalent to. And that's great, >valid, and useful. >But in some places, like Cantor's diagonal proof, the idea of an infinite >sized set of natural numbers gets treated in a logical argument as if it >were a finite sized set, as if it did exist and as if were possible to >actually construct the entire diagonal anti-value. If you look at that >argument about the infinite set of natural numbers like people look at >limits, you would not be so quick to assume that the application of proof >by contraction in the form used there is valid - as I tried to demonstrate >by showing how invalid the logic looks if you think of both the >construction of the mapping table and the construction of the diagonal >anti-value was done by a process which can never complete. >If you were given a description of the process which mapped the natural >numbers to the reals, say by a function such as f(n) = r, then you can >analyze what it will do without having to actually run the processes to >completion - as is commonly done with infinite series and which is the >foundation of calculus. >But in Cantor's argument, the actual mapping function is not given. It's >only assumed to exist. Then they argue that the diagonal anti-value can be >constructed for any mapping function provided - which is still a valid >idea. OK, stop right there. You said the diagonal anti-value can be constructed for any mapping function provided, *which is still a valid idea*. There, you said it: the construction is valid. >But then they make a conclusion that is invalid. They assume that >since the anti-diagonal value being constructed doesn't match any single >row, that it's valid to say that it doesn't match all the rows. And as >valid and as logical as that sounds as that sounds, it's not at all valid >when you are constructing infinite sized real values in a infinite sized >table. This is because it's impossible to construct the entire >anti-diagonal value, Whoa, whoa, whoa. Now you say you can't construct the entire anti-diagonal value. How come the construction was valid only a paragraph ago? Look, you seem to be really confused. The construction is simply a matter of composing functions. One assumes (as part of the proof by contradiction) that one has a table which can be presented as a function F N x N --> {0, 1, 2, ..., 9} and one then forms a composite function diag F s N ----> N x N --> {0, 1, 2, ..., 9} --> {0, 1, 2, ..., 9} where diag is defined by diag(n) = (n, n), and s is a certain function with no fixed point (e.g., s(i) = i+1 if i < 9; s(9) = 8). The anti-value as you call it is this composite function. No infinite process is involved in composing finitely many functions. In fact, it's really easy: g(n) = s(F(n, n)). As an engineer with an interest in AI (and presumably in computer science), you probably compose functions all the time, perhaps without realizing it. Did you realize that's all you're doing here? Todd Trimble === Subject: Re: Cantor's diagonal proof wrong? %IW48mQf3K=Ci&gZ7]]aazx@]Y-nq!r5{yH/#,?@lDdUDvOfByB2hVW0.@OM%{l/{cT'{w > OK, stop right there. You said the diagonal anti-value can be > constructed for any mapping function provided, *which is still a > valid idea*. There, you said it: the construction is valid. >But then they make a conclusion that is invalid. They assume that >since the anti-diagonal value being constructed doesn't match any single >row, that it's valid to say that it doesn't match all the rows. And as >valid and as logical as that sounds as that sounds, it's not at all >valid when you are constructing infinite sized real values in a infinite >sized table. This is because it's impossible to construct the entire >anti-diagonal value, > Whoa, whoa, whoa. Now you say you can't construct the entire > anti-diagonal value. How come the construction was valid only > a paragraph ago? I've already explained this about 10 times. But as long as someone is interested, I'll keep going. The problem is here is 100% language issues. What does constructed mean? How I was using it has a subtle but very important difference from how you were hearing it. What I say, is that it's perfectly valid to talk about the algorithm for constructing the diagonal. The algorithm is trivial, and can be written to run on any computer. Just extract the correct digit from a finite location of each row, change it, and use that to construct the anti-diagonal. But, whether a person is using that procedure, or a computer is using the procedure, it will NEVER FINISH constructing the anti-diagonal. It will always be a work in progress. You can specify the algorithm for constructing the anti-diagonal, but you can not built the entire anti-diagonal value. And this point, which you choose to ignore in your mind, because you have been trained to think like that, is a point which changes the argument from valid, to not valid. > Look, you seem to be really confused. I know you think I'm confused. I was confused at the start of this thread about how some important things are formally defined in mathematics. But about what I'm talking now, there is no confusion. Everything you read some of my words and it doesn't make sense, it's because you don't understand my message. Keep looking for a way to interpret my words until you find a meaning that does make sense, and then you will be able to see what I'm talking about. > The construction is simply > a matter of composing functions. One assumes (as part of the proof > by contradiction) that one has a table which can be presented as > a function > F > N x N --> {0, 1, 2, ..., 9} > and one then forms a composite function > diag F s > N ----> N x N --> {0, 1, 2, ..., 9} --> {0, 1, 2, ..., 9} > where diag is defined by diag(n) = (n, n), and s is a > certain function with no fixed point (e.g., s(i) = i+1 > if i < 9; s(9) = 8). > The anti-value as you call it is this composite function. > No infinite process is involved in composing finitely many > functions. In fact, it's really easy: g(n) = s(F(n, n)). > As an engineer with an interest in AI (and presumably in > computer science), you probably compose functions all the > time, perhaps without realizing it. Did you realize that's > all you're doing here? Do you realize what you are doing here? Do you understand that it's impossible in this universe to compose functions without an agent doing the actual work? Do you understand that the language you are using, which makes it easy to understand various aspects of math, is blinding you to what you are really talking about? Your functions are algorithms which, if they are to exist, and if they are to actually do what you say they do, must be implemented in some type of hardware, whether that's computer hardware, or neural brain hardware. The language you use to talk about these things hides that fact from you. It hides it so well, you don't even seem able to grasp what I'm talking about. Your function is just a description of how the missing value is constructed. And in order for it to be constructed, it must be given every digit from the diagonal, and the hardware which follows your function must take that digit, and produce the answer. And when you look at the logic of the hardware trying to actually construct the diagonal anti-value, it becomes clear that the proof which sounds so strong in the normal context, is no longer valid. Because it is not possible to construct the entire anti diagonal, it is not valid to say that the value is missing from the table. The value as constructed, can always be further down in the table. For example, what if I used a mapping function which, for each row, generated a new real value based on the same anti-diagonal algorithm you use in the proof. It would by definition be generating every value you generate, and placing it in the next row. Because it's infinite, your anti-diagonal construction algorithm would never be able to catch up to it. In this case, every value produced by your algorithm for constructing the anti-diagonal is guaranteed to be in the table. So, you have an algorithm for constructing the anti-diagonal which says it's not in any row, but yet my mapping function is the same algorithm, and it's able to guarantee that everything your function constructs _IS_ in the table in row N+1. So how is it possible to conclude that the diagonal is not in the table, when every number is guaranteed to be in the table and this construction never ends? If it ended, then I wouldn't have an N+1 row to put the next value in, and the argument would be valid. But since it doesn't end, it's infinite, my mapping function never fails to find a row to put the value in. -- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/ === Subject: Re: Cantor's diagonal proof wrong? at 06:08 PM, curt@kcwc.com (Curt Welch) said: >I was confused at the start of this thread >about how some important things are formally defined in mathematics. You still are. >But about what I'm talking now, there is no confusion. If there were no confusion then you wouldn't be writing about algorithms and procedures in a context where they don't exist. >Everything you read some of my words and it doesn't make sense, >it's because you don't understand my message. No, it's because the message is senseless. Your insistence that even though you don't understand the fundamentals you are still correct outs you firmly with the circle squarers and angle trisectors. >Your functions are algorithms No. That delusion is at the heart of your inability to communicate. >So, you have an algorithm for constructing the anti-diagonal which >says it's not in any row, but yet my mapping function is the same >algorithm, and it's able to guarantee that everything your function >constructs _IS_ in the table in row N+1. No. The partial diagonal has nothing to do with the Cantor diagonal argument. His function doesn't construct anything, and the output of his function isn't in the table. >So how is it possible to conclude that the diagonal is >not in the table, when every number is guaranteed to be in the table How is it possible to send a message when the Moon is made of green cheese? The answer is obvious; the question has an assumption contrary to fact. It is not the case that every number is guaranties to be in the table. -- 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: Cantor's diagonal proof wrong? %IW48mQf3K=Ci&gZ7]]aazx@]Y-nq!r5{yH/#,?@lDdUDvOfByB2hVW0.@OM%{l/{cT'{w > All you're showing is that a _different_ proof, one which looks the > same on the page, but where some of the words are given _different_ > meanings, is invalid. That's true, but so what? Yeah, I'm seeing that now. The so what is that any meaning other than the meaning I use becomes a contradiction for me. And though I kept running into the contradiction, I couldn't pin down it's source. But the real source is that I believe langauge is always about processes, and that's just the nature of languge which we can not escape. Everything you talk about is reference to process. It's impossible to talk about anything else using language. So, when the foundation of mathematics makes the assumption that langauge isn't process, they have created a contradiction, which comes out at the high level as this belief that there are different types of infinite sets. But if you believe like I do that langauge is always a reference to process, then the fall out is that there is only one type of infinite set - the processes which never terminates. And all the proofs which show there are more than one type of infinite set just become invalid questions. -- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/ === Subject: Re: Cantor's diagonal proof wrong? <3i11q0d3lbcdq8m9msaetpfdp1ur6ngtff@4ax.com> at 07:12 PM, curt@kcwc.com (Curt Welch) said: >Yeah, I'm seeing that now. The so what is that any meaning other >than the meaning I use becomes a contradiction for me. Rather egocentric, what? >But the real source is that I believe langauge is always about processes, What is the apple process? >So, when the foundation of mathematics makes the assumption that >langauge isn't process, they have created a contradiction, No. They've contradicted *YOU*, which isn't the same thing. -- 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: Cantor's diagonal proof wrong? >> All you're showing is that a _different_ proof, one which looks the >> same on the page, but where some of the words are given _different_ >> meanings, is invalid. That's true, but so what? >Yeah, I'm seeing that now. The so what is that any meaning other than >the meaning I use becomes a contradiction for me. There's nothing contradictory about the proof given the standard meanings. You need to simply _learn_ what it all means. >And though I kept >running into the contradiction, I couldn't pin down it's source. Simple ignorance. >But the >real source is that I believe langauge is always about processes, and >that's just the nature of languge which we can not escape. Everything you >talk about is reference to process. It's impossible to talk about anything >else using language. You keep saying this. Offering no reason anyone should believe it. It follows from what you say that _you_ know what everyone _means_ when they say something better than _they_ do! Seriously, if you're not just trolling you should see someone about this. >So, when the foundation of mathematics makes the assumption that langauge >isn't process, they have created a contradiction, which comes out at the >high level as this belief that there are different types of infinite sets. >But if you believe like I do that langauge is always a reference to >process, then the fall out is that there is only one type of infinite set - And if you believe like _I_ do that every word is a reference to a porcupine then it's also clear that almost everything everyone ever said is wrong. I can't understand why nobody's interested in the insights available in my universe, where everything's a porcupine. >the processes which never terminates. And all the proofs which show there >are more than one type of infinite set just become invalid questions. ************************ David C. Ullrich === Subject: Re: Cantor's diagonal proof wrong? %IW48mQf3K=Ci&gZ7]]aazx@]Y-nq!r5{yH/#,?@lDdUDvOfByB2hVW0.@OM%{l/{cT'{w > I can't understand why nobody's interested in the insights available > in my universe, where everything's a porcupine. I do understand why this group is not interested in my universe. That fact does not bother me. The group has helped me understand some new things about the language of math and that has been very helpful. I am a bit disappointed that no one here seems to have seen anything useful in what I have been talking about, but that does not really surprise me. What I've been talking about is all outside the field of math. I thought it was inside the field of math when I started the thread but after enough times of being told so what does that have to do with math, I was finally able to figure that out. The contradiction I was searching for wasn't here, it was just over the wall outside of math. It just causes interesting things to happen inside of math that I didn't understand. And the problem just outside of math I already knew about before coming here. What I didn't undestand was how it caused these interesting things to happen inside of math. But now I do. -- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/ === Subject: Re: Cantor's diagonal proof wrong? <3i11q0d3lbcdq8m9msaetpfdp1ur6ngtff@4ax.com> at 06:08 PM, curt@kcwc.com (Curt Welch) said: >I do understand why this group is not interested in my universe. We're not clinical psychologists and aren't into fantasy. Some here are into Automata theory, but I don't see what you have to offer them. You have offered no insights and no new techniques, but have simply obfuscated and misrepresented what is already known. You're in the position of someone in sci.chemistry trying to sell Phlogiston. >I am a bit disappointed that no one here seems to have seen anything >useful in what I have been talking about, That's because there was nothing useful in it. Without far more talent than most of us have, you're not going to come up with anything useful without first learning the vocabulary and the basic concepts. -- 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: Cantor's diagonal proof wrong? > And the problem just outside of math I already knew about before coming > here. What I didn't undestand was how it caused these interesting things > to happen inside of math. But now I do. Great. Now why don't you go away? Bob Kolker === Subject: Re: Cantor's diagonal proof wrong? > But if you believe like I do that langauge is always a reference to > process, then the fall out is that there is only one type of infinite set - > the processes which never terminates. And all the proofs which show there > are more than one type of infinite set just become invalid questions. What is invalid is your grasp of the concepts. Invalid did I say? Non-existent is more like it. Bob Kolker === Subject: Re: Cantor's diagonal proof wrong? > I've already explained this about 10 times. But as long as someone is > interested, I'll keep going. > The problem is here is 100% language issues. What does constructed mean? > How I was using it has a subtle but very important difference from how you > were hearing it. Do you realize you are arguing over a word that appears nowhere in the axioms? In set theory we do not talk about whether a set can be constructed, but only about whether a set exists. One of the axioms (the axiom of infinity) says there is a nonempty inductive set. The axiom does not say that this set can be constructed, but only that the set exists. Another axiom (actually an axiom schema) says that if you have a set X and a property P, then there exists a set Y = { x in X : P(x) }. Again, the axiom does not say that Y can be constructed, or that there is anything to finish, but merely that a Y exists with the property that for every x, x in Y <-> x in X and P(x). It is in this sense that the number described by the diagonal argument exists. Nobody is claiming that the number can be physically constructed. That expression has no meaning and is irrelevant to the proof. Therefore, the language issue that you mentioned is that you insist on dragging into the discussion a word that has no place there. -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. === Subject: Re: Cantor's diagonal proof wrong? %IW48mQf3K=Ci&gZ7]]aazx@]Y-nq!r5{yH/#,?@lDdUDvOfByB2hVW0.@OM%{l/{cT'{w > Because it is not possible to construct the entire anti diagonal, it is > not valid to say that the value is missing from the table. The value as > constructed, can always be further down in the table. > For example, what if I used a mapping function which, for each row, > generated a new real value based on the same anti-diagonal algorithm you > use in the proof. It would by definition be generating every value you > generate, and placing it in the next row. Because it's infinite, your > anti-diagonal construction algorithm would never be able to catch up to > it. In this case, every value produced by your algorithm for constructing > the anti-diagonal is guaranteed to be in the table. > So, you have an algorithm for constructing the anti-diagonal which says > it's not in any row, but yet my mapping function is the same algorithm, > and it's able to guarantee that everything your function constructs _IS_ > in the table in row N+1. So how is it possible to conclude that the > diagonal is not in the table, when every number is guaranteed to be in > the table and this construction never ends? > If it ended, then I wouldn't have an N+1 row to put the next value in, > and the argument would be valid. But since it doesn't end, it's > infinite, my mapping function never fails to find a row to put the value > in. I'm posting a follow-up to my own post because I think the argument above might open some people's eyes to what I'm talking about. It was at the bottom of my last long post so I thought it was likely that many people wouldn't see it. The point above is that in Cantor's diagonal argument, what happens when the unspecified mapping function from natural numbers to real, is the same algorithm used to construct the anti-diagonal? The N digit real constructed from rows 1 to N is always placed in row N+1. If that is the mapping function, then I can argue that everything generated by the diagonal construction function is in the table. And because the table is infinite, I never loose the argument. Everything constructed by the diagonal argument is in fact in the table. I would only use the argument if you PRETEND the task completes, and the game comes to an end, as it would if the table was finite in size. I believe people have pointed out to me a few times in this thread that when working with infinite sets, things aren't always as you would expect. I would argue that the thing which is not as you would expect is the validity of the diagonal argument. How is it possible in my example here that the diagonal being created can't be in any row, yet is also always in the table in some row? It's because when you play with infinity, things do not work the same as when you play with finite sized sets. -- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/ === Subject: Re: Cantor's diagonal proof wrong? > The point above is that in Cantor's diagonal argument, what happens when > the unspecified mapping function from natural numbers to real, is the same > algorithm used to construct the anti-diagonal? The N digit real > constructed from rows 1 to N is always placed in row N+1. That doesn't even make sense. The diagonal is given by a mapping from the naturals to the set of decimal digits, while the original mapping is from the naturals to the set of reals in [0,1]. They aren't even the same kind of mapping. Besides that, there's the fact that the diagonal argument depends on the original list in an essential way. You specify the list of reals first, and then the diagonal number is determined by it in a way that guarantees it is not in the list. It's like asking what happens if n is a number such that n+1 is the same number as n. What you are supposing is impossible. -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. === Subject: Re: Cantor's diagonal proof wrong? %IW48mQf3K=Ci&gZ7]]aazx@]Y-nq!r5{yH/#,?@lDdUDvOfByB2hVW0.@OM%{l/{cT'{w > The point above is that in Cantor's diagonal argument, what happens > when the unspecified mapping function from natural numbers to real, is > the same algorithm used to construct the anti-diagonal? The N digit > real constructed from rows 1 to N is always placed in row N+1. > That doesn't even make sense. The diagonal is given by a mapping from > the naturals to the set of decimal digits, while the original mapping is > from the naturals to the set of reals in [0,1]. They aren't even the > same kind of mapping. First, we can easily remove your issues in relation to natural numbers and reals from the debate by changing the argument to another domain. Lets do that. Pretend we have a infinite table made up of an infinite strings of 1s and 0s on each row. So every row in this table is just an infinite sequence of some combination of 1s and 0s. With this table, we make the argument that it is impossible for every combination of 1s and 0s to be listed in the table. We prove this by using the diagonal argument. So we start with the assumption that the table which includes all combinations of 1s and 0s does exist. Then, we build the anti-diagonal value by selecting the numbers from the diagonal, and inverting them. This anti-diagonal value can not be in the table, because every table entry will be different by at least one digit. Therefore, we have created a contradiction with the starting assumption, that such a table can exist. Therefore, we have proved that the staring assumption is wrong, the table can not contain every possible string of 0's and 1's. This is the exact same logic used in Cantor's diagonal proof, but this time, we are not dragging anything about math into it. (change 0 1 to A B if you like just to remove numbers from the picture). The result of this proof is the belief that any mapping function which maps table rows to a string, can not include every possible string, because the proof has constructed a string (from ANY mapping function) that is not in the table. But, I can specify one special mapping function that works like this. Fill the first row with any combination of 1's and 0's you like. Then, fill every following row, with a copy of the row above it, with the diagonal digit inverted. Now, what I can show about your diagonal value, is that every diagonal you construct is in fact in the table, in row N+1. So your argument that it is not in the table, is no stronger than my argument that it is in the table. If the table was finite in size, my argument would fall apart. When we reach the end of the table, I would have no place to put the N+1 value. But because it's infinite, my argument never fails. For every row you can show which does not contain the value, I can show you another row which does. > Besides that, there's the fact that the diagonal argument depends on the > original list in an essential way. You specify the list of reals first, Ok, in the above, I have specified the table first. Or if you want to be more exact, instead of starting with any set of 1's and 0's, let just say the first row is all 0s'. The second row is 1000... The third row is 110000... etc. > and then the diagonal number is determined by it in a way that guarantees > it is not in the list. Yes it does. But yet, I can also show that every diagonal number which you say is not in the table, is in fact in the table. So how can this be? It's because when dealing with the concept of infinity, things just don't work the same way as when dealing with finite objects. Arguments that are 100% valid for a finite sized table just make no sense when you try to apply them to a table that has no end. > It's like asking what happens if n is a number > such that n+1 is the same number as n. What you are supposing is > impossible. Now you are beginning to see the light. With the power of language, we can say things that are impossible. And if you hide the true meaning in enough layers of definitions, nothing you say by itself seems invalid, but the set of definitions, when taken together, can still create a contradiction, and be invalid. In the diagonal proof, we start with an infinite table. But that's already a trick of language because infinite tables can't exist. So we are not actually staring with an infinite table, we are starting with an algorithm for generating objects which never terminates and just pretending it's a table by only looking at the first N rows and writing ... at the end of it. Then, we specify the procedure for constricting the value from the diagonal. Then, by forgetting what the argument was really about, we use an argument that is only valid on finite tables, to try and prove something about the nature of procedures that never terminate. In the context of finite tables, the argument is valid. But, in the context of infinite tables, the argument is invalid. Now, you might notice I've gone back to my starting position that the logic used in Cantor's diagonal argument is just flat out invalid. What I don't know however, is what this really means for integers vs. reals. Cantor's diagonal proof, even if invalid, is not the only proof about integers and reals. And I do not yet know the full nature of those other proofs or the full nature of the language they are written in. -- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/ === Subject: Re: Cantor's diagonal proof wrong? at 09:19 PM, curt@kcwc.com (Curt Welch) said: >Now, what I can show about your diagonal value, is that every >diagonal you construct is in fact in the table, in row N+1. No. There is no value of N for which that is true. You are again confusing a statement about a sequence wits a statement about one of its subsequences. >If the table was finite in size, my argument would fall apart. It fall apart regardless, because you are looking at the wrong sequence. >For every row you can show which does not contain the value, I can >show you another row which does. No. You can show a row that contains a different, and irrelevant, value. >Ok, in the above, I have specified the table first. Or if you want >to be more exact, instead of starting with any set of 1's and 0's, >let just say the first row is all 0s'. The second row is 1000... >The third row is 110000... etc. That table does not contain 11... >Yes it does. But yet, I can also show that every diagonal number >which you say is not in the table, is in fact in the table. The value with all 1s is not in your table. >In the diagonal proof, we start with an infinite table. But that's >already a trick of language because infinite tables can't exist. That's an unwarranted assumption on your part. Further, Mathematics is not about physical objects, and the Mathematical usage of exists is quite different from the physical usage. >pretending That's you, not us. >by only looking at the first N rows That's you, not us. The Cantor diagonal argument looks at all rows concurrently. >writing ... That's you, not us. We use universal and existential quantifiers, functions, etc., to make the meaning precise. >only valid on finite tables No. >And I do not yet know the full nature of those other proofs or the >full nature of the language they are written in. Obviously. Yet in spite of not understanding the language, you make Rodin's The Thinker was in the key of G Major, would you not think that I was a crank? What you have written is fully as egregious. -- 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: Cantor's diagonal proof wrong? > Pretend we have a infinite table made up of an infinite strings of 1s and > 0s on each row. So every row in this table is just an infinite sequence of > some combination of 1s and 0s. It is well known that base-2 gives problems. > With this table, we make the argument that it is impossible for every > combination of 1s and 0s to be listed in the table. We prove this by using > the diagonal argument. > So we start with the assumption that the table which includes all > combinations of 1s and 0s does exist. > Then, we build the anti-diagonal value by selecting the numbers from the > diagonal, and inverting them. > This anti-diagonal value can not be in the table, because every table entry > will be different by at least one digit. > Therefore, we have created a contradiction with the starting assumption, > that such a table can exist. Therefore, we have proved that the staring > assumption is wrong, the table can not contain every possible string of 0's > and 1's. > This is the exact same logic used in Cantor's diagonal proof, but this > time, we are not dragging anything about math into it. (change 0 1 to A B > if you like just to remove numbers from the picture). > The result of this proof is the belief that any mapping function which maps > table rows to a string, can not include every possible string, because the > proof has constructed a string (from ANY mapping function) that is not in > the table. > But, I can specify one special mapping function that works like this. Fill > the first row with any combination of 1's and 0's you like. Then, fill > every following row, with a copy of the row above it, with the diagonal > digit inverted. Yes, that is why the diagonal argument does not work in base 2. > Now, what I can show about your diagonal value, is that every diagonal you > construct is in fact in the table, in row N+1. But it is very easy to construct a string that is not in that list. Take the first item and invert only the second digit, or any other digit but the first. -- 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: Cantor's diagonal proof wrong? > Pretend we have a infinite table made up of an infinite strings of 1s and > 0s on each row. So every row in this table is just an infinite sequence of > some combination of 1s and 0s. >It is well known that base-2 gives problems. If we're talking about binary representations of reals, yes. But here we've decided to ignore the reals and just talk about infinite sequences of 0's and 1's - no problem with that. > With this table, we make the argument that it is impossible for every > combination of 1s and 0s to be listed in the table. We prove this by using > the diagonal argument. > So we start with the assumption that the table which includes all > combinations of 1s and 0s does exist. > Then, we build the anti-diagonal value by selecting the numbers from the > diagonal, and inverting them. > This anti-diagonal value can not be in the table, because every table entry > will be different by at least one digit. > Therefore, we have created a contradiction with the starting assumption, > that such a table can exist. Therefore, we have proved that the staring > assumption is wrong, the table can not contain every possible string of 0's > and 1's. > This is the exact same logic used in Cantor's diagonal proof, but this > time, we are not dragging anything about math into it. (change 0 1 to A B > if you like just to remove numbers from the picture). > The result of this proof is the belief that any mapping function which maps > table rows to a string, can not include every possible string, because the > proof has constructed a string (from ANY mapping function) that is not in > the table. > But, I can specify one special mapping function that works like this. Fill > the first row with any combination of 1's and 0's you like. Then, fill > every following row, with a copy of the row above it, with the diagonal > digit inverted. >Yes, that is why the diagonal argument does not work in base 2. > Now, what I can show about your diagonal value, is that every diagonal you > construct is in fact in the table, in row N+1. >But it is very easy to construct a string that is not in that list. Take >the first item and invert only the second digit, or any other digit but >the first. ************************ David C. Ullrich === Subject: Re: Cantor's diagonal proof wrong? Originator: joshp@xoxy.net (joshp) >>It is well known that base-2 gives problems. >If we're talking about binary representations of reals, yes. What problems occur when using base 2 representations of reals that do not also occur when using other bases? -- Josh Purinton === Subject: Re: Cantor's diagonal proof wrong? :>>It is well known that base-2 gives problems. :>If we're talking about binary representations of reals, yes. : What problems occur when using base 2 representations of reals that do : not also occur when using other bases? : -- : Josh Purinton It has to do with the dual representation of reals. .011111111111111111111............. represents the same real as .100000000000000000000............. Using the simple change the diagonal rule, in base 2 there is no way to guarantee that the number represented by the diagonal is not in the list in a different representation. Given the list .100000000000000.......... .101000000000000.......... .100100000000000.......... .100010000000000.......... .100001000000000.......... ........... you would generate the value .011111111111111...... . Clearly this string is not in the list, but the number it represents (1/2) is in the list. In base 10 this can be avoided by not changing any digit to a 9. In general, for bases other than 2, it can be avoided by not changing any digit to the last digit in the base. Stephen === Subject: Re: Cantor's diagonal proof wrong? Originator: joshp@xoxy.net (joshp) >: What problems occur when using base 2 representations of reals that do >: not also occur when using other bases? >Using the simple change the diagonal rule, in base 2 there is no >way to guarantee that the number represented by the diagonal >is not in the list in a different representation. This problem could possibly be addressed by defining the diagonal in terms of digit-pairs, changing 01 to 10 and everything else to 01. In any event, this technical problem isn't likely to affect the persuasiveness of the simple diagonal argument on its intended audience, since the Cantor deniers and the 0.111... =/= 1.0 (base 2) crowd seem to overlap to a large degree. -- Josh Purinton === Subject: Re: Cantor's diagonal proof wrong? :>: What problems occur when using base 2 representations of reals that do :>: not also occur when using other bases? :>Using the simple change the diagonal rule, in base 2 there is no :>way to guarantee that the number represented by the diagonal :>is not in the list in a different representation. : This problem could possibly be addressed by defining the diagonal in : terms of digit-pairs, changing 01 to 10 and everything else to 01. : In any event, this technical problem isn't likely to affect the : persuasiveness of the simple diagonal argument on its intended audience, : since the Cantor deniers and the 0.111... =/= 1.0 (base 2) crowd seem to : overlap to a large degree. : -- : Josh Purinton Yes it is largely just a technical point, but there have been deniers who have fixated on that one technical point and claimed that it invalidated all versions of the proof in any base. Stephen === Subject: Re: Cantor's diagonal proof wrong? : > Pretend we have a infinite table made up of an infinite strings of 1s and : > 0s on each row. So every row in this table is just an infinite sequence of : > some combination of 1s and 0s. : It is well known that base-2 gives problems. In this case it does not cause any problems because he is just considering infinite strings os 1s and 0s. He is not claiming these are the binary representations of numbers. If you just consider them as strings than no two strings are the same. : > : > But, I can specify one special mapping function that works like this. Fill : > the first row with any combination of 1's and 0's you like. Then, fill : > every following row, with a copy of the row above it, with the diagonal : > digit inverted. : Yes, that is why the diagonal argument does not work in base 2. : > Now, what I can show about your diagonal value, is that every diagonal you : > construct is in fact in the table, in row N+1. : But it is very easy to construct a string that is not in that list. Take : the first item and invert only the second digit, or any other digit but : the first. Even using the simple rule you construct a string that is not in the list. This was demonstrated in an earlier post. Stephen === Subject: Re: Cantor's diagonal proof wrong? Originator: joshp@xoxy.net (joshp) > But, I can specify one special mapping function that works like this. Fill > the first row with any combination of 1's and 0's you like. Then, fill > every following row, with a copy of the row above it, with the diagonal > digit inverted. >Yes, that is why the diagonal argument does not work in base 2. The diagonal argument works for any base B >= 2. To see this, let S be a list of reals in [0,1], and let S_k denote the kth number in the list. Let S_k(i) denote the ith digit in the base B expansion of S_k. Let G be a real in [0,1], and let G(i) be the ith digit of the base B expansion of G, defined by the rule: / 0 if S(i,i) = 1 G(i) = | 0 otherwise By definition G(i) =/= S(i,i), and so G differs from S_i for all i. Therefore S does not contain all the reals in [0,1]. -- Josh Purinton === Subject: Re: Cantor's diagonal proof wrong? Originator: joshp@xoxy.net (joshp) > / 0 if S(i,i) = 1 >[...] By definition G(i) =/= S(i,i), and so G differs from S_i for all i. Replace S(i,i) with S_i(i). -- Josh Purinton === Subject: Re: Cantor's diagonal proof wrong? >> The point above is that in Cantor's diagonal argument, what happens >> when the unspecified mapping function from natural numbers to real, is >> the same algorithm used to construct the anti-diagonal? The N digit >> real constructed from rows 1 to N is always placed in row N+1. >> That doesn't even make sense. The diagonal is given by a mapping from >> the naturals to the set of decimal digits, while the original mapping is >> from the naturals to the set of reals in [0,1]. They aren't even the >> same kind of mapping. >First, we can easily remove your issues in relation to natural numbers and >reals from the debate by changing the argument to another domain. Lets do >that. >Pretend we have a infinite table made up of an infinite strings of 1s and >0s on each row. So every row in this table is just an infinite sequence of >some combination of 1s and 0s. >With this table, we make the argument that it is impossible for every >combination of 1s and 0s to be listed in the table. We prove this by using >the diagonal argument. >So we start with the assumption that the table which includes all >combinations of 1s and 0s does exist. >Then, we build the anti-diagonal value by selecting the numbers from the >diagonal, and inverting them. >This anti-diagonal value can not be in the table, because every table entry >will be different by at least one digit. >Therefore, we have created a contradiction with the starting assumption, >that such a table can exist. Therefore, we have proved that the staring >assumption is wrong, the table can not contain every possible string of 0's >and 1's. >This is the exact same logic used in Cantor's diagonal proof, but this >time, we are not dragging anything about math into it. (change 0 1 to A B >if you like just to remove numbers from the picture). So you have no idea what the word math means either. Never mind, that's not important here. >The result of this proof is the belief that any mapping function which maps >table rows to a string, can not include every possible string, because the >proof has constructed a string (from ANY mapping function) that is not in >the table. >But, I can specify one special mapping function that works like this. Fill >the first row with any combination of 1's and 0's you like. Then, fill >every following row, with a copy of the row above it, with the diagonal >digit inverted. >Now, what I can show about your diagonal value, is that every diagonal you >construct is in fact in the table, in row N+1. No, you can't show that. Let's actually do what I think you're saying. Let's start with 000000.... Now the next row should be the first row with the diagonal digit inverted - i take that to mean that the second row is the same as the first with the second digit swapped: [if that's not what you meant you need to explain again] 0100000... and the third row is then 0110000... and we get the table 000000... 010000... 011000... 011100... . . . Now apply the diagonal procedure to that table, and you get the string 100000... which sure enough is not a row in the table. >So your argument that it is not in the table, is no stronger than my >argument that it is in the table. Except that one argument is correct and the other is incorrect, yes. >[...] >Now, you might notice I've gone back to my starting position that the logic >used in Cantor's diagonal argument is just flat out invalid. What I don't >know however, is what this really means for integers vs. reals. Cantor's >diagonal proof, even if invalid, is not the only proof about integers and >reals. And I do not yet know the full nature of those other proofs or >the full nature of the language they are written in. ************************ David C. Ullrich === Subject: Re: Cantor's diagonal proof wrong? ... >But, I can specify one special mapping function that works like this. Fill >the first row with any combination of 1's and 0's you like. Then, fill >every following row, with a copy of the row above it, with the diagonal >digit inverted. > >Now, what I can show about your diagonal value, is that every diagonal you >construct is in fact in the table, in row N+1. > No, you can't show that. > Let's actually do what I think you're saying. Let's start with > 000000.... > Now the next row should be the first row with the diagonal > digit inverted - i take that to mean that the second row is > the same as the first with the second digit swapped: > [if that's not what you meant you need to explain again] I think that is not what he meant. I think he meant that it is the same as the first row with the *first* digit swapped. Similarly, the third row is the same as the second, with the *second* digit swapped. Using this algorithm we get: 00000... 10000... 11000... 11100... and the diagonal is: 11111... Now the interesting thing is that it looks like the diagonal is on the list. But it obviously is not, for the same reason that the infinite set of natural numbers does not contain an infinite number. But CW is thinking that you have to construct initial parts of the diagonal number sequentially, and that is where his statement every diagonal comes from. -- 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: Cantor's diagonal proof wrong? %IW48mQf3K=Ci&gZ7]]aazx@]Y-nq!r5{yH/#,?@lDdUDvOfByB2hVW0.@OM%{l/{cT'{w > I think that is not what he meant. I think he meant that it is the > same as the first row with the *first* digit swapped. Similarly, the > third row is the same as the second, with the *second* digit swapped. > Using this algorithm we get: > 00000... > 10000... > 11000... > 11100... > and the diagonal is: > 11111... > Now the interesting thing is that it looks like the diagonal is on > the list. But it obviously is not, for the same reason that the > infinite set of natural numbers does not contain an infinite number. > But CW is thinking that you have to construct initial parts of the > diagonal number sequentially, and that is where his statement > every diagonal comes from. Right. You have restored my faith in mainkind. :) You may not know why I'm thinking the way I think, but you at least show that you are smart enough and have enough of an open mind to understand something new and different. And you are right, the argument is exatly the same as my initial argument about infinite sized integers but the new form of the argument takes the definition of integers out of the picture. I thought taking integers out of the argument would be enought to clear up the confusion. But it wasn't. If you use the normal mathematical ideas about creation and existence, my argument still falls short even though integers have been removed from the language. So in the langauge of math, no version of my argument makes sense. Which is why I now say that what I've been talking about is actually an issue outside of math. -- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/ === Subject: Re: Cantor's diagonal proof wrong? > I think that is not what he meant. I think he meant that it is the > same as the first row with the *first* digit swapped. Similarly, the > third row is the same as the second, with the *second* digit swapped. > Using this algorithm we get: > 00000... > 10000... > 11000... > 11100... > and the diagonal is: > 11111... > Now the interesting thing is that it looks like the diagonal is on > the list. But it obviously is not, for the same reason that the > infinite set of natural numbers does not contain an infinite number. > But CW is thinking that you have to construct initial parts of the > diagonal number sequentially, and that is where his statement > every diagonal comes from. > Right. You have restored my faith in mainkind. :) You may not know why > I'm thinking the way I think, but you at least show that you are smart > enough and have enough of an open mind to understand something new and > different. > And you are right, the argument is exatly the same as my initial argument > about infinite sized integers but the new form of the argument takes the > definition of integers out of the picture. I thought taking integers out > of the argument would be enought to clear up the confusion. But it wasn't. > If you use the normal mathematical ideas about creation and existence, my > argument still falls short even though integers have been removed from the > language. So in the langauge of math, no version of my argument makes > sense. Which is why I now say that what I've been talking about is > actually an issue outside of math. Given the sequence of terminating rationals already discussed above: Can diagonalization, substituting 0 by 1, yield a number not contained in the sequence? Is anybody able to show at which natural number this argument fails. Or do we have to accept non-natural numbers enumerating the list? === Subject: Re: Cantor's diagonal proof wrong? !3KEIp?*w`|bL5qr,H)LFO6Q=qx~iH4DN;i;/yuIsqbLLCh/!U#X[S~(5eZ41to5f%E@'ELIi $t^ VcLWP@J5p^rst0+('>Er0=^1{]M9!p?&:z]|;&=NP3AhB!B_bi^]Pfkw >> I think that is not what he meant. I think he meant that it is the >> same as the first row with the *first* digit swapped. Similarly, the >> third row is the same as the second, with the *second* digit swapped. >> Using this algorithm we get: >> 00000... >> 10000... >> 11000... >> 11100... >> and the diagonal is: >> 11111... > Given the sequence of terminating rationals already discussed above: > Can diagonalization, substituting 0 by 1, yield a number not contained > in the sequence? Is anybody able to show at which natural number this > argument fails. Your question does not make sense since the diagonal is not associated with any natural number. > Or do we have to accept non-natural numbers enumerating the list? You are babbling. -- David Kastrup, Kriemhildstr. 15, 44793 Bochum === Subject: Re: Cantor's diagonal proof wrong? > I think that is not what he meant. I think he meant that it is the >> same as the first row with the *first* digit swapped. Similarly, the >> third row is the same as the second, with the *second* digit swapped. >> Using this algorithm we get: >> 00000... >> 10000... >> 11000... >> 11100... >> and the diagonal is: >> 11111... > Given the sequence of terminating rationals already discussed above: > Can diagonalization, substituting 0 by 1, yield a number not contained > in the sequence? Is anybody able to show at which natural number this > argument fails. > Your question does not make sense since the diagonal is not associated > with any natural number. Oh, is there any digit d_nn of the diagonal which is not associated with a natural number n? Is there any diagonal digit a_nn = 0 in a line which is not preceded by a string 111...111 with 0 < k < n digits a_nk = 1? Should there even be a digit of the diagonal which cannot be associated with a line at all, such that for some d_nn an a_nn is not existing at all? If these questions are answered as a mathematician should be expected to answer them, what does your statement mean, then? === Subject: Re: Cantor's diagonal proof wrong? !3KEIp?*w`|bL5qr,H)LFO6Q=qx~iH4DN;i;/yuIsqbLLCh/!U#X[S~(5eZ41to5f%E@'ELIi $t^ VcLWP@J5p^rst0+('>Er0=^1{]M9!p?&:z]|;&=NP3AhB!B_bi^]Pfkw > > I think that is not what he meant. I think he meant that it is the > same as the first row with the *first* digit swapped. Similarly, the > third row is the same as the second, with the *second* digit swapped. > Using this algorithm we get: > 00000... > 10000... > 11000... > 11100... > and the diagonal is: > 11111... > Given the sequence of terminating rationals already discussed above: >> Can diagonalization, substituting 0 by 1, yield a number not contained >> in the sequence? Is anybody able to show at which natural number this >> argument fails. >> Your question does not make sense since the diagonal is not associated >> with any natural number. > Oh, is there any digit d_nn of the diagonal which is not associated > with a natural number n? Each digit is, and so are the partial sums of the corresponding series. But the limit of the series is not associated with any n. > Is there any diagonal digit a_nn = 0 in a line which is not preceded > by a string 111...111 with 0 < k < n digits a_nk = 1? So what? > Should there even be a digit of the diagonal which cannot be > associated with a line at all, such that for some d_nn an a_nn is > not existing at all? Not at all. So what? > If these questions are answered as a mathematician should be > expected to answer them, what does your statement mean, then? That the value specified by the diagonal (which is basically the limit of the corresponding series) can't be completely specified if you stop at any digit. -- David Kastrup, Kriemhildstr. 15, 44793 Bochum === Subject: Re: Cantor's diagonal proof wrong? >> The point above is that in Cantor's diagonal argument, what happens >> when the unspecified mapping function from natural numbers to real, is >> the same algorithm used to construct the anti-diagonal? The N digit >> real constructed from rows 1 to N is always placed in row N+1. >> That doesn't even make sense. The diagonal is given by a mapping from >> the naturals to the set of decimal digits, while the original mapping is >> from the naturals to the set of reals in [0,1]. They aren't even the >> same kind of mapping. > First, we can easily remove your issues in relation to natural numbers and > reals from the debate by changing the argument to another domain. Lets do > that. I am happy to substitute the powerset form of the diagonal argument and dispense with digits altogether. > Pretend we have a infinite table made up of an infinite strings of 1s and > 0s on each row. So every row in this table is just an infinite sequence of > some combination of 1s and 0s. Cantor assumes instead that there is a mapping f: X -> P(X) for some X. The diagonal shows that f is not a surjection. > With this table, we make the argument that it is impossible for every > combination of 1s and 0s to be listed in the table. We prove this by using > the diagonal argument. Given f: X -> P(X), we simply observe that the set D = { x in X : not(x = f(x)) } is not in the range of f. > So we start with the assumption that the table which includes all > combinations of 1s and 0s does exist. Cantor makes no such assumption. If you think there is a flaw in Cantor's argument, then you should be able to point out where it lies in the direct form of the argument. > Then, we build the anti-diagonal value by selecting the numbers from the > diagonal, and inverting them. There are no numbers involved. Instead we have the set D defined above. > This anti-diagonal value can not be in the table, because every table entry > will be different by at least one digit. D is not equal to f(x) for any x in X, because x in D iff x not in f(x). > Therefore, we have created a contradiction with the starting assumption, > that such a table can exist. Therefore, we have proved that the staring > assumption is wrong, the table can not contain every possible string of 0's > and 1's. There is no contradiction involved. It's a direct proof. > This is the exact same logic used in Cantor's diagonal proof, but this > time, we are not dragging anything about math into it. (change 0 1 to A B > if you like just to remove numbers from the picture). Instead of arguing about whether your logic is the same as Cantor's, let's simply use Cantor's. > The result of this proof is the belief that any mapping function which maps > table rows to a string, can not include every possible string, because the > proof has constructed a string (from ANY mapping function) that is not in > the table. The result is that if f: X -> P(X) is given, then f is not a surjection. > But, I can specify one special mapping function that works like this. Fill > the first row with any combination of 1's and 0's you like. Then, fill > every following row, with a copy of the row above it, with the diagonal > digit inverted. Let's consider the case X = N and define f(0) = {}. Then according to your rule I believe I am supposed to define f(1) = {0} because 0 is the diagonal element in f(0), right? What then? Do we take f(2) = {0,1} because 1 is the diagonal element in f(1), or is that not what you meant? If we proceed by that scheme, then we are going to get f(0) = {}, f(1) = { 0 }, f(2) = { 0, 1 }, . . . f(k) = { 0, 1, ..., k-1 } . . . from which it follows that D = { n in N : not(n in f(n)) } = N, and sure enough, N is not a in the range of your function f. If you disagree, then tell me for which n is f(n) = N? > Now, what I can show about your diagonal value, is that every diagonal you > construct is in fact in the table, in row N+1. N is a set, not a number. What do you mean by N+1? You need to produce an n such that f(n) = N. > So your argument that it is not in the table, is no stronger than my > argument that it is in the table. It's Cantor's argument, not mine, and I suppose they are equally strong if you ignore the minor point that his actually works and yours is nonsense. > If the table was finite in size, my argument would fall apart. And also if the table is infinite in size. [ rest snipped ] -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. === Subject: Re: Cantor's diagonal proof wrong? %IW48mQf3K=Ci&gZ7]]aazx@]Y-nq!r5{yH/#,?@lDdUDvOfByB2hVW0.@OM%{l/{cT'{w > First, we can easily remove your issues in relation to natural numbers > and reals from the debate by changing the argument to another domain. > Lets do that. > I am happy to substitute the powerset form of the diagonal argument and > dispense with digits altogether. Good suggestion. However, I see no direct connection between my demonstration of the weakness of the diagonal argument with the powerset argument. My demonstration requires the construction to work the same way, and the construction of the D set doesn't work the same way as it does in the diagonal argument. I agree that if the diagonal argument has a problem, the powerset argument is likely to have a problem to. But where is that problem? Most likely, it lies outside of the argument. That is, in the basic assumptions set theory are built on. Which means that, as is well believed, axiomatic set theory is consistent given the starting axioms, and the starting assumptions about what sets are. Until I master the language of set theory and learn the exact meaning of all the ideas it's built on, I won't be able to even point to the problem, let alone argue the issue here. It's possible, as I have said, that the set theory form of the argument is valid, even if the diagonal argument is not. Also keep in mind that I'm only arguing that the diagonal argument itself is invalid. i.e., that the argument does not prove what it says it proves. My latest demonstration of the binary table does not say that there is a bijection from the integers to the reals, only that the logic used in the diagonal argument is invalid, so nothing in fact is proved by it. If I take the time to master the language and logic of set theory, what I expect to find is that they use a language that makes it trivial to talk about an infinite set as if it existed, and as if it worked exactly like a finite set. So, anything you build on top of that foundation, can be consistent, but yet incompatible with how I say the universe actually works. If this turns out to be the case, I should be able to point to the exact tools they use to allow this to happen, and I can point to what would have to be changed to bring set theory into line with view of reality. Then, I could rebuild all the work done on the current set theory to describe math under this new view of reality - under a different set of axioms. Google, I get the feeling that if you don't allow infinite sets, then you can't define the natural numbers. And if you can't define the natural numbers, then you really can't define much of anything useful. But that's not consistent with my problem. I know that most of what mathematics has done with the concept of infinity is valid. On a few areas seem to have taken a wrong turn. So if I'm right, there must be a way to bring in the power of the natural numbers without steping over the line. What I fear this means is that to solve what I consider to be the problem, I won't be able to use set theory at all. I would have to develop a new set-theory-like foundation, and duplicate all the work of creating formal proofs with this new foundation. And since doing that is years of work, and not a weekend project, and since I have no interest in becoming a mathematician, the odds of this getting done by me is near zero. However, what could happen, is that if I simply spent a little time to master the basics of set theory, I might be able to lay out what I consider the problems to be, and suggest how a different foundation of math which was in sync with my universe, could be defined. That might be enough to spark some interest in some real mathematicians to explore the idea to see where it takes them. So I'll see what I can do about taking that first step. And if I get anywhere, I'll come back and visit again. The real point you have made is that the diagonal argument is not important. If it's invalid, who cares? What's important is the formal proofs and arguments made with the set theory foundation. -- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/ === Subject: Re: Cantor's diagonal proof wrong? >Until I master the language of set theory and learn the exact meaning >of all the ideas it's built on, I won't be able to even point to the >problem, let alone argue the issue here. It's statements like that that show you to be a crank. You have faith that there is a problem in the discipline, even though you are aware that you lack the basic tools, and even though you have made it abundantly clear that you lack the necessary precision. >If I take the time to master the language and logic of set theory, >what I expect to find is that they use a language that makes it >trivial to talk about an infinite set as if it existed, and as if it >worked exactly like a finite set. You would be disappointed, since infinite sets do *not* work exactly like finite sets. >So, anything you build on top of that foundation, can be consistent, >but yet incompatible with how I say the universe actually works. Indeed, but the Universe doesn't care how you say that it actually works, nor do Mathematicians. The Universe is what it is, regardless of whether you understand it. Your beliefs about the universe actually works are a matter of faith and have no role in a discussion of Mathematics. >If this turns out to be the case, I should be able to point to the >exact tools they use to allow this to happen, and I can point to >what would have to be changed to bring set theory into line with >view of reality. Why would anybody want to bring Set Theory, or any other intellectual discipline, into line with your view of reality? Your view of reality is irrelevant. >However, what could happen, is that if I simply spent a little time >to master the basics of set theory, I might be able to lay out what >I consider the problems to be, and suggest how a different >foundation of math which was in sync with my universe, could be >defined. Why would anybody care about your Universe? >That might be enough to spark some interest in some real >mathematicians to explore the idea to see where it takes them. No. If you want real Mathematicians to take you seriously then you will have to take Mathematics seriously; that means that you will need to have a clearly reasoned argument as to why your idea makes sense[1] and why it is of Mathematical interest. [1] It currently doesn't, so you'll need to come up with a new 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: Cantor's diagonal proof wrong? >> First, we can easily remove your issues in relation to natural numbers >> and reals from the debate by changing the argument to another domain. >> Lets do that. >> I am happy to substitute the powerset form of the diagonal argument and >> dispense with digits altogether. > Good suggestion. However, I see no direct connection between my > demonstration of the weakness of the diagonal argument with the powerset > argument. My demonstration requires the construction to work the same way, > and the construction of the D set doesn't work the same way as it does in > the diagonal argument. The powerset argument is a diagonal argument. The set D = { x in X : not(x in f(x)) } is the diagonal in that argument. In fact, the powerset argument (for the case X = N) is identical to the base-2 form of the diagonal argument for real numbers, except that you don't have to worry about the dual representation problem (0.100000..._2 = 0.01111111..._2). Do you agree that |N| < |P(N)|? Do you also agree that |P(N)| = |R| by the Cantor-Bernstein theorem? Doesn't it follow that |N| < |R|? > I agree that if the diagonal argument has a problem, the powerset argument > is likely to have a problem to. But where is that problem? Most likely, > it lies outside of the argument. That is, in the basic assumptions set > theory are built on. Which means that, as is well believed, axiomatic set > theory is consistent given the starting axioms, and the starting > assumptions about what sets are. > Until I master the language of set theory and learn the exact meaning of > all the ideas it's built on, I won't be able to even point to the problem, > let alone argue the issue here. Then this discussion has concluded. Let me know if you think you find a problem in the axioms. -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. === Subject: Re: Cantor's diagonal proof wrong? %IW48mQf3K=Ci&gZ7]]aazx@]Y-nq!r5{yH/#,?@lDdUDvOfByB2hVW0.@OM%{l/{cT'{w > Do you agree that |N| < |P(N)|? For finite sets, it's obvious that the size of N is < size of the P(N). For infinite sets, the question seems to me to be invalid to ask. It's exactly like the following word problem: If we built one machine to count to infinity which can count one number per second, and a second machine which can count at the speed 2^T numbers per second, where T is how long the machines have been running, which machine will finish first? That question is just flat out invalid to ask. There is no answer. But, in set theory, it seems the question is not seen as invalid to ask, so I don't understand set theory yet. And if I don't understand set theory, I can't answer your questions about set theory. > Until I master the language of set theory and learn the exact meaning > of all the ideas it's built on, I won't be able to even point to the > problem, let alone argue the issue here. > Then this discussion has concluded. Let me know if you think you find a > problem in the axioms. Well, it's not a problem with the axioms I'm looking for. It's just a rift between the universe and the axioms I'm trying to identify. It's most likely in the langauge used to define the axioms and not the axioms themselves. -- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/ === Subject: Re: Cantor's diagonal proof wrong? > Do you agree that |N| < |P(N)|? > For finite sets, it's obvious that the size of N is < size of the P(N). It's EXACTLY EQUALLY obvious for infinite sets, because THE PROOF that the size of S is < size of the P(S) FOR ALL SETS, period; it works for AN ARBITRARY set: IT DOESN'T MAKE ANY DIFFERENCE if the set is infinite or finite. > For infinite sets, the question seems to me to be invalid to ask. Well, it isn't. Infinite sets have powersets just like finite ones; in ZF, that's axiomatic: EVERY set has a powerset. IT DOESN'T MATTER whether it's finite or infinite. > It's exactly like the following word problem: If we built one machine to > count to infinity which can count one number per second, and a second > machine which can count at the speed 2^T numbers per second, where T is how > long the machines have been running, which machine will finish first? THAT question is invalid, yes, because it presumes that infinity is one SINGLE place. THAT assumption is invalid. Unless you axiomatize it. > That question is just flat out invalid to ask. Sure it is, but only in the context of some axioms that define infinity more intelligently. > There is no answer. How would YOU know?? > But, in set theory, it seems the question is not seen as invalid to ask, Sure it is. In set theory, WE KNOW that there is NO SUCH THING as just plain infinity -- there are a GREAT MANY DIFFERENT infinities -- so set theory makes it CLEAR that that question cannotbe asked. > so I don't understand set theory yet. So STFU then. Jeezus. > And if I don't understand set theory, I > can't answer your questions about set theory. You understood enough set theory to know that it was obvious that n < 2^n for finite n. Stop PLAYING dumb. > Well, it's not a problem with the axioms I'm looking for. It's just a rift > between the universe and the axioms I'm trying to identify. Stop being so idiotically hubristic. You don't know about the universe. What little we DO know about the universe is the little that FITS INTO the theoretical approximations we've thus far been able to construct (those are called SCIENCE). If you want to allege a flaw in the science then you have to come up with a prediction-made-by-the-theory that is falsified by some relevant observation. You are not personally capable of observing that there is only 1 size of infinity. So give up. > It's most likely in the langauge used to define the axioms > and not the axioms themselves. It is indeed true that the traditional definition of a first-order language has some finitistic constraints that may be implicated in theoretical difficulties with infinity. But you are not likely to convince anybody to flex on that. The problem with allowing infinitary strings in the language is that finite humans only have finite amounts of time to parse them. For practical purposes,only finite proofs CAN be relevant. Proofs have to be surveyable. Proof-predicates are PRIMITIVE recursive. === Subject: Re: Cantor's diagonal proof wrong? at 05:54 PM, curt@kcwc.com (Curt Welch) said: >Well, it's not a problem with the axioms I'm looking for. It's just a >rift between the universe and the axioms I'm trying to identify. You can't, because you will never know what the Universe is, and because Mathematics is not about the Universe, any more than Music is. -- 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: Cantor's diagonal proof wrong? >>Do you agree that |N| < |P(N)|? > For finite sets, it's obvious that the size of N is < size of the P(N). > For infinite sets, the question seems to me to be invalid to ask. > It's exactly like the following word problem: If we built one machine to > count to infinity which can count one number per second, and a second > machine which can count at the speed 2^T numbers per second, where T is how > long the machines have been running, which machine will finish first? Constructability is not a requirement for theorizing about power sets. The way you deal with infinite sets is to use a static definition. A set is infinite if and only if there exists an injective surjection of the the set to a proper subset of itself. We know the set of integers is infinite because the correspondence n <-> 2*n is just such an injective surjection of the integers onto the even integers. Bob Kolker === Subject: Re: Cantor's diagonal proof wrong? > Constructability is not a requirement for theorizing about power sets. That probably should've said ... infinite sets. Finite powersets ARE constructible. > The way you deal with infinite sets is to use a static definition. That's problematic until you invoke the axiom of choice. At least 5 different definitions are available. > A set is infinite if and only if there exists an injective surjection of the > the set to a proper subset of itself. 1) that's not the only available definition; 2) relying on ANYthing to exist in a first-order context is problematic: sets can Exist but still get LEFT OUT OF the model of this particular theory. ZFC proves that p(N) is bigger than N, BUT IT HAS COUNTABLE MODELS. exist is just too problematic, unless nothing else can work. === Subject: Re: Cantor's diagonal proof wrong? >> Do you agree that |N| < |P(N)|? > For finite sets, it's obvious that the size of N is < size of the P(N). N is not a finite set. N is the set of natural numbers. Cantor's proof that |X| < |P(X)| makes no mention of whether X is finite or infinite, nor does it need to. > For infinite sets, the question seems to me to be invalid to ask. Nonsense. The question being asked is whether you agree that 1) there is an injection f: X -> P(X), and 2) there is no surjection from X onto P(X). You may possibly misunderstand the proof, but there is no doubt about whether the question is meaningful. The question doesn't even mention whether X is finite or infinite. Notice that 1) means |X| <= |P(X)|, and 2) implies there is no bijection, and therefore equality does not hold. > It's exactly like the following word problem: If we built one machine to > count to infinity which can count one number per second, and a second > machine which can count at the speed 2^T numbers per second, where T is how > long the machines have been running, which machine will finish first? No, it's not even remotely like that problem. You didn't even mention anything about injections or surjections. > That question is just flat out invalid to ask. There is no answer. Agreed. Now, can we get back to the question I originally asked? > But, in set theory, it seems the question is not seen as invalid to ask, so > I don't understand set theory yet. And if I don't understand set theory, I > can't answer your questions about set theory. Then perhaps the explanation above will help. -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. === Subject: Re: Cantor's diagonal proof wrong? >> Do you agree that |N| < |P(N)|? >For finite sets, it's obvious that the size of N is < size of the P(N). >For infinite sets, the question seems to me to be invalid to ask. >It's exactly like the following word problem: If we built one machine to >count to infinity which can count one number per second, and a second >machine which can count at the speed 2^T numbers per second, where T is how >long the machines have been running, which machine will finish first? No, it is nothing like that. >That question is just flat out invalid to ask. There is no answer. No, there's nothing invalid about the question. The answer is that neither machine would ever finish. Ok, if the answer is required to be first machine or second machine then the question is invalid. But it's also totally irrelevant. >But, in set theory, it seems the question is not seen as invalid to ask, so >I don't understand set theory yet. And if I don't understand set theory, Yet although you don't understand set theory you're confident that mathematicians have been wrong about set theory for centuries. That includes me, everyone else here, and actual honest mathematical geniuses down through the years - you don't understand the topic but you know that we're _all_ wrong about it. Wow. >can't answer your questions about set theory. >> Until I master the language of set theory and learn the exact meaning >> of all the ideas it's built on, I won't be able to even point to the >> problem, let alone argue the issue here. >> Then this discussion has concluded. Let me know if you think you find a >> problem in the axioms. >Well, it's not a problem with the axioms I'm looking for. It's just a rift >between the universe and the axioms I'm trying to identify. Are you DEAF or what? The axioms have nothing to do with the universe! Nobody said they did. People have explained repeatedly that they don't. > It's most >likely in the langauge used to define the axioms and not the axioms >themselves. ************************ David C. Ullrich === Subject: Re: Cantor's diagonal proof wrong? %IW48mQf3K=Ci&gZ7]]aazx@]Y-nq!r5{yH/#,?@lDdUDvOfByB2hVW0.@OM%{l/{cT'{w > Are you DEAF or what? The axioms have nothing to do with the universe! > Nobody said they did. People have explained repeatedly that they > don't. In my universe, that's an absurd statement. That's why I've been deaf to it. But as I've posted on 4 or 5 posts now, I think I understand what's really going on now and why I live in a different universe from the world of math. One of you guys posted some URLs about the connection between math and the universe. That's one of the 20 or so posts I've saved an not yet had time to go back to. I'd like to see what people have said about that in the past so I do want to follow those URLs and see what I find. -- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/ === Subject: Re: Cantor's diagonal proof wrong? > In my universe, that's an absurd statement. That's why I've been deaf to > it. But as I've posted on 4 or 5 posts now, I think I understand what's > really going on now and why I live in a different universe from the world > of math. You have already admitted that you either can't or you won't do mathematics. So why do you post here? > One of you guys posted some URLs about the connection between math and the > universe. That's one of the 20 or so posts I've saved an not yet had time > to go back to. I'd like to see what people have said about that in the > past so I do want to follow those URLs and see what I find. Mathematics makes quantum theory possible. Quantum theory makes computers possible. Computers make it possible for you to post complete dreck in this newsgroup. Bob Kolker === Subject: Re: Cantor's diagonal proof wrong? !3KEIp?*w`|bL5qr,H)LFO6Q=qx~iH4DN;i;/yuIsqbLLCh/!U#X[S~(5eZ41to5f%E@'ELIi $t^ VcLWP@J5p^rst0+('>Er0=^1{]M9!p?&:z]|;&=NP3AhB!B_bi^]Pfkw >> One of you guys posted some URLs about the connection between math >> and the universe. That's one of the 20 or so posts I've saved an >> not yet had time to go back to. I'd like to see what people have >> said about that in the past so I do want to follow those URLs and >> see what I find. > Mathematics makes quantum theory possible. Quantum theory makes > computers possible. Computers make it possible for you to post > complete dreck in this newsgroup. Uh, quantum theory is most definitely not what makes computers possible. There have been computers built purely from mechanical components. And for current computers, quantum theory is more involved with what makes computers hard to build rather than possible. Most quantum effects up to now have been more a hindrance than a gain for building computers. There will probably come a time when the tables are turned, but it will take a few decades the way it looks right now. -- David Kastrup, Kriemhildstr. 15, 44793 Bochum === Subject: Re: Cantor's diagonal proof wrong? > Uh, quantum theory is most definitely not what makes computers > possible. I meant computers made of solid state devices. I should have been more precise. Without quantum theory we would not know enough about semiconducts to make small computer components out of then. There have been computers built purely from mechanical > components. And for current computers, quantum theory is more > involved with what makes computers hard to build rather than possible. The crew at Bell Labs who invented transistors were all quantum physicists as well as engineers. > Most quantum effects up to now have been more a hindrance than a gain > for building computers. There will probably come a time when the > tables are turned, but it will take a few decades the way it looks > right now. Write us when it happens, will you? There's a good fellow. Bob Kolker === Subject: Re: Cantor's diagonal proof wrong? > If I take the time to master the language and logic of set theory, what I > expect to find is that they use a language that makes it trivial to talk > about an infinite set as if it existed, and as if it worked exactly like a > finite set. You need not invest very much time in this study. It's very simple. Let N represent the set of Natural numbers, that is, the usual counting numbers one learns about in grade school: {0, 1, 2, 3, 4, 5, 6, ...} That is an infinite set. It exists. Certainly not in the physical world, but in the world of concepts. It's an idea, the thought of all the counting numbers tossed into a box and considered as a whole. What do you find difficult to understand about that? Now when you say that infinite sets work exactly like finite sets, that is manifestly false. For example, an infinite set may be in 1-1 correspondence with a proper subset of itself; while a finite set can not. In fact that property is generally taken as the definition of an infinite set. === Subject: Re: Cantor's diagonal proof wrong? > Now when you say that infinite sets work exactly like finite sets, > that is manifestly false. For example, an infinite set may be in 1-1 > correspondence with a proper subset of itself; while a finite set can > not. In fact that property is generally taken as the definition of an > infinite set. Following an abstract, counter-intuitive and rigorous line of reasoning requires focus, discipline and concentrartion. Curtis does not have these. He gets diverted by his foolish non-logical fancies. The first thing one must give up to do hard math, is common sense. Common sense is a snare and a delusion. Bob Kolker === Subject: Re: Cantor's diagonal proof wrong? > I agree that if the diagonal argument has a problem, the powerset argument > is likely to have a problem to. But where is that problem? Most likely, > it lies outside of the argument. That is, in the basic assumptions set > theory are built on. Which means that, as is well believed, axiomatic set > theory is consistent given the starting axioms, and the starting > assumptions about what sets are. Since set theory has been purged of its original anomalies there has been no sign of inconsistency. This is not a proof, of course, but an observation. I don't know how it is possible to prove say the ZFC axioms are consistent. Maybe someone else does. Bob Kolker === Subject: Re: Cantor's diagonal proof wrong? |Since set theory has been purged of its original anomalies there has |been no sign of inconsistency. This is not a proof, of course, but an |observation. I don't know how it is possible to prove say the ZFC axioms |are consistent. Maybe someone else does. The problem is that in order to prove the consistency of ZFC, one needs axioms that are reasonably strong. There is, for instance, a proof of the consistency of ZFC in ZFC+there exists a measurable cardinal. But if one has any doubts about the consistency of ZFC, one is unlikely to find this proof adds anything to one's conviction that it is consistent. That is, of course, a somewhat subjective matter. If someone didn't know very much set theory, learning some about the notion of rank and seeing it proved that the sets below some suitable, and high, rank would form a model of ZFC (where a measurable cardinal is an example of a high enough rank of a suitable kind) *might* make them more comfortable with accepting the consistency of ZFC. By Goedel's incompleteness theorem, one needs of course *some* axiom that isn't a theorem of ZFC to prove the consistency of ZFC. That doesn't necessarily mean that the axiom is any less plausible than the axioms of ZFC, which leaves open a tiny opening for the hope that someday a proof of the consistency of ZFC, convincing to someone having some doubt, might be found. There's a famous proof by Gentzen of the consistency of PA, using induction up to an ordinal epsilon_0. I don't know whether anyone who seriously doubts the _truth_ of the axioms of PA has been persuaded that they are at least _consistent_ by this proof. Maybe someone has, though. Ordinal analyses having some kind of family resemblance to that proof have been made of various theories in between PA and PA_2 (which is a formal theory of natural numbers and sets of natural numbers). That leaves a long road to a happy ordinal analysis of ZFC. I think of it as an interesting sort of quest. Maybe there is no nice analysis of this kind (where is the guarantee that there is?) but there's no guarantee that there isn't. Keith Ramsay === Subject: Re: Cantor's diagonal proof wrong? : But, I can specify one special mapping function that works like this. Fill : the first row with any combination of 1's and 0's you like. Then, fill : every following row, with a copy of the row above it, with the diagonal : digit inverted. So your list possibly looks like 0000000000000000000000000000.... 0100000000000000000000000000.... 0110000000000000000000000000.... 0111000000000000000000000000.... 0111100000000000000000000000.... ............... : Now, what I can show about your diagonal value, is that every diagonal you : construct is in fact in the table, in row N+1. No, it is not. I am only going to construct a single diagonal value, which will be 10000000000.......... which is obviously nowhere in your list. Once again you have shown you do not understand what you are talking about. I can try your argument again with a different 'seed'. 1101101011010101010101010101.... 1001101011010101010101010101.... 1011101011010101010101010101.... 1010101011010101010101010101.... 1010001011010101010101010101.... ............... Again I am going to construct a single diagonal value which will be 01011........... which is obviously nowhere in the list. : So your argument that it is not in the table, is no stronger than my : argument that it is in the table. Given that your argument is obviously wrong and that I can provide a simply counter example showing it is wrong, I would say that my argument is a lot stronger than yours. Stephen === Subject: Re: Cantor's diagonal proof wrong? %IW48mQf3K=Ci&gZ7]]aazx@]Y-nq!r5{yH/#,?@lDdUDvOfByB2hVW0.@OM%{l/{cT'{w > : But, I can specify one special mapping function that works like this. > : Fill the first row with any combination of 1's and 0's you like. Then, > : fill every following row, with a copy of the row above it, with the > : diagonal digit inverted. > So your list possibly looks like > 0000000000000000000000000000.... > 0100000000000000000000000000.... > 0110000000000000000000000000.... > 0111000000000000000000000000.... > 0111100000000000000000000000.... > ............... > : Now, what I can show about your diagonal value, is that every diagonal > : you construct is in fact in the table, in row N+1. > No, it is not. I am only going to construct a single diagonal value, > which will be > 10000000000.......... > which is obviously nowhere in your list. > Once again you have shown you do not understand what you are talking > about. I shake my head in disbelief that you would actually write that. Well, it's been fun, but you are just not ready to understand what I'm talking about. Maybe in 10 years. I'll go back to my regular life and stop bothering the group. I learned quite I bit by my visit here. I'm sorry nobody else was able to learn anything useful. -- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/ === Subject: Re: Cantor's diagonal proof wrong? >> : But, I can specify one special mapping function that works like this. >> : Fill the first row with any combination of 1's and 0's you like. Then, >> : fill every following row, with a copy of the row above it, with the >> : diagonal digit inverted. >> So your list possibly looks like >> 0000000000000000000000000000.... >> 0100000000000000000000000000.... >> 0110000000000000000000000000.... >> 0111000000000000000000000000.... >> 0111100000000000000000000000.... >> ............... >> : Now, what I can show about your diagonal value, is that every diagonal >> : you construct is in fact in the table, in row N+1. >> No, it is not. I am only going to construct a single diagonal value, >> which will be >> 10000000000.......... >> which is obviously nowhere in your list. >> Once again you have shown you do not understand what you are talking >> about. >I shake my head in disbelief that you would actually write that. Fine. But you're ignoring the simple _proof_ he gave that what you say happens simply doesn't happen. (Which just by coincidence is exactly the same as the explanation I just gave before seeing his post.) >Well, it's been fun, but you are just not ready to understand what I'm >talking about. Maybe in 10 years. I'll go back to my regular life and >stop bothering the group. I learned quite I bit by my visit here. I'm >sorry nobody else was able to learn anything useful. That happens a lot around here. ************************ David C. Ullrich === Subject: Re: Cantor's diagonal proof wrong? %IW48mQf3K=Ci&gZ7]]aazx@]Y-nq!r5{yH/#,?@lDdUDvOfByB2hVW0.@OM%{l/{cT'{w >> : But, I can specify one special mapping function that works like >> : this. Fill the first row with any combination of 1's and 0's you >> : like. Then, fill every following row, with a copy of the row above >> : it, with the diagonal digit inverted. >> So your list possibly looks like >> 0000000000000000000000000000.... >> 0100000000000000000000000000.... >> 0110000000000000000000000000.... >> 0111000000000000000000000000.... >> 0111100000000000000000000000.... >> ............... >> : Now, what I can show about your diagonal value, is that every >> : diagonal you construct is in fact in the table, in row N+1. >> No, it is not. I am only going to construct a single diagonal value, >> which will be >> 10000000000.......... >> which is obviously nowhere in your list. >> Once again you have shown you do not understand what you are talking >> about. >I shake my head in disbelief that you would actually write that. > Fine. But you're ignoring the simple _proof_ he gave that what you > say happens simply doesn't happen. (Which just by coincidence is > exactly the same as the explanation I just gave before seeing > his post.) Yeah, it's hard to keep up with all the posts and not get behind in the comments. It's kinda like trying to have a conversation with 10 people at once. :) The point of my shake my head comment, is that his counter argument missed the point of what I was trying to show. I was arguing apples and he started to talk about oranges. I was NOT trying to show a one to one mapping of the natrual numbers to the reals, or that there was a one to one mapping from the natural numbers to all strings of 1s and 0s. I was only trying to demonstrate how (in my universe where everything is a procedure) that the diagonal argument is not a valid proof - that it proves nothing one way or the other about the mapping. And both of you misunderstood what table I was talking about - but I'll clear that up in another post in a minute. -- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/ === Subject: Re: Cantor's diagonal proof wrong? >[...] I was only trying to demonstrate how (in my >universe where everything is a procedure) that the diagonal argument is not >a valid proof - that it proves nothing one way or the other about the >mapping. You should stop stating that the proof is invalid, then. Invalid and Invalid in my universe are very different things. In _my_ universe it's invalid because everything is a gazebo. But I can't imagine why anyone would be interested in the way things work in my universe. >And both of you misunderstood what table I was talking about - but I'll >clear that up in another post in a minute. ************************ David C. Ullrich === Subject: Re: Cantor's diagonal proof wrong? :>[...] I was only trying to demonstrate how (in my :>universe where everything is a procedure) that the diagonal argument is not :>a valid proof - that it proves nothing one way or the other about the :>mapping. : You should stop stating that the proof is invalid, then. Invalid : and Invalid in my universe are very different things. : In _my_ universe it's invalid because everything is a gazebo. But : I can't imagine why anyone would be interested in the way things : work in my universe. And in my universe AI is invalid because only real things can be intelligent and anything that is artificial cannot be real. :) Stephen === Subject: Re: Cantor's diagonal proof wrong? > I was NOT trying to show a one to one mapping of the natrual numbers to the > reals, or that there was a one to one mapping from the natural numbers to > all strings of 1s and 0s. I was only trying to demonstrate how (in my > universe where everything is a procedure) that the diagonal argument is not > a valid proof - that it proves nothing one way or the other about the > mapping. Your rules are too restrictive. Mathamticians will not adopt them. Reasoning (I am being charitable here) as you do would have never lead us to the theory of real variables, to calculus or differential equations. Western civilization runs on the output of differential equations. Bob Kolker === Subject: Re: Cantor's diagonal proof wrong? %IW48mQf3K=Ci&gZ7]]aazx@]Y-nq!r5{yH/#,?@lDdUDvOfByB2hVW0.@OM%{l/{cT'{w > I was NOT trying to show a one to one mapping of the natrual numbers to > the reals, or that there was a one to one mapping from the natural > numbers to all strings of 1s and 0s. I was only trying to demonstrate > how (in my universe where everything is a procedure) that the diagonal > argument is not a valid proof - that it proves nothing one way or the > other about the mapping. > Your rules are too restrictive. Mathamticians will not adopt them. > Reasoning (I am being charitable here) as you do would have never lead > us to the theory of real variables, to calculus or differential > equations. Western civilization runs on the output of differential > equations. Ok, I think I can explain this better now. All that can be done without violating the rules of my universe. It's possible to talk about the behavior of an infinite procedure without having it run to completion. And all the above parts of mathematics you mention does just that. It talks about the behavior of infinite procedures (like the limit of a series) without making any assumptions that require the procedure to run to completion. This is, you can tell where it's headed, without it having to get there. However, arguments like Cantor's diagonal proof is based on the assumption that all the work completes - that the set fully exists. It's a subtle, but important difference. To see how it is different, you have to step out universe, it's trivial to see how calculus doesn't violate the rules, but equally valid, and you can walk over the my yellow foul line without even knowing it. To see the line I see, you have to accept as an axiom, that all creation is done by a procedure, and it always takes time. If my universe is in fact the correct and best description for our universe, what this means is that any work in math that is outside of my yellow foul line is totally useless to us as a tool for helping us understand our universe. All the work done in math outside of my yellow foul line is only there as a form of entertainment for the people that choose to visit there. It has the same value to us as science fiction stories do - and nothing more - and perhaps even less - because it would be science fiction which can never be true. What is useful to me, is to understand how to clearly paint this yellow foul line on various parts of mathematics. So, if you start with my theory of creation, we can talk about where the yellow foul line is, and what's inside the line, and what's outside the line. Of everything I know about math (clearly not much), the only things I've seen that seem to cross the line are this work with infinite sets, and G.9adel's incompleteness theorem. And G.9adel's work is too complex, and too related to all this logic calculus stuff for me to know for sure what's going on there. But it smells the same because it's based on a proof by contradiction trying to debate a type of existence that seems to make use of the infinite set of reals in a NOT FOR ALL type of argument. I suspect there is actually a large boddy of work over my yellow line, but I suspect it all ties in to the work in the same area that Cantor and G.9adel was working in. Oh, and I've seen evidence of it in computer science but once again, it just sems to be a computer science rewerite of the same ideas that these other guys were working with first and seems to have no real effect on what people are actually able to do with computers. -- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/ === Subject: Re: Cantor's diagonal proof wrong? <30ctcpF2uencaU3@uni-berlin.de> >It talks about the behavior of infinite procedures You keep making that claim; it's false. >and it always takes time. What is time? If you look closely at it you will find that the only way to give a usable answer is to employ Mathematics. >What is useful to me, is to understand how to clearly paint this >yellow foul line on various parts of mathematics. No. First you have to establish that your universe is correct and the best description. If, as seems clear, it is not, then there is no foul line to draw. -- 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: Cantor's diagonal proof wrong? !3KEIp?*w`|bL5qr,H)LFO6Q=qx~iH4DN;i;/yuIsqbLLCh/!U#X[S~(5eZ41to5f%E@'ELIi $t^ VcLWP@J5p^rst0+('>Er0=^1{]M9!p?&:z]|;&=NP3AhB!B_bi^]Pfkw > Ok, I think I can explain this better now. > All that can be done without violating the rules of my universe. > It's possible to talk about the behavior of an infinite procedure > without having it run to completion. And all the above parts of > mathematics you mention does just that. It talks about the behavior > of infinite procedures (like the limit of a series) without making > any assumptions that require the procedure to run to completion. > This is, you can tell where it's headed, without it having to get > there. This is shortsighted. > However, arguments like Cantor's diagonal proof is based on the > assumption that all the work completes - that the set fully exists. > It's a subtle, but important difference. Your mistake is that you are somehow connotating a set with a bunch or collection of items, and want to associate some characteristics of bunches or collections with it. This does not cut it, especially for infinite sets. A set is an entity which has one purpose: provide a unique question is a certain x a member of this set?. It is, so to say, an oracle that will always give the same answer when asked the same question. To know what the answers will be, you need to either ask the question explicitly (and you can't do that for every element of an infinite set), or know some _finite_ set of rules that you know characterize the answers completely. Now the set of real numbers obeys some rules that have the curious property that we as humans can't even ever state the question for the majority of specific members: we can only identify computable reals, and the computable reals have the same cardinality as the integers. But that does not change that once we lump a lot of the nonidentifiable reals together, we can again make statements about the resulting continuity. -- David Kastrup, Kriemhildstr. 15, 44793 Bochum === Subject: Re: Cantor's diagonal proof wrong? > However, arguments like Cantor's diagonal proof is based on the assumption > that all the work completes - that the set fully exists. Nonsense. Cantor's proof requires a finite number of lines. Given any countable list of infinite decimal expansions of numbers in the interval [0,1] it is always possible to construct an infinite decimal expasnsion not on the list. Take the n-th digit of the n-th item on the list and add 1 to it modulo 10. There. The procedure is complete defined, and in a finite number of words, too!. You will notice that the number constructed differs from the n-th item in the list in the n-th place for all n, so it cannot be in the list. Eight lines is all it took. It's a subtle, > but important difference. To see how it is different, you have to step out > of the normal universe of math and step into my universe. Why would anyone want to go into your universe? It produces no benefits to do so, and in fact restricts useful mathematics so it is a loosing proposition. > universe, it's trivial to see how calculus doesn't violate the rules, but > equally valid, and you can walk over the my yellow foul line without even > knowing it. To see the line I see, you have to accept as an axiom, that > all creation is done by a procedure, and it always takes time. Nonsense. I have just demonstrated that this is not the case. You are flat our wrong. I produced a finitary procedure (definable in a finite number of words) to produce a number not on a countable list. > If my universe is in fact the correct Well it isn't. The universe of standard mathematics produces emprically corroberated physical theories. Can Hermitean operators on Hilbert Spaces be defined in your universe of discourse. If the answer is no, say goodbye to quantum theory.. > and best description for our > universe, what this means is that any work in math that is outside of my > yellow foul line is totally useless to us as a tool for helping us > understand our universe. Egregiously wrong! Standard mathemetics is necessary to formulation of physica theories that work. In your universe of discourse you could not prove that solutions to Hamiltonians on symplectic manifolds exist. > All the work done in math outside of my yellow > foul line is only there as a form of entertainment for the people that > choose to visit there. It has the same value to us as science fiction > stories do - and nothing more - and perhaps even less - because it would be > science fiction which can never be true. Virtually all of physics requires mathematics that falls outside of your restrictions. > What is useful to me, is to understand how to clearly paint this yellow > foul line on various parts of mathematics. So, if you start with my theory > of creation, we can talk about where the yellow foul line is, and what's > inside the line, and what's outside the line. Starting with your theory (which is not well stated or defined, by the way) we would end up with no useful physics. In particular we would have no quantum theory. > Of everything I know about math (clearly not much), the only things I've > seen that seem to cross the line are this work with infinite sets, and > G.9adel's incompleteness theorem. And G.9adel's work is too complex, and too > related to all this logic calculus stuff for me to know for sure what's > going on there. But it smells the same because it's based on a proof by > contradiction trying to debate a type of existence that seems to make use > of the infinite set of reals in a NOT FOR ALL type of argument. The reasoning used in the theory of transfinite numbers is identical to the reasoning used in calculus. The same rules of logic are invoked. Using your rules, one could not sum and infinite series. Quickly now, using your rules what is SUM (n >= 1) [1/2^n]. Bob Kolker === Subject: Re: Cantor's diagonal proof wrong? >> : But, I can specify one special mapping function that works like this. >> : Fill the first row with any combination of 1's and 0's you like. Then, >> : fill every following row, with a copy of the row above it, with the >> : diagonal digit inverted. >> So your list possibly looks like >> 0000000000000000000000000000.... >> 0100000000000000000000000000.... >> 0110000000000000000000000000.... >> 0111000000000000000000000000.... >> 0111100000000000000000000000.... >> ............... >> : Now, what I can show about your diagonal value, is that every diagonal >> : you construct is in fact in the table, in row N+1. But there is only one diagonal value, not every. This has been pointed out to you several times before: one list is given and then exactly one value is then shown to be not on that list. [cut] >I shake my head in disbelief that you would actually write that. > Fine. But you're ignoring the simple _proof_ he gave that what you > say happens simply doesn't happen. (Which just by coincidence is > exactly the same as the explanation I just gave before seeing > his post.) I think Curt wants the following list: 0000000000000000000000000000.... 100000000000000000000000000.... 110000000000000000000000000.... 111000000000000000000000000.... 111100000000000000000000000.... ............... The diagonal value is then 11111... Sure enough, it is not in the above list. Curt wants the diagonal value(s) to be 10000..., 110000..., 111000..., etc. Of course, the list contains those values since that was the way the list was contructed. But the diagonal value 11111... given by Cantor's diagonal argument is not one of those values, and in fact does not appear in the above list. -- Bill Hale === Subject: Re: Cantor's diagonal proof wrong? %IW48mQf3K=Ci&gZ7]]aazx@]Y-nq!r5{yH/#,?@lDdUDvOfByB2hVW0.@OM%{l/{cT'{w > I think Curt wants the following list: > 0000000000000000000000000000.... > 100000000000000000000000000.... > 110000000000000000000000000.... > 111000000000000000000000000.... > 111100000000000000000000000.... > ............... > The diagonal value is then 11111... to. > Sure enough, it is not in the above list. > Curt wants the diagonal value(s) to be 10000..., 110000..., 111000..., > etc. Of course, the list contains those values since that was the > way the list was contructed. But the diagonal value 11111... > given by Cantor's diagonal argument is not one of those values, > and in fact does not appear in the above list. Right. The difference is in the foundation of what I believe vs the foundation of how math is defined. I don't want the diagonal valuds to be 100.. 1100.. I want the diagonal values to be something under construction that can never finish, so the sequence is: 1 11 111 1111 . . . And the value 111... never gets created in full because the infinite processes of construction can't complete in my universe. And that's the difference between how things work in my universe and in the universe of math. -- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/ === Subject: Re: Cantor's diagonal proof wrong? > And the value 111... never gets created in full because the infinite > processes of construction can't complete in my universe. And that's the > difference between how things work in my universe and in the universe of > math. You have just stated that you cannot cope with mathematics. That makes you less than human. Primitive savages cannot get past the number three. You are are not much better. Bob Kolker === Subject: Re: Cantor's diagonal proof wrong? %IW48mQf3K=Ci&gZ7]]aazx@]Y-nq!r5{yH/#,?@lDdUDvOfByB2hVW0.@OM%{l/{cT'{w > And the value 111... never gets created in full because the infinite > processes of construction can't complete in my universe. And that's > the difference between how things work in my universe and in the > universe of math. > You have just stated that you cannot cope with mathematics. You are funny. You don't seem to have grasped more than about 5% of what I've written. I understand math just fine. What I came here confused about was why my understanding of the universe didn't jive with math. If you like, I'll go back to only talking about the universe of math in this group. What I stated above is that now (with the help of this group) I know how to go back and forth between the two universes without tripping. > That makes > you less than human. Primitive savages cannot get past the number three. > You are are not much better. It's well known that rabbits can count to infinity: one two three four hrair. :) -- Curt Welch http://CurtWelch.Com/ curt@kcwc.com http://NewsReader.Com/ === Subject: Re: Cantor's diagonal proof wrong? : I think Curt wants the following list: : 0000000000000000000000000000.... : 100000000000000000000000000.... : 110000000000000000000000000.... : 111000000000000000000000000.... : 111100000000000000000000000.... : ............... : The diagonal value is then 11111... : Sure enough, it is not in the above list. : Curt wants the diagonal value(s) to be 10000..., 110000..., 111000..., : etc. Of course, the list contains those values since that was the : way the list was contructed. But the diagonal value 11111... : given by Cantor's diagonal argument is not one of those values, : and in fact does not appear in the above list. : -- Bill Hale Another way to try to make it crystal clear to the doubters that constructing the list in this fashion does not help is that there is more than one way to define the diagonal. The basic idea of the proof is that given a list I can describe an element not on the list. The exact details of how I describe that element are not important. So in this example we can consider pairs, replacing 11 with 00 and any other pair with 01. So given 000000000000000000000000000.... 100000000000000000000000000.... 110000000000000000000000000.... 111000000000000000000000000.... 111100000000000000000000000.... we look at 0000000000000000000000000000.... ^^ 100000000000000000000000000.... ^^ 110000000000000000000000000.... ^^ 111000000000000000000000000.... ^^ 111100000000000000000000000.... ^^ and the diagonal we end up with is 0101010101010101.... which is clearly not on the list. Stephen === Subject: Re: Cantor's diagonal proof wrong? : Another way to try to make it crystal clear to the doubters that : constructing the list in this fashion does not help is that there : is more than one way to define the diagonal. The basic idea of the proof : is that given a list I can describe an element not on the list. : The exact details of how I describe that element are not important. : So in this example we can consider pairs, replacing 11 with 00 ^^^^^^^^^^^^^^^^^^^^ : and any other pair with 01. That should be, replacing 01 with 00 and any other pair with 01. : So given : 000000000000000000000000000.... : 100000000000000000000000000.... : 110000000000000000000000000.... : 111000000000000000000000000.... : 111100000000000000000000000.... : we look at : 0000000000000000000000000000.... : ^^ : 100000000000000000000000000.... : ^^ : 110000000000000000000000000.... : ^^ : 111000000000000000000000000.... : ^^ : 111100000000000000000000000.... : ^^ : : and the diagonal we end up with is : 0101010101010101.... : which is clearly not on the list. : Stephen === Subject: Re: Cantor's diagonal proof wrong? : I think Curt wants the following list: : 0000000000000000000000000000.... : 100000000000000000000000000.... : 110000000000000000000000000.... : 111000000000000000000000000.... : 111100000000000000000000000.... : ............... : The diagonal value is then 11111... You are probably closer to what he had in mind than I was, but as you show it still makes no difference. He also said the first row could be anything. 10001110101010010101100.... 00001110101010010101100.... 01001110101010010101100.... 01101110101010010101100.... 01111110101010010101100.... 01110110101010010101100.... ...... The diagonal value is 011100... and this value is also not on the list. Of course now the argument becomes the same as the argument that claims that the list .3, .33, .333, ... must contain .33333....... Stephen === Subject: Re: Cantor's diagonal proof wrong? > Well, it's been fun, but you are just not ready to understand what I'm > talking about. Maybe in 10 years. I'll go back to my regular life and > stop bothering the group. I learned quite I bit by my visit here. I'm > sorry nobody else was able to learn anything useful. Mostly because you had nothing useful to say. Bob Kolker === Subject: Re: Cantor's diagonal proof wrong? > Now, you might notice I've gone back to my starting position that the logic > used in Cantor's diagonal argument is just flat out invalid. No it isn't. Your understanding is faulty. It is perfectly valid. It is claimed a countable list of decismal expansion for all real numbers is countable. That list contains all the decimal expansions possible. But then you exhibit an expansion which is not on the list. Contradiction! The assumption that there is a countable list leads to a contradiction therefore there is no such list. The set of real numbers is not countable (i.e. capable of being mapped one to one onto the integers). Bob Kolker === Subject: Re: SR consistency is crap. > Reliance on the concept of mathematical consistency is nonsense. > Consistency does not prove empirical truth. However mathematical > inconsistency is absolute proof of nonsense and balderdash. > We know SR is mathematically consistent being an excercise in the > algebra of Lorentz-Poincare transforms. > I also asked you to produce a single experiment that has ever falsified > a prediction of SR. Please only vetted reproducable experiments need > apply. Can you produce such an experiment or not? If you can, then do > and if not, shut the up. > Bob Kolker The planetary system is a on going experiment for millions of years and quite repeatable(!) that falsifies SR. Speed of gravity is (almost) infinite. If it were not, you would not be around. Now, the burden of proof is on you to prove vg = c. If you cannot, you just shut up. You have fooled people to try to setup experiments to falsify a mathematical theory where nature itsself provides all the evidence to falsify it a priori. Mike === Subject: Re: SR consistency is crap. > The planetary system is a on going experiment for millions of years > and quite repeatable(!) that falsifies SR. Speed of gravity is > (almost) infinite. Cite data please! Planetary systems work quite well without assuming infinite gravity wave propagation. === Subject: Re: SR consistency is crap. > The planetary system is a on going experiment for millions of years > and quite repeatable(!) that falsifies SR. Speed of gravity is > (almost) infinite. > Cite data please! Planetary systems work quite well without > assuming infinite gravity wave propagation. The copy & paste king who never presented any data now calls for data. The answer is in your high school physics book stupid. Mike === Subject: Re: SR consistency is crap. >> The planetary system is a on going experiment for millions of years >> and quite repeatable(!) that falsifies SR. Speed of gravity is >> (almost) infinite. >> Cite data please! Planetary systems work quite well without >> assuming infinite gravity wave propagation. >The copy & paste king who never presented any data now calls for data. >The answer is in your high school physics book stupid. That must have been one hell of a high school. My high school had three years of physics and the book we used was Halliday and Resnick. I don't believe that the tools we used were advanced enough to show that planetary systems do or do not require infinite gravity wave propagation. I await, with interest, your evidence to the contrary. Alan -- Defendit numerus === Subject: Re: SR consistency is crap. > The planetary system is a on going experiment for millions of years >> and quite repeatable(!) that falsifies SR. Speed of gravity is >> (almost) infinite. > Cite data please! Planetary systems work quite well without >> assuming infinite gravity wave propagation. >The copy & paste king who never presented any data now calls for data. >The answer is in your high school physics book stupid. > That must have been one hell of a high school. My high school had > three years of physics and the book we used was Halliday and Resnick. > I don't believe that the tools we used were advanced enough to show > that planetary systems do or do not require infinite gravity wave > propagation. > I await, with interest, your evidence to the contrary. > Alan If you teachers did not tell you about action_at_a_distance and the fact the gravitational potential function is time independent then you were deprived of fundational knoweledge, a common situation in all public schools. But there is enough in the book you mention to answer the question yourself. Just assume a cirnular orbit of the earth around the sun and that the changes in orbital speed are directed towards the center of forces with a delay equal to the spped of light propagation. You will soos find out that there is a Torquw which will kick the earth out of its orbit. A simple calculation Newton did almost 300 years ago to conclude that gravitation must be action_at_a_distance. Mike === Subject: Re: SR consistency is crap. > The planetary system is a on going experiment for millions of years >> and quite repeatable(!) that falsifies SR. Speed of gravity is >> (almost) infinite. > Cite data please! Planetary systems work quite well without >> assuming infinite gravity wave propagation. >The copy & paste king who never presented any data now calls for data. >The answer is in your high school physics book stupid. > That must have been one hell of a high school. My high school had > three years of physics and the book we used was Halliday and Resnick. > I don't believe that the tools we used were advanced enough to show > that planetary systems do or do not require infinite gravity wave > propagation. > I await, with interest, your evidence to the contrary. > Alan > If you teachers did not tell you about action_at_a_distance and the > fact the gravitational potential function is time independent then you > were deprived of fundational knoweledge, a common situation in all > public schools. > But there is enough in the book you mention to answer the question > yourself. Just assume a cirnular orbit of the earth around the sun and > that the changes in orbital speed are directed towards the center of > forces with a delay equal to the spped of light propagation. You will > soos find out that there is a Torquw which will kick the earth out of > its orbit. > A simple calculation Newton did almost 300 years ago to conclude that > gravitation must be action_at_a_distance. > Mike Mike have you studied GR? My books discuss the Newtonian limit of GR and the delay effect is shown as well as the other effects. GR acts as if in the limiting case it were action at a distance. Newton didn't like then, and most people who study GR find it to be a general improvement to remove action at a distance. === Subject: Re: SR consistency is crap. >> A simple calculation Newton did almost 300 years ago to conclude that >> gravitation must be action_at_a_distance. >> Mike >Mike have you studied GR? My books discuss the Newtonian limit of GR >and the delay effect is shown as well as the other effects. GR acts >as if in the limiting case it were action at a distance. Newton >didn't like then, and most people who study GR find it to be a general >improvement to remove action at a distance. Newton assumed the gravitational force between objects is purely central. If it is purely central, the force must propagate danged fast or an observable non-conservation of angular momentum would be exhibited in the Earth's orbit. I think the current numbers put it at around 10^10 c. As I recall reading, Newton understood this, and he didn't like the idea of an infinitely fast response, but he didn't have a better number to put in. So we got action at a distance. But for slower propagation speeds, the principle of relativity requires non-central forces, as in magnetism. And the analog in gravity. If the field has a finite propagation speed and the principle of relativity is true, it's impossible to imagine even a fictional force with finite propagation speed that doesn't have a magnetic analog, because that would create a contradiction. To see that, imagine a stationary electric charge S and a moving charge M. The force on M is directed at the instantaneous position of S. If you boost the system so S is moving and M is still, the force on M is still directed to the instantanous position of S (principle of relativity) even though it sees the electric field of S from some time d/c in the past. This is not a slow-speed limit. If to the instanteneous locations of the other, so energy is lost. But if energy is conserved, it must have been radiated away in the field. Those are rather stringent and universal theoretical requirements. And that argument doesn't bring in special or general relativity, except to get the details right. -- Is that plutonium on your gums? Shut up and kiss me! -- Marge and Homer Simpson === Subject: Re: SR consistency is crap. >> A simple calculation Newton did almost 300 years ago to conclude that > gravitation must be action_at_a_distance. Newtonian gravitation is empirically incorrect. Google Bob Kolker === Subject: Re: SR consistency is crap. > If you teachers did not tell you about action_at_a_distance and the > fact the gravitational potential function is time independent then you > were deprived of fundational knoweledge, a common situation in all > public schools. > But there is enough in the book you mention to answer the question > yourself. Just assume a cirnular orbit of the earth around the sun and > that the changes in orbital speed are directed towards the center of > forces with a delay equal to the spped of light propagation. You will > soos find out that there is a Torquw which will kick the earth out of > its orbit. > A simple calculation Newton did almost 300 years ago to conclude that > gravitation must be action_at_a_distance. > Mike The idea of speed of gravity doesn't come up in secondary school, as the gravitational field is more or less static. Gravity waves is not a concept at that level historically. === Subject: Re: SR consistency is crap. >The planetary system is a on going experiment for millions of years >and quite repeatable(!) that falsifies SR. Speed of gravity is >(almost) infinite. >> Cite data please! Planetary systems work quite well without >> assuming infinite gravity wave propagation. > The copy & paste king who never presented any data now calls for data. > The answer is in your high school physics book stupid. > Mike Perhaps that part of Mike's problem, thinking that high school physics books address gravity wave propagation. Mine was PSSC Physics, btw. === Subject: Re: SR consistency is crap. > The planetary system is a on going experiment for millions of years > and quite repeatable(!) that falsifies SR. Speed of gravity is > (almost) infinite. If it were not, you would not be around. Kopkein finds it otherwise. Bob Kolker === Subject: Re: SR consistency is crap. > The planetary system is a on going experiment for millions of years > and quite repeatable(!) that falsifies SR. Speed of gravity is > (almost) infinite. If it were not, you would not be around. > Kopkein finds it otherwise. > Bob Kolker Shame on you: http://arxiv.org/abs/astro-ph/0304006 http://arxiv.org/abs/astro-ph/0303346 Why don't you take a break from these ng's. You post crap. It's Kopeikin by the way. 'Kopkein' is what you think you have heard like the other stuff you post here. Mike === Subject: Re: SR consistency is crap. > Shame on you: > http://arxiv.org/abs/astro-ph/0304006 > http://arxiv.org/abs/astro-ph/0303346 > Why don't you take a break from these ng's. You post crap. It's > Kopeikin by the way. 'Kopkein' is what you think you have heard like > the other stuff you post here. > Mike Could mike be trying to insinuate that the above reference say that the speed of gravitational wave propagation is *not* the same as the speed of light? If so shame on Mike! === Subject: Re: SR consistency is crap. > Shame on you: > http://arxiv.org/abs/astro-ph/0304006 > http://arxiv.org/abs/astro-ph/0303346 > Why don't you take a break from these ng's. You post crap. It's > Kopeikin by the way. 'Kopkein' is what you think you have heard like > the other stuff you post here. > Mike > Could mike be trying to insinuate that the above reference say that the > speed of gravitational wave propagation is *not* the same as the speed of > light? If so shame on Mike! These papers contain rebutals to Kopeikin's claims and were given because of the reference made to him. Obviously, you missed the point. The papers say Kopeikin's clalculations were wrong. They do not contain an experiment that proves the speed of gravity equals the speed of light. They were presented because Kolker called on Kopeikin (since he has no other calls to make). Question: do you know how to have an intelligent conversation? Mike === Subject: Re: SR consistency is crap. >> Could mike be trying insinuate that the above reference say that the >> speed of gravitational wave propagation is *not* the same as the speed of >> light? If so shame on Mike! > These papers contain rebutals to Kopeikin's claims and were given > because of the reference made to him. Obviously, you missed the point. I know all about Kopeikin's paper and the counter arguments. Nobody is claiming that the speed of gravity wave propagation is any different than the speed of light. I repeat--Are you insinuating that the speed of gravitational wave propagation is *not* the same as the speed of Light? === Subject: Re: SR consistency is crap. >> Could mike be trying insinuate that the above reference say that the >> speed of gravitational wave propagation is *not* the same as the speed of >> light? If so shame on Mike! > These papers contain rebutals to Kopeikin's claims and were given > because of the reference made to him. Obviously, you missed the point. > I know all about Kopeikin's paper and the counter arguments. Nobody > is claiming that the speed of gravity wave propagation is any different > than the speed of light. I repeat--Are you insinuating that the speed of > gravitational wave propagation is *not* the same as the speed of Light? How stupid of you! This is not the subject of this thread. Since you asked the stupid question, my reply is I don't know since I have never detected, seen or touched a 'gravity wave'. If you are insinuating that the speed of gravitational wave propagation is the same as the speed of light you are mathemetically correct and at the same time an empirical fool. Mike === Subject: Re: SR consistency is crap. > If you are insinuating > that the speed of gravitational wave propagation is the same as the > speed of light you are mathemetically correct and at the same time an > empirical fool. === Subject: Re: SR consistency is crap. > One more obvious proof that Einstein's derivation in 1905 is just as > much > crap as his 1916/1962 derivation. > SR is an excercise in the algebra of Lorentz-Poincare transformations as > applied to electromagnetic fields. If it is mathematically inconsistent > then so is the theory real variables and linear algebra. That takes down > ALL of physics. > Reliance on the concept of mathematical consistency is nonsense. > Just consider the inconsistency as to which of two identically manufactured > and maintained objects is shorter/longer when in relative motion. You're > shorter! No! YOU are! Wrong, asshole, I can clearly see you are much > shorter than me! Idiot! Are you insane?! etc. No inconsistency there? > LOL. You assholes! Two people are facing each other at 100 meters. Each claims that he is at nomal size and it's the other guy that is smaller. The problem here is that you don't get that they disagree because the measuments by which they assign lengths do not have an absolute meaning. This just simply has to be taken into account to arrive at the proper length of a rod, say. All observers agree on the proper length of a rigid rod. Patrick === Subject: Re: SR consistency is crap. > Two people are facing each other at 100 meters. Each claims that he is > at nomal size and it's the other guy that is smaller. That would be Dinky van der Torquemada and devens, or Tit Pot and Kentucky Fried Kolker. Sane people would not claim that the other was smaller. > The problem here is that you don't get that they disagree because the > measuments by which they assign lengths do not have an absolute > meaning. No, the problem here is that the two people facing each other and claiming the other is smaller are not sane, and if you can't realise that then neither are you. > This just simply has to be taken into account to arrive at > the proper length of a rod, say. All observers agree on the proper > length of a rigid rod. > Patrick The whole concept of length contraction began with the insanity of Lorentz when he tried to reconcile aether with Michelson's experiment. the lengthenings and shortenings in question are extraordinarily small. We have v^2/c^2 = 1.0E-8, and thus, if epsilon = 0, the shortenings of the one diameter of the Earth would amount to 6.5 cm. - Michelson's Interference Experiment, HA Lorentz, 1895. What Lorentz failed to realize was that he was compressing the Earth with one jaw of a vise. Obviously he had never had any experience of mechanics in his life and had never heard of Newton's laws. What I suggest you do is perform the experiment of pushing a shopping cart with a snow blower to simulate the Earth passing through the aether wind and tell us how much it contracts. === Subject: Re: SR consistency is crap. > Two people are facing each other at 100 meters. Each claims that he is > at nomal size and it's the other guy that is smaller. > That would be Dinky van der Torquemada and devens, or Tit Pot > and Kentucky Fried Kolker. > Sane people would not claim that the other was smaller. Sane people can sanely disagree about what it means to make a measurement of length. It's the theory which requires such a measurement that contains in itself the instructions for making the measurement (usually unstated and thus left as conventional). All definitions of measuring things are arbitrary. As far as we can prove, Nature doesn't measure anything -- at least not as a visibly verifiable act, anyway. Patrick === Subject: Re: SR consistency is crap. >> Two people are facing each other at 100 meters. Each claims that he >> is >> at nomal size and it's the other guy that is smaller. >> That would be Dinky van der Torquemada and devens, or Tit Pot >> and Kentucky Fried Kolker. >> Sane people would not claim that the other was smaller. > Sane people can sanely disagree about what it means to make a > measurement of length. It's the theory which requires such a > measurement that contains in itself the instructions for making the > measurement (usually unstated and thus left as conventional). > All definitions of measuring things are arbitrary. As far as we can > prove, Nature doesn't measure anything -- at least not as a visibly > verifiable act, anyway. When I place Dinky back to back with devens, then give Dinky some elevator shoes and a top hat to make up the difference, it is those two morons that will decide the other is shorter at 100 paces, turn and fire, because the target shrank. I'll decide they are the same height. Deny it and I'll consider you insane as well. Androcles > Patrick === Subject: Re: SR consistency is crap. > What Lorentz failed to realize was that he was compressing the Earth > with one jaw of a vise. Obviously he had never had any experience > of mechanics in his life and had never heard of Newton's laws. > What I suggest you do is perform the experiment of pushing a shopping > cart with a snow blower to simulate the Earth passing through the aether > wind and tell us how much it contracts. Hmmm. Yes, it would be a strange thing resistance that could equally contract a whole body rather than just impact the leading edge of the body. eleaticus === Subject: Re: SR consistency is crap. One fumbler to another fumbler... === Subject: Re: SR consistency is crap. > What Lorentz failed to realize was that he was compressing the Earth > with one jaw of a vise. Lorentz was the greatest physicist in Europe between Maxwell and Einstein. He forgot more mechanics than you ever knew or could ever know. Bob Kolker === Subject: Re: SR consistency is crap. > What Lorentz failed to realize was that he was compressing the Earth > with one jaw of a vise. > Lorentz was the greatest physicist in Europe between Maxwell and > Einstein. He forgot more mechanics than you ever knew or could ever know. Such a person considers your above to be a rejonder? rofflmfao eleaticus > Bob Kolker > > === Subject: Re: SR consistency is crap. >> What Lorentz failed to realize was that he was compressing the >> Earth >> with one jaw of a vise. >> Lorentz was the greatest physicist in Europe between Maxwell and >> Einstein. He forgot more mechanics than you ever knew or could ever >> know. > Such a person considers your above to be a rejonder? > rofflmfao > eleaticus >> Bob Kolker Kolker sounds like he's Lorentz's greatest fan. I daresay he prefers the BeeGees to Brahms as well. I'd consider Michelson a far greater physicist to Lorentz. Michelson was honest and not stupid. Androcles === Subject: Re: SR consistency is crap. One fumbler to another fumbler... === Subject: Re: SR consistency is crap. > The problem here is that you don't get that they disagree because the > measuments by which they assign lengths do not have an absolute > meaning. This just simply has to be taken into account to arrive at > the proper length of a rod, say. All observers agree on the proper > length of a rigid rod. Gee. I wonder if the proper length of a rigid rod might just happen to be its uncontracted length? Gee, I wonder if there is an infinite number of idiotic avoidances of SR's absurb self-contradictions by True Believer SR-cult cretins, as it seems. eleaticus > Patrick === Subject: Re: SR consistency is crap. One more obvious proof that Einstein's derivation in 1905 is just as > much crap as his 1916/1962 derivation. > SR is an excercise in the algebra of Lorentz-Poincare transformations as > applied to electromagnetic fields. If it is mathematically inconsistent > then so is the theory real variables and linear algebra. That takes down > ALL of physics. > Reliance on the concept of mathematical consistency is nonsense. > Just consider the inconsistency as to which of two identically manufactured > and maintained objects is shorter/longer when in relative motion. You're > shorter! No! YOU are! Wrong, asshole, I can clearly see you are much > shorter than me! Idiot! Are you insane?! etc. No inconsistency there? > LOL. You assholes! > Two people are facing each other at 100 meters. Each claims that he is > at nomal size and it's the other guy that is smaller. > The problem here is that you don't get that they disagree because the > measuments by which they assign lengths do not have an absolute > meaning. This just simply has to be taken into account to arrive at > the proper length of a rod, say. All observers agree on the proper > length of a rigid rod. Yes, that's the killer argument against morons like Webster and Androcles. Alas, killer arguments don't convince people who are dead already. Dirk Vdm === Subject: Re: SR consistency is crap. > One more obvious proof that Einstein's derivation in 1905 is just as > much > crap as his 1916/1962 derivation. > SR is an excercise in the algebra of Lorentz-Poincare transformations as > applied to electromagnetic fields. If it is mathematically inconsistent > then so is the theory real variables and linear algebra. That takes down > ALL of physics. > Reliance on the concept of mathematical consistency is nonsense. > Just consider the inconsistency as to which of two identically manufactured > and maintained objects is shorter/longer when in relative motion. You're > shorter! No! YOU are! Wrong, asshole, I can clearly see you are much > shorter than me! Idiot! Are you insane?! etc. No inconsistency there? > LOL. You assholes! > Just consider the inconsistency of deriving spatial coorinate > transformations and not being able to actually use them with EM quantities > like E,B, D, H, etc. Or having 'cook the books' when you actually do try > to apply them to an equation. > The restort to 'mathematical consistency' reminds me of Chritian resort to > the Books of Moses to exclude their violence: immaterial, irrelevant, and > incompetent. > eleaticus Eleaticus, math (set theory) doesn't say that objects are shorter or longer when in relative motion. Minkowski geometry is consistent iff set theory is consistent. Humans cannot directly observe the length of an object, nor can we directly observe how old something else is, we can touch things, and we can look at light images of things that left a while ago, we can count and watch our own clocks, these are the real things and ALL ELSE is MEASURED (not observered) in terms of those things real things. S.R. makes a prediction about the REAL observations, what we TOUCH (coincident events) and what we SEE (light-like separated events), God only knows what A.E. does but A.E. it not what people are talking about when they discuss modern S.R. Minkowski geometry is contradictory iff set theory is contradictory. I think it is likely that your fixation on A.E.'s person has blinded your ability to learn the modern theory which is equiconsistent with set theory. People cite the consistency of set theory because they know that there is a $7 million bounty on disproving set theory, and they think you are a raving fool if you honestly think you have a disproof and aren't trying to collect that cash for yourself. Mangling the application of sight and touch into abstract concepts that you call length and time and such that you then make wild assumptions about how these ARTEFACTS of YOUR mind MUST behave is not science, it's just a waste of everyone's time even your own. Modern S.R. makes predictions about what you SEE, and it does it in a way that is equiconsistent with set theory, whose inconsistency has a $7 million bounty. === Subject: Re: SR consistency is crap. One more obvious proof that Einstein's derivation in 1905 is just as > much > crap as his 1916/1962 derivation. > SR is an excercise in the algebra of Lorentz-Poincare transformations as > applied to electromagnetic fields. If it is mathematically inconsistent > then so is the theory real variables and linear algebra. That takes down > ALL of physics. > Reliance on the concept of mathematical consistency is nonsense. > Just consider the inconsistency as to which of two identically manufactured > and maintained objects is shorter/longer when in relative motion. You're > shorter! No! YOU are! Wrong, asshole, I can clearly see you are much > shorter than me! Idiot! Are you insane?! etc. No inconsistency there? > LOL. You assholes! > . > Just consider the inconsistency of deriving spatial coorinate > transformations and not being able to actually use them with EM quantities > like E,B, D, H, etc. Or having 'cook the books' when you actually do try > to apply them to an equation. > The restort to 'mathematical consistency' reminds me of Chritian resort to > the Books of Moses to exclude their violence: immaterial, irrelevant, and > incompetent. > eleaticus > Eleaticus, math (set theory) doesn't say that objects are shorter or > longer when in relative motion. Minkowski geometry is consistent iff > set theory is consistent. Humans cannot directly observe the length > of an object, nor can we directly observe how old something else is, > we can touch things, and we can look at light images of things that > left a while ago, we can count and watch our own clocks, these are the > real things and ALL ELSE is MEASURED (not observered) in terms of > those things real things. > S.R. makes a prediction about the REAL observations, what we TOUCH > (coincident events) and what we SEE (light-like separated events), God > only knows what A.E. does but A.E. it not what people are talking > about when they discuss modern S.R. > Minkowski geometry is contradictory iff set theory is contradictory. > I think it is likely that your fixation on A.E.'s person has blinded > your ability to learn the modern theory which is equiconsistent with > set theory. > People cite the consistency of set theory because they know that there > is a $7 million bounty on disproving set theory, and they think you > are a raving fool if you honestly think you have a disproof and aren't > trying to collect that cash for yourself. Mangling the application of > sight and touch into abstract concepts that you call length and time > and such that you then make wild assumptions about how these ARTEFACTS > of YOUR mind MUST behave is not science, it's just a waste of > everyone's time even your own. Modern S.R. makes predictions about > what you SEE, and it does it in a way that is equiconsistent with set > theory, whose inconsistency has a $7 million bounty. Nice try. Instead of spending $1,000 years to prove set theory onconsistency, because you won't, like those thousands of monks died trying to dsprove the consistency of Euclidean geometry, it's a lot easier to SEE something that SR SEES otherwise. For explame: speed of gravity is almost infinite. End. Mike === Subject: Re: SR consistency is crap. >> One more obvious proof that Einstein's derivation in 1905 is just >> as >> much >> crap as his 1916/1962 derivation. >> SR is an excercise in the algebra of Lorentz-Poincare >> transformations as >> applied to electromagnetic fields. If it is mathematically >> inconsistent >> then so is the theory real variables and linear algebra. That takes >> down >> ALL of physics. >> Reliance on the concept of mathematical consistency is nonsense. >> Just consider the inconsistency as to which of two identically >> manufactured >> and maintained objects is shorter/longer when in relative motion. >> You're >> shorter! No! YOU are! Wrong, asshole, I can clearly see you are >> much >> shorter than me! Idiot! Are you insane?! etc. No inconsistency >> there? >> LOL. You assholes! >> . >> Just consider the inconsistency of deriving spatial coorinate >> transformations and not being able to actually use them with EM >> quantities >> like E,B, D, H, etc. Or having 'cook the books' when you actually >> do try >> to apply them to an equation. >> The restort to 'mathematical consistency' reminds me of Chritian >> resort to >> the Books of Moses to exclude their violence: immaterial, irrelevant, >> and >> incompetent. >> eleaticus > Eleaticus, math (set theory) doesn't say that objects are shorter or > longer when in relative motion. Minkowski geometry is consistent iff > set theory is consistent. UTTER CRAP!! Time is NOT a vector. Being able to manipulate symbols doesn't make set theory incorrect, it makes idiots incorrect. Androcles. Humans cannot directly observe the length > of an object, nor can we directly observe how old something else is, > we can touch things, and we can look at light images of things that > left a while ago, we can count and watch our own clocks, these are the > real things and ALL ELSE is MEASURED (not observered) in terms of > those things real things. > S.R. makes a prediction about the REAL observations, what we TOUCH > (coincident events) and what we SEE (light-like separated events), God > only knows what A.E. does but A.E. it not what people are talking > about when they discuss modern S.R. > Minkowski geometry is contradictory iff set theory is contradictory. > I think it is likely that your fixation on A.E.'s person has blinded > your ability to learn the modern theory which is equiconsistent with > set theory. > People cite the consistency of set theory because they know that there > is a $7 million bounty on disproving set theory, and they think you > are a raving fool if you honestly think you have a disproof and aren't > trying to collect that cash for yourself. Mangling the application of > sight and touch into abstract concepts that you call length and time > and such that you then make wild assumptions about how these ARTEFACTS > of YOUR mind MUST behave is not science, it's just a waste of > everyone's time even your own. Modern S.R. makes predictions about > what you SEE, and it does it in a way that is equiconsistent with set > theory, whose inconsistency has a $7 million bounty. === Subject: Re: SR consistency is crap. >> One more obvious proof that Einstein's derivation in 1905 is just >> as > much >> crap as his 1916/1962 derivation. >> SR is an excercise in the algebra of Lorentz-Poincare >> transformations as >> applied to electromagnetic fields. If it is mathematically >> inconsistent >> then so is the theory real variables and linear algebra. That takes >> down >> ALL of physics. >> Reliance on the concept of mathematical consistency is nonsense. >> Just consider the inconsistency as to which of two identically >> manufactured >> and maintained objects is shorter/longer when in relative motion. >> You're >> shorter! No! YOU are! Wrong, asshole, I can clearly see you are >> much >> shorter than me! Idiot! Are you insane?! etc. No inconsistency >> there? >> LOL. You assholes! >> . >> Just consider the inconsistency of deriving spatial coorinate >> transformations and not being able to actually use them with EM >> quantities >> like E,B, D, H, etc. Or having 'cook the books' when you actually >> do try >> to apply them to an equation. >> The restort to 'mathematical consistency' reminds me of Chritian >> resort to >> the Books of Moses to exclude their violence: immaterial, irrelevant, >> and >> incompetent. >> eleaticus > Eleaticus, math (set theory) doesn't say that objects are shorter or > longer when in relative motion. Minkowski geometry is consistent iff > set theory is consistent. > UTTER CRAP!! > Time is NOT a vector. Being able to manipulate symbols doesn't make set > theory incorrect, it makes idiots incorrect. > Androcles. Hmm I guess I should post again and snip where I said time is a vector, OH WAIT A MINUTE, I can't FIND that in my post because I did NOT say it. (Hey lurkers, why did the Androcles act like people said things that they didn't say?) Time is crap. A.E. is crap. Length is crap. We have a perfectly good theory about a correspondance between vectors in a Minkowski vector space and the inertial separations between events, and the vector space is equiconsistent with set theory. So once Androcles gets tired of shouting and making a fuss he can ASK about the correspondance BETWEEN the set theory model and the physical observations and START to be able to USE the theory, and THEN we can start COMPARING IT TO DATA. So far Androcles doesn't KNOW how to compare SR predictions to data, because he can't FIGURE OUT the Minkowski computations on the MATH end, let ALONE figure out what physical observations are predicted by those INVARIANT computations. === Subject: Re: SR consistency is crap. One more obvious proof that Einstein's derivation in 1905 is > just > as >> much > crap as his 1916/1962 derivation. > SR is an excercise in the algebra of Lorentz-Poincare > transformations as > applied to electromagnetic fields. If it is mathematically > inconsistent > then so is the theory real variables and linear algebra. That > takes > down > ALL of physics. Reliance on the concept of mathematical consistency is nonsense. Just consider the inconsistency as to which of two identically > manufactured > and maintained objects is shorter/longer when in relative motion. > You're > shorter! No! YOU are! Wrong, asshole, I can clearly see you > are > much > shorter than me! Idiot! Are you insane?! etc. No inconsistency > there? > LOL. You assholes! > . > Just consider the inconsistency of deriving spatial coorinate > transformations and not being able to actually use them with EM > quantities > like E,B, D, H, etc. Or having 'cook the books' when you > actually > do try > to apply them to an equation. The restort to 'mathematical consistency' reminds me of Chritian > resort to > the Books of Moses to exclude their violence: immaterial, > irrelevant, > and > incompetent. eleaticus >> Eleaticus, math (set theory) doesn't say that objects are shorter >> or >> longer when in relative motion. Minkowski geometry is consistent >> iff >> set theory is consistent. >> UTTER CRAP!! >> Time is NOT a vector. Being able to manipulate symbols doesn't make >> set >> theory incorrect, it makes idiots incorrect. >> Androcles. > Hmm I guess I should post again and snip where I said time is a > vector, OH WAIT A MINUTE, I can't FIND that in my post because I did > NOT say it. Ah, good. So you agree, then. Time is not a vector, so Minkowski's use of it as such is not legitimate. > (Hey lurkers, why did the Androcles act like people said > things that they didn't say?) You've just said above Minkowski geometry is consistent iff set theory is consistent. Set theory aside, I suggest you learn mathematics before you spout of words like consistent. Try googling for similar pages to this one http://www.math.ucla.edu/~tao/121.1.00s/vector_axioms.html In particular, notice For every x,y,z in X, we have (-x) + x = x + (-x) = 0. Time doesn't run backwards the last I heard. > Time is crap. No sonny. Time isn't crap. YOU are crap. A.E. is crap. Yes, he was crap. > Length is > crap. No sonny, Length is not crap. YOU are crap. > We have a perfectly good theory No you dont, you have a crap theory. about a correspondance between > vectors in a Minkowski vector space and the inertial separations > between events, When you can travel backwards in time as you can travel backwards in length, then you can use time as a vector. (The word is correspondence, BTW) > and the vector space is equiconsistent with set > theory. Learn some mathematics before you disgrace yourself even further. > So once Androcles gets tired of shouting Me shouting? Those are your capital letters in your ranting, not mine. > and making a fuss he > can ASK about the correspondance BETWEEN the set theory model and the > physical observations and START to be able to USE the theory, and THEN > we can start COMPARING IT TO DATA. What data do you have, sonny? You've never produced any. > So far Androcles doesn't KNOW how to compare SR predictions to data, That's right. I don't know how to compare crap to data. > because he can't FIGURE OUT the Minkowski computations on the MATH > end, Oh, I can quite competently travel from (0,0,0) to (x,y,z) and back again, but I never yet figured out how to travel back from (x,y,z,ct) to (0,0,0,0). It's a neat trick, you should build yourself a time machine since you can figure it out on the math end. > let ALONE figure out what physical observations are predicted by > those INVARIANT computations. The arrow of time is indeed invariant. Monotonic, too. Now why don't you be a good little boy and quit ranting about the mathematics you know nothing about? Androcles. === Subject: Re: SR consistency is crap. One more obvious proof that Einstein's derivation in 1905 is > just > as > much > crap as his 1916/1962 derivation. > SR is an excercise in the algebra of Lorentz-Poincare > transformations as > applied to electromagnetic fields. If it is mathematically > inconsistent > then so is the theory real variables and linear algebra. That > takes > down > ALL of physics. Reliance on the concept of mathematical consistency is nonsense. Just consider the inconsistency as to which of two identically > manufactured > and maintained objects is shorter/longer when in relative motion. > You're > shorter! No! YOU are! Wrong, asshole, I can clearly see you > are > much > shorter than me! Idiot! Are you insane?! etc. No inconsistency > there? > LOL. You assholes! > . > Just consider the inconsistency of deriving spatial coorinate > transformations and not being able to actually use them with EM > quantities > like E,B, D, H, etc. Or having 'cook the books' when you > actually > do try > to apply them to an equation. The restort to 'mathematical consistency' reminds me of Chritian > resort to > the Books of Moses to exclude their violence: immaterial, > irrelevant, > and > incompetent. eleaticus >> Eleaticus, math (set theory) doesn't say that objects are shorter >> or >> longer when in relative motion. Minkowski geometry is consistent >> iff >> set theory is consistent. >> UTTER CRAP!! >> Time is NOT a vector. Being able to manipulate symbols doesn't make >> set >> theory incorrect, it makes idiots incorrect. >> Androcles. > Hmm I guess I should post again and snip where I said time is a > vector, OH WAIT A MINUTE, I can't FIND that in my post because I did > NOT say it. > Ah, good. > So you agree, then. Time is not a vector, I agree time is not a vector. Time is a label, you can't add labels. > so Minkowski's use of > it as such is not legitimate. A Minkowski space can add vectors and scale vectors and find the proper magnitude of a vector. SR asserts that there exists a correspondance between events and vectors such that the three operations of minkowski space can be used in a particular way to compute observables (the existance of certain events). If Minkowksi did the mapping correctly, and the operations correctly, then what he does was legitimate. For instance the way I do it is legitimate. If Minkowski did it wrongly, then it was not legitimate, for instance the way you compute proper magnititudes is fallacious, so it is illegitimate. > (Hey lurkers, why did the Androcles act like people said > things that they didn't say?) > You've just said above Minkowski geometry is consistent iff > set theory is consistent. Minkowksi geometry says that there exists a set with particular properties. I can prove with the set theory axioms that such a set exists. So if you find an internal inconsistency in that set, then set theory is inconsistent. Similarly if you find an inconsistency in set theory, I can use to and the definition of minkowski space to make a set that satisies the definitions of minkowksi space but which is internally inconsistent. I stand behind what I said. > Set theory aside, I suggest you learn mathematics before you spout > of words like consistent. > Try googling for similar pages to this one > http://www.math.ucla.edu/~tao/121.1.00s/vector_axioms.html > In particular, notice > For every x,y,z in X, we have (-x) + x = x + (-x) = 0. > Time doesn't run backwards the last I heard. Minkowksi geometry doesn't say that time is a vector, or that you can add times, or that time runs backwards. Those are Androcles-claims, and like many Androcles-claims they are baseless. I know the vector space axioms. And you know I know it. To take events and correspond events to vectors. There is no addition of events. There is addition of vectors, and YES that gives another vector, and YES that corresponds to another event. Your axioms translates to For every event x there is another event y such that there is a third event z such that g(y) + g(x) = g(z) = 0 where g(x) is the vector corresponding to the event x, g(y) is the vector corresponding to the event y, and g(z) is the vector corresponding to the event z, NO CONTRADICTION, and NO CLAIM THAT TIME RUNS BACKWARDS. As he has done many times before, Androcles is making baseless claims that are disprovable, and I have disproven the claim now as I have before. > Time is crap. > No sonny. Time isn't crap. YOU are crap. Ad Hominen, what a great response, did you TRY to listen to my point and come to a fair understanding of it. > A.E. is crap. > Yes, he was crap. Good, let's not mention him again and discuss the modern SR theory instead, or better yet something more basic like my newtonian physics basketball example. > Length is > crap. > No sonny, Length is not crap. YOU are crap. Ad Hominen, what a great response, did you TRY to listen to my point and come to a fair understanding of it. Length isn't an observable Androcles, so cut the crap, and I mean cut A.E., cut time, and cut length, none of those are observable. > We have a perfectly good theory > No you dont, you have a crap theory. You don't even understand my basketball example in newtonian physics, so there is simply NO WAY you could comprehend SR. > about a correspondance between > vectors in a Minkowski vector space and the inertial separations > between events, > When you can travel backwards in time as you can travel backwards > in length, then you can use time as a vector. Time is a label, you can't travel forward in a label anymore than you can travel backwords in a label, your assertions are meaningless, irrelevant, and ill-defined. I never said I wanted to use time as a vector, YOU said that. I use vectors as vectors, to compute whether certain other vectors exist with certain properties because the PRECITION is that if certain vectors exist with vcertain properties than certain EVENTS exist with corresponding specific properties. > (The word is correspondence, BTW) You either understand what I say or you don't. You don't seem to understand me when I DO spell correctly, so why bother? > and the vector space is equiconsistent with set > theory. > Learn some mathematics before you disgrace yourself even further. I know much much mathematics, enough to build a minkowski vector space up from scratch based only on the set theory axioms and FOL. Should I do that? Will it matter? Will it make a difference to you? > So once Androcles gets tired of shouting > Me shouting? Those are your capital letters in your ranting, not mine. Shouting is talking over someone, interrupting, and not listening. In written speech caps are emphasis, talking over someone is sniping unread, interrupting is impossible, and not listening is sniping unread and/or not bothering to try to understand what you read. Those are things you seem to do regularly and that I try to avoid. I use caps ONLY because you seem to have difficultly understanding the meaning of my words. > and making a fuss he > can ASK about the correspondance BETWEEN the set theory model and the > physical observations and START to be able to USE the theory, and THEN > we can start COMPARING IT TO DATA. > What data do you have, sonny? You've never produced any. That's a perfect example of not listening. I was saying that you need to understand the theory first. You don't understand the theory yet. Try the basketball example of Newtonian physics first. > So far Androcles doesn't KNOW how to compare SR predictions to data, > That's right. I don't know how to compare crap to data. No one can compare crap to data Androcles. But only you produce crap and think that your Androcles-crap is a prediction of SR. It isn't, and it never will be, what you produce is crap, crappy crap even. SR makes valid predictions, but since you can even understand the valid basketball example of a NEWTONIAN prediction, obviously SR is beyond your grasp. > because he can't FIGURE OUT the Minkowski computations on the MATH > end, > Oh, I can quite competently travel from (0,0,0) to (x,y,z) and back > again, but You can't travel from a VECTOR to another VECTOR. They are SETS. > I never yet figured out how to travel back from (x,y,z,ct) to (0,0,0,0). > It's > a neat trick, you should build yourself a time machine since you can > figure it out > on the math end. There is NOTHING to figure out on the math end the existance of a vector doesn't mean the existance of a way to go ANYWHERE. You should now better Androcles. A vector space is a SET and you KNOW the axioms of set theory don't mention travel, they are propositional functions, they don't say anything except that some set may or may exist that belong in some other sets. > let ALONE figure out what physical observations are predicted by > those INVARIANT computations. > The arrow of time is indeed invariant. Monotonic, too. > Now why don't you be a good little boy and quit ranting about the > mathematics > you know nothing about? > Androcles. Invariant is a set theory term for a number produced from operations on a vector space without selecting a basis for that vector space. Your terms arrow time monotonic and invariant must be totally different words than my use of invariant if you mean something about the physical world and not about vectors. I'm always curious why you think I don't know math. Do you have a rationale? === Subject: Re: SR consistency is crap. > (Hey lurkers, why did the Androcles act like people said > things that they didn't say?) > You've just said above Minkowski geometry is consistent iff > set theory is consistent. > Set theory aside, I suggest you learn mathematics before you spout > of words like consistent. I suggest you learn mathematics before you spout nonsense like you always do: Androcles and equations: http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/SetSolve2.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Persuasive.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/AndroDistri.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Pythagoras.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ToothlessBite.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Competent.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/UseTrans.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Sheesh.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/SetSolve.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/DivZero.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Think.html Androcles and square roots: http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/STILL.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/CanSpecify.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Nearly.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Quadratic.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/GrowUp.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Tautology.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Material.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/GIVEN.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/PythagoRescue.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/SqrtRev.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/NegSqrt.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/SqrtAnswers.html Androcles and exclusive ors: http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Gibberish.html Androcles and partial differential equations: http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/PartialDiff.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/PartialDiff2.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/PartialDiff3.html Dirk Vdm === Subject: Re: SR consistency is crap. > (Hey lurkers, why did the Androcles act like people said >things that they didn't say?) >>You've just said above Minkowski geometry is consistent iff >>set theory is consistent. >>Set theory aside, I suggest you learn mathematics before you spout >>of words like consistent. > I suggest you learn mathematics before you spout nonsense like you > always do: > Androcles and equations: > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/SetSolve2.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Persuasive.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/AndroDistri.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Pythagoras.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/ToothlessBite.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Competent.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/UseTrans.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Sheesh.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/SetSolve.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/DivZero.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Think.html > Androcles and square roots: > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/STILL.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/CanSpecify.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Nearly.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Quadratic.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/GrowUp.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Tautology.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Material.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/GIVEN.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/PythagoRescue.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/SqrtRev.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/NegSqrt.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/SqrtAnswers.html > Androcles and exclusive ors: > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Gibberish.html > Androcles and partial differential equations: > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/PartialDiff.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/PartialDiff2.html > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/PartialDiff3.html > Dirk Vdm No wonder Androcles is dummy@dummy.net! === Subject: Re: SR consistency is crap. > Eleaticus, math (set theory) doesn't say that objects are shorter or > longer when in relative motion. Minkowski geometry is consistent iff > set theory is consistent. > UTTER CRAP!! > Time is NOT a vector. Being able to manipulate symbols doesn't make set > theory incorrect, it makes idiots incorrect. > Androcles. A fox! http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/UTTERCRAP.html Dirk Vdm === Subject: Re: SR consistency is crap. > Eleaticus, math (set theory) doesn't say that objects are shorter or > longer when in relative motion. Minkowski geometry is consistent iff > set theory is consistent. > UTTER CRAP!! > Time is NOT a vector. Being able to manipulate symbols doesn't make set > theory incorrect, it makes idiots incorrect. > Androcles. > A fox! > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/UTTERCRAP.html > Dirk Vdm I'm annoyed that Androcles assume I said time is a vector, I think he should get a better newsreader, or maybe just finish reading a post of mine would be sufficient, I really explain what I say but he never gets that far, I guess he only cares about lurkers with no attention span, that's all he has hopes of convincing. Or maybe he's just trying to be funny. === Subject: Re: SR consistency is crap. Eleaticus, math (set theory) doesn't say that objects are shorter or > longer when in relative motion. Minkowski geometry is consistent iff > set theory is consistent. UTTER CRAP!! > Time is NOT a vector. Being able to manipulate symbols doesn't make set > theory incorrect, it makes idiots incorrect. > Androcles. > A fox! > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/UTTERCRAP.html > Dirk Vdm > I'm annoyed that Androcles assume I said time is a vector, I think > he should get a better newsreader, or maybe just finish reading a post > of mine would be sufficient, I really explain what I say but he never > gets that far, I guess he only cares about lurkers with no attention > span, that's all he has hopes of convincing. Or maybe he's just > trying to be funny. He's asshole number 1, nothing more ;-) Never let him annoy you - he is too stupid for that. Dirk Vdm === Subject: Re: SR consistency is crap. > Eleaticus, math (set theory) doesn't say that objects are shorter or > longer when in relative motion. Minkowski geometry is consistent iff > set theory is consistent. > UTTER CRAP!! > Time is NOT a vector. Being able to manipulate symbols doesn't make set > theory incorrect, it makes idiots incorrect. > Androcles. > A fox! > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/UTTERCRAP.html Post your idiocy here, morontill doomsday. > Dirk Vdm === Subject: Re: SR consistency is crap. Eleaticus, math (set theory) doesn't say that objects are shorter or > longer when in relative motion. Minkowski geometry is consistent iff > set theory is consistent. UTTER CRAP!! > Time is NOT a vector. Being able to manipulate symbols doesn't make set > theory incorrect, it makes idiots incorrect. > Androcles. > A fox! > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/UTTERCRAP.html > Post your idiocy here, morontill doomsday. > Dirk Vdm Did you READ my entire post Eleaticus, the part Androcles didn't respond to because he'd lose (like he usually does)? === Subject: Re: SR consistency is crap. > Did you READ my entire post Eleaticus, the part Androcles didn't > respond to because he'd lose (like he usually does)? As a matter of fact, yes. Indeed, I also have put aside most of your recent posts till I am not burdened with other matters. Your manner is very much appreciated in this quarter. BTW, have you actually read any of morontill forever's stuff? Would you say he contributes ANYTHING besides animus? would have become something along this line: SR is supposed to be physics, a theory about the physical. Hence, its basic effects must be physical or it is complete nonsense. Contraction is one of those basic effects and the PoR says both of two bodies in relative motion must be contracted relative to the other. Hence, of two bodies that were of identical size and shape when at rest wrt each other and are in motion in the same attitude, body A Did you READ my entire post Eleaticus, the part Androcles didn't > respond to because he'd lose (like he usually does)? > As a matter of fact, yes. I mentioned that the modern theory is an assert that the patterns in a certain branch of set theory match the patterns in certain physical *observations*. > Indeed, I also have put aside most of your recent posts till I am not > burdened with other matters. Your manner is very much appreciated in this > quarter. have time. > BTW, have you actually read any of morontill forever's stuff? Would you say > he contributes ANYTHING besides animus? I don't know anyone by the name morontill, sorry that I coudn't be of help. > would have become something along this line: > SR is supposed to be physics, a theory about the physical. Hence, its basic > effects must be physical or it is complete nonsense. You lost me. To avoid being a useless tautology like what we a observe is what we observe or we will observe what we will observe, a theory must start with something known or knowable and assert that nature follows the same patterns. Some modern physical theories take set theory as the known and assert that certain patterns in set theory mirror certain patterns in the physical world. For instance F=ma is about how the solutions of certain differential equations (a seen, then you can predict patterns about what an observer would see. latter show to be untrue because their were observations that did not of the correct type. It's nice that the theory was falsifiable, and it was falsified. > Contraction is one of those basic effects and the PoR says both of two > bodies in relative motion must be contracted relative to the other. I don't fully understand your above paragraph, but I can follow enough to tell that you did not read my post carefully or that you have absolutely no memory of it, or that it just was not clear to you. Contraction is NOT a prediction of the modern theory, because it is impossible to observe contraction (or length), and the modern theory is about ACTUAL observations (like all theories should be IMO). The modern theory of SR says that it is possible to find a 1-1 correspondance from a minkowski vector space to physical events (note that it does say that the physical events (or time) ARE vectors, just future pointing tangent vectors at every event and such that for two that there exist an event C, such that (C-B) is future-pointing time-like (or zero) and (A-C) is space-like (or zero) and (A-B) is light-like (or zero). V is time-like means B(V,V) > 0 V is space-like means B(V,V) < 0 V is light-like means B(V,V) = 0 Future-pointing means that there is a proper minkowski rotation from the time-like vector into a fixed non-zero time-like vector. Sometimes people say null instead of light-like but that confuses Germans and causes them to say isotropic and so on, so I used the more clear terms and defined them for you. You may have noticed some point is that certain parts of the model (set theory) are given names that SOUND LIKE physical things to act as a COGNITIVE AID in following the LATER 1-1 correspondance about OBSERVATIONS. It really is ALL about math the goal of which is to produce patterns of observations, and those OBSERVATIONS are compared to PHYSICAL observations. The ALWAYS about what you feel (including sight). The falsification of the modern SR theory would be to say that no such 1-1 correspondance exists that produces the patterns we OBSERVE. Neither you nor Androcles ever seems to discuss this that I've seen. > Hence, of two bodies that were of identical size and shape when at rest wrt > each other and are in motion in the same attitude, body A lengthwise. Nope, length simply isn't an observation. The modern theory is about what things FEEL and SEE (which is really a special way to feel at the other end of a rod, but the theory is just about what you SEE, and clearly because light moves at less than an infinite speed, the OBSERVATIONS as if they belonged to one and the same object is silly AT BEST. EVEN NEWTONIAN theory says that two trains moving away from each other on a track see train images that appear shorter, and in fact that EACH sees the other appear shorter. It's not a contradiction, a contradiction is if the observations contradict each other, NOT if two existance of the something else called length that then happens to not have the same properties that someone else expects. It is unfair to Newtonian theory to take the predictions of what people SEE and from it build an inconsistent ADDITIONAL theory (NOT in the Newtonian theory) called length and THEN blame Newtonian theory. It is similarly unfair to do so to SR. > Any talk about modern SR vs AE that is asserted to obviate the absurdity > must necessarily be 'schizoid' - out of touch with the physical (per > Alexander Lowen's usage). Any claim that either SR or AE is absurb by claiming things that are not about observation is silly and besides the point. One could choose to ADD inconsistent structures (like constant observed lengths) to ANY theory, but such structures are IRRELEVENT to the soundness or accuracy of the ORIGINAL theory, you then are ONLY analyzing some OTHER structure you ADDED to the theory that wasn't there to begin with, so claims of contradiction cannot be leveled any more at the original theory. If you WANT to complain about or test the ORIGINAL theory, then you must USE that theory, not something that YOU add in addition. If Alexander Lowen disagrees with that, then he is not a scientist. > Do not speak to sane and intelligent people about how schizoid (abstract) > math has anything to say that contradicts the (supposed) physical. Read above about the avoidance of meaningless tautologies. There might be other ways to avoid meaningless tautologies, but you have to use something, what do YOU propose we use instead? > I did not reread - just glance at - the post you ask about so maybe it is > another to which I was to make some such response as this. This certainly > does constitute a proper response to much of what I have been seeing this > past week. > eleaticus The only reason I post AT ALL is because I find the posts of other people to be besides the actual points. If you read JUST my posts I think it would benefit you, since most other people simply talk past each other about things that have nothing to do with actual science. Of course I don't read EVERY post by other people, so I'm not actually trying to discourage you from finding conversation or assistance or open ears or minds or anything like that in absolutely whatever way that you think is best, in fact I wish you the best success in your invesitigations, I do however suggest that you stick to observables. === Subject: Re: SR consistency is crap. >> Did you READ my entire post Eleaticus, the part Androcles didn't >> respond to because he'd lose (like he usually does)? >> As a matter of fact, yes. > I mentioned that the modern theory is an assert that the patterns in a > certain branch of set theory match the patterns in certain physical > *observations*. >> Indeed, I also have put aside most of your recent posts till I am not >> burdened with other matters. Your manner is very much appreciated in >> this >> quarter. > have time. >> BTW, have you actually read any of morontill forever's stuff? Would >> you say >> he contributes ANYTHING besides animus? > I don't know anyone by the name morontill, sorry that I coudn't be of > help. That's moortel, the bitterest idiot of the newsgroup. Like you, he doesn't understand physics. >> Innyhoo, in short, as best as I can remember, my response to this >> would have become something along this line: >> SR is supposed to be physics, a theory about the physical. Hence, its >> basic >> effects must be physical or it is complete nonsense. > You lost me. To avoid being a useless tautology like what we a > observe is what we observe or we will observe what we will observe, > a theory must start with something known or knowable and assert that > nature follows the same patterns. LOL! Yes, you are right, actually. So where does SR begin with something known or knowable? Certainly you do NOT know light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body and neither did Einstein. All the evidence points to the velocity of light being dependent on the velocity of the source. It takes aether to make it independent, just as it takes air for sound to be source independent. Even then the velocity of sound is dependent on the velocity of the observer, relative to the observer. That's why Doppler's equation is f' = f ( m+u)/(m+v). > Some modern physical theories take > set theory as the known and assert that certain patterns in set > theory mirror certain patterns in the physical world. For instance > F=ma is about how the solutions of certain differential equations (a > seen, then you can predict patterns about what an observer would see. But it is NOT seen. Therefore the theory is crap. > latter show to be untrue because their were observations that did not > of the correct type. It's nice that the theory was falsifiable, and > it was falsified. That's right. SR is falsified. >> Contraction is one of those basic effects and the PoR says both of >> two >> bodies in relative motion must be contracted relative to the other. > I don't fully understand your above paragraph, Then you do not even know what the PoR is. > but I can follow enough > to tell that you did not read my post carefully or that you have > absolutely no memory of it, or that it just was not clear to you. You were gabbing on about set theory being wrong, which is nonsense. > Contraction is NOT a prediction of the modern theory, because it is > impossible to observe contraction (or length), and the modern theory > is about ACTUAL observations (like all theories should be IMO). Good. No x' = (x-vt)/sqrt(1-v^2/c^2). Both eleaticus and myself agree, so what on earth are you arguing about? Oh, and so does John Kennaugh, Henri Wilson, Bob Fritzius, Prof Dingle, Petr Beckmann, Albert Michelson. And since you do not allow for a real length contraction, you have no answer to MMX. > The > modern theory of SR says that it is possible to find a 1-1 > correspondance from a minkowski vector space to physical events (note > that it does say that the physical events (or time) ARE vectors, just > future pointing tangent vectors at every event and such that for two > that there exist an event C, such that (C-B) is future-pointing > time-like (or zero) and (A-C) is space-like (or zero) and (A-B) is > light-like (or zero). What modern theory are you ranting on about? One that has no explanation for MMX at all? The only reason I post AT ALL is because I find the posts of other people to be besides the actual points. Just what IS the point ? Rest of rant snipped. Write up your modern theory and explain MMX. Androcles. === Subject: Re: SR consistency is crap. >> Did you READ my entire post Eleaticus, the part Androcles didn't >> respond to because he'd lose (like he usually does)? >> As a matter of fact, yes. > I mentioned that the modern theory is an assert that the patterns in a > certain branch of set theory match the patterns in certain physical > *observations*. >> Indeed, I also have put aside most of your recent posts till I am not >> burdened with other matters. Your manner is very much appreciated in >> this >> quarter. > have time. >> BTW, have you actually read any of morontill forever's stuff? Would >> you say >> he contributes ANYTHING besides animus? > I don't know anyone by the name morontill, sorry that I coudn't be of > help. > That's moortel, the bitterest idiot of the newsgroup. Like you, he > doesn't > understand physics. Make up your mind, does Mootel understand physics, or is he like me, he can't be both. >> Innyhoo, in short, as best as I can remember, my response to this >> would have become something along this line: >> SR is supposed to be physics, a theory about the physical. Hence, its >> basic >> effects must be physical or it is complete nonsense. > You lost me. To avoid being a useless tautology like what we a > observe is what we observe or we will observe what we will observe, > a theory must start with something known or knowable and assert that > nature follows the same patterns. > LOL! > Yes, you are right, actually. > So where does SR begin with something known or knowable? Set theory, you knew that too, why do you play dumb? You start with the known, set theory, and then claim that the universe behaves LIKE certain structures in set theory. But set theory seems to be too advanced for you Androcles, try the basketball example first. When you can count basketballs, then you will be ready for the next step. > Certainly you do NOT know light is always propagated in empty space > with a definite velocity c which is independent of the state of motion > of the emitting body and neither did Einstein. All the evidence points > to the velocity of light being dependent on the velocity of the source. > It takes aether to make it independent, just as it takes air for sound > to > be source independent. Even then the velocity of sound is dependent > on the velocity of the observer, relative to the observer. > That's why Doppler's equation is > f' = f ( m+u)/(m+v). Speed is not observable, red shifts and blue shifts are. Durations are not observable, ticks on a clock are. Get real Androcles, stick to observables, and START by observing how many basketballs Stella and Terrance throw on their little 10 second pre-takeoff game. > Some modern physical theories take > set theory as the known and assert that certain patterns in set > theory mirror certain patterns in the physical world. For instance > F=ma is about how the solutions of certain differential equations (a > seen, then you can predict patterns about what an observer would see. > But it is NOT seen. Therefore the theory is crap. I understand the theory and it's patterns. You are incapable of producing the predictions. When I produce them, then are not only the correct predictions of the theory, they are matched by the experiments I've done. What experiments have you done Androcles? > latter show to be untrue because their were observations that did not > of the correct type. It's nice that the theory was falsifiable, and > it was falsified. > That's right. SR is falsified. I was talking about Newtonisn physics assumption of space and time being falsified, Androcles. Try reading a post for intended meaning for once. >> Contraction is one of those basic effects and the PoR says both of >> two >> bodies in relative motion must be contracted relative to the other. > I don't fully understand your above paragraph, > Then you do not even know what the PoR is. I'm sure you MEANT to say Principle of Relativity which means that the laws of physics have the same form in all inertial frames of reference. It's a stupid principle which the modern theory makes unnecissary. It's a waste of time and just confuses people like you. > but I can follow enough > to tell that you did not read my post carefully or that you have > absolutely no memory of it, or that it just was not clear to you. > You were gabbing on about set theory being wrong, which is nonsense. I was saying that Minkowksi geometry is based on set theory. SR is based on Minkowksi geometry. The irony is that when talking to Androcles I can't GET as far as discussing SR, because Androcles keeps thinking that there are contradictions in Minkowski geometry, if that were the case, then there would be paradoxes in the basketball problem in Newtonian physics and then Newtonian physics is wrong too. You are trapped Androcles, you are going to be proven wrong unless you snip me or killfile me or otherwise don't read what I say. > Contraction is NOT a prediction of the modern theory, because it is > impossible to observe contraction (or length), and the modern theory > is about ACTUAL observations (like all theories should be IMO). > Good. No x' = (x-vt)/sqrt(1-v^2/c^2). Eck! Blecky-eck, coordinates are lame. > Both eleaticus and myself agree, so what on earth are you arguing about? > Oh, and so does John Kennaugh, Henri Wilson, Bob Fritzius, Prof > Dingle, Petr Beckmann, Albert Michelson. And since you do not allow > for a real length contraction, you have no answer to MMX. I did an experiment similar to MMX, and my theory held up just fine. Produce any of those persons, and I if they believe in the Modern theory, and they take the time to read my posts, then I will converse with them and convince then that length is uneccissary. Proper length is real, length is not. And proper length doesn't contract. > The > modern theory of SR says that it is possible to find a 1-1 > correspondance from a minkowski vector space to physical events (note > that it does say that the physical events (or time) ARE vectors, just > future pointing tangent vectors at every event and such that for two > that there exist an event C, such that (C-B) is future-pointing > time-like (or zero) and (A-C) is space-like (or zero) and (A-B) is > light-like (or zero). > What modern theory are you ranting on about? One that has no > explanation for MMX at all? It has explanations for anything that isn't affected by gravity or QM. Do you really not even know what the modern theory is Androcles? > The only reason I post AT ALL is because I find the posts of other > people to be besides the actual points. > Just what IS the point ? If you don't listen to me, then at least maybe the others will start replying more properly about invariant dynamics instead of coordinate crap. But I'm new here, so for all I know they started out proper and became improper to try to appeal to your antics. > Rest of rant snipped. Write up your modern theory and > explain MMX. Ha Ha, I explained it multiple times already, you always snip it. Use level. === Subject: Re: SR consistency is crap. J.E.: >> Then you do not even know what the PoR is. >I'm sure you MEANT to say Principle of Relativity which means that >the laws of physics have the same form in all inertial frames of >reference. It's a stupid principle which the modern theory makes >unnecissary. It's a waste of time and just confuses people like you. Except for the part about androsleaze being confused, I disagree and I would say that your comment below is inconsistent with your comment about inertial frames. [...] >I was saying that Minkowksi geometry is based on set theory. SR is >based on Minkowksi geometry. Sure, but without the principle of relativity to connect that geometry to physics, all you have is minkowski geometry with no physical meaning. I could equally well say that any geometry is based on set theory, but in order to decide which one applies to the universe, I also need a connection to physical phenomena. That connection is the principle of relativity, since what it requires is that physics be unchanged by an infinitesimal displacement of the spacetime variables. >The irony is that when talking to Androcles I can't GET as far as >discussing SR, because Androcles keeps thinking that there are >contradictions in Minkowski geometry, if that It gets worse. His tour de farce argument is that writing, x' = x - vt means x' = x - (x/t)t = x - x = 0 in all seriousness. See, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Infinitesimal.html http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Assertion.html (which is only a cross section of androsleaze' misconceptions. If you're the eternal optimist, there's always the entire collection ``black.'' If you say ``white'', androsleaze will say ``mo''. The exact question and his answer are uncorrelated (note that I didn't say anti-correlated, which would be way too generous). >were the case, then there would be paradoxes in the basketball problem >in Newtonian physics and then Newtonian physics is wrong too. You are >trapped Androcles, you are going to be proven wrong unless you snip me >or killfile me or otherwise don't read what I say. That has no impact on androsleaze - trust me. He is simply not a conscious organism. He's been proven wrong so many times that he's become a carrier for bull disease. === Subject: Re: SR consistency is crap. > J.E.: > >> Then you do not even know what the PoR is. > >I'm sure you MEANT to say Principle of Relativity which means that > >the laws of physics have the same form in all inertial frames of > >reference. It's a stupid principle which the modern theory makes > >unnecissary. It's a waste of time and just confuses people like you. > Except for the part about androsleaze being confused, I disagree and > I would say that your comment below is inconsistent with your comment about > inertial frames. What IS there to be inconsistent. I don't USE the PoR. I use Minkowski geometry, so there are EVEN two things TO contradict each other, just ONE thing, Minkowksi geometry. > [...] > >I was saying that Minkowksi geometry is based on set theory. SR is > >based on Minkowksi geometry. > Sure, but without the principle of relativity to connect that geometry > to physics, all you have is minkowski geometry with no physical meaning. > I could equally well say that any geometry is based on set theory, but > in order to decide which one applies to the universe, I also need a > connection to physical phenomena. That connection is the principle of > relativity, since what it requires is that physics be unchanged by an > infinitesimal displacement of the spacetime variables. I disagree wholeheartedly and completely. What you need is a mapping between physical events and minkowski geometry, and then a procedure for computing future observables in the geometry, which can then be mapped back to observations in reality. PoR is redundant, unecissary and confusing. Drop it. The symmetries of Minkowski geometry do all the work FOR you, you don't NEED to do anything else. Did Terrance's clock tick? Find the event. Did Stella see it? Trace a line to find out what event corresponds to Stella seeing it. What OTHER events that Stella saw did see observe it BETWEEN, that is ALL you need, the rest is fluff and if fluff confuses people, bag it. Body bag it. [snip disparagements against Androcles] === Subject: Re: SR consistency is crap. J.E.: [...] >> Sure, but without the principle of relativity to connect that geometry >> to physics, all you have is minkowski geometry with no physical meaning. >> I could equally well say that any geometry is based on set theory, but >> in order to decide which one applies to the universe, I also need a >> connection to physical phenomena. That connection is the principle of >> relativity, since what it requires is that physics be unchanged by an >> infinitesimal displacement of the spacetime variables. >I disagree wholeheartedly and completely. What you need is a mapping >between physical events and minkowski geometry, and then a procedure >for computing future observables in the geometry, which can then be >mapped back to observations in reality. That only attempts to hide the physics. You cannot use the minkowski geometry to predict anything without first having some theory of mechanics to which it should be applied. The principle of relativity imposes such a requirement by stating that certain observers should be equivalent and defines those observers as ``inertial.'' You cannot define inertial observers using just the minkowski geometry as anything but observers related by a coordinate transformation between coordiates that have no a priori connection to any physics. Otherwise, you are implicitly using the principle of relativity to give meaning to the geometry, but leaving out the physical connection in the explanation. > PoR is redundant, unecissary and confusing. Drop it. The symmetries >of Minkowski geometry do all the work FOR you, you don't NEED to do >anything else. Did Terrance's clock tick? Find the event. OK. Terrence and stella each start with N radioactive nuclei and define equal clock ticks as the interval required for 1 nucleus to decay. I'll eliminate the inherent probem with the decays being probabilistic by simply defining the time in terms of a kurie plot, which is linear in N vs t, not logrithmic. Nothing in the geometry or in set theory prevents me from doing that. You can't argue that it doesn't agree with observation, since you haven't specified the correspondence between what stella and terrence observe. Stella and terrence could simply decide they aren't related by a simple lorentz boost. The minkowski geometry allows for a great many different physical realizations. See, for example, http://arxiv.org/abs/gr-qc/0007036 which is a partial summary of locally lorentz invariant theories in which `c' is constant but may or may not be directly interpreted as the speed of anything. For example, one might take beta = a/(dc/dt) as a constant. >Did Stella see it? Trace a line to find out what event corresponds >to Stella seeing it. What OTHER events that Stella saw did see observe >it BETWEEN, that is ALL you need, the rest is fluff and if fluff confuses >people, bag it. Body bag it. Depends upon what you mean by ``see.'' Do you mean terrence and stella are connected by a null ray or a light ray? Null rays are defined by the minkowski geometry. The equivalence between a light ray and a null ray is an experimental issue. Defining null rays to be light rays, is circular. I can construct a perfectly good relativistic theory of E&M using the minkowski geometry in which the photon mass is neither zero nor a null ray. It's a standard example used to illustrate the higgs mechanism in most field theory textbooks. I can't construct every theory with the minkowski geometry by defining light to correspond to a null ray. The only way to relate the minkowski geometry to the physical universe is to have a suitable theory of mechanics to which the geometry can be applied. The principle of relativity specifies that equivalent observers should define the same quantities in the same way. === Subject: Re: SR consistency is crap. > J.E.: > [...] > >> Sure, but without the principle of relativity to connect that geometry > >> to physics, all you have is minkowski geometry with no physical meaning. > >> I could equally well say that any geometry is based on set theory, but > >> in order to decide which one applies to the universe, I also need a > >> connection to physical phenomena. That connection is the principle of > >> relativity, since what it requires is that physics be unchanged by an > >> infinitesimal displacement of the spacetime variables. > >I disagree wholeheartedly and completely. What you need is a mapping > >between physical events and minkowski geometry, and then a procedure > >for computing future observables in the geometry, which can then be > >mapped back to observations in reality. > That only attempts to hide the physics. I wasn't trying to hide it, but it's obvious it was hidden to you. Sorry dude. > You cannot use the minkowski geometry to predict anything without > first having some theory of mechanics to which it should be applied. WRONG. Watch me. If Stella and Terrance observe the same spectral lines from distant stars (as each other and over time) and pass light signals back of forth to synchronize clocks, and THEN Stella decides to move towards Terrance (so the spectral lines now start changing over time for her), then Stella's clock will be behind Terrances' see the same sepctral lines from distant stars. An observation. And the degree to which Stella's clock disagrees will be realted to the degree to which the spectral lines changed, i.e. how fast she goes. > The principle of relativity imposes such a requirement by stating that > certain observers should be equivalent and defines those observers as > ``inertial.'' You cannot define inertial observers using just the > minkowski geometry as anything but observers related by a coordinate > transformation between coordiates that have no a priori connection to any > physics. You can't do it ever dude. You don't observe coordinates. Inertial observer is an ill-defined concept, it's equivalent to going in a straight line it's true in a limited sense (locally) for all bodies, and otherwise it's fictional. > Otherwise, you are implicitly using the principle of relativity to give > meaning to the geometry, but leaving out the physical connection in the > explanation. The physical connection is where I say this straight line is a series of events that observe the distant stars having a homogeneous spectral distribution. And then start drawing other straight lines corresponding to other series of events, and so on. > > PoR is redundant, unecissary and confusing. Drop it. The symmetries > >of Minkowski geometry do all the work FOR you, you don't NEED to do > >anything else. Did Terrance's clock tick? Find the event. > OK. Terrence and stella each start with N radioactive nuclei and > define equal clock ticks as the interval required for 1 nucleus to > decay. I'll eliminate the inherent probem with the decays being > probabilistic by simply defining the time in terms of a kurie plot, > which is linear in N vs t, not logrithmic. Nothing in the geometry > or in set theory prevents me from doing that. Nothing in geometry stops you from doing anything. Either those people are moving in straight lines in the geometry in your model or they aren't, that's what matters, not how they measure time. The measure time based on what curve in the model represents them, the nuclie observation will match that, because the physical theory says that if a local physical process happen at a rate of n per unit of proper time on one part of a curve then it happens at a rate of n per unit of proper time on another part of the curve. It's homogeneity. > You can't argue that it doesn't agree with observation, since you haven't > specified the correspondence between what stella and terrence observe. They observe all things that happen that they SEE, I did specify that, and besides it's pretty darn obvious. The question is, what events happen. I just described how to determine the timing of a local event. The timing of the observation by TS of a distant event E is to draw two time-like lines from the E to the worldline of TS. The lines will intersect the TS in two places unless the TS was actually AT the event E themself. The two places will be the event D that event E saw at event E, and the event F where TS was event E. > Stella and > terrence could simply decide they aren't related by a simple lorentz > boost. Stella and Terrance could simply decide that they are children and don't KNOW what a Lorentz boost is, and it won't affect my predictions, yes. > The minkowski geometry allows for a great many different physical > realizations. See, for example, > http://arxiv.org/abs/gr-qc/0007036 > which is a partial summary of locally lorentz invariant theories in > which `c' is constant but may or may not be directly interpreted as > the speed of anything. For example, one might take beta = a/(dc/dt) > as a constant. I can't tell if you are deliberately misreading me. I could have made a theory in a EUCLIDEAN space, but then my formula for proper time would be complicated. I chose Minkowski geometry so that proper time and striaght lines could be the things I based physical predictions on, and they are simplest in Minkowski geometry. Sure I could do it in another geometry just to be more complicated. Sure you could do other theories in Minkowski geometry and be more complicated. I never said you couldn't. I was discussing the SR theory with people that couldn't EVEN compare SR to data because they couldn't understand the SR predictions, so I wanted the SIMPLEST POSSIBLE WAY to get the SR predictions. I stand behind that method. > >Did Stella see it? Trace a line to find out what event corresponds > >to Stella seeing it. What OTHER events that Stella saw did see observe > >it BETWEEN, that is ALL you need, the rest is fluff and if fluff confuses > >people, bag it. Body bag it. > Depends upon what you mean by ``see.'' Do you mean terrence and stella > are connected by a null ray or a light ray? Null rays are defined by > the minkowski geometry. The equivalence between a light ray and a null > ray is an experimental issue. Yes it is, but we haven't gotten as far as discussing what Terrance and Stella SEE in REALITY, we are STILL discussing what the theory of SR would PREDICT that they SEE. And yes, I use null lines and proper time to predict this. > Defining null rays to be light rays, is circular. I can construct a perfectly > good relativistic theory of E&M using the minkowski geometry in which the > photon mass is neither zero nor a null ray. One is an element of geometry, another is as a wave, they have different definitions, so how can ANYTHING I DO be circular. The E&M theory says that waves travel a vacuum at constant speed. Since I have to make A MODEL using geometry to MODEL the physical REALITY, I choose something IN THE MODEL to correspond to the wave IN REALITY. I choose null line segments. That's my perogative in making a model. No one can make predictions without a model, and if you make a bad model, then of course you don't agree with experiment, but it's NOT like you can AVOID making a model. If I make a model where the sun is a ball of gas and it turns out that aliens live inside and just create the illusion of a ball of gas, well, my bad, models are sometimes wrong, but you can't DO anything WITHOUT ONE. > It's a standard example used to illustrate the higgs > mechanism in most field theory textbooks. I can't construct every theory > with the minkowski geometry by defining light to correspond to a null ray. I didn't say you could. I'm trying to make normal vanilla garden variety SR predictions to people who have had ... bad luck with the math. Why does this bother you? > The only way to relate the minkowski geometry to the physical universe > is to have a suitable theory of mechanics to which the geometry can > be applied. Not required. My principle of homogeneity is enough to get the basic SR predictions, and we can leave out questions about what thrusters Stella has to fire to actually do the experiment, because WE DON'T CARE what thrusters she fires. People move on curves where the tangents are future-pointing. Light moves on null lines. That's ENOUGH to make the prediction I WANT TO MAKE RIGHT NOW. > The principle of relativity specifies that equivalent > observers should define the same quantities in the same way. That sounds circular, you'd have to say what you mean by same quantities. And it doesn't matter, I've explained my goals, I've explained my methods, they work. Check out the finacial twin paradox where I use dollars and tickers instead of light and clocks, I'm trying to explain BASIC PREDICTIONS to people with a MINIMAL MODEL. I simply do NOT care about fancy theories of force and momentum and dynamics for this task, and I don't need them for this task. === Subject: Re: SR consistency is crap. > What IS there to be inconsistent. I don't USE the PoR. I use > Minkowski geometry, so there are EVEN two things TO contradict each > other, just ONE thing, Minkowksi geometry. rofflmfao! Two objects at motion wrt each other? Screw them! Well, screw one of them, physics is only about one object, not two! rofflmfao! eleaticus === Subject: Re: SR consistency is crap. > What IS there to be inconsistent. I don't USE the PoR. I use > Minkowski geometry, so there are EVEN two things TO contradict each > other, just ONE thing, Minkowksi geometry. > rofflmfao! > Two objects at motion wrt each other? Screw them! > Well, screw one of them, physics is only about one object, not two! > rofflmfao! > eleaticus Physics makes PREDICTIONS. The thing you make predictions with is the theory. For modern SR, that thing is Minkowski geometry. Which is proven consistent. So you just aren't going to find internal inconsistencies. The best you can hope to do is show that it doesn't agree with experiments, but BEFORE you do that, you have to understand it well enough to KNOW what predictions it makes. Did you figure out the math behind the financial twin paradox yet eleaticus? === Subject: Re: SR consistency is crap. Did you READ my entire post Eleaticus, the part Androcles didn't > respond to because he'd lose (like he usually does)? As a matter of fact, yes. >> I mentioned that the modern theory is an assert that the patterns >> in a >> certain branch of set theory match the patterns in certain physical >> *observations*. > Indeed, I also have put aside most of your recent posts till I am > not > burdened with other matters. Your manner is very much appreciated > in > this > quarter. >> finally >> have time. > BTW, have you actually read any of morontill forever's stuff? > Would > you say > he contributes ANYTHING besides animus? >> I don't know anyone by the name morontill, sorry that I coudn't be >> of >> help. >> That's moortel, the bitterest idiot of the newsgroup. Like you, he >> doesn't >> understand physics. > Make up your mind, does Mootel understand physics, or is he like me, > he can't be both. I have made up my mind. You don't understand physics and neither does Dinky van de Torquemada. You are both idiots. Pretty soon you'll be as full of animus as he is, as eleaticus will soon observe. > Innyhoo, in short, as best as I can remember, my response to this > would have become something along this line: SR is supposed to be physics, a theory about the physical. Hence, > its > basic > effects must be physical or it is complete nonsense. >> You lost me. To avoid being a useless tautology like what we a >> observe is what we observe or we will observe what we will >> observe, >> a theory must start with something known or knowable and assert >> that >> nature follows the same patterns. >> LOL! >> Yes, you are right, actually. >> So where does SR begin with something known or knowable? > Set theory, you knew that too, why do you play dumb? Well, I do draw a slight distinction between Venn diagrams, Boolean Algebra and Linear Algebra, although I accept the real numbers are a set. > You start with > the known, set theory, and then claim that the universe behaves LIKE > certain structures in set theory. Good grief, no. Ever heard of the Russell's Barber Paradox? In a certain village, all men are clean shaven and those that are not shaved by the barber shave themselves. If he shaves himself, then he is not shaved by the barber. If he does not shave himself, then he is shaved by the barber. Who shaves the barber? > But set theory seems to be too > advanced for you Androcles, try the basketball example first. When > you can count basketballs, then you will be ready for the next step. I know a hell of lot more set theory than you ever will, you flaming moron. >> Certainly you do NOT know light is always propagated in empty space >> with a definite velocity c which is independent of the state of >> motion >> of the emitting body and neither did Einstein. All the evidence >> points >> to the velocity of light being dependent on the velocity of the >> source. >> It takes aether to make it independent, just as it takes air for >> sound >> to >> be source independent. Even then the velocity of sound is dependent >> on the velocity of the observer, relative to the observer. >> That's why Doppler's equation is >> f' = f ( m+u)/(m+v). > Speed is not observable, LOL! Ok, moron, tell that to the cop! (or in Britain, to the magistrate when the cop produces a picture of two images of your car taken 0.5 seconds apart with 5 feet apart road markers and a radar readout.) I'm done with you, speed is not observable. Androcles. === Subject: Re: SR consistency is crap. Did you READ my entire post Eleaticus, the part Androcles didn't > respond to because he'd lose (like he usually does)? As a matter of fact, yes. >> I mentioned that the modern theory is an assert that the patterns >> in a >> certain branch of set theory match the patterns in certain physical >> *observations*. > Indeed, I also have put aside most of your recent posts till I am > not > burdened with other matters. Your manner is very much appreciated > in > this > quarter. >> finally >> have time. > BTW, have you actually read any of morontill forever's stuff? > Would > you say > he contributes ANYTHING besides animus? >> I don't know anyone by the name morontill, sorry that I coudn't be >> of >> help. >> That's moortel, the bitterest idiot of the newsgroup. Like you, he >> doesn't >> understand physics. > Make up your mind, does Mootel understand physics, or is he like me, > he can't be both. > I have made up my mind. You don't understand physics and neither > does Dinky van de Torquemada. You are both idiots. Pretty soon you'll > be as full of animus as he is, as eleaticus will soon observe. Interesting. So if someone refutes you, your response is to pretend that they have no credibility. Wow, the lurkers must think you are a God! > Innyhoo, in short, as best as I can remember, my response to this > would have become something along this line: SR is supposed to be physics, a theory about the physical. Hence, > its > basic > effects must be physical or it is complete nonsense. >> You lost me. To avoid being a useless tautology like what we a >> observe is what we observe or we will observe what we will >> observe, >> a theory must start with something known or knowable and assert >> that >> nature follows the same patterns. >> LOL! >> Yes, you are right, actually. >> So where does SR begin with something known or knowable? > Set theory, you knew that too, why do you play dumb? > Well, I do draw a slight distinction between Venn diagrams, Boolean > Algebra and Linear Algebra, although I accept the real numbers > are a set. You agree the reals are a set? How about 4? (By which I mean {{}, {{}} {{},{{}}}, {{},{{}},{{},{{}}}}.) How about the set of functions from 4 to R? Give be something to start with Androcles. Can I use the axiom of separation on sets with the same cardinality as R? > You start with > the known, set theory, and then claim that the universe behaves LIKE > certain structures in set theory. > Good grief, no. Ever heard of the Russell's Barber Paradox? > In a certain village, all men are clean shaven and those that > are not shaved by the barber shave themselves. > If he shaves himself, then he is not shaved by the barber. > If he does not shave himself, then he is shaved by the barber. > Who shaves the barber? There are many possibilities that can be ascribed to that scenario. (1) The barber is a woman (2) There is no such village You didn't prove the existence of such a village OR such a barber, and you know it. You think the lurkers are impressed with your non-sequitors, I doubt it? > But set theory seems to be too > advanced for you Androcles, try the basketball example first. When > you can count basketballs, then you will be ready for the next step. > I know a hell of lot more set theory than you ever will, you flaming > moron. That's something I really really doubt Androcles. I mean, I don't know you, but the things you say and knowledge of set theory just don't go together. Maybe you *know* set theory the same way you *know* SR, that I'd believe. >> Certainly you do NOT know light is always propagated in empty space >> with a definite velocity c which is independent of the state of >> motion >> of the emitting body and neither did Einstein. All the evidence >> points >> to the velocity of light being dependent on the velocity of the >> source. >> It takes aether to make it independent, just as it takes air for >> sound >> to >> be source independent. Even then the velocity of sound is dependent >> on the velocity of the observer, relative to the observer. >> That's why Doppler's equation is >> f' = f ( m+u)/(m+v). > Speed is not observable, > LOL! > Ok, moron, tell that to the cop! (or in Britain, to the magistrate when > the cop produces a picture of two images of your car taken 0.5 seconds > apart with 5 feet apart road markers and a radar readout.) > I'm done with you, speed is not observable. > Androcles. I can discuss two events, one being a camera seeing my car and a clock, and another one being a camera seeing my car and a clock a different time. That's the level I will discuss things with you at, UNobservables. Have you explained the basketball example? The financial twin paradox example? Those are BOTH based on your precious Newtonian theory Androcles, can you not handle it? === Subject: Re: SR consistency is crap. > I know a hell of lot more set theory than you ever will, you flaming > moron. > That's something I really really doubt Androcles. I mean, I don't > know you, but the things you say and knowledge of set theory just > don't go together. Maybe you *know* set theory the same way you > *know* SR, that I'd believe. He knows set theory like here: http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Gibberish.html See at the end, the part with the Venn-diagram :-)) Dirk Vdm === Subject: Re: SR consistency is crap. > He knows set theory like here: > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Gibberish.html > See at the end, the part with the Venn-diagram :-)) Did I read that correctly. He thinks xor is the same as or? Apparently he does not know disjunctive normal form. AvB = A&B v A&-B v -A&B whereas x!=y (denoting xor by !=) is A&-B v -A&B. The two boolean functions differn when A is true and B is true. Bob Kolker === Subject: Re: SR consistency is crap. > He knows set theory like here: > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Gibberish.html > See at the end, the part with the Venn-diagram :-)) > Did I read that correctly. He thinks xor is the same as or? You read that correctly. Even with 3 different ways of 'proving', he called it gibberish :-) Dirk Vdm > Apparently he does not know disjunctive normal form. > AvB = A&B v A&-B v -A&B > whereas > x!=y (denoting xor by !=) is A&-B v -A&B. The two boolean functions > differn when A is true and B is true. > Bob Kolker === Subject: Re: SR consistency is crap. He knows set theory like here: > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Gibberish.html > See at the end, the part with the Venn-diagram :-)) > Did I read that correctly. He thinks xor is the same as or? > You read that correctly. > Even with 3 different ways of 'proving', he called it gibberish :-) Did you try discussing it in latin? === Subject: Re: SR consistency is crap. > He knows set theory like here: > http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Gibberish.html > See at the end, the part with the Venn-diagram :-)) Did I read that correctly. He thinks xor is the same as or? > You read that correctly. > Even with 3 different ways of 'proving', he called it gibberish :-) > Did you try discussing it in latin? hm, no, we tried discussing it in English and in Mathematics. He didn't understand, so I decided not to try Latin or Greek. Dirk Vdm === Subject: Re: SR consistency is crap. Dirk Van de moortel: >> Did you try discussing it in latin? >hm, no, we tried discussing it in English and in Mathematics. >He didn't understand, so I decided not to try Latin or Greek. We could try pig latin. === Subject: Re: SR consistency is crap. > Dirk Van de moortel: > > >> Did you try discussing it in latin? > >hm, no, we tried discussing it in English and in Mathematics. > >He didn't understand, so I decided not to try Latin or Greek. > We could try pig latin. Yes. Perhaps some suitable combination of oinks, snorts and farts might do it. Dirk Vdm === Subject: Re: SR consistency is crap. > Good grief, no. Ever heard of the Russell's Barber Paradox? > In a certain village, all men are clean shaven and those that > are not shaved by the barber shave themselves. > If he shaves himself, then he is not shaved by the barber. > If he does not shave himself, then he is shaved by the barber. > Who shaves the barber? > There are many possibilities that can be ascribed to that scenario. > (1) The barber is a woman (2) There is no such village > You didn't prove the existence of such a village OR such a barber, and > you know it. You think the lurkers are impressed with your > non-sequitors, I doubt it? Goddess forbid he should have impressed us more than you impressed us with your response! rofflmfao! eleaticus === Subject: Re: SR consistency is crap. Hey demented retard, you should not reply to someone you just killfiled: | Why don't you just off, imbecile? | This newsgroup is for beating up idiots and you are such an | easy target it's getting boring as shooting fish in a barrel. | Tell you what... I'll help you. | *plonk* | Androcles. | PS... you are so stupid I doubt you can understand the meaning | of *plonk*. It means I can no longer read your noise. You are | kill filed. Dirk Vdm === Subject: Re: SR consistency is crap. > BTW, have you actually read any of morontill forever's stuff? Would you say > he contributes ANYTHING besides animus? There are lots of people who say the same about you. > would have become something along this line: > SR is supposed to be physics, a theory about the physical. Hence, its basic > effects must be physical or it is complete nonsense. > Contraction is one of those basic effects and the PoR says both of two > bodies in relative motion must be contracted relative to the other. > Hence, of two bodies that were of identical size and shape when at rest wrt > each other and are in motion in the same attitude, body A lengthwise. are in motion in the same attitude? WTF does that mean? If the two ships are in relative motion then they will measure that the other ship will be shorter than the proper length of their own ship, by a factor gamma. If however they do the calculation sigma^2 = (speed of light x elapsed time)^2 - (observed length)^2 they will get the same answer and can therefore calculate that the proper length of the other ship is indeed the same as their own. > Any talk about modern SR vs AE that is asserted to obviate the absurdity > must necessarily be 'schizoid' - out of touch with the physical (per > Alexander Lowen's usage). > Do not speak to sane and intelligent people about how schizoid (abstract) > math has anything to say that contradicts the (supposed) physical. Nope. Instead we'll talk about real repeatable experiments using display path length contraction and time dilation. And you'll ignore every one. > I did not reread - just glance at - the post you ask about so maybe it is > another to which I was to make some such response as this. This certainly > does constitute a proper response to much of what I have been seeing this > past week. Fortunately physics is not constrained by your personal incredulity. === Subject: Re: SR consistency is crap. > Did you READ my entire post Eleaticus, the part Androcles didn't > respond to because he'd lose (like he usually does)? > As a matter of fact, yes. > Indeed, I also have put aside most of your recent posts till I am not > burdened with other matters. Your manner is very much appreciated in this > quarter. > BTW, have you actually read any of morontill forever's stuff? Would you say > he contributes ANYTHING besides animus? > would have become something along this line: > SR is supposed to be physics, a theory about the physical. Hence, its basic > effects must be physical or it is complete nonsense. > Contraction is one of those basic effects and the PoR says both of two > bodies in relative motion must be contracted relative to the other. Thats not what the principle of relativity states. That is a result derived from special relativity. Learn the difference. > Hence, of two bodies that were of identical size and shape when at rest wrt > each other and are in motion in the same attitude, body A lengthwise. > Any talk about modern SR vs AE that is asserted to obviate the absurdity > must necessarily be 'schizoid' - out of touch with the physical (per > Alexander Lowen's usage). > Do not speak to sane and intelligent people about how schizoid (abstract) > math has anything to say that contradicts the (supposed) physical. > I did not reread - just glance at - the post you ask about so maybe it is > another to which I was to make some such response as this. This certainly > does constitute a proper response to much of what I have been seeing this > past week. > eleaticus I am consistantly amused by your premise that since length contraction is not directly observed to your satisfaction, SR is supposedly falsified. http://math.ucr.edu/home/baez/relativity.html Go read. === Subject: Re: SR consistency is crap. > SR is supposed to be physics, a theory about the physical. Hence, its basic > effects must be physical or it is complete nonsense. > Contraction is one of those basic effects and the PoR says both of two > bodies in relative motion must be contracted relative to the other. > Thats not what the principle of relativity states. That is a result > derived from special relativity. Learn the difference. How do you manage to be such an idiot on what must be such short notice? SR says no such thing. SR says a inertialy moving object contracts. Period. It is the PoR that says if that is so then the stationary object must also contract because it too is moving inertially, wrt the supposed moving object. eleaticus === Subject: Re: SR consistency is crap. > SR is supposed to be physics, a theory about the physical. Hence, its > basic > effects must be physical or it is complete nonsense. > Contraction is one of those basic effects and the PoR says both of two > bodies in relative motion must be contracted relative to the other. > Thats not what the principle of relativity states. That is a result > derived from special relativity. Learn the difference. Mark your snips. I am not sure why I complain because you have made it obvious that intellectual honesty is not one of your strong suites. > How do you manage to be such an idiot on what must be such short notice? The same way you have managed to be an idiot your whole life. Which is to say there is no reason, that is just how I am. > SR says no such thing. SR says a inertialy moving object contracts. Period. No. Again, that is a result derived from SR not an initial assumption. > It is the PoR that says if that is so then the stationary object must also > contract because it too is moving inertially, wrt the supposed moving > object. No, it is you who says that - not the PoR. It is never surprising to see a false conclusion drawn from an invalid premise. Tell us, eleaticus: How long have you been misinterpeting relativity? If you have been doing math before Robert Kolker was born, you would have to be in your 80's, at least. > eleaticus [Google cries 'internal server error', Repost #1] === Subject: Re: SR consistency is crap. > SR is supposed to be physics, a theory about the physical. Hence, its > basic > effects must be physical or it is complete nonsense. > Contraction is one of those basic effects and the PoR says both of two > bodies in relative motion must be contracted relative to the other. > Thats not what the principle of relativity states. That is a result > derived from special relativity. Learn the difference. > How do you manage to be such an idiot on what must be such short notice? > SR says no such thing. SR says a inertialy moving object contracts. Period. Nope it doesn't. Give up on length contraction and time dilation eleaticus, neither are claims about observations, focus on the observations, the ONLY way to keep the baggage about lengths and such is to live and breath new SR definitions of the terms and for you I don't think it's worth it, and they'd have different meanings anyway, you have to talk about terrance-years and stella-meters. If you focus on invariant observations predicted by the theory, you can avoid these endless discussions that frankly go nowhere where you are misunderstanding phrases about the numerical value of a CALCULATION in units of stella-meters and comparing it to another number (in terrance-meters) and saying things like since x < y, PoR claims y < x, it doesn't. It doesn't saying ANYTHING like that. The PoR says that Stella imagines that Terrance's stomache is x stella-meters and Terrance imagines that it's y terrance-meters. And YES x < y. But the PoR says that Terrance imagines that STELLA'S stomache is r terrance-meters and Stella imagines that it's s stella-meters. And YES r < s. There is NO contradiction here for a whole CITY full of reason, namely that they are measuring different things, and I don't mean JUST that they are measuring different stomaches each time, I mean that the whole concept of stomache length is ill-defined and unobservable, note that I was compelled to use the word imagine, they make OTHER observations and had to COMPUTE what they DEFINED as a length, and each one makes DIFFERENT definitions. And the whole QUESTION is stupid because the definition of how big is my stomache is NOT invariant, and there IS no answer. It's twice as big as the distance from the middle of your stomache to the outside. The whole idea of discussing lengths and such instead of invariant observable quantities is riddled with linguisitic difficulties, it's not worth it unless you can do it right. You eleaticus cannot. That doesn't make you a bad person. Maybe after doing it the invariant way enough you'll figure out how, but you aren't yet ready, and it's not going to get you anywhere to just do it wrong. Do invariant math instead eleaticus. > It is the PoR that says if that is so then the stationary object must also > contract because it too is moving inertially, wrt the supposed moving > object. > eleaticus Stick to observables. You are throwing around words like stationary and moving and such that have no invariant meaning. You are just going to burn yourself and not go anywhere doing that. There is simply no such thing as a rigid body in SR, if you assume one, you are going to get logical contradictions. Imagine a train that thinks a hole in the level tracks is approaching it very fast. _ __ _o =:==:==> ------------------ ------ S| |T It says, that hole is very small, and my train is a rigid body, I won't hit the cliff face T. But imagine someone standing next to the cliff T, they imagine a different picture. | ------- ------- S | | T this person thinks the train is very very short, and that of course it will hit the cliff face T. The second person *is* correct that the train hits the cliff face T. So does the person on the train say relativity is wrong, NO. The person on the train notes that as the tip of the train starts to go over the cliff face S, the assumption that it was a rigid body is shattered like stressed metal as the tip starts to dip down down and down and hits cliff face T which train person still imagines that the train is still partly to the left of cliff face S. The problem with this story is that BOTH fantasy imaginations are equally bonkers, talking about where one part of the train is at at the same time when a different part is someplace else is just a STUPID question. And it's unscientific, since it isn't about any observation. And observation is about what something FEELS at a surface, then that's an observation, it means a Faraday field existed at the events corresponding to the locations and times when and where the retina surface was stimulated by the light. You don't SEE time dilation. You don't SEE length contradtion. You don't SEE time. You don't SEE length. You do SEE light, which according to SR is caused by the events on your backwards light cone. Stick to observables. === Subject: Re: SR consistency is crap. > SR says no such thing. SR says a inertialy moving object contracts. Period. > It is the PoR that says if that is so then the stationary object must also > contract because it too is moving inertially, wrt the supposed moving > object. If you look at a stick orthogonally you see its full length. If you rotate the stick about its midpoint to see a -projection- which is less than the full length. Length contractions (so-called) is a rotation which interchanges the time and space-axis. Hence when the -spatial- distance between the end-points is measured it appears smaller. There is not actual stretching of squeezing. Look at the matrix for the Lorentz transformation and see how the boosts work. But you won't. You simply will not do the mathematics, will you. Bob Kolker === Subject: Re: SR consistency is crap. In sci.math, robert j. kolker <30e1d6F2u9di4U1@uni-berlin.de>: >> SR says no such thing. SR says a inertialy moving object contracts. Period. >> It is the PoR that says if that is so then the stationary object must also >> contract because it too is moving inertially, wrt the supposed moving >> object. > If you look at a stick orthogonally you see its full length. Pedant point: Actually, I'm not sure about that. The only bit one sees orthogonally is at the center of the stick; the rest is angularly displaced, requiring one to move one's head and/or off the center of the viewing area/retina. However, it turns out this won't affect its observed length, if it's travelling at the observer orthogonally. The Lorentz Transformation only affects the x and t coordinates, when the item is travelling on the x axis; the y and z are unchanged. (At least, so goes the theory. But it does make a bit of a mess when doing lightpath computations. :-) ) > If you > rotate the stick about its midpoint to see a -projection- which is less > than the full length. Length contractions (so-called) is a rotation > which interchanges the time and space-axis. Hence when the -spatial- > distance between the end-points is measured it appears smaller. There is > not actual stretching of squeezing. Look at the matrix for the Lorentz > transformation and see how the boosts work. > But you won't. You simply will not do the mathematics, will you. I'm not sure math is the problem here; we simply can't perceive time directly, and if the coordinate system is rotating 4-dimensionally (with one of the coordinates being treated as an imaginary, to boot), we'll be lucky if we can see 3 of them. > Bob Kolker -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: SR consistency is crap. > If you look at a stick orthogonally you see its full length. If you > rotate the stick about its midpoint to see a -projection- which is less > than the full length. Length contractions (so-called) is a rotation > which interchanges the time and space-axis. Hence when the -spatial- > distance between the end-points is measured it appears smaller. There is > not actual stretching of squeezing. Look at the matrix for the Lorentz > transformation and see how the boosts work. Jerk. I was probably doing the math before you were born. I was too young and naive then to understand how ridiculous it was. Do physics, not schizoid math. There is no god damned rotation, schizophenia-man. Neither the rear nor the front of a cylinder passing in a length-wise direction becomes visible. There is no suggestion even in your schizo math that the side of the cylinder is what would impact at high velocity should it approach a target bar front/'straight' on. Get real. Get your head out of some schizophrenic mathematician's ass. eleaticus === Subject: Re: SR consistency is crap. > If you look at a stick orthogonally you see its full length. If you > rotate the stick about its midpoint to see a -projection- which is less > than the full length. Length contractions (so-called) is a rotation > which interchanges the time and space-axis. Hence when the -spatial- > distance between the end-points is measured it appears smaller. There is > not actual stretching of squeezing. Look at the matrix for the Lorentz > transformation and see how the boosts work. > Jerk. I was probably doing the math before you were born. I was too young > and naive then to understand how ridiculous it was. So what was the breaking point? This ought to be amusing, considering you are old enough to have been around for every fundamental experiment that supports SR save for the MMX. Perhaps you had a mentor that was of the old guard who could never accept SR and passed his beliefs on to you, which stuck because of your massive ignorance of all things mathematical and physical? If what you say is true, you have been stupid for a better fraction of a century - Uncle Al was right, stupidity is forever. === Subject: Re: SR consistency is crap. > One more obvious proof that Einstein's derivation in 1905 is just as > much > crap as his 1916/1962 derivation. > SR is an excercise in the algebra of Lorentz-Poincare transformations as > applied to electromagnetic fields. If it is mathematically inconsistent > then so is the theory real variables and linear algebra. That takes down > ALL of physics. > Reliance on the concept of mathematical consistency is nonsense. > Just consider the inconsistency as to which of two identically manufactured > and maintained objects is shorter/longer when in relative motion. You're > shorter! No! YOU are! Wrong, asshole, I can clearly see you are much > shorter than me! Idiot! Are you insane?! etc. No inconsistency there? > LOL. You assholes! > Just consider the inconsistency of deriving spatial coorinate > transformations and not being able to actually use them with EM quantities > like E,B, D, H, etc. Or having 'cook the books' when you actually do try > to apply them to an equation. > The restort to 'mathematical consistency' reminds me of Chritian resort to > the Books of Moses to exclude their violence: immaterial, irrelevant, and > incompetent. > eleaticus Tell us, eleaticus. Since you have disproven SR and calculus by your stunning arguments against SR and limits, what is left of modern physics that you don't feel like destroying? Lets see whats left. Quantum anything? Nope, gone. It uses partial differential equations, which requires calculus, which requires limits. Modern QFT also has SR embedded into it through Shrodinger's equation, so thats out. I doubht you could crunch a PDE if your life depended on it, anyway. SR, GR? Gone. Newtonian mechanics? Gone! You need calculus to use that effectively. All we have left is philsophical rambling from idiots such as Jeff Relf, Mike Helland, and yourself. === Subject: Re: SR consistency is crap. > Reliance on the concept of mathematical consistency is nonsense. > Just consider the inconsistency as to which of two identically manufactured > and maintained objects is shorter/longer when in relative motion. You're > shorter! No! YOU are! Wrong, asshole, I can clearly see you are much > shorter than me! Idiot! Are you insane?! etc. No inconsistency there? > LOL. You assholes! . > Just consider the inconsistency of deriving spatial coordinate > transformations and not being able to actually use them with EM quantities > like E,B, D, H, etc. Or having to 'cook the books' when you actually do try > to apply them to an equation. > eleaticus > Tell us, eleaticus. Since you have disproven SR and calculus by your > stunning arguments against SR and limits, what is left of modern > physics that you don't feel like destroying? Another of the strawman arguments typical of True Believer SR-cult cretins. I have no problems with, nor even hinted or mistakenly implied problems with, caluclus and limits. I just pointed out that a physical process is a physical process that occurs over time and that formulae that are not process cannot argue against the results of a process argument. They can only show what some value -WOULD BE. In the Zeno Stadium case, what the given distance would be, which is quite a triumph: the distance it would be is the distance specified that it would be! WOW! It is lucky that you cretins aren't even one percent as hot as you think you are, else you'd burn yourselves to death with all the strawmen with which you surround yourselves. eleaticus === Subject: Re: SR consistency is crap. > Reliance on the concept of mathematical consistency is nonsense. > Just consider the inconsistency as to which of two identically > manufactured > and maintained objects is shorter/longer when in relative motion. > You're > shorter! No! YOU are! Wrong, asshole, I can clearly see you are much > shorter than me! Idiot! Are you insane?! etc. No inconsistency there? > LOL. You assholes! > . > Just consider the inconsistency of deriving spatial coordinate > transformations and not being able to actually use them with EM > quantities > like E,B, D, H, etc. Or having to 'cook the books' when you actually do > try > to apply them to an equation. > eleaticus > Tell us, eleaticus. Since you have disproven SR and calculus by your > stunning arguments against SR and limits, what is left of modern > physics that you don't feel like destroying? > Another of the strawman arguments typical of True Believer SR-cult cretins. > I have no problems with, nor even hinted or mistakenly implied problems > with, caluclus and limits. I just pointed out that a physical process is a > physical process that occurs over time and that formulae that are not > process cannot argue against the results of a process argument. They can > only show what some value -WOULD BE. In the Zeno Stadium case, what the > given distance would be, which is quite a triumph: the distance it would be > is the distance specified that it would be! WOW! If you have no problem with limits why were you arguing about how wrong they are? It is a simple problem to solve using limits but you failed to understand. > It is lucky that you cretins aren't even one percent as hot as you think you > are, else you'd burn yourselves to death with all the strawmen with which > you surround yourselves. > eleaticus === Subject: Re: SR consistency is crap. > Reliance on the concept of mathematical consistency is nonsense. > Just consider the inconsistency as to which of two identically > manufactured > and maintained objects is shorter/longer when in relative motion. > You're > shorter! No! YOU are! Wrong, asshole, I can clearly see you are much > shorter than me! Idiot! Are you insane?! etc. No inconsistency there? > LOL. You assholes! > . > Just consider the inconsistency of deriving spatial coordinate > transformations and not being able to actually use them with EM > quantities > like E,B, D, H, etc. Or having to 'cook the books' when you actually do > try > to apply them to an equation. > eleaticus > Tell us, eleaticus. Since you have disproven SR and calculus by your > stunning arguments against SR and limits, what is left of modern > physics that you don't feel like destroying? > Another of the strawman arguments typical of True Believer SR-cult cretins. > I have no problems with, nor even hinted or mistakenly implied problems > with, caluclus and limits. I just pointed out that a physical process is a > physical process that occurs over time and that formulae that are not > process cannot argue against the results of a process argument. They can > only show what some value -WOULD BE. In the Zeno Stadium case, what the > given distance would be, which is quite a triumph: the distance it would be > is the distance specified that it would be! WOW! > If you have no problem with limits why were you arguing about how wrong they are? Idiot, I have no problems with, nor even hinted at nor mistakenly implied problems with, calculus and limits. I just pointed out that a physical process is a physical process that occurs over time and that formulae that are not process cannot argue against the results of a process argument. They can only show what some value -WOULD BE. In the Zeno Stadium case, what the given distance would be, which is quite a triumph: the distance it would be is the distance specified that it would be! WOW! It is lucky that you cretins aren't even one percent as hot as you think you are, else you'd burn yourselves to death with all the strawmen with which you surround yourselves. eleaticus === Subject: Re: SR consistency is crap. > One more obvious proof that Einstein's derivation in 1905 is just as > much > crap as his 1916/1962 derivation. > SR is an excercise in the algebra of Lorentz-Poincare transformations as > applied to electromagnetic fields. If it is mathematically inconsistent > then so is the theory real variables and linear algebra. That takes down > ALL of physics. > Reliance on the concept of mathematical consistency is nonsense. > Just consider the inconsistency as to which of two identically manufactured > and maintained objects is shorter/longer when in relative motion. You're > shorter! No! YOU are! Wrong, asshole, I can clearly see you are much > shorter than me! Idiot! Are you insane?! etc. No inconsistency there? > LOL. You assholes! > Just consider the inconsistency of deriving spatial coorinate > transformations and not being able to actually use them with EM quantities > like E,B, D, H, etc. Or having 'cook the books' when you actually do try > to apply them to an equation. > The restort to 'mathematical consistency' reminds me of Chritian resort to > the Books of Moses to exclude their violence: immaterial, irrelevant, and > incompetent. > eleaticus You both all idiots giving wrong answers for the right reasons and right answers for the wrong reasons. A theory about math must be consistent but cannot be complete. Thus it always incorporates a paradox: Goedel A theory about physics must be complete, i.e. contain no paradox but as a result it is always inconsistent. Thus, idiot Einstein, not understanding the right domain for the application of math, has twin paradox and black holes in his theories. They are consistent math theories stupid eleticus (you'll never become an 'eleatis'), but not complete to qualify for physical theories because they incorporate paradoxes. This settles the Einstein Affair once for all:. He applied mathemetics to come up with a physical theory without using self evident propositions as axioms, as the Greeks have already taught us to do and Galileo and Newton afterwards, but non-provable mathematical statements, such as the analytic proposition that 'For all moving inertial observers the speed of light is constant'. Analytic propositions cannot be proved since they are universally quantified. If they also fail to be self-evident, they should not be used in a physical theory. (using them as such is straight forward paranoia) Above material is (c) copyright Eleatis. It can be used only by mentioning the name 'Eleatis'. Mike === Subject: Re: SR consistency is crap. > A theory about math must be consistent but cannot be complete. Thus it > always incorporates a paradox: Goedel G.9adel's Incompleteness Theorem http://mathworld.wolfram.com/GoedelsIncompletenessTheorem.html === Subject: Re: SR consistency is crap. > A theory about math must be consistent but cannot be complete. Thus it > always incorporates a paradox: Goedel > G.9adel's Incompleteness Theorem > http://mathworld.wolfram.com/GoedelsIncompletenessTheorem.html Huh, I bet you don't even understand what's written there. Posting links is an act of great stupidity. Do you got anything to say to prove that you are a thinking person? Mike === Subject: Re: SR consistency is crap. G.9adel's Incompleteness Theorem http://mathworld.wolfram.com/GoedelsIncompletenessTheorem.html Suggest you read G.9adel's Proof Revised edition, Nagel & Newman, edited and with a new foreword by Douglas R. Hofstadter, New York University Press (2001). Hofstadter updated this classic text, clarifying ambiguities, made arguements clearer... and the text is more accessible.... maybe even for Micky! === Subject: Re: SR consistency is crap. > > A theory about math must be consistent but cannot be complete. Thus it >> always incorporates a paradox: Goedel > G.9adel's Incompleteness Theorem > http://mathworld.wolfram.com/GoedelsIncompletenessTheorem.html Goedel's incompleteness results apply to a particular class of formal systems which are powerful enough to formulate arithmetic. Goedels results do not apply to physics theories, which in general are not formal, but applications of existing theories in geometry and function theory. Bob Kolker === Subject: Re: SR consistency is crap. > > A theory about math must be consistent but cannot be complete. Thus it >> always incorporates a paradox: Goedel > G.9adel's Incompleteness Theorem > http://mathworld.wolfram.com/GoedelsIncompletenessTheorem.html > Goedel's incompleteness results apply to a particular class of formal > systems which are powerful enough to formulate arithmetic. Goedels > results do not apply to physics theories, which in general are not > formal, but applications of existing theories in geometry and function > theory. Yes they are, since math tarts still have figured that there is a difference between and a formal theory, and a formal system. Since formal systems don't apply to anything, except set theory. Which is not only not physics, it's not even math. It's MATHS, and the category slanters keep pointing in their hopeless proof that Einstone was wrong, and Quantum Mechanics is like anything other a misapplication of the Central Limit Theorem, and some revivalist economics by the Bush, the UN, and The International Center For Recursive Recombinant Eve Forecasting on ext 16 of The Born-Again Boston Beltway. So the only thing any geomery has to with science is actually: Take three steps to the left, take three steps to the right, cross yourself with the sign of PI, say three Yeah, Verilys, and take a discontinous quantum leap into the nearest Brown Hole. > Bob Kolker === Subject: Re: SR consistency is crap. > > A theory about math must be consistent but cannot be complete. Thus it >> always incorporates a paradox: Goedel > G.9adel's Incompleteness Theorem > http://mathworld.wolfram.com/GoedelsIncompletenessTheorem.html > Goedel's incompleteness results apply to a particular class of formal > systems which are powerful enough to formulate arithmetic. Goedels > results do not apply to physics theories, which in general are not > formal, but applications of existing theories in geometry and function > theory. > Bob Kolker How stupid are you going to get? Now you claim Einstein's theories are physical theories? What is a physical theory? Those are just mathematical theories. They are incomplete but consistent. Every consistent formal system contains antinomies or paradox(es). Every complete formal system does not contain antinomies but it is incosistent. SR incompletness is well known. It contains the twin paradox. GR's incompletness arises from locality. It leads to antinomies and I have shown that in these ng's. the arfument is simple and straight forward. Pure formal systems in the spirit of logical positivism of early 20th century. Both theories are failures. Their survival is solely due to a huge publicity effort and media involvement. Plenty of empirical evidence says they are trash. You are playing your last card. Mike === Subject: Re: SR consistency is crap. > > A theory about math must be consistent but cannot be complete. Thus it >> always incorporates a paradox: Goedel I'm really curious as to what you think the word paradox means. The word complete can mean many things, like deductively complete, or semantically complete. A theory about math can mean many things too. Are you talking about a list oFOL formulas? There is no proof that set theory is consistent, btw. That's why Goedel's result is that oFOL based set theory is deductively incomplete (by a fixed method of proof) if it is consistent. > G.9adel's Incompleteness Theorem > http://mathworld.wolfram.com/GoedelsIncompletenessTheorem.html > Goedel's incompleteness results apply to a particular class of formal > systems which are powerful enough to formulate arithmetic. Goedels > results do not apply to physics theories, which in general are not > formal, but applications of existing theories in geometry and function > theory. > Bob Kolker How stupid are you going to get? Now you claim Einstein's theories are > physical theories? What is a physical theory? Those are just > mathematical theories. They are incomplete but consistent. A physical theory is a generator of a list of predictions. If you use a consistent source to generator your list then you don't have to worry about predicting contradictory things. If you use an incomplete generator, then there might be experiemnts where your theory makes no prediction. > Every > consistent formal system contains antinomies or paradox(es). Every > complete formal system does not contain antinomies but it is > incosistent. Now I wonder what your definition of antinomies are. > SR incompletness is well known. It contains the twin paradox. SR contains now contradictions. The experiment where two twins leave and see the same red-shift factor followed by the same blue shift factor has the case where one twin ages more than the other. This is not a contradiction because the one who ages less sees the red shift for a smaller propotion of the trip than the one who ages more. There is simply NO contradiction in that experiment OR in it's UNambigious prediction. Anyone who told you otherwise was either incompetant or a liar. I'd have to know them to know which they were. > GR's > incompletness arises from locality. It leads to antinomies and I have > shown that in these ng's. the arfument is simple and straight forward. An incomplete generator just fails to make predictions. Based on your previous useage about twin paradox I suspect that you think that GR makes contradictory predictions. This is not the case either, if so set theory would be inconsistent, because set theory is the essential part of the generator of GR. > Pure formal systems in the spirit of logical positivism of early 20th > century. Both theories are failures. Their survival is solely due to a > huge publicity effort and media involvement. Plenty of empirical > evidence says they are trash. Interesting theory. How come things hold up in the lab then? Does the media mess with my equipment when I'm not there? Your thoughts are very interesting Mike, I'd love to see you back up what you say. === Subject: Re: SR consistency is crap. > How stupid are you going to get? Now you claim Einstein's theories are > physical theories? Any theory that leads to testable quantitative predictions about what happens in the world, under specified circumstance is a physical theory. The word physics in a physics theory pertains to the domain of application, not the methodology. GTR has not yet been falsified by empirical means. What is a physics theory. It is a verbal artifact which is used to grind out testable predictions of what will happen in the world, under specified condition. It is a predictor. Nothing more, nothing less. Bob Kolker === Subject: Re: SR consistency is crap. > A theory about math must be consistent but cannot be complete. Thus it > always incorporates a paradox: Goedel > A theory about physics must be complete, i.e. contain no paradox but > as a result it is always inconsistent. A physics theory need not apply to all phenomena nor explain every phenomena. Quantum theory does not explain gravitation, for instance. > Thus, idiot Einstein, not understanding the right domain for the > application of math, has twin paradox and black holes in his theories. > They are consistent math theories stupid eleticus (you'll never become > an 'eleatis'), but not complete to qualify for physical theories > because they incorporate paradoxes. What paradoxes? Do you mean inconsistency. None of Einstein's theories nor any mainline physics theory of any kind is mathematically inconsistent. None of them are complete. No one single theory explains all the known forces for example. > This settles the Einstein Affair once for all:. He applied mathemetics > to come up with a physical theory without using self evident > propositions as axioms, Oh bull. Reality cannot be deduced a priori from self-evident axioms. The postulates chose where chose to predict certain classes of phenomena. There is nothing self evident about them at all. For example Newton's theird law of motion is not self evident, which is to say the conservation of momentum is not self evident. One could have a theory in which momentum is not conserved and it would be perfectly consistent (internally). It would also be emprically wrong. Bob Kolker === Subject: Re: SR consistency is crap. > A theory about math must be consistent but cannot be complete. Thus it > always incorporates a paradox: Goedel > A theory about physics must be complete, i.e. contain no paradox but > as a result it is always inconsistent. > A physics theory need not apply to all phenomena nor explain every > phenomena. Quantum theory does not explain gravitation, for instance. > Thus, idiot Einstein, not understanding the right domain for the > application of math, has twin paradox and black holes in his theories. > They are consistent math theories stupid eleticus (you'll never become > an 'eleatis'), but not complete to qualify for physical theories > because they incorporate paradoxes. > What paradoxes? Do you mean inconsistency. None of Einstein's theories > nor any mainline physics theory of any kind is mathematically > inconsistent. None of them are complete. No one single theory explains > all the known forces for example. > This settles the Einstein Affair once for all:. He applied mathemetics > to come up with a physical theory without using self evident > propositions as axioms, > Oh bull. Reality cannot be deduced a priori from self-evident > axioms. The postulates chose where chose to predict certain classes of > phenomena. There is nothing self evident about them at all. For example > Newton's theird law of motion is not self evident, which is to say the > conservation of momentum is not self evident. One could have a theory in > which momentum is not conserved and it would be perfectly consistent > (internally). It would also be emprically wrong. > Bob Kolker You are a very confused individual. Conservation of linear momentum arises from the second law: integral from t1 to t2 of (Fdt) = integral from t1 to t2 of (dp/dt)dt = (p1) - (p2) If F = 0 then p1=p2 =mv = constant. And again stupid, Newton's third law is self evident. You seem not to understand what 'self-evident' means. I do not blame you since the books you have read were written by idiots. A generation of people who should have gone to law school but because the standards were high they got involved with Physics and turned it into the greatest Sophism of all times. Self-evident means exactly that. It does not mean evident to you or empirically evident. Otherwise it would have been called just 'evident'. Neither stupid Einstein understood this. Newton did understand it. 100 years of bull**** is enough. Enough is enough. YOu cannot fool nobody any longer. Mike === Subject: Re: SR consistency is crap. > = (p1) - (p2) THird Law force of action = force of reaction. or dp_1/dt = -dp_2/dt hence dp_1/dt + dp_2/dt = 0 which implies d(p_1 + p_2)/dt = 0 which implies p_1 + p_2 = const. That is your conservation of momentum from the third law. Bob Kolker === Subject: Re: SR consistency is crap. > = (p1) - (p2) > THird Law force of action = force of reaction. > or dp_1/dt = -dp_2/dt hence dp_1/dt + dp_2/dt = 0 Correct. But in the absence of the second law you wouldn't be able to make that step. You lack basic understanding of what is a primitive in science and what is a direct consequence versus a deduction. which implies > d(p_1 + p_2)/dt = 0 which implies p_1 + p_2 = const. That is your > conservation of momentum from the third law. You have showed that the momentum of an isolated system of two former is a deduction, the latter is a direct consequence of the second law and the assumptions that lead to it regarding the properties of space and time, and of course the property of inertia (first law). > Bob Kolker Another misunderstanding of Mr. Bob Kolker. It shows that physics is more than symbol manipulation and arbitrary conclusions like Einstein and his modern followers preach. Science must be founded on self-evident principles otherwise is nothing more than religion and paranoia, whether or not predictions come out right. This is because: every false formula implies a true formula. Example: 3 > 4 ---> 5 > 4 is a true conditional. The world must isolate Bob Kolkerism and eliminate it before it is too late and chaos prevails over common sense. Mike === Subject: Re: SR consistency is crap. > You have showed that the momentum of an isolated system of two > former is a deduction, the latter is a direct consequence of the > second law and the assumptions that lead to it regarding the > properties of space and time, and of course the property of inertia > (first law). Actually the first law. No force means uniform velocity which means velocity don't change and the mass is constant the momentum is constant because momentum = m*v (classically) or m*v/sqrt(1 -v^2) relativistically. Bob Kolker === Subject: Re: SR consistency is crap. > You have showed that the momentum of an isolated system of two > former is a deduction, the latter is a direct consequence of the > second law and the assumptions that lead to it regarding the > properties of space and time, and of course the property of inertia > (first law). > Actually the first law. No force means uniform velocity which means > velocity don't change and the mass is constant the momentum is constant > because momentum = m*v (classically) or m*v/sqrt(1 -v^2) relativistically. > Bob Kolker Again, the first law cannot be a primitive law. It is a deduction from the second law. This is the reason in some books Lex secunda is stated as Lex prima. If the quantity of motion P = mv remains constant when no force acts, it immediately means that dp/dt = F is given. Thus, Lex secunda is Lex prima and Lex prima is Lex secunda. Many generations have been fooled by the British school of philosophy using this trick to enforce the empirical nature of Newton's laws of motion. Continental schools remained unconvnined about that. Corect laws: 1st: F = d(mv)/dt is an axiom, cannot be proved empirically. F. M, V cannot be measured independently of one another. 2nd: If F =0 then mv = constant, is a simple theorem proved using 1st law 3rd: F12 = - F21, is an axiom or a theorem depending on the approach (complicated issue, has to do with metaphysics, cannot be proved) Let's stop fooling people. It's time to go forward. Many generations of brain washed pupils is enough. Mike === Subject: Re: SR consistency is crap. > Many generations have been fooled by the British school of philosophy > using this trick to enforce the empirical nature of Newton's laws of > motion. Continental schools remained unconvnined about that. Corect > laws: > 1st: F = d(mv)/dt is an axiom, cannot be proved empirically. F. M, V > cannot be measured independently of one another. This above statement assumes many other prior theories about the nature of sapce and time, lengths, etc. Assuming a known force (like gravitation) then you can apply fixed forces to achieve a system in stasis (there come the assumptions about simultaneousness) like electro-static forces to figure out how much mass something has. You can then use a clock to see how far it goes in with a fixed force (say, roll the ball on an incline) and see how far it goes, much much verification is possible. It is not self-evident, you make it sound like most of historical science was done by thought experiments. The problem is that that the whole foundation doesn't hold up to the patterns of electrodynamics phenomena. The pattern described by the first law DID hold up for a wide variety of experiments, but then it failed. > Let's stop fooling people. It's time to go forward. Many generations > of brain washed pupils is enough. I'm all for improving education, I'm not sure that closing my eyes and pretending that Newton's patterns are universal laws HELPS that any when there is evidence to the contrary. Whereas SR when taught correctly is a very useful theory, one that you can EVEN derive Newton's patterns from as special limiting cases. Why can't we work on improving SR education Mike? === Subject: Re: SR consistency is crap. >I see Mike is at his old tricks again. Newton's laws contain some aspects >that are nothing but tautologies but Newton's 3rd law for example has >empirical content that can be tested. Also those bits that are tautologies >can easily be converted into forms that are not eg Newton's first law can be >reformulated as inertial frames exist where inertial frames are defined by >their symmetry properties. Not to encourage the woo-woos, but can I take a moment to examine this? What would it mean for the 3rd law to be violated? A gun that can fire a bullet without recoil, a rocket that gains more momentum than the exhaust, an ice skater that might push off a wall and the entire Earth moves while the skater stays still, etc. Reduce the problem to two identical masses with a compressed spring between them. Assume the spring will exert a force on one or both masses, but we don't know yet whether it will be equal and opposite. Now rotate the system by 180 degrees, and it goes to an identical system because the masses are equal, the distance of each from the center of the spring is equal, even the handedness of the spring stays the same. There's no way to distinguish one orientation from the other such that we can say a force is exerted on one mass but not on the other, unless something breaks the symmetry of the system. That symmetry could be broken by an external force like gravity. Then the masses could accelerate differently. But we'd say that there are two forces acting on the masses; the spring, and gravity. A rocket can certainly gain more momentum than its exhaust if it's falling down. -- The preferred method of entering a building is to use a tank main gun round, direct fire artillery round, or TOW, Dragon, or Hellfire missile to clear the first room. -- THE RANGER HANDBOOK U.S. Army, 1992 === Subject: Re: SR consistency is crap. > Many generations have been fooled by the British school of philosophy > using this trick to enforce the empirical nature of Newton's laws of > motion. Continental schools remained unconvnined about that. Corect > laws: > 1st: F = d(mv)/dt is an axiom, cannot be proved empirically. F. M, V > cannot be measured independently of one another. > This above statement assumes many other prior theories about the > nature of sapce and time, lengths, etc. Assuming a known force (like > gravitation) then you can apply fixed forces to achieve a system in > stasis (there come the assumptions about simultaneousness) like > electro-static forces to figure out how much mass something has. You > can then use a clock to see how far it goes in with a fixed force > (say, roll the ball on an incline) and see how far it goes, much much > verification is possible. It is not self-evident, you make it sound > like most of historical science was done by thought experiments. The > problem is that that the whole foundation doesn't hold up to the > patterns of electrodynamics phenomena. The pattern described by the > first law DID hold up for a wide variety of experiments, but then it > failed. > Let's stop fooling people. It's time to go forward. Many generations > of brain washed pupils is enough. > I'm all for improving education, I'm not sure that closing my eyes and > pretending that Newton's patterns are universal laws HELPS that any > when there is evidence to the contrary. Whereas SR when taught > correctly is a very useful theory, one that you can EVEN derive > Newton's patterns from as special limiting cases. Why can't we work > on improving SR education Mike? SR is kinematics. You got a problem right from the start. SR came to challenge the Copernican view of the world (see Hans Reichenbach, The Philosophy of Space and Time) the cornerstone of Newton's dynamics. Ptolemaic and Copernican systems are kinematically equivalent according to Relativity. Yet, while admitting SR, the educational status quo refuses to drop Newtonian dynamics, claiming there is ample emprirical evidence to support it. Actually, sicne Newton's laws are mere tautologies, in non-relativistic limits they will always conform to experiment. I took Physics 101 and Modern Phycsi 101 together during the same semester as soon as I started undergraduate. The mentor protested and argued I should take Modern Physics (Relativity) after I take Classical Mechanics, because that was a prerequisite. I protested, I argued it must be my choice not theirs. I won. I got a A- in Classical and an A+ in Modern. I think this is the way to go. Teach students everything together as competing theories and not relativity as an advance extension to Newtonian Dynamics. But remember, you still have a problem. SR+GR are axiomatic systems. No different from Euclidean geometry in that respect. You gain understanding of the theories early on but also you raise the doubt in their foundations. Eventually, someone will lose. Those that are afraid of ending up with a loser keep SR+GR as advance subjects. Remember what happened to Euclidean geometry? As soos as they started teaching it, thousands attempted to disprove the Playfair axiom (parallel lines never meet). The result was a relative-consistency with spherical and hypoerbolic geometries. The same will happen to SR+GR as soon as they became a target of the masses. The current approach is to keep the theory for the few and feed the supposed prediction to the masses via the media. Silly but works due to hype. Mike === Subject: Re: SR consistency is crap. > Many generations have been fooled by the British school of philosophy > using this trick to enforce the empirical nature of Newton's laws of > motion. Continental schools remained unconvnined about that. Corect > laws: 1st: F = d(mv)/dt is an axiom, cannot be proved empirically. F. M, V > cannot be measured independently of one another. > This above statement assumes many other prior theories about the > nature of sapce and time, lengths, etc. Assuming a known force (like > gravitation) then you can apply fixed forces to achieve a system in > stasis (there come the assumptions about simultaneousness) like > electro-static forces to figure out how much mass something has. You > can then use a clock to see how far it goes in with a fixed force > (say, roll the ball on an incline) and see how far it goes, much much > verification is possible. It is not self-evident, you make it sound > like most of historical science was done by thought experiments. The > problem is that that the whole foundation doesn't hold up to the > patterns of electrodynamics phenomena. The pattern described by the > first law DID hold up for a wide variety of experiments, but then it > failed. > Let's stop fooling people. It's time to go forward. Many generations > of brain washed pupils is enough. > I'm all for improving education, I'm not sure that closing my eyes and > pretending that Newton's patterns are universal laws HELPS that any > when there is evidence to the contrary. Whereas SR when taught > correctly is a very useful theory, one that you can EVEN derive > Newton's patterns from as special limiting cases. Why can't we work > on improving SR education Mike? > SR is kinematics. You got a problem right from the start. SR came to > challenge the Copernican view of the world (see Hans Reichenbach, The > Philosophy of Space and Time) the cornerstone of Newton's dynamics. SR challenges the idea of absolute time regardless of what Hans Reichenbach may or may not say. Since you seem to like to quote eminent philosophers you might tike to actually check out what an eminent physicist has to say - see Landau - Mechanics - page 6 and 8 where the true bases is discussed. > Ptolemaic and Copernican systems are kinematically equivalent > according to Relativity. Yet, while admitting SR, the educational > status quo refuses to drop Newtonian dynamics, claiming there is ample > emprirical evidence to support it. Actually, sicne Newton's laws are > mere tautologies, in non-relativistic limits they will always conform > to experiment. I see Mike is at his old tricks again. Newton's laws contain some aspects that are nothing but tautologies but Newton's 3rd law for example has empirical content that can be tested. Also those bits that are tautologies can easily be converted into forms that are not eg Newton's first law can be reformulated as inertial frames exist where inertial frames are defined by their symmetry properties. Bill > I took Physics 101 and Modern Phycsi 101 together during the same > semester as soon as I started undergraduate. The mentor protested and > argued I should take Modern Physics (Relativity) after I take > Classical Mechanics, because that was a prerequisite. I protested, I > argued it must be my choice not theirs. I won. I got a A- in Classical > and an A+ in Modern. > I think this is the way to go. Teach students everything together as > competing theories and not relativity as an advance extension to > Newtonian Dynamics. But remember, you still have a problem. SR+GR are > axiomatic systems. No different from Euclidean geometry in that > respect. You gain understanding of the theories early on but also you > raise the doubt in their foundations. Eventually, someone will lose. > Those that are afraid of ending up with a loser keep SR+GR as advance > subjects. Remember what happened to Euclidean geometry? As soos as > they started teaching it, thousands attempted to disprove the Playfair > axiom (parallel lines never meet). The result was a > relative-consistency with spherical and hypoerbolic geometries. The > same will happen to SR+GR as soon as they became a target of the > masses. The current approach is to keep the theory for the few and > feed the supposed prediction to the masses via the media. Silly but > works due to hype. Countless good books explaining classical mechanics, SR and GR exist for any who are interested to find out what is happening. For classical mechanics I recommend Landau - Mechanics, for SR Rindler - Introduction to Sepia;Relativity, for GR Wald - General Relativity. Bill > Mike === Subject: Re: SR consistency is crap. > recommend Landau - Mechanics, for SR Rindler - Introduction to > Sepia;Relativity, for GR Wald - General Relativity. Wald is a bear to read. It requires some mathematical cojones. For an introduction I prefer Sean Carrol's book. It is somewhat gentler. Bob Kolker === Subject: Re: SR consistency is crap. > Many generations have been fooled by the British school of philosophy > using this trick to enforce the empirical nature of Newton's laws of > motion. Continental schools remained unconvnined about that. Corect > laws: > 1st: F = d(mv)/dt is an axiom, cannot be proved empirically. F. M, V > cannot be measured independently of one another. > This above statement assumes many other prior theories about the > nature of sapce and time, lengths, etc. Assuming a known force (like > gravitation) then you can apply fixed forces to achieve a system in > stasis (there come the assumptions about simultaneousness) like > electro-static forces to figure out how much mass something has. You > can then use a clock to see how far it goes in with a fixed force > (say, roll the ball on an incline) and see how far it goes, much much > verification is possible. It is not self-evident, you make it sound > like most of historical science was done by thought experiments. The > problem is that that the whole foundation doesn't hold up to the > patterns of electrodynamics phenomena. The pattern described by the > first law DID hold up for a wide variety of experiments, but then it > failed. > Let's stop fooling people. It's time to go forward. Many generations > of brain washed pupils is enough. > I'm all for improving education, I'm not sure that closing my eyes and > pretending that Newton's patterns are universal laws HELPS that any > when there is evidence to the contrary. Whereas SR when taught > correctly is a very useful theory, one that you can EVEN derive > Newton's patterns from as special limiting cases. Why can't we work > on improving SR education Mike? > SR is kinematics. I disagree. SR is about a proposed symmetry of nature. > You got a problem right from the start. SR came to > challenge the Copernican view of the world (see Hans Reichenbach, The > Philosophy of Space and Time) the cornerstone of Newton's dynamics. > Ptolemaic and Copernican systems are kinematically equivalent > according to Relativity. Yet, while admitting SR, the educational > status quo refuses to drop Newtonian dynamics, claiming there is ample > emprirical evidence to support it. Actually, sicne Newton's laws are > mere tautologies, in non-relativistic limits they will always conform > to experiment. Newtonian dynamics are not dropped. They are derived locally, you already conceded that below that they are local tautologies. A dynamic isn't much without a law about elementary forces. > I took Physics 101 and Modern Phycsi 101 together during the same > semester as soon as I started undergraduate. The mentor protested and > argued I should take Modern Physics (Relativity) after I take > Classical Mechanics, because that was a prerequisite. I protested, I > argued it must be my choice not theirs. I won. I got a A- in Classical > and an A+ in Modern. Good for you. I didn't even realize I liked physics until Modern Physics (which for us covered QM, solid state, Stat mech, etc. too) I just took it as an easy class since I was good at math. > I think this is the way to go. Teach students everything together as > competing theories and not relativity as an advance extension to > Newtonian Dynamics. I'd rather teach QM from the start, and get special relativity as a limiting case of that, and then Newtonian dynamics as a special case of that. > But remember, you still have a problem. SR+GR are > axiomatic systems. No different from Euclidean geometry in that > respect. You gain understanding of the theories early on but also you > raise the doubt in their foundations. Huh? You want to avoid doubt? Science has doubt, predictions are made, the predictions can be compared to data, they might pass or fail. > Eventually, someone will lose. Only theories can lose, not people, please explain more what you mean. > Those that are afraid of ending up with a loser keep SR+GR as advance > subjects. I'd love to have GR and SR as grade-school subjects, does that mean I'm not afraid of losing? I don't know what you mean by afraid of losing or lose, I do hope my predictions match the data, that's because if it's easy to be wrong, so why bother learning a theory if it makes wrong predictions? > Remember what happened to Euclidean geometry? What happened? It's still around! > As soos as > they started teaching it, thousands attempted to disprove the Playfair > axiom (parallel lines never meet). The result was a > relative-consistency with spherical and hypoerbolic geometries. Elemetary euclidean geometry was proved consistent, you can drop relative-consistency and just say consistent if what you mean is that elementary hyperbolic geometry is as consistent as elementary Euclidean geometry. And if you mean something other than elementary, then that useally means bringing in sets and once you've done that then all become equiconsistent with set theory. > The > same will happen to SR+GR as soon as they became a target of the > masses. What will happen to SR+GR (which is GR, unless you meant the same will happen to SR and the same will happen to GR as soon as each becomes a target of the masses)? And what masses are currently kept away from it? > The current approach is to keep the theory for the few and > feed the supposed prediction to the masses via the media. Silly but > works due to hype. > Mike I actively try to teach physics at as early a stage as possible, and books on relatively are freely sold in stores, there is no conspiracy going on. Anyone can learn. Heck, I'm on Usenet because I want to help people learn SR, among other reasons, this is a public forum where anyone can read it. === Subject: Re: SR consistency is crap. >I'd rather teach QM from the start, and get special relativity as a >limiting case of that, and then Newtonian dynamics as a special case >of that. How do you expect to get special relativity as a limiting case of QM? David ----- === Subject: Re: SR consistency is crap. >I'd rather teach QM from the start, and get special relativity as a >limiting case of that, and then Newtonian dynamics as a special case >of that. > How do you expect to get special relativity as a limiting case of QM? > David comes as a limiting case. Many of the so-called quantum corrections are actually present in classical SR, so in a sense QM has always been SR theory. === Subject: Re: SR consistency is crap. > comes as a limiting case. Many of the so-called quantum corrections > are actually present in classical SR, so in a sense QM has always been > SR theory. Which quantities in non-relativistic QM are Lorentz invariant? Bob Kolker === Subject: Re: SR consistency is crap. > comes as a limiting case. Many of the so-called quantum corrections > are actually present in classical SR, so in a sense QM has always been > SR theory. > Which quantities in non-relativistic QM are Lorentz invariant? > Bob Kolker i It's the spin bivector, but in the non-relativistic constant-spin limit the Dirac theory becomes the Schrodinger theory and the spatial bivector becomes a constant. But what I was discussing was various factors of 2 differences between QM and classical mechanics, SR has the same factors of 2. === Subject: Re: SR consistency is crap. > comes as a limiting case. Many of the so-called quantum corrections > are actually present in classical SR, so in a sense QM has always been > SR theory. > Which quantities in non-relativistic QM are Lorentz invariant? > Bob Kolker > It's the spin bivector, but in the non-relativistic constant-spin > limit the Dirac theory becomes the Schrodinger theory and the spatial > bivector becomes a constant. No, the nonrelativistic limit of the Dirac theory is the Pauli theory. There's no getting away from spin. === Subject: Re: SR consistency is crap. > comes as a limiting case. Many of the so-called quantum corrections > are actually present in classical SR, so in a sense QM has always been > SR theory. > Which quantities in non-relativistic QM are Lorentz invariant? > Bob Kolker > i > It's the spin bivector, but in the non-relativistic constant-spin > limit the Dirac theory becomes the Schrodinger theory and the spatial > bivector becomes a constant. > No, the nonrelativistic limit of the Dirac theory is the Pauli theory. > There's no getting away from spin. Have you ever noted that i is isomorphic to an element of the pauli algebra, ever noted that the pauli algebra is isomorphic to the dirac algebra. You can take a non-relativistic limit of dirac to get Pauli and a constant spin limit of pauli to get schrodinger, the holdever from dirac includes i. Do dirac algebra symbolically starting with gt gx gy gz and getting the rest from mulitplation and addition, for instance 1 = (gt)(gt). Then the pauli matrix px can be px := (gt)(gx), py := (gt)(gy). pz:=(gt)(gz), it's been done before. Quantum mechanics is IMO about spin, and in that sense there is no getting around it. But I'd also therefore say that spin is inherent in the schrodinger theory. Why do YOU think i appears in schrodinger theory? === Subject: Re: SR consistency is crap. > comes as a limiting case. Many of the so-called quantum corrections > are actually present in classical SR, so in a sense QM has always been > SR theory. > Which quantities in non-relativistic QM are Lorentz invariant? > Bob Kolker > i > It's the spin bivector, but in the non-relativistic constant-spin > limit the Dirac theory becomes the Schrodinger theory and the spatial > bivector becomes a constant. > No, the nonrelativistic limit of the Dirac theory is the Pauli theory. > There's no getting away from spin. > Have you ever noted that i is isomorphic to an element of the pauli > algebra, ever noted that the pauli algebra is isomorphic to the dirac > algebra. You can take a non-relativistic limit of dirac to get Pauli > and a constant spin limit of pauli to get schrodinger, the holdever > from dirac includes i. > Do dirac algebra symbolically starting with gt gx gy gz and getting > the rest from mulitplation and addition, for instance 1 = (gt)(gt). > Then the pauli matrix px can be px := (gt)(gx), py := (gt)(gy). > pz:=(gt)(gz), it's been done before. Quantum mechanics is IMO about > spin, and in that sense there is no getting around it. But I'd also > therefore say that spin is inherent in the schrodinger theory. Why do > YOU think i appears in schrodinger theory? ANSWER Because, duh, it's a differential wave equation, and if you try to make or solve differential equations about waves without using i, you are letting yourself in for a lot of unnecessary mathematical pain. That doesn't mean there's anything specifically physical about the i= sqrt(-1) that denotes spin. This is easily proved. The Shroedinger equation is the non-relativistic limit of the Klein-Gordon *scalar* wave equation, which explicitly does not include room for spin. Therefore neither does its low-energy limit, the Shroedinger eq. To be sure there is no i in the K-G equation, but that's not because the K-G doesn't describe spin. Rather it's because in some sense the K-G equation as we know it with -1 has been prettied up by squaring both sides of a relativisitic QM equation that contains the familiar relativistic square root relations for energy, and which does contain an i as the square root of that -1 you see in K-G. Thus, both positive and negative energy solutions are implicit in this squared stucture of the K-G equation, just as in Dirac, but provisions for spin, sorry, no. SBH === Subject: Re: SR consistency is crap. J.E.: >> >> comes as a limiting case. Many of the so-called quantum corrections >> are actually present in classical SR, so in a sense QM has always been >> SR theory. >> >> Which quantities in non-relativistic QM are Lorentz invariant? >> >> Bob Kolker >It's the spin bivector, but in the non-relativistic constant-spin >limit the Dirac theory becomes the Schrodinger theory and the spatial >bivector becomes a constant. But what I was discussing was various Hindsight is 20-20, but it doesn't constitute a derivation of anything. In particular, a relativistic quantum wave equation did exist in 1920, the klein-gordon equation. Despite being relativistic, it doesn't contain the electron spin, so I don't think it's fair to conclude that spin leads to relativity, just because in hindsight, you can make some tentative connection between spin and relativity. A counter-example is the weak interaction. The W+/- and Z are also described by the SU(2) algebra, yet the W+/- and Z are spin 1 rotation in the form of a guge transformation, not the spatial part of bivector. Indeed, the weak interaction is a vector-axial vector and is proportional to gamma^u(1 - gamma^5), not sigma^uv. >factors of 2 differences between QM and classical mechanics, SR has >the same factors of 2. E^2 = p^2 + m^2 IF, you insert the quantum mechanical operators for p and E, you get the relativistic wave equation. The wave equation you get does not contain the pauli matrices in any kind of limit, so it wouldn't be very convincing to suggest there is some connection. If it had been convincing, someone would have done it before dirac, since dirac's motivation was to find _a_ relativistic wave equation that was compatible with quantum mechanics, not explain spin based on any intuition gleened from the pauli matrices. === Subject: Re: SR consistency is crap. > J.E.: > >> comes as a limiting case. Many of the so-called quantum corrections > >> are actually present in classical SR, so in a sense QM has always been > >> SR theory. > >> Which quantities in non-relativistic QM are Lorentz invariant? > >> Bob Kolker > >i > >It's the spin bivector, but in the non-relativistic constant-spin > >limit the Dirac theory becomes the Schrodinger theory and the spatial > >bivector becomes a constant. But what I was discussing was various > Hindsight is 20-20, but it doesn't constitute a derivation of > anything. In particular, a relativistic quantum wave equation did > exist in 1920, the klein-gordon equation. Despite being relativistic, > it doesn't contain the electron spin, so I don't think it's fair > to conclude that spin leads to relativity, just because in hindsight, > you can make some tentative connection between spin and relativity. I didn't mean to say that spin leads to relativity. The dirac equation has spin and relativity, and even in the constant spin limit, the spin direction which singled out a preffered direction exists, in the form of the scalar i. So either relativity never fully goes away, or spin never fully goes away. I'm not sure there is that much of a difference. I'm a strong believer in doing invariant SR all the time, If most wordlines point all in almost the same direction, so be it, no one forces you to take non-relativistic limits. > A counter-example is the weak interaction. The W+/- and Z are also > described by the SU(2) algebra, yet the W+/- and Z are spin 1 > rotation in the form of a guge transformation, not the spatial part > of bivector. Indeed, the weak interaction is a vector-axial vector > and is proportional to gamma^u(1 - gamma^5), not sigma^uv. Counter-example to what? There is no non-relativistic limit of the W+/0 and Z interaction. I'm saying that the i in the electron theory of schrodinger isn't arbitrary because it generalizes in a SPECIFIC way to the full dirac theory. There isn't a schrodinger theory of the W or the Z, so there is no analogous claim. So I didn't MAKE an analogous claim. > >factors of 2 differences between QM and classical mechanics, SR has > >the same factors of 2. > E^2 = p^2 + m^2 > IF, you insert the quantum mechanical operators for p and E, you get > the relativistic wave equation. The wave equation you get does not > contain the pauli matrices in any kind of limit, so it wouldn't be > very convincing to suggest there is some connection. If it had been > convincing, someone would have done it before dirac, since dirac's > motivation was to find _a_ relativistic wave equation that was compatible > with quantum mechanics, not explain spin based on any intuition gleened > from the pauli matrices. Let's say you want and object X, such that XX=m*m, then go to the dirac algebra and find X= E gt + px gx + py gy + pz gz. Then you get X*X = m*m. This is a space-time algebra, if you want a spatial algebra relative to an observer comovingn with gt, then just take the basis ((gt)(gx)) ((gt)(gy)) and ((gt)(gz)), you'll note that the algebra they span is isomorphic, as an algebra, to the pauli algebra. Why didn't Dirac know that? Well Gibbs won a general debate on whether to use Hamilon's quaternians (which were related to Clifford's algebras which include the algebras later known as the pauli algebra and the dirac algebra) or to use Gibbs own vector system. Gibbs's sytem didn't generalize to 4-d (too bad for Einstein) whereas Hamilton's system DID generalize to the ALREADY KNOWN Clifford algebras, WHICH DIRAC AND PAULI HAD TO REINVENT ANYWAY, but Gibbs won, and since math-land was overwought with classification of algebras at the time and separated from physics development, no one at all cared about abstract clifford algebras once the theorem every clifford algebra is (isomorphic to) a matrix algebra was proven. And later Pauli and Dirac had to come looking for a matrix algebra to handle spacetime mechanics. That's the historical story about why Dirac didn't know that. Maybe if Clifford hadn't died so young, then things would have been different, but there's no use debating what ifs. === Subject: Re: SR consistency is crap. J.E.: >> A counter-example is the weak interaction. The W+/- and Z are also >> described by the SU(2) algebra, yet the W+/- and Z are spin 1 >> rotation in the form of a guge transformation, not the spatial part >> of bivector. Indeed, the weak interaction is a vector-axial vector >> and is proportional to gamma^u(1 - gamma^5), not sigma^uv. >Counter-example to what? There is no non-relativistic limit of the >W+/0 and Z interaction. Sure there is. It's called nuclear beta decay. The extent to which the calculation is relativistic depends upon the precision you want to obtain. That is true for atomic spectra as well. In the non-relativistic limit, you get the fermi operator, which just `1' and the gamow-teller operator which is delta.tau, delta being the pauli matrices and tau being a weak isovector. >I'm saying that the i in the electron >theory of schrodinger isn't arbitrary because it generalizes in a >SPECIFIC way to the full dirac theory. There isn't a schrodinger >theory of the W or the Z, so there is no analogous claim. Look up the non-relativistic weak hamiltonian for simple beta decay in nuclei. You can get by in lots of cases with very little relativity. >So I didn't MAKE an analogous claim. >> >factors of 2 differences between QM and classical mechanics, SR has >> >the same factors of 2. >> >> >> E^2 = p^2 + m^2 >> >> IF, you insert the quantum mechanical operators for p and E, you get >> the relativistic wave equation. The wave equation you get does not >> contain the pauli matrices in any kind of limit, so it wouldn't be >> very convincing to suggest there is some connection. If it had been >> convincing, someone would have done it before dirac, since dirac's >> motivation was to find _a_ relativistic wave equation that was compatible >> with quantum mechanics, not explain spin based on any intuition gleened >> from the pauli matrices. >Let's say you want and object X, such that XX=m*m, then go to the >dirac algebra and find X= E gt + px gx + py gy + pz gz. Then you get >X*X = m*m. Hindsight is 20-20. I think you fail to appreciate the fact that dirac did not have the benefit of seeing his equation in textbooks after tens of thousands of physicists studied it for 70 years. What dirac did was quite remarkable. Dirac's primary justification for the dirac equation was that he considered it too beutiful to be incorrect. He obviously had no real idea how to interpret it, since he tried to identify the negative energy states with the proton at first and tried for a while to obtain that result. It wasn't until he realized that idea was destined to fail that he predicted the positron. >This is a space-time algebra, if you want a spatial >algebra relative to an observer comovingn with gt, then just take the >basis ((gt)(gx)) ((gt)(gy)) and ((gt)(gz)), you'll note that the >algebra they span is isomorphic, as an algebra, to the pauli algebra. Yes, I am aware of all of that. I've read several of hestenes papers and I have pertti lounesto's book on clifford algebras, which mentions hestene's program, but slides by the issue of the `i' in quantum theory. I don't find that approach very physically illuminating. I think the claim that `i' represents a unit pseudoscalar in quantum theory, is a bit of a stretch. For example, `i' is what quantizes quantum mechanics. First quantization doesn't entail any relativistic concepts nor even [p, q] = -ihbar. >Why didn't Dirac know that? Well Gibbs won a general debate on >whether to use Hamilon's quaternians (which were related to Clifford's >algebras which include the algebras later known as the pauli algebra >and the dirac algebra) or to use Gibbs own vector system. Gibbs's >sytem didn't generalize to 4-d (too bad for Einstein) whereas >Hamilton's system DID generalize to the ALREADY KNOWN Clifford >algebras, WHICH DIRAC AND PAULI HAD TO REINVENT ANYWAY, but Gibbs won, Again, hindsight is 20-20. To have an appreciation for what dirac didn't rather than all of the clues that hindsight tells you were staring everyone in the face, you have to try to imagine what it was like in an era when bohr was still trying to figure out atomic electron and proton. (The neutron wasn't discovered until around 1931). >and since math-land was overwought with classification of algebras >at the time and separated from physics development, no one at all >cared about abstract clifford algebras once the theorem every Well, up until around 1918 when noether published her famous theorems, the reason for conservation laws, like conservation of energy, weren't understood, so I imagine that a physical basis for using group theory was not readily apparent. Since practically all of the physics since then is directly or inderectly a result of recognizing the importance of noether's theorem, it's easy to forget it didn't always exist. If you look in goldstein, in the section on hamilton-jacobi theory, you'll find a couple of pages that discusses precisely why hamilton could not have proposed the schroedinger equation. >clifford algebra is (isomorphic to) a matrix algebra was proven. And >later Pauli and Dirac had to come looking for a matrix algebra to >handle spacetime mechanics. That's the historical story about why OK, so what precisely, would lead anyone to identify clifford algebras with relativity in 1920? >Dirac didn't know that. Maybe if Clifford hadn't died so young, then >things would have been different, but there's no use debating what >ifs. The utility of clifford algebras and other aspects of group theory is a consequence of noether's work, which showed that continuous symmetries of the lagrangian can be identified with conserved currents. Once symmetry was recogized as being even more important than it had been, group theory became important. === Subject: Re: SR consistency is crap. >>I'd rather teach QM from the start, and get special relativity as a >>limiting case of that, and then Newtonian dynamics as a special case >>of that. > How do you expect to get special relativity as a limiting case of QM? You don't. You have to formulate a quantum theory that incorporates QM, as did Dirac. Relativity is not deducible from classical wave mechanics or Heisenberg matrices. Bob Kolker === Subject: Re: SR consistency is crap. >I'd rather teach QM from the start, and get special relativity as a >limiting case of that, and then Newtonian dynamics as a special case >of that. >> How do you expect to get special relativity as a limiting case of QM? >You don't. You have to formulate a quantum theory that incorporates QM, >as did Dirac. Relativity is not deducible from classical wave mechanics >or Heisenberg matrices. Well, *I* *never* thought that you could get special relativity as a limiting case of QM. It was J.E. who made the ridiculous assertion, not me. I was rather surprised that you answered this. I was directly addressing my question to J.E., and to nobody else, so that he explain where he got his weird idea from, and why he made such a statement. I asked J.E. why he (i.e. J.E.) thought that special relativity was a limiting case of QM. meant J.E. Please correctly attribute the ideas to the people who originated them. It was J.E. who had the idea that special relativity was a limiting case to QM, not me. And anybody who takes the trouble to read my posting and takes the trouble to comprehend it would know this. ----- === Subject: Re: SR consistency is crap. >>I'd rather teach QM from the start, and get special relativity as a >>limiting case of that, and then Newtonian dynamics as a special case >>of that. > How do you expect to get special relativity as a limiting case of QM? >>You don't. You have to formulate a quantum theory that incorporates QM, >>as did Dirac. Relativity is not deducible from classical wave mechanics >>or Heisenberg matrices. >Well, *I* *never* thought that you could get special relativity as a >limiting case of QM. It was J.E. who made the ridiculous assertion, >not me. >I was rather surprised that you answered this. I was directly addressing >my question to J.E., and to nobody else, so that he explain where he got >his weird idea from, and why he made such a statement. I asked J.E. why >he (i.e. J.E.) thought that special relativity was a limiting case of QM. >meant J.E. >Please correctly attribute the ideas to the people who originated them. >It was J.E. who had the idea that special relativity was a limiting case >to QM, not me. And anybody who takes the trouble to read my posting and >takes the trouble to comprehend it would know this. The main reason why anybody, who takes the trouble to comprehend what I expect in my original question. This means that Bob Kolker gave completely the wrong answer to my question to J.E. I asked J.E. a question about *himself* - however, Bob Kolker answered my query to J.E. as though the question was about something I was personally wondering about. I do not expect to derive special relativity as a limiting case of QM, and it is obvious that Bob Kolker does not expect to derive special relativity as a limiting case of QM. However, it is obvious that J.E. does expect to do so. My question was - why did J.E. expect it, and in what manner would J.E. expect to do it. Bob, I do not need you to explain to me material which I already know (this is something which you have also done previouly, and in a quite condescending manner). This is not the first time that Bob Kolker has made it look as though my intentions in a posting were the exact opposite to what my actual intentions were (remember Bob Kolker's insulting responses to a couple of my posts in the Another Bogus Claim by the SR Experts thread in February 2002 - a thread in which Bob Kolker appeared as though he was selectively choosing those of my postings to which he could respond in such a way way as to belittle me, and ignoring all my other postings which gave ample proof that my knowledge was in no need of his condescending help). Bob, if you did not think that I was saying that special relativity is a limiting case of QM, then why don't you say so. If you did think that I was saying that special relativity is a limiting case of QM, then I would appreciate an apology from you. David ----- === Subject: Re: SR consistency is crap. > Please correctly attribute the ideas to the people who originated them. It was not incorrectly attributed to you. eleaticus === Subject: Re: SR consistency is crap. > I disagree. SR is about a proposed symmetry of nature. Explain the twin paradox then. By the way, introducing accelerations or boosts is a departure from SR and a move into the Dynamics domain. > You got a problem right from the start. SR came to > challenge the Copernican view of the world (see Hans Reichenbach, The > Philosophy of Space and Time) the cornerstone of Newton's dynamics. > Ptolemaic and Copernican systems are kinematically equivalent > according to Relativity. Yet, while admitting SR, the educational > status quo refuses to drop Newtonian dynamics, claiming there is ample > emprirical evidence to support it. Actually, sicne Newton's laws are > mere tautologies, in non-relativistic limits they will always conform > to experiment. > Newtonian dynamics are not dropped. They are derived locally, you > already conceded that below that they are local tautologies. A > dynamic isn't much without a law about elementary forces. > I took Physics 101 and Modern Phycsi 101 together during the same > semester as soon as I started undergraduate. The mentor protested and > argued I should take Modern Physics (Relativity) after I take > Classical Mechanics, because that was a prerequisite. I protested, I > argued it must be my choice not theirs. I won. I got a A- in Classical > and an A+ in Modern. > Good for you. I didn't even realize I liked physics until Modern > Physics (which for us covered QM, solid state, Stat mech, etc. too) I > just took it as an easy class since I was good at math. Yesy, interesting to see that while it is an easy subject for some people it is beyond comprehension for others. > I think this is the way to go. Teach students everything together as > competing theories and not relativity as an advance extension to > Newtonian Dynamics. > I'd rather teach QM from the start, and get special relativity as a > limiting case of that, and then Newtonian dynamics as a special case > of that. Well, you are talking 1000 years from now when we will understand better how quantum uncertainty gives rise to macrocosmic certainty. For now, such approach can result only in confusion. > But remember, you still have a problem. SR+GR are > axiomatic systems. No different from Euclidean geometry in that > respect. You gain understanding of the theories early on but also you > raise the doubt in their foundations. > Huh? You want to avoid doubt? Science has doubt, predictions are > made, the predictions can be compared to data, they might pass or > fail. > Eventually, someone will lose. > Only theories can lose, not people, please explain more what you mean. I meant that popularization of SR, GR will turn out more questioning and eventually abandoment. This is the fate of every theory that becomes pupolarized. > Those that are afraid of ending up with a loser keep SR+GR as advance > subjects. > I'd love to have GR and SR as grade-school subjects, does that mean > I'm not afraid of losing? I don't know what you mean by afraid of > losing or lose, I do hope my predictions match the data, that's > because if it's easy to be wrong, so why bother learning a theory if > it makes wrong predictions? > Remember what happened to Euclidean geometry? > What happened? It's still around! > As soos as > they started teaching it, thousands attempted to disprove the Playfair > axiom (parallel lines never meet). The result was a > relative-consistency with spherical and hypoerbolic geometries. > Elemetary euclidean geometry was proved consistent, you can drop > relative-consistency and just say consistent if what you mean is > that elementary hyperbolic geometry is as consistent as elementary > Euclidean geometry. And if you mean something other than elementary, > then that useally means bringing in sets and once you've done that > then all become equiconsistent with set theory. I agree. But I hope you recall that the consistency of Euclidean geometry was under question for some time. > The > same will happen to SR+GR as soon as they became a target of the > masses. > What will happen to SR+GR (which is GR, unless you meant the same > will happen to SR and the same will happen to GR as soon as each > becomes a target of the masses)? And what masses are currently kept > away from it? The majority of people fails math and you should know that. The majority works using a common sense basis. Anything as advanced as GR will create a reaction and eventually will be dropped, creating more problems than the intended solution. Another solution recently proposed is to make physics a subject for selected few. > The current approach is to keep the theory for the few and > feed the supposed prediction to the masses via the media. Silly but > works due to hype. > Mike > I actively try to teach physics at as early a stage as possible, and > books on relatively are freely sold in stores, there is no conspiracy > going on. Anyone can learn. Heck, I'm on Usenet because I want to > help people learn SR, among other reasons, this is a public forum > where anyone can read it. You are wasting your time. If 95% of your student can remember all three Newton's laws 2 years after graduation from any level exept grad school then you have accomplished your task. You probably aiming for a small % while frustrating the rest of the class and ending up with the opposite that what you aim, i.e. making people dislike physics. Mike === Subject: Re: SR consistency is crap. > I disagree. SR is about a proposed symmetry of nature. > Explain the twin paradox then. By the way, introducing accelerations > or boosts is a departure from SR and a move into the Dynamics domain. I'd be happy to explain the twin paradox. Start with the financial twin paradox that I just explained to eleaticus. And I disagree about accelerations and boosts being outside SR, altough I understand why people ignore it. SR is a theory about how the symmetries of spacetime are similar to the symmetries of Minkowksi geometry. That's why the financial twin paradox using an indefinite quadratic form to determine the rate at which money is sucked out our your pocket and sent to someone else. > You got a problem right from the start. SR came to > challenge the Copernican view of the world (see Hans Reichenbach, The > Philosophy of Space and Time) the cornerstone of Newton's dynamics. > Ptolemaic and Copernican systems are kinematically equivalent > according to Relativity. Yet, while admitting SR, the educational > status quo refuses to drop Newtonian dynamics, claiming there is ample > emprirical evidence to support it. Actually, sicne Newton's laws are > mere tautologies, in non-relativistic limits they will always conform > to experiment. > Newtonian dynamics are not dropped. They are derived locally, you > already conceded that below that they are local tautologies. A > dynamic isn't much without a law about elementary forces. > I took Physics 101 and Modern Phycsi 101 together during the same > semester as soon as I started undergraduate. The mentor protested and > argued I should take Modern Physics (Relativity) after I take > Classical Mechanics, because that was a prerequisite. I protested, I > argued it must be my choice not theirs. I won. I got a A- in Classical > and an A+ in Modern. > Good for you. I didn't even realize I liked physics until Modern > Physics (which for us covered QM, solid state, Stat mech, etc. too) I > just took it as an easy class since I was good at math. > Yesy, interesting to see that while it is an easy subject for some > people it is beyond comprehension for others. I think it's bad teaching. If I had a good background to easily understand a fixed way of teaching the subject, that doesn't make the subject inherently hard for others or easy for me, in means by background and the teaching lined up well. > I think this is the way to go. Teach students everything together as > competing theories and not relativity as an advance extension to > Newtonian Dynamics. > I'd rather teach QM from the start, and get special relativity as a > limiting case of that, and then Newtonian dynamics as a special case > of that. > Well, you are talking 1000 years from now when we will understand > better how quantum uncertainty gives rise to macrocosmic certainty. > For now, such approach can result only in confusion. You seem to have strong opinions about things you obviously don't know. Bohm did a good job of explaining maro-certaintanty as a was decades ago. Teaching is always behind the cutting edge. > But remember, you still have a problem. SR+GR are > axiomatic systems. No different from Euclidean geometry in that > respect. You gain understanding of the theories early on but also you > raise the doubt in their foundations. > Huh? You want to avoid doubt? Science has doubt, predictions are > made, the predictions can be compared to data, they might pass or > fail. > Eventually, someone will lose. > Only theories can lose, not people, please explain more what you mean. > I meant that popularization of SR, GR will turn out more questioning > and eventually abandoment. This is the fate of every theory that > becomes pupolarized. I seriously doubt that. I think that when the correct SR theory is finally popularized the incorrect alleged SR theories will FINALLY be adandoned, and not a moment too soon, yeak! > Those that are afraid of ending up with a loser keep SR+GR as advance > subjects. > I'd love to have GR and SR as grade-school subjects, does that mean > I'm not afraid of losing? I don't know what you mean by afraid of > losing or lose, I do hope my predictions match the data, that's > because if it's easy to be wrong, so why bother learning a theory if > it makes wrong predictions? > Remember what happened to Euclidean geometry? > What happened? It's still around! > As soos as > they started teaching it, thousands attempted to disprove the Playfair > axiom (parallel lines never meet). The result was a > relative-consistency with spherical and hypoerbolic geometries. > Elemetary euclidean geometry was proved consistent, you can drop > relative-consistency and just say consistent if what you mean is > that elementary hyperbolic geometry is as consistent as elementary > Euclidean geometry. And if you mean something other than elementary, > then that useally means bringing in sets and once you've done that > then all become equiconsistent with set theory. > I agree. But I hope you recall that the consistency of Euclidean > geometry was under question for some time. Well, the same grounding to elementary euclidean geometry applies to elementary hyperbolic geometry, and I can do SR predictions with ELEMENTARY hyperbolic geometry. If you want not instantaneous accelerations, then I need FULL hyperbolic geometry, which is as consistent as FULL euclidean geometry. > The > same will happen to SR+GR as soon as they became a target of the > masses. > What will happen to SR+GR (which is GR, unless you meant the same > will happen to SR and the same will happen to GR as soon as each > becomes a target of the masses)? And what masses are currently kept > away from it? > The majority of people fails math and you should know that. The > majority works using a common sense basis. Anything as advanced as GR People fail at math because of math is taught badly. Did you know that you can multiply vectors? Life is easier with that, and hard without it. > will create a reaction and eventually will be dropped, creating more > problems than the intended solution. Another solution recently > proposed is to make physics a subject for selected few. I will concede that fixing math eduation is paramount to fixing physics education, there isn't a strong reason not to do both by fixing the education of geometry to be incorporated the cutting edge from the 19th century, which frankly we have yet to do and that's just sad sad sad. > The current approach is to keep the theory for the few and > feed the supposed prediction to the masses via the media. Silly but > works due to hype. Mike > I actively try to teach physics at as early a stage as possible, and > books on relatively are freely sold in stores, there is no conspiracy > going on. Anyone can learn. Heck, I'm on Usenet because I want to > help people learn SR, among other reasons, this is a public forum > where anyone can read it. > You are wasting your time. If 95% of your student can remember all > three Newton's laws 2 years after graduation from any level exept grad > school then you have accomplished your task. You probably aiming for a > small % while frustrating the rest of the class and ending up with the > opposite that what you aim, i.e. making people dislike physics. Physics education should start out with modeling in general, and comparing models to data, with computers you can bury most of the math until a later epistological phase that COULD be reserved for the few that care, where the class discusses the foundations of the models used earlier. If someone isn't going to remember the basics of how to make or test a model, then you shouldn't BOTHER teaching science at all, just drill job skills instead. === Subject: Re: SR consistency is crap. >> Many generations have been fooled by the British school of >> philosophy >> using this trick to enforce the empirical nature of Newton's laws >> of >> motion. Continental schools remained unconvnined about that. >> Corect >> laws: >> 1st: F = d(mv)/dt is an axiom, cannot be proved empirically. F. >> M, V >> cannot be measured independently of one another. >> This above statement assumes many other prior theories about the >> nature of sapce and time, lengths, etc. Assuming a known force >> (like >> gravitation) then you can apply fixed forces to achieve a system in >> stasis (there come the assumptions about simultaneousness) like >> electro-static forces to figure out how much mass something has. >> You >> can then use a clock to see how far it goes in with a fixed force >> (say, roll the ball on an incline) and see how far it goes, much >> much >> verification is possible. It is not self-evident, you make it >> sound >> like most of historical science was done by thought experiments. >> The >> problem is that that the whole foundation doesn't hold up to the >> patterns of electrodynamics phenomena. The pattern described by >> the >> first law DID hold up for a wide variety of experiments, but then >> it >> failed. >> Let's stop fooling people. It's time to go forward. Many >> generations >> of brain washed pupils is enough. >> I'm all for improving education, I'm not sure that closing my eyes >> and >> pretending that Newton's patterns are universal laws HELPS that >> any >> when there is evidence to the contrary. Whereas SR when taught >> correctly is a very useful theory, one that you can EVEN derive >> Newton's patterns from as special limiting cases. Why can't we >> work >> on improving SR education Mike? >> SR is kinematics. > I disagree. SR is about a proposed symmetry of nature. >> You got a problem right from the start. SR came to >> challenge the Copernican view of the world (see Hans Reichenbach, The >> Philosophy of Space and Time) the cornerstone of Newton's dynamics. >> Ptolemaic and Copernican systems are kinematically equivalent >> according to Relativity. Yet, while admitting SR, the educational >> status quo refuses to drop Newtonian dynamics, claiming there is >> ample >> emprirical evidence to support it. Actually, sicne Newton's laws are >> mere tautologies, in non-relativistic limits they will always conform >> to experiment. > Newtonian dynamics are not dropped. They are derived locally, you > already conceded that below that they are local tautologies. A > dynamic isn't much without a law about elementary forces. >> I took Physics 101 and Modern Phycsi 101 together during the same >> semester as soon as I started undergraduate. The mentor protested and >> argued I should take Modern Physics (Relativity) after I take >> Classical Mechanics, because that was a prerequisite. I protested, I >> argued it must be my choice not theirs. I won. I got a A- in >> Classical >> and an A+ in Modern. > Good for you. I didn't even realize I liked physics until Modern > Physics (which for us covered QM, solid state, Stat mech, etc. too) I > just took it as an easy class since I was good at math. If you are as good at math as you claim, tell me the value of c in ü[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v)). Einstein thinks it is infinity. He even says so. we shall, however, find in what follows, that the velocity of light in our theory plays the part, physically, of an infinitely great velocity. Reference http://www.fourmilab.ch/etexts/einstein/specrel/www/ Androcles. >> I think this is the way to go. Teach students everything together as >> competing theories and not relativity as an advance extension to >> Newtonian Dynamics. > I'd rather teach QM from the start, and get special relativity as a > limiting case of that, and then Newtonian dynamics as a special case > of that. >> But remember, you still have a problem. SR+GR are >> axiomatic systems. No different from Euclidean geometry in that >> respect. You gain understanding of the theories early on but also you >> raise the doubt in their foundations. > Huh? You want to avoid doubt? Science has doubt, predictions are > made, the predictions can be compared to data, they might pass or > fail. >> Eventually, someone will lose. > Only theories can lose, not people, please explain more what you mean. >> Those that are afraid of ending up with a loser keep SR+GR as advance >> subjects. > I'd love to have GR and SR as grade-school subjects, does that mean > I'm not afraid of losing? I don't know what you mean by afraid of > losing or lose, I do hope my predictions match the data, that's > because if it's easy to be wrong, so why bother learning a theory if > it makes wrong predictions? >> Remember what happened to Euclidean geometry? > What happened? It's still around! >> As soos as >> they started teaching it, thousands attempted to disprove the >> Playfair >> axiom (parallel lines never meet). The result was a >> relative-consistency with spherical and hypoerbolic geometries. > Elemetary euclidean geometry was proved consistent, you can drop > relative-consistency and just say consistent if what you mean is > that elementary hyperbolic geometry is as consistent as elementary > Euclidean geometry. And if you mean something other than elementary, > then that useally means bringing in sets and once you've done that > then all become equiconsistent with set theory. >> The >> same will happen to SR+GR as soon as they became a target of the >> masses. > What will happen to SR+GR (which is GR, unless you meant the same > will happen to SR and the same will happen to GR as soon as each > becomes a target of the masses)? And what masses are currently kept > away from it? >> The current approach is to keep the theory for the few and >> feed the supposed prediction to the masses via the media. Silly but >> works due to hype. >> Mike > I actively try to teach physics at as early a stage as possible, and > books on relatively are freely sold in stores, there is no conspiracy > going on. Anyone can learn. Heck, I'm on Usenet because I want to > help people learn SR, among other reasons, this is a public forum > where anyone can read it. === Subject: Re: SR consistency is crap. > If you are as good at math as you claim, tell me the value of c in > ü[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v)). > Einstein thinks it is infinity. He even says so. > we shall, however, find in what follows, that the velocity of light > in our theory plays the part, physically, of an infinitely great > velocity. > Reference http://www.fourmilab.ch/etexts/einstein/specrel/www/ > Androcles. c is the speed of the signal in K-coordinate-system that moves from the origin of the k-coordinate-system at time t and thence at constant speed in the K-coordinate-system to the point x' in the k-coordinate-system and then instantly turns around and travels back to the origin of the k-coordinate-system at the same constant speed in the K-coordinate-system. tau is an at-this-point unkown function of the K-coordinate system, and the equation ü[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v)) si what Einstein uses to derive the formula for tau. His words are heuristics, the point about whether his function tau(x,y,z,t) satisifies the properties he wants it to have are available for direct examinition and the derivation of the said function is purely a matter for those with curiousity. Einstein could have simply asserted the formula for tau and would be within his rights to do so. As I said earlier, the fact that eta(x,y,z,t), nu(x,y,z,t), kcsee(x,y,z,t) and tau(x,y,z,t) have the property that for any two events A=(x1,y2,y2,t1) and B=(x1,x2,z2,t2) sqrt([x2-x1]^2+[y2-y1]^2+[z2-z1]^2)=c[t2-t2] <=> sqrt([eta(x1,x2,z2,t2)-eta(x1,y2,y2,t1)]^2 + [nu(x1,x2,z2,t2)-nu(x1,y2,y2,t1)]^2 + [kcsee(x1,x2,z2,t2)-kcsee(x1,y2,y2,t1)]^2) = c[tau(x1,x2,z2,t2)-tau(x1,y2,y2,t1)] is the property Einstein wanted, and can be verified from the explicit forms of eta, nu, kcsee, and tau, and the derivation of tau can be ignored. As for your claims that Einstein meant c to be infinitely great in that formula, I am strained to come up with any explanation for your comment other than dishonesty. Einstein doesn't say your quote until a completely different section, and in THAT section he says that that is demonstrated in an EVEN LATER part, which I suspect is when he shows that relativisitic velocities form a group with the relativistic velocity addition formula. And then c has the property that a(v,c)=c where a(v,w) is the relativistic addition of two relativisitic velocities v and w into a new relativistic velocity. THAT is the context in which Einstein means that, where me means that c is unattainable from an infinite number of additions of a finite (non-zero) velocity .... the same as an infinitely great velocity in the Newtonian theory. And reference to this applying to the tau derivation seems to be misguided at best, and likely dishonest. Are you a sociologist doing a study on scientists recognizing dishonesty Androcles? I try to be polite, but I my imagination has limits and if dishonesty is the only explanation I can come up with for the things you say then the most gracious thing I can say is that I have NO IDEA why you think Einstein thought c was infinite in the derivation of tau. None really. I can understand Einstein better than you Androcles, and he think he has a very poor writing style, but I don't mean that as a discredit to him, maybe that was how people to me than your Androcles. === Subject: Re: SR consistency is crap. >> If you are as good at math as you claim, tell me the value of c in >> ü[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v)). >> Einstein thinks it is infinity. He even says so. >> we shall, however, find in what follows, that the velocity of light >> in our theory plays the part, physically, of an infinitely great >> velocity. >> Reference http://www.fourmilab.ch/etexts/einstein/specrel/www/ >> Androcles. It is interesting that Androcles has missed an alternative interpretation light *plays* the part, physically, of an infinitely great velocity. Androcles effectively states that the only viable interpretation is that Einstein states that c is infinite. Here is an alternative interpretation for Androcles to consider. In classical mechanics, infinite speed is the unattainable supremum for attainable speeds (i.e. all finite speeds are theoretically attainable, infinite speed is unattainable for material bodies, and all material bodies travel at less than infinite speed). In special relativity, c is the unattainable supremum for attainable speeds speed (i.e. all speeds less than c are theoretically attainable, c is unattainable for material bodies, and all material bodies travel at speed less than c). This means that, from a physical point of view, the role of c in special relativity as the unattainable maximum possible speed (i.e. an unattainable supremum) is analogous to the role of infinite speed in classical mechanics as the unattainable maximum possible speed (i.e. an unattainable supremum). infinite speed in classical mechanics (from the point of view of both being unattainable suprema for attainable speeds for material bodies in their respective theories), it is reasonable to suggest that it was paper that we shall, however, find in what follows, that the velocity of light in our theory plays the part, physically, of an infinitely great velocity. David ----- === Subject: Re: SR consistency is crap. > If you are as good at math as you claim, tell me the value of c in > ü[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = > tau(x',0,0,t+x'/(c-v)). > Einstein thinks it is infinity. He even says so. > we shall, however, find in what follows, that the velocity of light > in our theory plays the part, physically, of an infinitely great > velocity. > Reference http://www.fourmilab.ch/etexts/einstein/specrel/www/ > Androcles. > It is interesting that Androcles has missed an alternative > interpretation > of > light *plays* the part, physically, of an infinitely great velocity. Yeah, and Bottom plays the part of the ass in A Midsummer Night's Dream. > Androcles effectively states that the only viable interpretation is > that > Einstein states that c is infinite. or v = 0. I notice you've ignored the equation. > Here is an alternative interpretation for Androcles to consider. In > classical mechanics, infinite speed is the unattainable supremum for > attainable speeds (i.e. all finite speeds are theoretically > attainable, > infinite speed is unattainable for material bodies, and all material > bodies travel at less than infinite speed). In special relativity, c > is > the unattainable supremum for attainable speeds speed (i.e. all speeds > less than c are theoretically attainable, c is unattainable for > material > bodies, and all material bodies travel at speed less than c). This > means > that, from a physical point of view, the role of c in special > relativity > as the unattainable maximum possible speed (i.e. an unattainable > supremum) > is analogous to the role of infinite speed in classical mechanics as > the > unattainable maximum possible speed (i.e. an unattainable supremum). It takes finite time to travel from (0,0,0) to (x',0,0) and the tip of the ray returns to (0,0,0) IN THE MOVING SYSTEM. Therefore either the moving system has not moved or the velocity of light is infinite as Einstein clearly states in his theory. Androcles. > infinite speed in classical mechanics (from the point of view of both > being unattainable suprema for attainable speeds for material bodies > in > their respective theories), it is reasonable to suggest that it was > paper that > we shall, however, find in what follows, that the velocity of > light in our theory plays the part, physically, of an infinitely > great velocity. > David > ----- === Subject: Re: SR consistency is crap. > Here is an alternative interpretation for Androcles to consider. In > classical mechanics, infinite speed is the unattainable supremum for > attainable speeds (i.e. all finite speeds are theoretically attainable, > infinite speed is unattainable for material bodies, and all material > bodies travel at less than infinite speed). In special relativity, c is > the unattainable supremum for attainable speeds speed (i.e. all speeds > less than c are theoretically attainable, c is unattainable for material > bodies, and all material bodies travel at speed less than c). This means > that, from a physical point of view, the role of c in special relativity > as the unattainable maximum possible speed (i.e. an unattainable supremum) > is analogous to the role of infinite speed in classical mechanics as the > unattainable maximum possible speed (i.e. an unattainable supremum). > infinite speed in classical mechanics (from the point of view of both > being unattainable suprema for attainable speeds for material bodies in > their respective theories), it is reasonable to suggest that it was > paper that > we shall, however, find in what follows, that the velocity of > light in our theory plays the part, physically, of an infinitely > great velocity. Especially since the unattainable aspect of c for material bodies is what is discussed in the next section, which is consistent with in what follows. === Subject: Re: SR consistency is crap. > I think this is the way to go. Teach students everything together as > competing theories and not relativity as an advance extension to > Newtonian Dynamics. But remember, you still have a problem. SR+GR are > axiomatic systems. Which have been corroberated experimentally. Whereas Galilean invariant mechanics is emprically incorrect. The first Lorentz invariant theory of dynamics as invented by Maxwell (although he could not have characterized it that way). Einstein taught us how to make all mechanisc Lorentz invariant. The last word, the bottom line the sine qua non of a scientific theory is how well it predicts. Nothing else matters. Bob Kolker === Subject: Re: SR consistency is crap. > I think this is the way to go. Teach students everything together as > competing theories and not relativity as an advance extension to > Newtonian Dynamics. But remember, you still have a problem. SR+GR are > axiomatic systems. > Which have been corroberated experimentally. Whereas Galilean invariant > mechanics is emprically incorrect. The first Lorentz invariant theory of > dynamics as invented by Maxwell (although he could not have > characterized it that way). Einstein taught us how to make all mechanisc > Lorentz invariant. > The last word, the bottom line the sine qua non of a scientific theory > is how well it predicts. Nothing else matters. > Bob Kolker Now, please justify as to why all mechanics must be Lorentz invariant. You know this is grounded in epistemology and can easily be subject to skepticism. It seems that although making all mechanics Lorentz invariant results in a methematical attractive formulation and some predictions of values, there are some troublesome consequences both at the prediction and philosophical level. Ex. twin paradox and a timeless universe. Maybe science is not about predictions but about comprehension. Have you thought of that? Mike === Subject: Re: SR consistency is crap. I think this is the way to go. Teach students everything together as > competing theories and not relativity as an advance extension to > Newtonian Dynamics. But remember, you still have a problem. SR+GR are > axiomatic systems. > Which have been corroberated experimentally. Whereas Galilean invariant > mechanics is emprically incorrect. The first Lorentz invariant theory of > dynamics as invented by Maxwell (although he could not have > characterized it that way). Einstein taught us how to make all mechanisc > Lorentz invariant. > The last word, the bottom line the sine qua non of a scientific theory > is how well it predicts. Nothing else matters. > Bob Kolker > Now, please justify as to why all mechanics must be Lorentz invariant. SR PREDICTS that all of mechanics is Lorentz covariant (not invariant). There is no justification required. The prediction can be tested by experiment. That's science. Theories have to be testable and supported by experiments. If they aren't supported then they're wrong. You don't understand the scientific method. John Anderson === Subject: Re: SR consistency is crap. > I think this is the way to go. Teach students everything together as > competing theories and not relativity as an advance extension to > Newtonian Dynamics. But remember, you still have a problem. SR+GR are > axiomatic systems. Which have been corroberated experimentally. Whereas Galilean invariant > mechanics is emprically incorrect. The first Lorentz invariant theory of > dynamics as invented by Maxwell (although he could not have > characterized it that way). Einstein taught us how to make all mechanisc > Lorentz invariant. The last word, the bottom line the sine qua non of a scientific theory > is how well it predicts. Nothing else matters. Bob Kolker > Now, please justify as to why all mechanics must be Lorentz invariant. > SR PREDICTS that all of mechanics is Lorentz covariant (not invariant). > There is no justification required. The prediction can be tested by > experiment. That's science. Theories have to be testable > and supported by experiments. If they aren't supported then they're > wrong. You don't understand the scientific method. > John Anderson Since you don't understand what we are talking about, you better not spew crap. Mike === Subject: Re: SR consistency is crap. > Since you don't understand what we are talking about, you better not spew crap. No. He is quite corret. A scientific theory is just as good as its predictions and no better. A scientific theory must be testable and tested. If it is falsified by experiment then it is wrong. If it is supported by experiment then it might be right or it might be wrong. Science is quantitative testable falsifiable prediction. That is it. There ain't no more. Bob Kolker === Subject: Re: SR consistency is crap. >> Since you don't understand what we are talking about, you better not >spew crap. >No. He is quite corret. A scientific theory is just as good as its >predictions and no better. A scientific theory must be testable and >tested. If it is falsified by experiment then it is wrong. If it is >supported by experiment then it might be right or it might be wrong. >Science is quantitative testable falsifiable prediction. That is it. >There ain't no more. >Bob Kolker No, there's more. Otherwise we'd still be happily using Lorentz's aether, with additional postulates tacked on as needed. We prefer a theory with a small set of postulates of wide scope. We want a new theory to encompass phenomena that an old theory hadn't. There's an aesthetic appeal that is of over-riding importance for some. We want a fecund theory-- one that suggests lots of tests to do that nobody had thought of doing before. We also ask it to pass those tests. People are still trying to figure out what a good theory is, and there's no single right answer, although all the lists seem to share some of the same sentiments as expressed above. But the correct theory is still not part of the list. Even if it makes sense to say that there is a single theory that is correct, we can't test it exhaustively, and we can't peek at the Cosmic Blueprints, so any claims that one theory seems to work but is actually wrong, while another one is correct, is unfounded hubris that can't be defended except by personal preference. -- The result of this experiment was inconclusive, so we had to use statistics. (Overheard at international physics conference) === Subject: Re: SR consistency is crap. > Now, please justify as to why all mechanics must be Lorentz invariant. As a heuristic matter, Galilean mechanics can be used in a low velocity regime. That is because the Lorentz Transform becomes Galilean when the ratio v/c goes to zero. > You know this is grounded in epistemology and can easily be subject to > skepticism. It seems that although making all mechanics Lorentz > invariant results in a methematical attractive formulation and some > predictions of values, there are some troublesome consequences both at > the prediction and philosophical level. Ex. twin paradox and a > timeless universe. There is no twin paradox. If you intergrate the differential of the Minkowski integral along a world line that is close to the null light world line you get a small number. If you integrate the differention along a world line where the spatial posiition does not change you get a larger number. > Maybe science is not about predictions but about comprehension. Have > you thought of that? Yes. We comprehend our theories, and we predict events as measurables. We comprehend very little of Nature because we perceive so little directly so must make inferences and hypothesize causes. So what we end up understanding is our theories or models of what is going on. Most of nature is out of sight for us, but not out of mind. When heat was believed to be a fluid, people understood heat as the flow of a subtle fluid, Caloric. Now we know better. We think heat is predictions made from the hypothesis are correct and they lead to good technology. And that is what it is all about. Modeling nature sufficiently well to get good technology. Bob Kolker === Subject: Re: SR consistency is crap. > Now, please justify as to why all mechanics must be Lorentz invariant. > As a heuristic matter, Galilean mechanics can be used in a low velocity > regime. That is because the Lorentz Transform becomes Galilean when the > ratio v/c goes to zero. > You know this is grounded in epistemology and can easily be subject to > skepticism. It seems that although making all mechanics Lorentz > invariant results in a methematical attractive formulation and some > predictions of values, there are some troublesome consequences both at > the prediction and philosophical level. Ex. twin paradox and a > timeless universe. > There is no twin paradox. If you intergrate the differential of the > Minkowski integral along a world line that is close to the null light > world line you get a small number. If you integrate the differention > along a world line where the spatial posiition does not change you get a > larger number. > Maybe science is not about predictions but about comprehension. Have > you thought of that? > Yes. We comprehend our theories, and we predict events as measurables. > We comprehend very little of Nature because we perceive so little > directly so must make inferences and hypothesize causes. So what we end > up understanding is our theories or models of what is going on. Most > of nature is out of sight for us, but not out of mind. > When heat was believed to be a fluid, people understood heat as the > flow of a subtle fluid, Caloric. Now we know better. We think heat is > predictions made from the hypothesis are correct and they lead to good > technology. And that is what it is all about. Modeling nature > sufficiently well to get good technology. > Bob Kolker Technology has little to do with science. Maybe improving technology but discovery is fairly uncoupled from scientific inquiry. How much physics you have to know to build a good mouse trap? Mike === Subject: Re: SR consistency is crap. >Technology has little to do with science. Maybe improving technology >but discovery is fairly uncoupled from scientific inquiry. >How much physics you have to know to build a good mouse trap? Less than you need to know to build a good plasma TV. -- In any case, don't stress too much--cortisol inhibits muscular hypertrophy. -- Eric Dodd === Subject: Re: SR consistency is crap. > How much physics you have to know to build a good mouse trap? Very little. Long before Newton, bridges and cathedrals were built and cannons were forged. The development of a good theory expanded the horizons of the engineers. They were no longer bound to highly restrictive rules of thumb. Bob Kolker === Subject: Re: SR consistency is crap. >> Many generations have been fooled by the British school of philosophy >> using this trick to enforce the empirical nature of Newton's laws of >> motion. Continental schools remained unconvnined about that. Corect >> laws: >> 1st: F = d(mv)/dt is an axiom, cannot be proved empirically. F. M, V >> cannot be measured independently of one another. >This above statement assumes many other prior theories about the >nature of sapce and time, lengths, etc. Assuming a known force (like >gravitation) then you can apply fixed forces to achieve a system in >stasis (there come the assumptions about simultaneousness) like >electro-static forces to figure out how much mass something has. You No, he has that one right. Force in relativity is still dp/dt, momentum is still conserved. Relativistic force is found by going to the transforming the acceleration to whatever frame you please. Relativity mucks around with the geometry, not with the dynamics. -- Outside the camp you shall have a place set aside to be used as a latrine. You shall keep a trowel in your equipment and with it, when you go outside to ease nature, you shall first dig a hole and afterward cover up your excrement. -- Deuteronomy 23:13-14 === Subject: Re: SR consistency is crap. >> Many generations have been fooled by the British school of philosophy >> using this trick to enforce the empirical nature of Newton's laws of >> motion. Continental schools remained unconvnined about that. Corect >> laws: > 1st: F = d(mv)/dt is an axiom, cannot be proved empirically. F. M, V >> cannot be measured independently of one another. >This above statement assumes many other prior theories about the >nature of sapce and time, lengths, etc. Assuming a known force (like >gravitation) then you can apply fixed forces to achieve a system in >stasis (there come the assumptions about simultaneousness) like >electro-static forces to figure out how much mass something has. You > No, he has that one right. Force in relativity is still dp/dt, momentum > is still conserved. Relativistic force is found by going to the > transforming the acceleration to whatever frame you please. Relativity > mucks around with the geometry, not with the dynamics. I will only discuss the invariant theory, go here, jump coordinates here, and look Newton's law is the same, that's unnecisarily complicated AND it makes people with Newtonian bagagge bring it into SR. Just use proper time. Just use proper length. Drop all discussion of frames, it isn't necissary and it causes confusion to some people, so do it invariantly. Once I see the letter t I know that it's a different theory than the one I use, because I don't use coodinates. === Subject: Re: SR consistency is crap. > I will only discuss the invariant theory, go here, jump coordinates > here, and look Newton's law is the same, that's unnecisarily > complicated AND it makes people with Newtonian bagagge bring it into > SR. Just use proper time. Just use proper length. Drop all > discussion of frames, it isn't necissary and it causes confusion to > some people, so do it invariantly. Once I see the letter t I know > that it's a different theory than the one I use, because I don't use > coodinates. Suppose you need corroberation from another person and to get it you had to tell him to look for an event of some sort. How do you specify the event (which consists of WHERE and WHEN) without specifying a fiducial frame of reference which you both share. How do you tell the post office where to deliver your mail without giving an address (which is a set of co-ordinates wrt to some standard location frame). Bob Kolker === Subject: Re: SR consistency is crap. > I will only discuss the invariant theory, go here, jump coordinates > here, and look Newton's law is the same, that's unnecisarily > complicated AND it makes people with Newtonian bagagge bring it into > SR. Just use proper time. Just use proper length. Drop all > discussion of frames, it isn't necissary and it causes confusion to > some people, so do it invariantly. Once I see the letter t I know > that it's a different theory than the one I use, because I don't use > coodinates. > Suppose you need corroberation from another person and to get it you had > to tell him to look for an event of some sort. How do you specify the > event (which consists of WHERE and WHEN) without specifying a fiducial > frame of reference which you both share. You could describe a series of events and what would happen next. You could even say that the series of events are laying a meter-stick end-to-end 500 times and then waiting until the watch he wears goes off. His watch could tick uninformly and the meter stick could have a battery that heats it up causing it to expand, the point is that if you take those things into account, then it doesn't matter that the watch and meter stick aren't a suitable to define an actual frame. > How do you tell the post office where to deliver your mail without > giving an address (which is a set of co-ordinates wrt to some standard > location frame). You describe events relative to other events. My house is between Joe's house and Bob's house. If they know Bob's house and Joe's house and know what a house is and there aren't other houses between them, then that's sufficient. And these labels don't have to be a full frame, you only need two. Inbetweenness is a concept of all frames. It's like doing elementary geometry, they DID somehow manage to describe a triangle before Decartes introduced coordinates. > Bob Kolker I can't tell you if you are even trying to take me seriously the idea of a postal address being a standard frame is frankly absurd to me. The point is that a physical model just requires that you predict events. The events that can be observered all on the world-lines of future-pointing curves and you COULD inroduce a proper time relative to that curve, but that'd be equivalent to imaging that the person has a clock and just saying which clock-ticking EVENTS the new event happened BETWEEN or coincident with. If you want to fix someone's motion, then the usual easiest way is to tell them to move such that they get spectral line A from star A and B from star B and C from star C, and then you know that they are at rest. If you want them to move another way you could give the A,B, and C spectras as a fucntion of proper time. These are all observable. Length and location is not. In the Gauge Theory of Gravity, physical observables are independant of arbitrary local smooth minkowski rotations and displacements. Your location in space doesn't matter, your redshifts do. === Subject: Re: SR consistency is crap. rofflmfao One more obvious proof that Einstein's derivation in 1905 is just as > much > crap as his 1916/1962 derivation. > SR is an excercise in the algebra of Lorentz-Poincare transformations as > applied to electromagnetic fields. If it is mathematically inconsistent > then so is the theory real variables and linear algebra. That takes down > ALL of physics. > Reliance on the concept of mathematical consistency is nonsense. > Just consider the inconsistency as to which of two identically manufactured > and maintained objects is shorter/longer when in relative motion. You're > shorter! No! YOU are! Wrong, asshole, I can clearly see you are much > shorter than me! Idiot! Are you insane?! etc. No inconsistency there? > LOL. You assholes! > . > Just consider the inconsistency of deriving spatial coorinate > transformations and not being able to actually use them with EM quantities > like E,B, D, H, etc. Or having 'cook the books' when you actually do try > to apply them to an equation. > The restort to 'mathematical consistency' reminds me of Chritian resort to > the Books of Moses to exclude their violence: immaterial, irrelevant, and > incompetent. > eleaticus > You both all idiots giving wrong answers for the right reasons and > right answers for the wrong reasons. > A theory about math must be consistent but cannot be complete. Thus it > always incorporates a paradox: Goedel > A theory about physics must be complete, i.e. contain no paradox but > as a result it is always inconsistent. > Thus, idiot Einstein, not understanding the right domain for the > application of math, has twin paradox and black holes in his theories. > They are consistent math theories stupid eleticus (you'll never become > an 'eleatis'), but not complete to qualify for physical theories > because they incorporate paradoxes. > This settles the Einstein Affair once for all:. He applied mathemetics > to come up with a physical theory without using self evident > propositions as axioms, as the Greeks have already taught us to do and > Galileo and Newton afterwards, but non-provable mathematical > statements, such as the analytic proposition that 'For all moving > inertial observers the speed of light is constant'. Analytic > propositions cannot be proved since they are universally quantified. > If they also fail to be self-evident, they should not be used in a > physical theory. (using them as such is straight forward paranoia) > Above material is (c) copyright Eleatis. It can be used only by > mentioning the name 'Eleatis'. > Mike === Subject: Re: SR consistency is crap. : > : > : > : > One more obvious proof that Einstein's derivation in 1905 is just as : > much : > crap as his 1916/1962 derivation. : > : > : > SR is an excercise in the algebra of Lorentz-Poincare transformations as : > applied to electromagnetic fields. If it is mathematically inconsistent : > then so is the theory real variables and linear algebra. That takes down : > ALL of physics. : > Reliance on the concept of mathematical consistency is nonsense. : > Just consider the inconsistency as to which of two identically manufactured : > and maintained objects is shorter/longer when in relative motion. You're : > shorter! No! YOU are! Wrong, asshole, I can clearly see you are much : > shorter than me! Idiot! Are you insane?! etc. No inconsistency there? : > LOL. You assholes! : > . : > Just consider the inconsistency of deriving spatial coorinate : > transformations and not being able to actually use them with EM quantities : > like E,B, D, H, etc. Or having 'cook the books' when you actually do try : > to apply them to an equation. : > The restort to 'mathematical consistency' reminds me of Chritian resort to : > the Books of Moses to exclude their violence: immaterial, irrelevant, and : > incompetent. : > eleaticus : : : You both all idiots giving wrong answers for the right reasons and : right answers for the wrong reasons. : : : A theory about math must be consistent but cannot be complete. Thus it : always incorporates a paradox: Goedel : : A theory about physics must be complete, i.e. contain no paradox but : as a result it is always inconsistent. : : Thus, idiot Einstein, not understanding the right domain for the : application of math, has twin paradox and black holes in his theories. : They are consistent math theories stupid eleticus (you'll never become : an 'eleatis'), but not complete to qualify for physical theories : because they incorporate paradoxes. : : This settles the Einstein Affair once for all:. He applied mathemetics : to come up with a physical theory without using self evident : propositions as axioms, as the Greeks have already taught us to do and : Galileo and Newton afterwards, but non-provable mathematical : statements, such as the analytic proposition that 'For all moving : inertial observers the speed of light is constant'. Analytic : propositions cannot be proved since they are universally quantified. : If they also fail to be self-evident, they should not be used in a : physical theory. (using them as such is straight forward paranoia) : : Above material is (c) copyright Eleatis. It can be used only by : mentioning the name 'Eleatis'. : : Mike For velocities greater than that of light our deliberations become meaningless; we shall, however, find in what follows, that the velocity of light in our theory plays the part, physically, of an infinitely great velocity. -- Einstein. You are always insane when you are in love. -- Sigmund Freud The best-known character, Bottom, is transformed into an ass and becomes the butt of jokes. - A Midsummer Night's Dream, by William Shakespeare, as interpreted by Ed Friedlander M.D. There are a lot of people in love with Einstein's ridiculous ideas. The velocity of light plays the part, physically, of the ass's head Bottom wears. In fact it is 299,792,458 meters per second relative to the source, not infinite. Bottom is played by Einstein. Androcles. === Subject: Re: SR consistency is crap. One more obvious proof that Einstein's derivation in 1905 is just as > much > crap as his 1916/1962 derivation. > SR is an excercise in the algebra of Lorentz-Poincare transformations as > applied to electromagnetic fields. If it is mathematically inconsistent > then so is the theory real variables and linear algebra. That takes down > ALL of physics. > Reliance on the concept of mathematical consistency is nonsense. > Just consider the inconsistency as to which of two identically manufactured > and maintained objects is shorter/longer when in relative motion. You're > shorter! No! YOU are! Wrong, asshole, I can clearly see you are much > shorter than me! Idiot! Are you insane?! etc. No inconsistency there? > LOL. You assholes! > . > Just consider the inconsistency of deriving spatial coorinate > transformations and not being able to actually use them with EM quantities > like E,B, D, H, etc. Or having 'cook the books' when you actually do try > to apply them to an equation. > The restort to 'mathematical consistency' reminds me of Chritian resort to > the Books of Moses to exclude their violence: immaterial, irrelevant, and > incompetent. > eleaticus > You both all idiots giving wrong answers for the right reasons and > right answers for the wrong reasons. > A theory about math must be consistent but cannot be complete. Thus it > always incorporates a paradox: Goedel > A theory about physics must be complete, i.e. contain no paradox but > as a result it is always inconsistent. > Thus, idiot Einstein, not understanding the right domain for the > application of math, has twin paradox and black holes in his theories. > They are consistent math theories stupid eleticus (you'll never become > an 'eleatis'), but not complete to qualify for physical theories > because they incorporate paradoxes. > This settles the Einstein Affair once for all:. He applied mathemetics > to come up with a physical theory without using self evident > propositions as axioms, as the Greeks have already taught us to do and > Galileo and Newton afterwards, but non-provable mathematical > statements, such as the analytic proposition that 'For all moving > inertial observers the speed of light is constant'. Analytic > propositions cannot be proved since they are universally quantified. > If they also fail to be self-evident, they should not be used in a > physical theory. (using them as such is straight forward paranoia) > Above material is (c) copyright Eleatis. It can be used only by > mentioning the name 'Eleatis'. aka Mike aka Undeniable aka Bill Smith, so it can de facto be used without mentioning any name at all. Dirk Vdm === Subject: Re: please help me >A baseball is popped straight up with an initial velocity of 32 >feet per second, Giving KE = 1/2 m v^2 = 1/2 m * (32fps)^2 >What is the maximum height >reached by this baseball? It is the height at which PE=KE, and PE+KE=k throughout the trajectory. PE = mgh = m*32fpsps*h 1/2 m * (32 ft / sec)^2 = m * (32 ft/sec^2) * h m factors out 1/2 * 1024 ft^2/sec^2 = 32 ft/sec^2 * h(ft) 512 ft^2/sec^2 / 32 ft/sec^2 = h 16 ft = h. It's an energy balance. Now apply KE=PE throughout the trajectory to determine > its height above the ground is a function of >time I tolerance everything and tolerate everyone. I love: Dona, Jeff, Kim, Kimmie, Mom, Neelix, Tasha, and Teri, alphabetically. I drive: A double-step Thunderbolt with 657% range. I fight terrorism by: Using less gasoline. === Subject: Re: please help me - simple reasoning Simpler, but nevertheless correct reasoning: Initial speed 32 feet/s, deceleration 32 feet/s/s -> stopping time 1.00 s; average speed during climb 16 feet/s -> distance travelled = height reached is 16 feet. Johan E. Mebius >>A baseball is popped straight up with an initial velocity of 32 >>feet per second, >> >Giving KE = 1/2 m v^2 = 1/2 m * (32fps)^2 >>What is the maximum height >>reached by this baseball? >> >It is the height at which PE=KE, and PE+KE=k throughout the trajectory. >PE = mgh = m*32fpsps*h >1/2 m * (32 ft / sec)^2 = m * (32 ft/sec^2) * h >m factors out >1/2 * 1024 ft^2/sec^2 = 32 ft/sec^2 * h(ft) >512 ft^2/sec^2 / 32 ft/sec^2 = h >16 ft = h. >It's an energy balance. >Now apply KE=PE throughout the trajectory to determine >>its height above the ground is a function of >>time >> >I tolerance everything and tolerate everyone. >I love: Dona, Jeff, Kim, Kimmie, Mom, Neelix, Tasha, and Teri, alphabetically. >I drive: A double-step Thunderbolt with 657% range. >I fight terrorism by: Using less gasoline. === Subject: algebraic extension... hello.....doctor~ this is a problem of Fraleigh book. T, F problem. if E is an algebraically closed extension field of F, then E is an algebraic extension of F. answer is false. ------------------------------------------------- counter-example of this is C and Q. right ?? but i can't understand that C is not an algebraic extension of Q. so, i need your advice. thank you very much for your advice. === Subject: Re: algebraic extension... versus transcendental extension It is the existence of trancendental numbers that makes the proposition in the T/F problem false. See Fraleigh 35.2 (p. 290) for the definition of transcendental number. The reasoning: Fact: C is algebraically closed. Fact: C is an extension field of Q, i.e. C is a field containing Q as a subfield. Fact: Because there exist transcendental reals (e and pi being the most well-known) R is not an algebraic extension of Q. Finally, C = R + iR cannot be algebraic over Q because its subfield R is not. So the correct answer is indeed false. Johan E. Mebius >hello.....doctor~ >this is a problem of Fraleigh book. >T, F problem. >if E is an algebraically closed extension field of F, >then E is an algebraic extension of F. >answer is false. >------------------------------------------------- >counter-example of this is C and Q. >right ?? >but i can't understand that >C is not an algebraic extension of Q. >so, i need your advice. >thank you very much for your advice. === Subject: Re: algebraic extension... > this is a problem of Fraleigh book. > T, F problem. What does this mean? > if E is an algebraically closed extension field of F, > then E is an algebraic extension of F. > answer is false. > ------------------------------------------------- > counter-example of this is C and Q. > right ?? Right! > but i can't understand that > C is not an algebraic extension of Q. Because there are complex numbers which are transcendental over Q. For instance, pi or e. Jose Carlos Santos === Subject: Re: algebraic extension... > this is a problem of Fraleigh book. > T, F problem. > What does this mean? > if E is an algebraically closed extension field of F, > then E is an algebraic extension of F. > answer is false. > ------------------------------------------------- > counter-example of this is C and Q. > right ?? > Right! > but i can't understand that > C is not an algebraic extension of Q. > Because there are complex numbers which are transcendental over Q. > For instance, pi or e. oh.....easy.....thank you very much for your advice. === Subject: group Let G be the additive group of all polynomials in x with interger coefficients. Show that G is isomorphic to the group Q* of all positive rationals under multiplication. === Subject: Re: group - Construct a homomorphism of the integer polynomials onto the integers as follows: Map 1, 2, 3, 4, ... onto 2, 4, 8, 16 ... Map x, 2x, 3x, ... onto 3, 9, 27 ... Map xx, 2xx, 3xx, ... onto 5, 25, 125, ... etc., etc., and extend in the obvious way to sums and opposites of these monomials. Use the unique factorization property of integers to prove that you actually constructed an isomorphism. Johan E. Mebius >Let G be the additive group of all polynomials in x with interger >coefficients. >Show that G is isomorphic to the group Q* of all positive rationals >under multiplication. === Subject: Re: group > Let G be the additive group of all polynomials in x with interger > coefficients. > Show that G is isomorphic to the group Q* of all positive rationals > under multiplication. Let p_1, p_2, p_3, ... be the natural primes. If a and b are natural numbers, then you can write a/b as p_1^{k_1}*p_2^{k_2}*p_3^{k_3}*... Now it's easy to define the isomorphism f: f(a/b) = k_1 + k_2x + k_3x^2 + ... Jose Carlos Santos === Subject: Re: inverse of a block matrix Originator: harris@tcs.inf.tu-dresden.de (Mitchell Harris) >>Let A, B, and C be three square, symmetric matrices of compatible size so that >>M = { {A,B}, {B,C} } >>forms a square symmetric and invertible >>matrix. Is there a simple formula for the inverse of M in terms of >>A, B, and C? pedantic and unedifying exceptions to come... >Yes, providing the needed inverses exist. (Perhaps it is the case that >if M is invertible, then they do). what about 0 1 1 1 ? I was about to say at least one of A or C must be invertible but then 0 1 1 0 still is problematic >It is not necessary that B be square. if B must be symmetric (as the OP requested) then it needs to be square. maybe you meant that B doesn't have to be symmetric? >The method: Do a matrix Gaussian elimination. That is, transform the >following: >A B | I 0 >B^T C | 0 I >being careful to multiply on the correct side. If my algebra is >correct, I get the following: Let D = - A^(-1) B, and let E = (C >+ B^T D)^(-1). Then the inverse is >A^(-1) + D E D^T D E > E D^T E If A is not invertible you could change this appropriately to dealing with the inverse of C (but the example above shows that that might not always work). I don't see immediately how to fix it though. Mitch === Subject: Re: inverse of a block matrix > Let A, B, and C be three square, symmetric matrices > of compatible size so that > M = { {A,B}, {B,C} } > forms a square symmetric and invertible matrix. Is there a > simple formula for the inverse of M in terms of A, B, and C? The inverse of the partitioned symmetric matrix {{A,B},{B',C}}, where A and C are symmetric, B may be nonsquare, and ' denotes a transpose, is {{ (A-BC^B')^, -A^B(C-B'A^B)^}, {-C^B'(A-BC^B')^, (C-B'A^B)^}} where ^ denotes an inverse. Note that the offdiagonal block is expressed in two different ways. === Subject: Re: inverse of a block matrix > Let A, B, and C be three square, symmetric matrices > of compatible size so that > M = { {A,B}, {B,C} } > forms a square symmetric and invertible matrix. Is there a > simple formula for the inverse of M in terms of A, B, and C? > The inverse of the partitioned symmetric matrix {{A,B},{B',C}}, > where A and C are symmetric, B may be nonsquare, > and ' denotes a transpose, is > {{ (A-BC^B')^, -A^B(C-B'A^B)^}, > {-C^B'(A-BC^B')^, (C-B'A^B)^}} > where ^ denotes an inverse. Note that the offdiagonal block > is expressed in two different ways. Hmmm, this seems like it's only the right inverse (M M^ = I). When I try M^ M, it does not equal 1 even if B = square symmetric. Rod === Subject: Re: inverse of a block matrix >Hmmm, this seems like it's only the right inverse (M M^ = I). >When I try M^ M, it does not equal 1 even if B = square symmetric. Impossible. Suppose a square matrix A has a right inverse B. Then A is nonsingular, hence it has left inverse C. C A B = C (A B) = C I = C C A B = (C A) B = I B = B. I.e., B = C. -- Stephen J. Herschkorn sjherschko@netscape.net === Subject: A simple proof for the following? Is there for the following statement a simple proof (or a way to show that it is plausible)? Statement: Any 8-bit word can be stored as a 14-bit word, with the 14-bit word having at least two zeros between every one. Carl === Subject: Re: A simple proof for the following? |Statement: Any 8-bit word can be stored as a 14-bit word, with the |14-bit word having at least two zeros between every one. You need to count how many such 14-bit strings there are. Let A_n be the number of n-bit strings that have at least two zeros between any two consecutive 1-bits. Those can be divided into the strings that start with a 0, and the strings that start with a 1. Any n-1-bit string of this kind can be extended to one of n bits by prepending a 0, so there are A_{n-1} that start with a 0. If an n bit string of this kind starts with a 1, then the next two bits are 0s (if n>=3). Any n-3 bit string of this kind for n>=3 can be extended to one of n bits that starts with a 1 by prepending 100. Hence the number of n bit strings of this kind starting with 1 is A_{n-3}. Putting it all together, we get the recurrence relation for n>=3: A_n = A_{n-1} + A_{n-3}. What you want to know is whether A_14 >= 2^8: A_0=1 A_1=2 A_2=3 A_3=4 A_4=6 A_5=9 A_6=13 A_7=19 A_8=28 A_9=41 A_10=60 A_11=88 A_12=129 A_13=189 A_14=277 > 256 = 2^8. It seems it's correct. Keith Ramsay === Subject: Re: A simple proof for the following? Originator: joshp@xoxy.net (joshp) >Is there for the following statement a simple proof (or a way to show >that it is plausible)? >Statement: Any 8-bit word can be stored as a 14-bit word, with the >14-bit word having at least two zeros between every one. This is hardly a formal proof, but the following Unix command should print the number of 14-bit words with at least two zeros between every one. It prints 277. Since there are only 256 8-bit words, it's certainly possible to losslessly convert each 8-bit word to a suitable 14-bit word. perl -e 'for ($i = 0; $i < 2 ** 14; $i++) {print substr(unpack(B*, pack(N, $i)), -14), n}' | grep -v 101 | grep -v 11 | sort -u | wc -l -- Josh Purinton === Subject: definition heterotic? I'm trying to read a paper, can someone define this term *as pertains to math* for me? kwallace See http://en.wikipedia.org/wiki/Heterotic_string and http://en.wikipedia.org/wiki/Heterosis > I'm trying to read a paper, can someone define this term *as pertains > to math* for me? > kwallace === Subject: tetrahelix model Here's another model. Comments welcome. http://www.freewebtown.com/randome/tetrahelix.lg.jpg Dick === Subject: what's wrong with this proof? Hausdorff's maximality theorem: Every nonempty partially ordered set P has a maximal linearly ordered subset. Proof: Let L be a linearly ordered subset of P. Let F be the collection of all linearly ordered subsets of P that are also supersets of L. Then the union of all the elements of F is a linearly ordered subset of P and is maximal. === Subject: Re: what's wrong with this proof? === >Subject: what's wrong with this proof? You need to apply Zorn's Lemma. >Let L be a linearly ordered subset of P. Let F be the collection of >all linearly ordered subsets of P that are also supersets of L. >Then the union of all the elements of F is a linearly ordered subset >of P Not in general. -- 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: what's wrong with this proof? |Hausdorff's maximality theorem: |Every nonempty partially ordered set P has a maximal linearly ordered |subset. | |Proof: |Let L be a linearly ordered subset of P. Let F be the collection of |all linearly ordered subsets of P that are also supersets of L. Then |the union of all the elements of F is a linearly ordered subset of P |and is maximal. The union is not always linearly ordered. Keith Ramsay === Subject: Re: what's wrong with this proof? > Hausdorff's maximality theorem: > Every nonempty partially ordered set P has a maximal linearly ordered > subset. > Proof: > Let L be a linearly ordered subset of P. Let F be the collection of > all linearly ordered subsets of P that are also supersets of L. Then > the union of all the elements of F is a linearly ordered subset of P > and is maximal. Why is the union of such sets linearly ordered? for example consider the poset {a,b,c,d} with a If gcd(a,b,c) = 1, and a possibility that rather than phi(a)/2, phi(b)/2, and phi(c)/2 are > distinct. There are more number involved and so the condition is > closer. I'd like to read some opinions on this. > Perhaps you wouldn't mind reading some facts, instead. > phi(36391) = phi(36661) = phi(37231) = 36000, > 36391 = 151 x 241, 36661 = 61 x 601, 37231 = 31 x 1201. a=36391; b=36661; c=37231. gcd(a,b,c)=1. a t (mod c) = t (mod b) = t (mod a) = 2. This is shown only in tests. I don't have any proof of it. It has something to do with the way the additive generator mod c can degenerate and the two subtractive generators mod b and mod a cannot. That, and the fact that the triple coincidence ( a^n + b^n ) mod c == 0 ( c^n + a^n ) mod b == 0 ( c^n + b^n ) mod a == 0 happens at other than the node value of 2 for the generator mod c at n=0. So I'm concentrating on the subtractive generators for now and wonder about some kind of offset in the additive generator. I do know that if I took specific values of a, b, and c from a list of Pythagorean triangles I could show that for each, the triple coincidence happens at n=2 because I know it is necessary for a solution to a^n + b^n = c^n. That would prove nothing but could expand the limits of a search and lead to faster programs. Still, the patterns are clear at lower numbers and I just wonder why. One counterexample would do for me, let me let go of this, just as one solution for n = 3 would disprove FLT. But FLT is proved, and this is just an exploration into a pattern I see which has some beauty. That's all. No proof here. I am certainly learning a lot about modular arithmetic. conditions apply. Off to reread Mathworld's totient page. === Subject: Golf Statistics Article http://home.austin.rr.com/reedbender/golf/golf%20statistics.htm Validation of Various Methods of Handicapping Golfers Including the USGA System and Other Golf Statistics === Subject: Re: The decimal system is outlawed now ! ! ! In sci.math, JEMebius <419C955C.2080004@xs4all.nl>: >>We have to use the hexadecimal system now or the math-cops will arrest >>us! >>So start using it now , because in $07D5 , all offenders still using >>the decimal system will be executed ! Note: $07D5 = next year. >> > Please let this threat become a thread in a different newsgroup. Followups redirected to alt.politics.usa.misc. (It's about the only country that might seriously give any thought at all to this proposal outside of engineering circles... :-) ) > This is against the current trend of using more and more paper year by year! > Paper manufacturers have been advocating the binary system since times > immemorable. > To put an end to joking for now: > In the 1950s chess champion Max Euwe made an issue of teaching binary > arithmetic in primary schools. Well, one has to admire its simplicity. :-) + 0 1 x 0 1 0 0 1 0 0 0 1 1 0 1 0 1 Makes memorization of the multiplication tables a *lot* easier. Of course one drawback is that the national debt becomes harder US national debt is estimated to be $1101100011010111000101010000000101110011100.1010000 base 2. (from http://www.brillig.com/debt_clock/) > Johan E. Mebius -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: The decimal system is outlawed now ! ! ! - Etymology The Germans have the correct word: hexadekadisches System. BTW, the Latin word is decem = ten; the Greek is .83å.83Ì.83é.83À = deka, in English transliterated as deca. In Cymru: ten = deg, in French: dix; a heavily worn-out form of decem; etc. etc. It is all Indo-European. Johan E. Mebius >> Hans-Marc Olsen scribbled the following: > We have to use the hexadecimal system now or the math-cops will arrest > us! > So start using it now , because in $07D5 , all offenders still using > the decimal system will be executed ! >> If the decimal system is so evil, why are you writing the year as $07D5? >> That shows an underlying decimal bias. Why not simply write it as 7D5? >> Actually even the name hexadecimal itself has a decimal bias. Hexa >> is Greek for six and deca is Latin for ten, yet when you add those two >> numbers together, the hexadecimal number you get is 10, not 16. > You are understanding! A+6=10. === Subject: Re: The decimal system is outlawed now ! ! ! - Etymology > The Germans have the correct word: hexadekadisches System. > BTW, the Latin word is decem = ten; the Greek is í¡.8còí[Hyphen][A Ring]Çí¡.8cò[Capit alIGrave][Hyphen].8c[Micro]í¡.8c[CapitalU Acute]í[Hyphen].8c.bcí¡.8c òí[Hyphen].8c± = deka, in English transliterated as deca. > In Cymru: ten = deg, in French: dix; a heavily worn-out form of decem; > etc. etc. It is all Indo-European. or dhasa=10 in Sanskrit(vowel a short and long). But base 10 may remain even if or after 10 fingers of the hands are genetically modified. BTW,it is a surprise(to me) Greek letters could show correctly in Compose or Preview modes here. === Subject: Re: The decimal system(...) - Etymology - Greek alphabet About Greek and other non-Latin alphabets in webpages and in Email: (1) under MS Windows you can select several different input locales via >>Start >Settings >Control Panel >Regional Options >Tab Input Locales. Once you are back in text typing mode you obtain the desired keyboard setting among the input locales you selected previously by keying LeftAlt-LeftShift as often as needed. Watch the blue square in the system tray. The Netscape Email and HTML composer programs generate the official W3C tokens, for instance α for lowercase letter alpha and ω for lowercase letter omega. If in Email both the sending and the receiving parties have the correct character encoding settings, then EMail letters will be shown as intended by the sender. With HTML the browser will do its work. No special settings needed there. BTW, when viewing the raw EMail text in hexadecimal you will find the W3C tokens transformed into Unicode tokens. For instance, lowercase alpha is CEB1h. You really need a basic viewer program that does not perform any interpretation; just shows the characters in (extended) ASCII and in hexadecimal. BTW, about modification, genetic or otherwise: you may know that the Simpson family uses the octal number system. >>The Germans have the correct word: hexadekadisches System. >>BTW, the Latin word is decem = ten; the Greek is í.8e.8cÇí.8e.8c[Mic ro]í.8e.8c.bcí.8e.8c± = deka, in English transliterated as deca. >>In Cymru: ten = deg, in French: dix; a heavily worn-out form of decem; >>etc. etc. It is all Indo-European. >> >or dhasa=10 in Sanskrit(vowel a short and long). But base 10 may >remain even if or after 10 fingers of the hands are genetically >modified. >BTW,it is a surprise(to me) Greek letters could show correctly in >Compose or Preview modes here. === Subject: Re: The decimal system is outlawed now ! ! ! - Etymology JEMebius scribbled the following: > The Germans have the correct word: hexadekadisches System. > BTW, the Latin word is decem = ten; the Greek is .91Ç.91[Micro].91.bc[EDoubleD ot]± = deka, in English > transliterated as deca. > In Cymru: ten = deg, in French: dix; a heavily worn-out form of decem; > etc. etc. It is all Indo-European. I don't think you understand. If the hexadecimal system were free of decimal bias, it wouldn't have a two-part name, one part meaning six, the other ten, at all, no matter what language those words are in. In contrast, its name would simply be based on a word meaning ten or something. Not of course ten as we know it - the number of fingers on our hands - but a similar name. -- /-- Joona Palaste (palaste@cc.helsinki.fi) ------------- Finland -------- -------------------------------------------------------- rules! --------/ To err is human. To really louse things up takes a computer. - Anon === Subject: Re: The decimal system is outlawed now ! ! ! - Etymology the chicken-egg format can be utilized: base of four to the second-power? > I don't think you understand. If the hexadecimal system were free of > decimal bias, it wouldn't have a two-part name, one part meaning six, > the other ten, at all, no matter what language those words are in. --Give Earth a Trickier Dick Cheeny -- out of office, after gigayears! http://tarpley.net/bush12.htm http://www.benfranklinbooks.com/ http://members.tripod.com/~american_almanac http://www.wlym.com/pdf/iclc/howthenation.pdf http://www.rand.org/publications/randreview/issues/rr.12.00/ http://www.rwgrayprojects.com/synergetics/plates/figs/plate02.html === Subject: Re: The Paradox of Zeno In sci.math, Jim Greenfield Jim G >> c'=c+v >> How right you are! (Probabaly) > Remember; I am always referring to c in vacuum. Refraction and prisms > incline me to the view that things are not right in material light > velocity either (source dependency), but I'm not going there. Just let > a space-race of two pulses of EMR, one from a stationary source, and > another simultaneous from a source moving ref us, decide the matter of > c'=c+v And the reason supernovae don't satisfy this condition is precisely why? >> eleaticus > Just a stab :-) > Matter is just markers too, eh? If it is in motion, we can use that to > see how time is passing. Something at absolute zero with no relative > motion to anything we can see might be useless as a clock, but would > still age in my credo. Something at absolute zero wouldn't function very well as an observer. :-) > Jim G > c'=c+v -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: The Paradox of Zeno > In sci.math, Jim Greenfield > > c'=c+v > How right you are! (Probabaly) > Remember; I am always referring to c in vacuum. Refraction and prisms > incline me to the view that things are not right in material light > velocity either (source dependency), but I'm not going there. Just let > a space-race of two pulses of EMR, one from a stationary source, and > another simultaneous from a source moving ref us, decide the matter of > c'=c+v > And the reason supernovae don't satisfy this condition is > precisely why? (when discussing comparative flight times of EMR from supernova ? ) ........-1051548 secs--------- almost two weeks ahead ........+1052249 secs---------AGAIN almost two weeks ahead Ghost PROVED c'=c+v RIGHT THERE with his own calculation. His inability to accept his own conclusion is noted. It was also noted that he exited that thread (DHR's Invited on a Space Trip) > Just a stab :-) > Matter is just markers too, eh? If it is in motion, we can use that to > see how time is passing. Something at absolute zero with no relative > motion to anything we can see might be useless as a clock, but would > still age in my credo. > Something at absolute zero wouldn't function very well as an observer. :-) It isn't the observer; I am, but as it is not emitting EMR, might be invisible (undetectable) > Jim G > c'=c+v === Subject: Re: The Paradox of Zeno > In sci.math, Jim Greenfield > c'=c+v > How right you are! (Probabaly) >> Remember; I am always referring to c in vacuum. Refraction and prisms >> incline me to the view that things are not right in material light >> velocity either (source dependency), but I'm not going there. Just >> let >> a space-race of two pulses of EMR, one from a stationary source, and >> another simultaneous from a source moving ref us, decide the matter >> of >> c'=c+v > And the reason supernovae don't satisfy this condition is > precisely why? Here's a supernova (several images). http://www.star.ucl.ac.uk/~apod/apod/ap040220.html http://www.star.ucl.ac.uk/~apod/apod/ap000512.html http://www.star.ucl.ac.uk/~apod/apod/ap020331.html And the reason you don't believe supernovae don't satisfy the condition is precisely why? What is it about those images is it that tells you the speed of light is precisely c? Androcles. > eleaticus >> Just a stab :-) >> Matter is just markers too, eh? If it is in motion, we can use that >> to >> see how time is passing. Something at absolute zero with no relative >> motion to anything we can see might be useless as a clock, but >> would >> still age in my credo. > Something at absolute zero wouldn't function very well as an observer. > :-) >> Jim G >> c'=c+v > -- > #191, ewill3@earthlink.net > It's still legal to go .sigless. === Subject: Re: The Paradox of Zeno In sci.math, Androcles : >> In sci.math, Jim Greenfield >> Jim G >> c'=c+v >> How right you are! (Probabaly) > Remember; I am always referring to c in vacuum. Refraction and prisms > incline me to the view that things are not right in material light > velocity either (source dependency), but I'm not going there. Just > let > a space-race of two pulses of EMR, one from a stationary source, and > another simultaneous from a source moving ref us, decide the matter > of > c'=c+v >> And the reason supernovae don't satisfy this condition is >> precisely why? > Here's a supernova (several images). > http://www.star.ucl.ac.uk/~apod/apod/ap040220.html > http://www.star.ucl.ac.uk/~apod/apod/ap000512.html > http://www.star.ucl.ac.uk/~apod/apod/ap020331.html > And the reason you don't believe supernovae don't satisfy the > condition is precisely why? > What is it about those images is it that tells you the speed of > light is precisely c? > Androcles. It's hard to say what exactly things would look like were c' = c+v, but the problem is that the nebula of the Crab Nebula is estimated (presumably by simple trig) to be 10 lightyears in diameter, and is known to have exploded 950 years ago (our time), thus leads to gases moving about 1/190 c from the explosion, and a 73+-year delta, give or take, assuming that the supernova is exactly 7,000 light-years distant. If one doesn't like the Crab, one can go with SN1987A, which is estimated to be 170,00 light-years distant. Assuming similar parameters for the gases, the object would glow for almost 1800 years given the ballistic light theory. There's also the little problem of the neutrino precursor. We were lucky and caught 19 of them, apparently: http://csep10.phys.utk.edu/guidry/violence/sn87a.html and then the light show began 3 hours later, approximately. The SR explanation is relatively simple, even accounting for the neutrinos having a small amount of mass. The star in its final death throes collapses, then in one gigantic energy burst the neutrinos come flying out as it explodes on the rebound, along with a lot of other crap (the above does not mention gamma rays but I wonder). The light show, of course, is from the very hot gases of the explosion. Now, how do these observations reconcile with the ballistic light theory? Bear in mind the gasses are moving at 1/190 c, if Crab Nebula estimates are correct (but even if they're not they're not that far off, presumably). The leading edge of the explosion would therefore come well ahead of the neutrino burst. As for lightspeed being precisely c, I cannot show this; I can only show with these supernova that the lightspeed is approximately c, and very constant whatever its speed actually is. Since the theoretic discrepancy between SR and the ballistic theory is so great an approximate result seems good enough for now. [rest snipped] -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: The Paradox of Zeno > In sci.math, Androcles > : >> in > In sci.math, Jim Greenfield > Jim G > c'=c+v How right you are! (Probabaly) >> Remember; I am always referring to c in vacuum. Refraction and >> prisms >> incline me to the view that things are not right in material light >> velocity either (source dependency), but I'm not going there. Just >> let >> a space-race of two pulses of EMR, one from a stationary source, >> and >> another simultaneous from a source moving ref us, decide the matter >> of >> c'=c+v > And the reason supernovae don't satisfy this condition is > precisely why? >> Here's a supernova (several images). >> http://www.star.ucl.ac.uk/~apod/apod/ap040220.html >> http://www.star.ucl.ac.uk/~apod/apod/ap000512.html >> http://www.star.ucl.ac.uk/~apod/apod/ap020331.html >> And the reason you don't believe supernovae don't satisfy the >> condition is precisely why? >> What is it about those images is it that tells you the speed of >> light is precisely c? >> Androcles. > It's hard to say what exactly things would look like were > c' = c+v, Those images ARE what it looks like, because the velocity of light IS source dependent. > but the problem is that the nebula of > the Crab Nebula is estimated (presumably by simple > trig) to be 10 lightyears in diameter, and is known > to have exploded 950 years ago (our time), > thus leads to gases moving about 1/190 c from the explosion, > and a 73+-year delta, give or take, assuming that the > supernova is exactly 7,000 light-years distant. Why is that a problem? > If one doesn't like the Crab, one can go with SN1987A, which is > estimated to be 170,00 light-years distant. Assuming similar > parameters for the gases, the object would glow for almost 1800 > years given the ballistic light theory. Are you going to stick around for 1800 years to see if goes out? > There's also the little problem of the neutrino precursor. > We were lucky and caught 19 of them, apparently: > http://csep10.phys.utk.edu/guidry/violence/sn87a.html > and then the light show began 3 hours later, approximately. Yes, that event would indicate neutrinos travel FTL, wouldn't it? > The SR explanation is relatively simple, even accounting for the > neutrinos having a small amount of mass. The star in its > final death throes collapses, then in one gigantic energy burst > the neutrinos come flying out as it explodes on the rebound, > along with a lot of other crap (the above does not mention > gamma rays but I wonder). The light show, of course, is from > the very hot gases of the explosion. > Now, how do these observations reconcile with the ballistic light > theory? > Bear in mind the gasses are moving at 1/190 c, if Crab Nebula > estimates > are correct (but even if they're not they're not that far off, > presumably). > The leading edge of the explosion would therefore come well ahead of > the neutrino burst. You do a lot of guessing, don't you? The velocity of the neutrinos is also added to the velocity of their source. > As for lightspeed being precisely c, I cannot show this; I can > only show with these supernova that the lightspeed is approximately > c, and very constant whatever its speed actually is. Since > the theoretic discrepancy between SR and the ballistic theory is > so great an approximate result seems good enough for now. In other words you are claiming that the velocity of the neutrino is less that c but they win the race, therefore they had at least a three hour head start on the light. Next time we decide to explode a thermonuclear device at the top of a tower, there should be a three hour warning of neutrino emission before the main event. To be honest with you, I think you are one teat short of an udder. Androcles. > [rest snipped] > -- > #191, ewill3@earthlink.net > It's still legal to go .sigless. === Subject: Re: The Paradox of Zeno In sci.math, Androcles : >> In sci.math, Androcles >> : > in >> In sci.math, Jim Greenfield >> Jim G >> c'=c+v >> How right you are! (Probabaly) Remember; I am always referring to c in vacuum. Refraction and > prisms > incline me to the view that things are not right in material light > velocity either (source dependency), but I'm not going there. Just > let > a space-race of two pulses of EMR, one from a stationary source, > and > another simultaneous from a source moving ref us, decide the matter > of > c'=c+v >> And the reason supernovae don't satisfy this condition is >> precisely why? > Here's a supernova (several images). > http://www.star.ucl.ac.uk/~apod/apod/ap040220.html > http://www.star.ucl.ac.uk/~apod/apod/ap000512.html > http://www.star.ucl.ac.uk/~apod/apod/ap020331.html > And the reason you don't believe supernovae don't satisfy the > condition is precisely why? > What is it about those images is it that tells you the speed of > light is precisely c? > Androcles. >> It's hard to say what exactly things would look like were >> c' = c+v, > Those images ARE what it looks like, because the velocity of light IS > source dependent. Of course it is, that's why the Crab Nebula glowed in the daytime for almost 50 years. Erm...wait. It didn't. >> but the problem is that the nebula of >> the Crab Nebula is estimated (presumably by simple >> trig) to be 10 lightyears in diameter, and is known >> to have exploded 950 years ago (our time), >> thus leads to gases moving about 1/190 c from the explosion, >> and a 73+-year delta, give or take, assuming that the >> supernova is exactly 7,000 light-years distant. > Why is that a problem? This is problem setup. >> If one doesn't like the Crab, one can go with SN1987A, which is >> estimated to be 170,00 light-years distant. Assuming similar >> parameters for the gases, the object would glow for almost 1800 >> years given the ballistic light theory. > Are you going to stick around for 1800 years to see if goes out? It's already violated the light curve. Try slicing up an orange, for example, using a cleaver or paper cutter (if it's sharp enough). The orange slices represent the nascent glowing gasball expanding from the explosion; for various reasons all points on the edge have the same speed relative to Earth and will arrive at the same time in either theory. Therefore, the perimeter of the slice represents the intensity of the glow. As the slices get larger, the perimeter gets brighter, but gradually, then dim just as gradually. This does not fit the intensity profile of the explosion, which is a sudden increase of brightness, followed by a gradual dropoff. Also, the size of the sphere, assuming my assumptions of gas speed are correct, would result in a 50+ year interval of this increase in brightness. >> There's also the little problem of the neutrino precursor. >> We were lucky and caught 19 of them, apparently: >> http://csep10.phys.utk.edu/guidry/violence/sn87a.html >> and then the light show began 3 hours later, approximately. > Yes, that event would indicate neutrinos travel FTL, wouldn't it? I don't have enough information to state either way at this point. A more logical (or consistent with SR; take your pick) conclusion is that the event generating neutrinos, whatever it is, predates the actual collapse/expansion by about 3 hours. I do know that the Si => Fe fusion event takes at most 1 day. >> The SR explanation is relatively simple, even accounting for the >> neutrinos having a small amount of mass. The star in its >> final death throes collapses, then in one gigantic energy burst >> the neutrinos come flying out as it explodes on the rebound, >> along with a lot of other crap (the above does not mention >> gamma rays but I wonder). The light show, of course, is from >> the very hot gases of the explosion. >> Now, how do these observations reconcile with the ballistic light >> theory? >> Bear in mind the gasses are moving at 1/190 c, if Crab Nebula >> estimates >> are correct (but even if they're not they're not that far off, >> presumably). >> The leading edge of the explosion would therefore come well ahead of >> the neutrino burst. > You do a lot of guessing, don't you? > The velocity of the neutrinos is also added to the velocity of their > source. Which means we'd be treated to a steady shower of them as well, in the c' = c+v world. Funny thing, though; nobody's noticed such a steady shower. We got a single burst of 19; that's it. >> As for lightspeed being precisely c, I cannot show this; I can >> only show with these supernova that the lightspeed is approximately >> c, and very constant whatever its speed actually is. Since >> the theoretic discrepancy between SR and the ballistic theory is >> so great an approximate result seems good enough for now. > In other words you are claiming that the velocity of the neutrino is > less that c but they win the race, therefore they had at least a three > hour head start on the light. > Next time we decide to explode a thermonuclear device at the top > of a tower, there should be a three hour warning of neutrino emission > before the main event. > To be honest with you, I think you are one teat short of an udder. If you wish FTL travel of neutrinos, fine. I think other experiments ran through our detectors at one point, with a phenomenal (for a However, I don't know if anyone was able to measure its actual speed. It's clear, however, that Galilean physics predicts that we can accelerate a phenomenal number of protons with little more than a flashlight battery's worth of energy. We should be doing so routinely by now -- and we're not. [rest snipped] -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: The Paradox of Zeno > However, I don't know if anyone was able to measure its actual speed. > It's clear, however, that Galilean physics predicts that we can > accelerate a phenomenal number of protons with little more than > a flashlight battery's worth of energy. We should be doing so > routinely by now -- and we're not. and requires no accelerating over time. There is no contradiction between light c+v and the behavior of massive bodies. eleaticus === Subject: Re: The Paradox of Zeno > In sci.math, Androcles > : >> in > In sci.math, Androcles > : >> The Ghost In The Machine >> in > In sci.math, Jim Greenfield > Jim G > c'=c+v How right you are! (Probabaly) >> Remember; I am always referring to c in vacuum. Refraction and >> prisms >> incline me to the view that things are not right in material >> light >> velocity either (source dependency), but I'm not going there. >> Just >> let >> a space-race of two pulses of EMR, one from a stationary source, >> and >> another simultaneous from a source moving ref us, decide the >> matter >> of >> c'=c+v And the reason supernovae don't satisfy this condition is > precisely why? >> Here's a supernova (several images). >> http://www.star.ucl.ac.uk/~apod/apod/ap040220.html >> http://www.star.ucl.ac.uk/~apod/apod/ap000512.html >> http://www.star.ucl.ac.uk/~apod/apod/ap020331.html >> And the reason you don't believe supernovae don't satisfy the >> condition is precisely why? >> What is it about those images is it that tells you the speed of >> light is precisely c? >> Androcles. > It's hard to say what exactly things would look like were > c' = c+v, >> Those images ARE what it looks like, because the velocity of light IS >> source dependent. > Of course it is, that's why the Crab Nebula glowed in the daytime > for almost 50 years. > Erm...wait. It didn't. You are really good at manufacturing fake evidence, are you not? Whoever said it should? You, obviously. Why would you claim it should and did not, when you haven't a clue what you are going on about? > but the problem is that the nebula of > the Crab Nebula is estimated (presumably by simple > trig) to be 10 lightyears in diameter, and is known > to have exploded 950 years ago (our time), > thus leads to gases moving about 1/190 c from the explosion, > and a 73+-year delta, give or take, assuming that the > supernova is exactly 7,000 light-years distant. >> Why is that a problem? > This is problem setup. > If one doesn't like the Crab, one can go with SN1987A, which is > estimated to be 170,00 light-years distant. Assuming similar > parameters for the gases, the object would glow for almost 1800 > years given the ballistic light theory. >> Are you going to stick around for 1800 years to see if goes out? > It's already violated the light curve. Try slicing up an orange, > for example, using a cleaver or paper cutter (if it's sharp enough). > The orange slices represent the nascent glowing gasball expanding > from the explosion; for various reasons all points on the edge have > the same speed relative to Earth and will arrive at the same time > in either theory. > Therefore, the perimeter of the slice represents the intensity > of the glow. > As the slices get larger, the perimeter gets brighter, but > gradually, then dim just as gradually. This does not fit > the intensity profile of the explosion, which is a sudden > increase of brightness, followed by a gradual dropoff. > Also, the size of the sphere, assuming my assumptions of > gas speed are correct, would result in a 50+ year interval > of this increase in brightness. > There's also the little problem of the neutrino precursor. > We were lucky and caught 19 of them, apparently: > http://csep10.phys.utk.edu/guidry/violence/sn87a.html > and then the light show began 3 hours later, approximately. >> Yes, that event would indicate neutrinos travel FTL, wouldn't it? > I don't have enough information to state either way at this point. > A more logical (or consistent with SR; take your pick) conclusion > is that the event generating neutrinos, whatever it is, predates > the actual collapse/expansion by about 3 hours. Logic is where SR breaks down completely, and so does your argument > I do know that the Si => Fe fusion event takes at most 1 day. > The SR explanation is relatively simple, even accounting for the > neutrinos having a small amount of mass. The star in its > final death throes collapses, then in one gigantic energy burst > the neutrinos come flying out as it explodes on the rebound, > along with a lot of other crap (the above does not mention > gamma rays but I wonder). The light show, of course, is from > the very hot gases of the explosion. > Now, how do these observations reconcile with the ballistic light > theory? > Bear in mind the gasses are moving at 1/190 c, if Crab Nebula > estimates > are correct (but even if they're not they're not that far off, > presumably). > The leading edge of the explosion would therefore come well ahead of > the neutrino burst. >> You do a lot of guessing, don't you? >> The velocity of the neutrinos is also added to the velocity of their >> source. > Which means we'd be treated to a steady shower of them as well, > in the c' = c+v world. Funny thing, though; nobody's noticed such a > steady shower. We got a single burst of 19; that's it. How on earth do you come to that conclusion? > As for lightspeed being precisely c, I cannot show this; I can > only show with these supernova that the lightspeed is approximately > c, and very constant whatever its speed actually is. Since > the theoretic discrepancy between SR and the ballistic theory is > so great an approximate result seems good enough for now. >> In other words you are claiming that the velocity of the neutrino is >> less that c but they win the race, therefore they had at least a >> three >> hour head start on the light. >> Next time we decide to explode a thermonuclear device at the top >> of a tower, there should be a three hour warning of neutrino emission >> before the main event. >> To be honest with you, I think you are one teat short of an udder. > If you wish FTL travel of neutrinos, fine. I think other experiments > ran through our detectors at one point, with a phenomenal (for a > However, I don't know if anyone was able to measure its actual speed. > It's clear, however, that Galilean physics predicts that we can > accelerate a phenomenal number of protons with little more than > a flashlight battery's worth of energy. We should be doing so > routinely by now -- and we're not. So you really do think that we get a 3 hour warning of a neutrino burst if we are going to explode a bomb. What happens if we get the neutrino burst and then decide not to do it? Androcles. > [rest snipped] > -- > #191, ewill3@earthlink.net > It's still legal to go .sigless. === Subject: Re: The Paradox of Zeno In sci.math, Androcles <2G6od.37907$Y7.36407@fe1.news.blueyonder.co.uk>: >> In sci.math, Androcles >> : > in >> In sci.math, Androcles >> : The Ghost In The Machine > In sci.math, Jim Greenfield >> Jim G >> c'=c+v >> How right you are! (Probabaly) Remember; I am always referring to c in vacuum. Refraction and > prisms > incline me to the view that things are not right in material > light > velocity either (source dependency), but I'm not going there. > Just > let > a space-race of two pulses of EMR, one from a stationary source, > and > another simultaneous from a source moving ref us, decide the > matter > of > c'=c+v >> And the reason supernovae don't satisfy this condition is >> precisely why? Here's a supernova (several images). > http://www.star.ucl.ac.uk/~apod/apod/ap040220.html > http://www.star.ucl.ac.uk/~apod/apod/ap000512.html > http://www.star.ucl.ac.uk/~apod/apod/ap020331.html And the reason you don't believe supernovae don't satisfy the > condition is precisely why? > What is it about those images is it that tells you the speed of > light is precisely c? > Androcles. >> It's hard to say what exactly things would look like were >> c' = c+v, > Those images ARE what it looks like, because the velocity of light IS > source dependent. >> Of course it is, that's why the Crab Nebula glowed in the daytime >> for almost 50 years. >> Erm...wait. It didn't. > You are really good at manufacturing fake evidence, are you not? > Whoever said it should? You, obviously. Why would you claim it > should and did not, when you haven't a clue what you are going on > about? Well, I'd have to go look at the records, but AIUI the nova was observed during the *day* for a few weeks. How does one reconcile this with gas speeds of 1/190 c and an estimated distance of 7,000 ly? >> but the problem is that the nebula of >> the Crab Nebula is estimated (presumably by simple >> trig) to be 10 lightyears in diameter, and is known >> to have exploded 950 years ago (our time), >> thus leads to gases moving about 1/190 c from the explosion, >> and a 73+-year delta, give or take, assuming that the >> supernova is exactly 7,000 light-years distant. > Why is that a problem? >> This is problem setup. >> If one doesn't like the Crab, one can go with SN1987A, which is >> estimated to be 170,00 light-years distant. Assuming similar >> parameters for the gases, the object would glow for almost 1800 >> years given the ballistic light theory. > Are you going to stick around for 1800 years to see if goes out? >> It's already violated the light curve. Try slicing up an orange, >> for example, using a cleaver or paper cutter (if it's sharp enough). >> The orange slices represent the nascent glowing gasball expanding >> from the explosion; for various reasons all points on the edge have >> the same speed relative to Earth and will arrive at the same time >> in either theory. >> Therefore, the perimeter of the slice represents the intensity >> of the glow. >> As the slices get larger, the perimeter gets brighter, but >> gradually, then dim just as gradually. This does not fit >> the intensity profile of the explosion, which is a sudden >> increase of brightness, followed by a gradual dropoff. >> Also, the size of the sphere, assuming my assumptions of >> gas speed are correct, would result in a 50+ year interval >> of this increase in brightness. >> There's also the little problem of the neutrino precursor. >> We were lucky and caught 19 of them, apparently: >> http://csep10.phys.utk.edu/guidry/violence/sn87a.html >> and then the light show began 3 hours later, approximately. > Yes, that event would indicate neutrinos travel FTL, wouldn't it? >> I don't have enough information to state either way at this point. >> A more logical (or consistent with SR; take your pick) conclusion >> is that the event generating neutrinos, whatever it is, predates >> the actual collapse/expansion by about 3 hours. > Logic is where SR breaks down completely, and so does your argument Yes, of course. Supernovae do not disprove c' = c+v, and the observations thereof merely show strong evidence that all light rays have source-invariant speed. (And I have bridges for sale.) >> I do know that the Si => Fe fusion event takes at most 1 day. >> The SR explanation is relatively simple, even accounting for the >> neutrinos having a small amount of mass. The star in its >> final death throes collapses, then in one gigantic energy burst >> the neutrinos come flying out as it explodes on the rebound, >> along with a lot of other crap (the above does not mention >> gamma rays but I wonder). The light show, of course, is from >> the very hot gases of the explosion. >> Now, how do these observations reconcile with the ballistic light >> theory? >> Bear in mind the gasses are moving at 1/190 c, if Crab Nebula >> estimates >> are correct (but even if they're not they're not that far off, >> presumably). >> The leading edge of the explosion would therefore come well ahead of >> the neutrino burst. > You do a lot of guessing, don't you? > The velocity of the neutrinos is also added to the velocity of their > source. >> Which means we'd be treated to a steady shower of them as well, >> in the c' = c+v world. Funny thing, though; nobody's noticed such a >> steady shower. We got a single burst of 19; that's it. > How on earth do you come to that conclusion? I'm assuing neutrinos have a similar speed distribution to light quanta. It is admittedly possible that they do not. >> As for lightspeed being precisely c, I cannot show this; I can >> only show with these supernova that the lightspeed is approximately >> c, and very constant whatever its speed actually is. Since >> the theoretic discrepancy between SR and the ballistic theory is >> so great an approximate result seems good enough for now. > In other words you are claiming that the velocity of the neutrino is > less that c but they win the race, therefore they had at least a > three > hour head start on the light. > Next time we decide to explode a thermonuclear device at the top > of a tower, there should be a three hour warning of neutrino emission > before the main event. > To be honest with you, I think you are one teat short of an udder. >> If you wish FTL travel of neutrinos, fine. I think other experiments >> ran through our detectors at one point, with a phenomenal (for a >> However, I don't know if anyone was able to measure its actual speed. >> It's clear, however, that Galilean physics predicts that we can >> accelerate a phenomenal number of protons with little more than >> a flashlight battery's worth of energy. We should be doing so >> routinely by now -- and we're not. > So you really do think that we get a 3 hour warning of a neutrino > burst if we are going to explode a bomb. What happens if we get the > neutrino burst and then decide not to do it? > Androcles. The bomb in this case is a large ball of silicon -- the remnants of a star. Since we can't even contemplate manufacturing one you probably needn't worry overmuch. :-) [rest snipped] -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: The Paradox of Zeno > In sci.math, Androcles > : >> in > In sci.math, Androcles > : >> The Ghost In The Machine >> in > In sci.math, Androcles > : >> The Ghost In The Machine in > In sci.math, Jim Greenfield > Jim G > c'=c+v How right you are! (Probabaly) >> Remember; I am always referring to c in vacuum. Refraction and >> prisms >> incline me to the view that things are not right in material >> light >> velocity either (source dependency), but I'm not going there. >> Just >> let >> a space-race of two pulses of EMR, one from a stationary >> source, >> and >> another simultaneous from a source moving ref us, decide the >> matter >> of >> c'=c+v And the reason supernovae don't satisfy this condition is > precisely why? >> Here's a supernova (several images). >> http://www.star.ucl.ac.uk/~apod/apod/ap040220.html >> http://www.star.ucl.ac.uk/~apod/apod/ap000512.html >> http://www.star.ucl.ac.uk/~apod/apod/ap020331.html >> And the reason you don't believe supernovae don't satisfy the >> condition is precisely why? >> What is it about those images is it that tells you the speed of >> light is precisely c? >> Androcles. It's hard to say what exactly things would look like were > c' = c+v, >> Those images ARE what it looks like, because the velocity of light >> IS >> source dependent. > Of course it is, that's why the Crab Nebula glowed in the daytime > for almost 50 years. > Erm...wait. It didn't. >> You are really good at manufacturing fake evidence, are you not? >> Whoever said it should? You, obviously. Why would you claim it >> should and did not, when you haven't a clue what you are going on >> about? > Well, I'd have to go look at the records, but AIUI the > nova was observed during the *day* for a few weeks. So what? That doesn't make emission theory wrong. Why do you imagine it does? > How does one reconcile this with gas speeds of 1/190 c > and an estimated distance of 7,000 ly? How many weeks do you want for a single explosion? Of course it lasted for several weeks, that's what emission theory predicts. Acording to relativity, the glow should have been a single flash, over in a second. How do YOU reconcile the fact that it lasted for several weeks? > but the problem is that the nebula of > the Crab Nebula is estimated (presumably by simple > trig) to be 10 lightyears in diameter, and is known > to have exploded 950 years ago (our time), > thus leads to gases moving about 1/190 c from the explosion, > and a 73+-year delta, give or take, assuming that the > supernova is exactly 7,000 light-years distant. >> Why is that a problem? > This is problem setup. > > If one doesn't like the Crab, one can go with SN1987A, which is > estimated to be 170,00 light-years distant. Assuming similar > parameters for the gases, the object would glow for almost 1800 > years given the ballistic light theory. >> Are you going to stick around for 1800 years to see if goes out? > It's already violated the light curve. Try slicing up an orange, > for example, using a cleaver or paper cutter (if it's sharp enough). > The orange slices represent the nascent glowing gasball expanding > from the explosion; for various reasons all points on the edge have > the same speed relative to Earth and will arrive at the same time > in either theory. > Therefore, the perimeter of the slice represents the intensity > of the glow. > As the slices get larger, the perimeter gets brighter, but > gradually, then dim just as gradually. This does not fit > the intensity profile of the explosion, which is a sudden > increase of brightness, followed by a gradual dropoff. > Also, the size of the sphere, assuming my assumptions of > gas speed are correct, would result in a 50+ year interval > of this increase in brightness. > > There's also the little problem of the neutrino precursor. > We were lucky and caught 19 of them, apparently: http://csep10.phys.utk.edu/guidry/violence/sn87a.html and then the light show began 3 hours later, approximately. >> Yes, that event would indicate neutrinos travel FTL, wouldn't it? > I don't have enough information to state either way at this point. > A more logical (or consistent with SR; take your pick) conclusion > is that the event generating neutrinos, whatever it is, predates > the actual collapse/expansion by about 3 hours. >> Logic is where SR breaks down completely, and so does your argument > Yes, of course. Supernovae do not disprove c' = c+v, and > the observations thereof merely show strong evidence that > all light rays have source-invariant speed. > (And I have bridges for sale.) I'm not buying one from someone that thinks an explosion lasts for weeks. > I do know that the Si => Fe fusion event takes at most 1 day. > The SR explanation is relatively simple, even accounting for the > neutrinos having a small amount of mass. The star in its > final death throes collapses, then in one gigantic energy burst > the neutrinos come flying out as it explodes on the rebound, > along with a lot of other crap (the above does not mention > gamma rays but I wonder). The light show, of course, is from > the very hot gases of the explosion. Now, how do these observations reconcile with the ballistic light > theory? > Bear in mind the gasses are moving at 1/190 c, if Crab Nebula > estimates > are correct (but even if they're not they're not that far off, > presumably). > The leading edge of the explosion would therefore come well ahead > of > the neutrino burst. >> You do a lot of guessing, don't you? >> The velocity of the neutrinos is also added to the velocity of >> their >> source. > Which means we'd be treated to a steady shower of them as well, > in the c' = c+v world. Funny thing, though; nobody's noticed such a > steady shower. We got a single burst of 19; that's it. >> How on earth do you come to that conclusion? > I'm assuing neutrinos have a similar speed distribution to > light quanta. It is admittedly possible that they do not. Good at assuming, aren't you? You also assume that a neutrino has a 3 hour head start on the light and I'm gullible enough to believe it. Guess what? I've got a bridge for sale. Interested? Pay now and I'll deliver to your doorstep in three hours. > > As for lightspeed being precisely c, I cannot show this; I can > only show with these supernova that the lightspeed is > approximately > c, and very constant whatever its speed actually is. Since > the theoretic discrepancy between SR and the ballistic theory is > so great an approximate result seems good enough for now. >> In other words you are claiming that the velocity of the neutrino >> is >> less that c but they win the race, therefore they had at least a >> three >> hour head start on the light. >> Next time we decide to explode a thermonuclear device at the top >> of a tower, there should be a three hour warning of neutrino >> emission >> before the main event. >> To be honest with you, I think you are one teat short of an udder. > If you wish FTL travel of neutrinos, fine. I think other > experiments > ran through our detectors at one point, with a phenomenal (for a > However, I don't know if anyone was able to measure its actual > speed. > It's clear, however, that Galilean physics predicts that we can > accelerate a phenomenal number of protons with little more than > a flashlight battery's worth of energy. We should be doing so > routinely by now -- and we're not. >> So you really do think that we get a 3 hour warning of a neutrino >> burst if we are going to explode a bomb. What happens if we get the >> neutrino burst and then decide not to do it? >> Androcles. > The bomb in this case is a large ball of silicon -- the remnants of a > star. > Since we can't even contemplate manufacturing one you probably needn't > worry overmuch. :-) Get yourself a detector, and when your fridge starts emitting neutrinos leave and come back three hours later. It will have turned to gold, alchemist. Androcles > [rest snipped] > -- > #191, ewill3@earthlink.net > It's still legal to go .sigless. === Subject: Re: The Paradox of Zeno In sci.math, Androcles : >> In sci.math, Androcles >> <2G6od.37907$Y7.36407@fe1.news.blueyonder.co.uk>: > in >> In sci.math, Androcles >> : The Ghost In The Machine > In sci.math, Androcles >> : The Ghost In The Machine > In sci.math, Jim Greenfield >> Jim G >> c'=c+v >> How right you are! (Probabaly) Remember; I am always referring to c in vacuum. Refraction and > prisms > incline me to the view that things are not right in material > light > velocity either (source dependency), but I'm not going there. > Just > let > a space-race of two pulses of EMR, one from a stationary > source, > and > another simultaneous from a source moving ref us, decide the > matter > of > c'=c+v >> And the reason supernovae don't satisfy this condition is >> precisely why? Here's a supernova (several images). > http://www.star.ucl.ac.uk/~apod/apod/ap040220.html > http://www.star.ucl.ac.uk/~apod/apod/ap000512.html > http://www.star.ucl.ac.uk/~apod/apod/ap020331.html And the reason you don't believe supernovae don't satisfy the > condition is precisely why? > What is it about those images is it that tells you the speed of > light is precisely c? > Androcles. >> It's hard to say what exactly things would look like were >> c' = c+v, Those images ARE what it looks like, because the velocity of light > IS > source dependent. >> Of course it is, that's why the Crab Nebula glowed in the daytime >> for almost 50 years. >> Erm...wait. It didn't. > You are really good at manufacturing fake evidence, are you not? > Whoever said it should? You, obviously. Why would you claim it > should and did not, when you haven't a clue what you are going on > about? >> Well, I'd have to go look at the records, but AIUI the >> nova was observed during the *day* for a few weeks. > So what? > That doesn't make emission theory wrong. Why do you imagine it does? Not sure what you mean by emission theory. >> How does one reconcile this with gas speeds of 1/190 c >> and an estimated distance of 7,000 ly? > How many weeks do you want for a single explosion? > Of course it lasted for several weeks, that's what emission > theory predicts. Acording to relativity, the glow should have > been a single flash, over in a second. Emission theory predicts over 50 years from a point source 7,000 light years away with gasses moving at 1/190 c. SR does not predict a single flash, except perhaps for the neutrinos, as the star's gasses glow for several weeks anyway -- and are still glowing now, only much more faintly. There are also gamma-ray bursts. The working hypothesis is that these are from supernova explosions -- a logical explanation, as far as I can tell. > How do YOU reconcile the fact that it lasted for several weeks? By noting that something hot will radiate for a certain amount of time. A cooling iron ingot, for example, does not lose all of its energy at once. > > but the problem is that the nebula of >> the Crab Nebula is estimated (presumably by simple >> trig) to be 10 lightyears in diameter, and is known >> to have exploded 950 years ago (our time), >> thus leads to gases moving about 1/190 c from the explosion, >> and a 73+-year delta, give or take, assuming that the >> supernova is exactly 7,000 light-years distant. Why is that a problem? >> This is problem setup. > >> If one doesn't like the Crab, one can go with SN1987A, which is >> estimated to be 170,00 light-years distant. Assuming similar >> parameters for the gases, the object would glow for almost 1800 >> years given the ballistic light theory. Are you going to stick around for 1800 years to see if goes out? >> It's already violated the light curve. Try slicing up an orange, >> for example, using a cleaver or paper cutter (if it's sharp enough). >> The orange slices represent the nascent glowing gasball expanding >> from the explosion; for various reasons all points on the edge have >> the same speed relative to Earth and will arrive at the same time >> in either theory. >> Therefore, the perimeter of the slice represents the intensity >> of the glow. >> As the slices get larger, the perimeter gets brighter, but >> gradually, then dim just as gradually. This does not fit >> the intensity profile of the explosion, which is a sudden >> increase of brightness, followed by a gradual dropoff. >> Also, the size of the sphere, assuming my assumptions of >> gas speed are correct, would result in a 50+ year interval >> of this increase in brightness. > >> There's also the little problem of the neutrino precursor. >> We were lucky and caught 19 of them, apparently: >> http://csep10.phys.utk.edu/guidry/violence/sn87a.html >> and then the light show began 3 hours later, approximately. Yes, that event would indicate neutrinos travel FTL, wouldn't it? >> I don't have enough information to state either way at this point. >> A more logical (or consistent with SR; take your pick) conclusion >> is that the event generating neutrinos, whatever it is, predates >> the actual collapse/expansion by about 3 hours. > Logic is where SR breaks down completely, and so does your argument >> Yes, of course. Supernovae do not disprove c' = c+v, and >> the observations thereof merely show strong evidence that >> all light rays have source-invariant speed. >> (And I have bridges for sale.) > I'm not buying one from someone that thinks an explosion lasts > for weeks. It's a very *big* explosion. [rest snipped] -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: Two new math jokes (Physicist's vector space, and compact math curriculum) In sci.math, Snis Pilbor Q: What is the physicist's definition of a vector space? > A: A set V satisfying the axiom that for any x in V, x has a little > arrow drawn over it > Ok now for the second one! > I was talking with a friend in my graph theory class and he pointed > out that a lot of the material is review from his geometric topology > class. I thought about this for a moment and said, Ah! Mathematics > curriculum is compact! He asked me what I meant and I answered: > Any material covered by an infinite number of math courses can be > covered by some finite subset of those courses > Ok let's see some other original jokes on this thread... :-) > Snis Pilbor A mathematician, engineer, and average Joe walk into a bar. The mathematician immediately orders a pie. The engineer immediately orders an 'e', since it's Euler's number, after all, and many engineers have to oil things. The average Joe doesn't exist, being a statistical anomaly. :-) (Well, you wanted a new joke....you got one. I can't say it's *good*... :-) ) -- #191, ewill3@earthlink.net -- insert random good joke here, if one can be found It's still legal to go .sigless. === Subject: Re: Need Help With A Problem > If I could travel 186,000 mph in a nanosecond, how long would it > take me to reach the Virgo Star Cluster? > Assume that VSC is X billion light years away. Since a nanosecond is > one billionth of a second, it would take X years to reach VSC. > Are you saying he's travelling at 1 billion times the speed of light? > Such that a 5 billion light year distance would take 5 years? YES. > First, he said 186000 miles per HOUR. The speed of light is 186000 > miles per SECOND. Touche' I assumed that the OP meant to say 186,000 miles/nanoscond > Second, miles per hour per nanosecond is acceleration, not velocity. True! > Thirdly, the Virgo cluster is only 50 MILLION light years away. > The answer is 29.6 hours. At 1 billion times the speed of light, the trip to Virgo would take 50,000,000/1,000,000,000 = 0.05 years or about 18.25 days. How do you get 29.6 hours? === Subject: Re: Need Help With A Problem === >Subject: Re: Need Help With A Problem >> If I could travel 186,000 mph in a nanosecond, how long would it >> take me to reach the Virgo Star Cluster? >> Assume that VSC is X billion light years away. Since a nanosecond is >> one billionth of a second, it would take X years to reach VSC. >> Are you saying he's travelling at 1 billion times the speed of light? >> Such that a 5 billion light year distance would take 5 years? >YES. >> First, he said 186000 miles per HOUR. The speed of light is 186000 >> miles per SECOND. >Touche' I assumed that the OP meant to say 186,000 miles/nanoscond >> Second, miles per hour per nanosecond is acceleration, not velocity. >True! >> Thirdly, the Virgo cluster is only 50 MILLION light years away. >> The answer is 29.6 hours. >At 1 billion times the speed of light, the trip to Virgo would take >50,000,000/1,000,000,000 = 0.05 years or about 18.25 days. >How do you get 29.6 hours? Well, he never said the acceleration stopped after 1 nanosecond, so I applied constant acceleration. And he didn't say to stop when you arrive there, so I didn't figure in deceleration. -- Mensanator Ace of Clubs === Subject: Re: Need Help With A Problem === >Subject: Re: Need Help With A Problem >> If I could travel 186,000 mph in a nanosecond, how long would it > take me to reach the Virgo Star Cluster? >> Assume that VSC is X billion light years away. Since a nanosecond is >> one billionth of a second, it would take X years to reach VSC. > Are you saying he's travelling at 1 billion times the speed of light? > Such that a 5 billion light year distance would take 5 years? >>YES. >> First, he said 186000 miles per HOUR. The speed of light is 186000 >> miles per SECOND. >>Touche' I assumed that the OP meant to say 186,000 miles/nanoscond >> Second, miles per hour per nanosecond is acceleration, not velocity. >>True! >> Thirdly, the Virgo cluster is only 50 MILLION light years away. >> The answer is 29.6 hours. >At 1 billion times the speed of light, the trip to Virgo would take >50,000,000/1,000,000,000 = 0.05 years or about 18.25 days. >How do you get 29.6 hours? > Well, he never said the acceleration stopped after 1 nanosecond, > so I applied constant acceleration. > And he didn't say to stop when you arrive there, so I didn't figure > in deceleration. Makes sense. === Subject: Re: Turing Machines and Physical Computation > The latter camp has the precise terminology. >> There is no >> physical time constraint applied to when the calculation has to be >> completed. > If you mean *any* computation. But a Turing Machine is a *particular* > computer. Not just *any* computer. Let's pay attention to our > language. http://www.mulhauser.net/research/tutorials/turing/ The capabilities of Turing Machines, Universal Turing Machines, and finite automata are easily confused, and usage outside the specialist literature doesn't help. Of the three, Universal Turing Machines are the most powerful. The Universal Turing Machine was originally described independently but equivalently by Alan Turing and Emil Post (see Davis 1965 or van Heijenoort 1967 for the original papers). It is a general purpose digital computer which can simulate any other digital computer. Formally, this means that for any other computer M, a program p for M can be prefixed with a fixed length segment of code s for Universal Turing Machine U such that sp causes U to perform the same computation as p for M. The fixed length segment s just tells U how to simulate the behaviour of M. This is much like the piece of software which enables a Macintosh personal computer to emulate computers based on an entirely different Intel chip set and thus to run their software unmodified. It is widely -- and incorrectly -- held that a Universal Turing Machine can simulate any physical process at all. The name 'Turing Machine' is often used to include all kinds of Turing Machines (Universal, uniform, non-uniform, oracle machines, etc.), but used narrowly it simply picks out the class of ordinary Turing Machines which lack the universal computational abilities described above. Finally, the class of finite automata is set apart by the fact that they may exist in only a finite number of distinct states. Unlike the Universal Turing Machine, which may write any of an infinite set of binary strings on its infinitely long tape, finite automata can display only a strictly finite number of distinct states. Whereas the Universal Turing Machine can, for intance, enumerate infinitely many natural numbers by virtue of its unlimited tape capacity, any finite automaton for enumerating natural numbers will always be limited by some largest number beyond which it cannot continue. Relations Between Computation Models Their finiteness guarantees that for any finite automaton, there exists some Turing Machine which can calculate the same function (i.e., which can simulate it). Likewise, the definition of Universal Turing Machine guarantees that for any Turing Machine, any Universal Turing Machine can simulate it. Similarly, any Universal Turing Machine can simulate any finite automaton. Some Universal Turing Machines running particular programs compute functions equivalent to those computed by less powerful (non-universal) Turing Machines or even finite automata, but no program can give a non-universal Turing Machine universal power, and no finite automaton has universal power. === Subject: Re: Turing Machines and Physical Computation >http://www.mulhauser.net/research/tutorials/turing/ >The capabilities of Turing Machines, Universal Turing Machines, and finite >automata are easily confused, and usage outside the specialist literature >doesn't help. ... > but no program can >give a non-universal Turing Machine universal power, and no finite automaton >has universal power. Well, this author makes his own words come true, for he completely confuses the ideas himself. The principle of the UTM finds its use in emulation programs of all kinds. If this doesn't fit some transcendental sense of the term universal, that's a minor point. Even the specialist literature, perhaps most urgently of all the specialist literature, needs to be rationalized. J. === Subject: Re: Turing Machines and Physical Computation >>http://www.mulhauser.net/research/tutorials/turing/ >>The capabilities of Turing Machines, Universal Turing Machines, and >>finite >>automata are easily confused, and usage outside the specialist literature >>doesn't help. > ... >> but no program can >>give a non-universal Turing Machine universal power, and no finite >>automaton >>has universal power. > Well, this author makes his own words come true, for he completely > confuses the ideas himself. > The principle of the UTM finds its use in emulation programs of all > kinds. If this doesn't fit some transcendental sense of the term > universal, that's a minor point. One can change emulating programs to emulating machines without error. I think he means in comparison to Finite Automatas which have a finite limitation that Turing Machines do not. FAs do not have the same computational power as TMs meaning a UTM. I am not sure he committed this transgression: http://plato.stanford.edu/entries/church-turing/ A myth seems to have arisen concerning Turing's paper of 1936, namely that he there gave a treatment of the limits of mechanism and established a fundamental result to the effect that the universal Turing machine can simulate the behaviour of any machine. The myth has passed into the philosophy of mind, generally to pernicious effect. > Even the specialist literature, perhaps most urgently of all the > specialist literature, needs to be rationalized. > J. I found this/his statement a bit awkward also. Suppose you decided to explore the decimal expansion of the square root of prime numbers. There is a Turing machine for each such operation. I think the author means it is the hardwired, that is the non-programmable aspect of the construction of the TM which accounts for the computation. Or that instructions on Turing Machine A will not run on Turing Machine B, not because the instructions are in a different logical format, but because the machine is the instruction set. I think the author is trying to distinguish between a static hardwired program that only runs on one exact machine and the dynamic portable idea of a program. The idea of a word processor that will work on any PC versus a word processor that only works with the hardware specific to a particular PC. I've read this idea before which I suppose the author did not express well. You can't take the instruction set which serves for input for TM A, and use it for input to TM B. Because the input is what describes the machine. There is no program that makes input from TM A and makes it run on TM B. A UTM can be thought of as a dynamic, reconfigurable, hardware specification. So that if you had a word processor that only worked on one computer, because of the computer's hardware, a UTM works by metamorphosizing its internal hardware so that it can read the unique word processor. The idea is not that the unique word processor has its software translated into something generically readable by many other possible computer hardwares. http://www.infrastructures.org/papers/turing/turing.html 8.2- Because a Turing machine's program is hardwired, it is common practice to say that the program _describes_ or _is_ the machine. A Turing machine's program is stated in a descriptive language which we will call the machine language. Using this language, we describe the actions the machine should take when certain conditions are discovered. We will call each atom of description an instruction. [SH: the emphasis is the author's.] SH: I probably dwelt on this too much and too long. It seemed to me that thinking about that a TM's program is hardwired, not portable, which isn't the traditional assumption of the more logical, portable usage of 'program'. I think the author should rewrite the statement, it is a bit too condensed. Also since the machine admits an abstract, logical/mathematical formulation, the line blurs between program and machine. Probably when I research this, I wil find no universal agreement. I tend to think of this as emulating a machine rather than a program because that is how I learned it, but it could probably be taught differently too. I included a quote which uses your terminology. >> but no program can >>give a non-universal Turing Machine universal power I think he means a true TM cannot function as another true TM where true means non-universal. That the change of function that comes a (special)Universal TM, is not a program change, the instructions that are being run, but that the change in function comes from assuming the hardware identity of another/different true TM description. I didn't produce this quote because of the point you bring up. But because it supports another position. Quantum computers have the potential to solve computable problems that are considered to be intractable for conventional computers because of a time constraint. I don't think a TM comes equipped with any time (or physical) constraint as described in Turing's 1936 paper. My point was that Turing machines could compute some problems that a conventional digital computer could not, rather than the expected justification of why TMs can actually compute as much as physical digital computers. Thus some abacus-computable functions will not be computable by any physical machine. http://plato.stanford.edu/entries/turing-machine/ A Turing machine is a kind of state machine. Turing machines are not physical objects but mathematical ones. Devices with different capabilities may be able to complete different instruction sets, and therefore may result in different classes of computable tasks. One way to think of a UTM is as a programmable computer. When a UTM is given a program (a description of another machine), it makes itself behave as if it were that machine while processing the input. [SH: not the only way though] The action of a Turing machine is determined completely by (1) the current state of the machine (2) the symbol in the cell currently being scanned by the head and (3) a table of transition rules, which serve as the program for the machine. [SH: Notice that program is put in quotes, I think because of the hardware method of implementation.] ------------------------------------------------------------------- http://plato.stanford.edu/entries/turing-machine/ In modern terms, the tape serves as the memory of the machine, while the read-write head is the memory bus through which data is accessed (and updated) by the machine. There are two important things to notice about the definition. The first is that the machine's tape is infinite in length, corresponding to an assumption that the memory of the machine is infinite. The second is similar in nature, but not explicit in the definition of the machine, namely that a function will be Turing-computable if there exists a set of instructions that will result in the machine computing the function regardless of the amount of time it takes. One can think of this as assuming the availability of infinite time to complete the computation. These two assumptions are intended to ensure that the definition of computation that results is not too narrow. This is, it ensures that no computable function will fail to be Turing-computable solely because there is insufficient time or memory to complete the computation. If a function is not Turing-computable it is because Turing machines lack the computational machinery to carry it out, not because of a lack of spatio-temporal resources. -------------------------------------------------------------------- These are called abacus computers by Lambek (Lambek 1961), and are known to be equivalent to Turing machines. The modern digital computer is subject to finiteness constraints that we have abstracted away in the definition of abacus machines, just as we did in the case of Turing machines. Physical computers are limited in the number of memory locations that they have, and in the storage capacity of each of those locations, while abacus machines are not subject to those constraints. Thus some abacus-computable functions will not be computable by any physical machine. (We won't consider whether Turing machines and modern digital computers remain equivalent when both are given external inputs, since that would require us to change the definition of a Turing machine.) ---------------------------------------------------------------------------- - http://www.alanturing.net/turing_archive/pages/Reference%20Articles/What%20i s%20a%20Turing%20Machine.html#head Commercially available computers are hard-wired to perform primitive operations considerably more sophisticated than those of a Turing machine --add, multiply, decrement, store-at-address, branch, and so forth. The precise constitution of the list of primitives varies from manufacturer to manufacturer. It is a remarkable fact that none of these computers can outdo a Turing machine. Despite the Turing machine's austere simplicity, it is capable of computing anything that any computer on the market can compute. Indeed, since it is an abstract or notional machine, a Turing machine can compute more than any physical computer. This is because (1) the physical computer has access to only a bounded amount of memory, and (2) the physical computer's speed of operation is limited by various real-world constraints. It is sometimes said, incorrectly, that a Turing machine is necessarily slow, since the head is continually shuffling backwards and forwards, one square at a time, along a tape of unbounded length. But since a Turing machine is an idealised device, it has no real-world constraints on its speed of operation. Stephen === Subject: Re: Turing Machines and Physical Computation >One can change emulating programs to emulating machines without error. Agreed. >I think he means in comparison to Finite Automatas which have >a finite limitation that Turing Machines do not. FAs do not have >the same computational power as TMs meaning a UTM. He should say what he means. As should I, I suppose. Perhaps what I am interested in is a class on the fuzzy boundary between FA and UTM, large FA's, equivalent to this here machine I am typing on. I suspect many others would be interested in this same class, if indeed it is distinguishable in principle from either smaller FA's or UTMs. I suppose it is distinguishable, but perhaps not interestingly so. >http://plato.stanford.edu/entries/turing-machine/ >A Turing machine is a kind of state machine. >Turing machines are not physical objects but mathematical ones. Fascinating, a non-physical state machine. I'm a big fan of SEP, but I believe the idealist interpretation they >These two assumptions are intended to ensure that the definition of >computation that results is not too narrow. OK, and let us also worry that it not be too broad. J. === Subject: Re: Turing Machines and Physical Computation >http://plato.stanford.edu/entries/turing-machine/ >A Turing machine is a kind of state machine. >Turing machines are not physical objects but mathematical ones. > Fascinating, a non-physical state machine. > I'm a big fan of SEP, but I believe the idealist interpretation they Agreed. Turing seems to be a concrete physicalist. This talk of non-physical machines is an open invitation to substance dualism, which we should not favor on comp.ai.philosophy. And neither on comp.theory. I guess sci.math readers want to have the privilege to talk about counter-factuals, and I'll happily grant that, but they must know what it means. >These two assumptions are intended to ensure that the definition of >computation that results is not too narrow. > OK, and let us also worry that it not be too broad. I know you worry about this, but I am not too concerned. -- Eray Ozkural === Subject: Re: Turing Machines and Physical Computation >Agreed. Turing seems to be a concrete physicalist. More of a positivist, considering the context of his time and place. Which I like to try to reinterpret as instrumentalist. And constructivist. Postivism implies some sort of physicalism, I think, or at least it should. Unfortunately, Turing never give a fig about being nominalist or not, which is another reinterpretation I like to give to OCN. J. === Subject: Re: Turing Machines and Physical Computation >Agreed. Turing seems to be a concrete physicalist. > More of a positivist, considering the context of his time and place. > Which I like to try to reinterpret as instrumentalist. > And constructivist. > Postivism implies some sort of physicalism, I think, or at least it > should. > Unfortunately, Turing never give a fig about being nominalist or not, > which is another reinterpretation I like to give to OCN. Personally, I do not condone those idealist re-readings of Turing which litter these newsgroups. They are just as bad as braindead behaviorism for what it's worth. Although Turing does not make it clear where he stands, well, he clearly is not part of the Vienna Circle, but his works can be conceived as part of the larger paradigm of positivism, if not logical positivism. I would also like to interpret his work as nominalist, and it certainly reads as if it were instrumentalist, because of the style of arguments in Computing Machinery and Intelligence. At any rate, these idealist revisionists like Stephen Harris will find it difficult to understand the necessary conditions for computation. What they are doing is no philosophy of computation, it is theology. TURING WAS NO THEOLOGIST, HE WAS AN INTELLIGENT MAN. In particular, Harris and several others here do not seem to understand the distinction between unbounded and infinite. They claim they understand the distinction, but that is not the case. ------------------------------------------------------------------------ Stephen, now I do not wish to seem sore or unsympathetic, but you are not understanding a very simple fact of the matter, perhaps for the 100th time. 1. The ID of a TM is finite at all times. Do you agree or not? 2. The space of a physical computer is finite at all times. Do you agree or not? 3. There is no machine in the world that is larger than the universe. Do you agree or not? Where is your purported discrepancy then? Because, the following easy scientific arguments follow. 4. Therefore *IF* the universe is finite (WHICH WE DO NOT HAVE CONCLUSIVE PHYSICAL EVIDENCE OF, ONLY SOME EVIDENCE THAT POINTS TO THAT!), THEN, it is absurd to talk of ANY MACHINES WITH INFINITE SIZE. 5. However, since a theory is not concerned with how large that finite size is, the theory depicts in principle AN UNBOUNDED SPACE. That does not mean it shows the EXISTENCE OF MACHINES LARGER THAN THE UNIVERSE. It only says that, WELL IF OUR UNIVERSE WERE LARGER, WE COULD CONSTRUCT LARGER MACHINES. 6. If on the other hand the universe if INFINITE (WHICH WE DO NOT KNOW!), then Turing Machines make unconditional predictions for the causal structures of all possible machines (requires separate argumentation and acception of C-T but easy to see) I think you do not understand any of the 6 steps of argumentation. 5 clearly exceeds your toolkit, but even 1, I don't think you understand it. I don't think you or any of these idealist crowd here truly understand the distinction between actual infinite space and unbounded space. (And I don't expect you to understand the conditional nature of 4-6) Let me repeat if for you so that you get a permanent fix. THE TURING MACHINE DOES NOT HAVE AN INFINITE TAPE. IT HAS AN UNBOUNDED TAPE. THIS IS SO BECAUSE ITS DESCRIPTION IS NEVER ACTUALLY INFINITE AT ANY TIME OF OPERATION. IT IS ALWAYS FINITE WHICH MEANS IT IS REPRESENTABLE IN FINITE SPACE. Note that I also think you have a gross misunderstanding of scientific theories in general. Consider geometry. The theory of spaces, discrete or continuous, does not matter, are in fact theories of physical spaces as well as spaces of possible worlds. However, the latter metaphysical character of geometry does not reduce its value in depicting the physical world. This is a much more difficult issue, and you can't get around it by your irrelevant quoting and misinterpretation of some web pages you -- Eray Ozkural === Subject: Re: Turing Machines and Physical Computation & TM 'S REVISIONISTS You've not yet read Copeland, EZzz ? Friendly. Po;-Á) >Agreed. Turing seems to be a concrete physicalist. > More of a positivist, considering the context of his time and place. > Which I like to try to reinterpret as instrumentalist. > And constructivist. > Postivism implies some sort of physicalism, I think, or at least it > should. > Unfortunately, Turing never give a fig about being nominalist or not, > which is another reinterpretation I like to give to OCN. > Personally, I do not condone those idealist re-readings of Turing > which litter these newsgroups. They are just as bad as braindead > behaviorism for what it's worth. > Although Turing does not make it clear where he stands, well, he > clearly is not part of the Vienna Circle, but his works can be > conceived as part of the larger paradigm of positivism, if not logical > positivism. > I would also like to interpret his work as nominalist, and it > certainly reads as if it were instrumentalist, because of the style of > arguments in Computing Machinery and Intelligence. > At any rate, these idealist revisionists like Stephen Harris will find > it difficult to understand the necessary conditions for computation. > What they are doing is no philosophy of computation, it is theology. > TURING WAS NO THEOLOGIST, HE WAS AN INTELLIGENT MAN. > In particular, Harris and several others here do not seem to > understand the distinction between unbounded and infinite. They claim > they understand the distinction, but that is not the case. > ------------------------------------------------------------------------ > Stephen, now I do not wish to seem sore or unsympathetic, but you are > not understanding a very simple fact of the matter, perhaps for the > 100th time. > 1. The ID of a TM is finite at all times. > Do you agree or not? > 2. The space of a physical computer is finite at all times. > Do you agree or not? > 3. There is no machine in the world that is larger than the universe. > Do you agree or not? > Where is your purported discrepancy then? Because, the following easy > scientific arguments follow. > 4. Therefore *IF* the universe is finite (WHICH WE DO NOT HAVE > CONCLUSIVE PHYSICAL EVIDENCE OF, ONLY SOME EVIDENCE THAT POINTS TO > THAT!), THEN, it is absurd to talk of ANY MACHINES WITH INFINITE SIZE. > 5. However, since a theory is not concerned with how large that finite > size is, the theory depicts in principle AN UNBOUNDED SPACE. That does > not mean it shows the EXISTENCE OF MACHINES LARGER THAN THE UNIVERSE. > It only says that, WELL IF OUR UNIVERSE WERE LARGER, WE COULD > CONSTRUCT LARGER MACHINES. > 6. If on the other hand the universe if INFINITE (WHICH WE DO NOT > KNOW!), then Turing Machines make unconditional predictions for the > causal structures of all possible machines (requires separate > argumentation and acception of C-T but easy to see) > I think you do not understand any of the 6 steps of argumentation. 5 > clearly exceeds your toolkit, but even 1, I don't think you understand > it. I don't think you or any of these idealist crowd here truly > understand the distinction between actual infinite space and unbounded > space. (And I don't expect you to understand the conditional nature of > 4-6) > Let me repeat if for you so that you get a permanent fix. > THE TURING MACHINE DOES NOT HAVE AN INFINITE TAPE. IT HAS AN UNBOUNDED > TAPE. THIS IS SO BECAUSE ITS DESCRIPTION IS NEVER ACTUALLY INFINITE AT > ANY TIME OF OPERATION. IT IS ALWAYS FINITE WHICH MEANS IT IS > REPRESENTABLE IN FINITE SPACE. > Note that I also think you have a gross misunderstanding of scientific > theories in general. > Consider geometry. The theory of spaces, discrete or continuous, does > not matter, are in fact theories of physical spaces as well as spaces > of possible worlds. However, the latter metaphysical character of > geometry does not reduce its value in depicting the physical world. > This is a much more difficult issue, and you can't get around it by > your irrelevant quoting and misinterpretation of some web pages you === Subject: Re: Turing Machines and Physical Computation >>Agreed. Turing seems to be a concrete physicalist. > More of a positivist, considering the context of his time and place. > Which I like to try to reinterpret as instrumentalist. > And constructivist. > Postivism implies some sort of physicalism, I think, or at least it > should. > Unfortunately, Turing never give a fig about being nominalist or not, > which is another reinterpretation I like to give to OCN. > J. I decided to try a different approach. They have already simulated TMs on a PC and even built a physical TM which is pretty much like the TM in Turing's paper. Except for the tape. http://en.wikipedia.org/wiki/Turing_machine A physical Turing machine It is not difficult to simulate a Turing machine on a modern computer except for the limited memory of actually existing computers. It is also possible to build a Turing machine on a purely mechanical basis. The mathematician Karl Scherer has indeed built such a machine in 1986 using metal and plastic construction sets, and some wood. The 1.5 meter high machine uses the pulling of strings to read, move and write the data (which is represented using ball bearings). SH: The physical TM, or a PC simulation of a TM, are always going to have finite memory, a limitation which can be temporarily expanded, but in principle, there is a finite limit to the physical storage available. The physical storage determines how big or how deep the computations can get. A 100 mile tape can perform calcuations to a much greater depth than a 10 inch tape because the calculations have to be stored. Like a really really long number would exceed the ram and hard drive capacity of your computer. Mathematics can always generate numbers bigger than the capacity of physical storage needed to move operations. So in theory not in physical practice, a TM equipped with a potentially infinitely long tape is going to compute the value of some numerical operation that far exceeds the capacity of a finite tape. If some physical turing machine with physical tape can compute a number with a billion, billion, billion digits digits it will eventually hit a roadblock of the number of digits which exceeds its capacities. The abstract turing machine with eventually always be able to surpass the physical turing machine tape imposed boundary. If a physical turing machine can compute a zillion finite digits of Pi, an abstract turing machine with infinite tape can compute a zillion + 1 finite digits of Pi a zillion +2 finite digits of PI ; a zillion +3 finite digits of Pi; and so on and so on: a zillion + {1, 2, 3, 4, ...} countably infinite more digits of Pi than its counterpart the physical TM constrained by a finitely long tape. I just let a zillion represent the largest number of digits a physical TM could compute of Pi (infinite) using the longest finite tape existing or possible to exist in the physical universe. An abstract TM can always compute more than a zillion digits because it is using the abstract storage potential of the unbounded expansion/storage potential of its hypothetical tape. Physical machines (PCs) suffer from intractability of hugely complex operations while abstract TMs don't suffer from intractibility caused by time constraints or lack of memory. So abstract TMs can compute a large class of intractible PC computations due to unbounded tape/memory. The large class is infinite in size because there is no limit to the TM tape arbitrary selection of finite numbers, each one just 1 digit longer than the one before. If a PC can calculate twenty jillion digits of Pi before it exhausts its storage capacity to represent all those digit, a TM which can never exhaust its storage capacity (potentially infinite tape), can always compute one more digit than twenty jillion, two more digits, three more digits and so on. Not to the end of time, because there is no time assigned to how long a computation takes on the abstract Turing machine. Stephen === Subject: Re: Turing Machines and Physical Computation >>Agreed. Turing seems to be a concrete physicalist. > More of a positivist, considering the context of his time and place. > Which I like to try to reinterpret as instrumentalist. > And constructivist. > Postivism implies some sort of physicalism, I think, or at least it > should. > Unfortunately, Turing never give a fig about being nominalist or not, > which is another reinterpretation I like to give to OCN. > J. Turing did not call his description a Turing machine, that name was conferred by others later. He called it a Logical Computing Machine LCM And the LCM was equivalent to Church's logical formalism: The Princeton logician Alonzo Church had slightly outpaced Turing in finding a satisfactory definition of what he called 'effective calculability.' Church's definition required the logical formalism of the lambda-calculus. This meant that from the outset Turing's achievement merged with and superseded the formulation of Church's Thesis, namely the assertion that the lambda-calculus formalism correctly embodied the concept of effective process or method. Very rapidly it was shown that the mathematical scope of Turing computability coincided with Church's definition (and also with the scope of the general recursive functions defined by G.9adel). === Subject: Re: Turing Machines and Physical Computation >>Agreed. Turing seems to be a concrete physicalist. > More of a positivist, considering the context of his time and place. > Which I like to try to reinterpret as instrumentalist. > And constructivist. In the philosophy of mathematics, constructivism asserts that it is necessary to find (or construct) a mathematical object to prove that it exists. When one assumes that an object does not exist, and derive a contradiction from that assumption, one still has not found it, and therefore not proved its existence, according to constructivists. I'm trying to see how discussion of Turing's person philosophy ties into the issues he presented in his 1936 paper (he was a minimalist). Almost all mathematicians prefer a constructive proof to a non-constructive proof. I think the 4-color proof relies on brute force computer search of a huge amount of possibilities which a human can't follow. There is alway some distrust of computer aided proofs. Turing was interested in the foundations of Mathematics. His paper is a response to Hilbert's program and in particular question #10. He mentions Godel's result which also disproved question #10 but says his proof is clearer. Godel received a lot of flak rejecting his proof and Turing wanted to mitigate this perception. His other purpose was to clarify the meaning of algorithm, which is also called an effective procedure. Turing used the word mechanical. This meant repetitive, by rote, not the movement of parts in a machine. He also used the word computer which meant a human clerk who did calculations with pencil and paper. Another way you can tell that Turing did not mean a physical machine, but rather a mathematical object, an idea, was that he gave the TM an infinite tape which was one-dimensional. This condition cannot be physically realized in the ordinary usage of machine. All evenly educated people know this (not mostly self-taught). It is not a matter of opinion, it does not depend Turing's philosophical inclination. It is a matter of fact. That is why I can keep providing variations of the same definition, because it is a fact. There are finite mathematical numbers which are so large that they exceed the capacity of the universe to store requirement or correlation which says mathematical finiteness of a huge number matches up with the finite storage capacity of the universe. There are ways of condensing a number so that you don't write out all the zeros. Even these methods (or one ultimate method) will eventually exceed the storage capacity of the physical universe and so not be computed because it is intractable. Because the Turing Machine has an infinite tape and not time restraint, it can chug along and compute any finite number no matter how large because it has an infinite tape which surpasses finite universe storage capacity. I'm providing a definitional fact. Just like there are no married bachelors is a fact because the definition of a bachelor means not married. Infinite does not mean finite no matter what your philosphical inclination is if one is of sound mind. Definition: Common term for computer, usually when considered at the hardware level. The Turing Machine, an early example of this usage, was however neither hardware nor software, but only an idea. http://www.hyperdictionary.com/dictionary/machine === Subject: Re: Turing Machines and Physical Computation Originator: tchow@lagrange.mit.edu.mit.edu (Timothy Chow) >I think the 4-color proof relies on brute force computer search of a huge >amount of possibilities which a human can't follow. There is alway some >distrust of computer aided proofs. Dissatisfaction, maybe, but distrust, not really---not nowadays, anyway. >Turing was interested in the foundations of Mathematics. His paper >is a response to Hilbert's program and in particular question #10. He >mentions Godel's result which also disproved question #10 but says his >proof is clearer. What do you mean by question #10? Do you mean Hilbert's 10th problem? That wasn't solved until much later, by Davis, Putnam, Robinson, and Matiyasevich. What you probably intended was Hilbert's Entscheidungsproblem. The unsolvability of this was *not* proved by Goedel, as Turing points out in his paper. Goedel showed that the naive method of searching for a proof of either X or ~X would not solve the Entscheidungsproblem, but didn't rule out some other method. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Turing Machines and Physical Computation >>I think the 4-color proof relies on brute force computer search of a huge >>amount of possibilities which a human can't follow. There is alway some >>distrust of computer aided proofs. > Dissatisfaction, maybe, but distrust, not really---not nowadays, anyway. I thought there were cases of theorems considered to be proven that were later discovered not to be proven, because the computer was programmed in error? So how do you know for sure. >>Turing was interested in the foundations of Mathematics. His paper >>is a response to Hilbert's program and in particular question #10. He >>mentions Godel's result which also disproved question #10 but says his >>proof is clearer. > What do you mean by question #10? Do you mean Hilbert's 10th problem? > That wasn't solved until much later, by Davis, Putnam, Robinson, and > Matiyasevich. > What you probably intended was Hilbert's Entscheidungsproblem. The I didn't want to type it so substituted erroneously (didn't know about 1928) http://en.wikipedia.org/wiki/Entscheidungsproblem The Entscheidungsproblem (German: decision problem) is the challenge in symbolic logic to find a general algorithm which decides for given first-order statements whether they are universally valid or not. Alonzo Church and independently Alan Turing showed in 1936 that this is impossible. As a consequence, it is in particular impossible to algorithmically decide whether statements in arithmetic are true or false. The question goes back to Gottfried Leibniz, who in the seventeenth century, after having constructed a successful mechanical calculating machine, dreamt of building a machine that could manipulate symbols in order to determine the truth values of mathematical statements. He realized that the first step would have to be a clean formal language, and much of his subsequent work was directed towards that goal. In 1928, David Hilbert and Wilhelm Ackermann posed the question in the form outlined above. In 1900, at a mathematical conference in Paris, David Hilbert presented his famous 23 unsolved problems of Mathematics, the second problem of which was to determine whether the axioms of Mathematics were consistent or not. In 1928 he proposed a related question that whether it was possible to determine the truth of any mathematical statement. > unsolvability of this was *not* proved by Goedel, as Turing points out > in his paper. Goedel showed that the naive method of searching for a > proof of either X or ~X would not solve the Entscheidungsproblem, but > didn't rule out some other method. Stephen === Subject: Re: Turing Machines and Physical Computation Originator: tchow@lagrange.mit.edu.mit.edu (Timothy Chow) [Re: distrust of computer-assisted proofs] >I thought there were cases of theorems considered to be proven that >were later discovered not to be proven, because the computer was >programmed in error? So how do you know for sure. There are also cases of theorems considered to be proven that were later discovered to have erroneous proofs, where no computer was involved, and the only error involved was human error. The attitude of most mathematicians nowadays is that every proof has some risk of being wrong. The computer-assisted part of a proof, if properly managed, tends to be *less* likely to have errors than the human part. (Not that everyone properly manages their computer-assisted proofs. Then again, not everyone properly manages their non-computer-assisted proofs either.) The dissatisfaction with computer-assisted proofs stems mostly from the feeling that they don't give a lot of insight. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Turing Machines and Physical Computation <41a38073$0$564$b45e6eb0@senator-bedfellow.mit.edu> <41a3ef28$0$576$b45e6eb0@senator-bedfellow.mit.edu[Re: distrust of computer-assisted proofs] >>I thought there were cases of theorems considered to be proven that >>were later discovered not to be proven, because the computer was >>programmed in error? So how do you know for sure. >There are also cases of theorems considered to be proven that were later >discovered to have erroneous proofs, where no computer was involved, and >the only error involved was human error. >The attitude of most mathematicians nowadays is that every proof has some >risk of being wrong. The computer-assisted part of a proof, if properly >managed, tends to be *less* likely to have errors than the human part. >(Not that everyone properly manages their computer-assisted proofs. >Then again, not everyone properly manages their non-computer-assisted >proofs either.) >The dissatisfaction with computer-assisted proofs stems mostly from the >feeling that they don't give a lot of insight. This is a point which has been elaborated at some length within c.a.p over the years in the explication of the empirical, fallibilistic nature of the extensional stance. Sadly, the most vociferous detractors clearly have not grasped what the banality (and ultimately intensionalism or mentalism) of analyticity means for GOFAI (and more widely, for so called cognitive science). Instead, these true believers cling to an anachronistic (veiled mono or pluralistic deistic metaphysics whilst clearly demonstrating that they simply don't understand what they're objecting to. This ignorance has been empirically demonstrated time after time with each and every one of them, usually to no avail. Which is why I begin Fragments with the three quotes that I do (and why one of the living luminaries in the field was awarded a Nobel a couple of years ago). The facts are there for all to see. These folk just ignore them and keep deluding themselves, solipsistically denigrating precisely what they should be trying to come to grips with - namely, how epistemology or the theory of science has been naturalised as radical, or evidential behaviourism. The last century will, I predict be looked back upon by future generations with some consternation, as they will see how, especially in its latter part, hoards of apparently educated folk, got the temporal order of cognitivism and behaviourism completely the wrong way round, not for rational reasons, but for entirely irrational politically correct reasons. In a nutshell, they confabulate what they don't understand, with what they don't agree with (or like). -- David Longley http://www.longley.demon.co.uk/Frag.htm http://www.longley.demon.co.uk/Frag.htm === Subject: Re: Turing Machines and Physical Computation >> [Re: distrust of computer-assisted proofs] > I thought there were cases of theorems considered to be proven that > were later discovered not to be proven, because the computer was > programmed in error? So how do you know for sure. >> There are also cases of theorems considered to be proven that were later >> discovered to have erroneous proofs, where no computer was involved, and >> the only error involved was human error. >> The attitude of most mathematicians nowadays is that every proof has some >> risk of being wrong. The computer-assisted part of a proof, if properly >> managed, tends to be *less* likely to have errors than the human part. >> (Not that everyone properly manages their computer-assisted proofs. >> Then again, not everyone properly manages their non-computer-assisted >> proofs either.) >> The dissatisfaction with computer-assisted proofs stems mostly from the >> feeling that they don't give a lot of insight. > This is a point which has been elaborated at some length within c.a.p > over the years in the explication of the empirical, fallibilistic nature > of the extensional stance. Sadly, the most vociferous detractors clearly > have not grasped what the banality (and ultimately intensionalism or > mentalism) of analyticity means for GOFAI (and more widely, for so > called cognitive science). Instead, these true believers cling to an > anachronistic (veiled mono or pluralistic deistic metaphysics whilst > clearly demonstrating that they simply don't understand what they're > objecting to. This ignorance has been empirically demonstrated time > after time with each and every one of them, usually to no avail. Which > is why I begin Fragments with the three quotes that I do (and why one > of the living luminaries in the field was awarded a Nobel a couple of > years ago). The facts are there for all to see. These folk just ignore > them and keep deluding themselves, solipsistically denigrating precisely > what they should be trying to come to grips with - namely, how > epistemology or the theory of science has been naturalised as radical, > or evidential behaviourism. The last century will, I predict be looked > back upon by future generations with some consternation, as they will > see how, especially in its latter part, hoards of apparently educated > folk, got the temporal order of cognitivism and behaviourism > completely the wrong way round, not for rational reasons, but for > entirely irrational politically correct reasons. Your bombastic message might have had more impact here had it addressed the topic of computer assisted proofs in some slight measure. Your message leaves the pertinent question of what the extensional stance has to say relevant to computer assisted proofs open for us to guess. In other words you are perversely pandering to the inscrutability of reference of what you refer to as this. Shame on you ! patty === Subject: Re: Turing Machines and Physical Computation <41a38073$0$564$b45e6eb0@senator-bedfellow.mit.edu> <41a3ef28$0$576$b45e6eb0@senator-bedfellow.mit.edu> > I thought there were cases of theorems considered to be proven that >> were later discovered not to be proven, because the computer was >> programmed in error? So how do you know for sure. > There are also cases of theorems considered to be proven that were later > discovered to have erroneous proofs, where no computer was involved, and > the only error involved was human error. > The attitude of most mathematicians nowadays is that every proof has some > risk of being wrong. The computer-assisted part of a proof, if properly > managed, tends to be *less* likely to have errors than the human part. > (Not that everyone properly manages their computer-assisted proofs. > Then again, not everyone properly manages their non-computer-assisted > proofs either.) > The dissatisfaction with computer-assisted proofs stems mostly from the > feeling that they don't give a lot of insight. >> This is a point which has been elaborated at some length within >>c.a.p over the years in the explication of the empirical, >>fallibilistic nature of the extensional stance. Sadly, the most >>vociferous detractors clearly have not grasped what the banality (and >>ultimately intensionalism or mentalism) of analyticity means for >>GOFAI (and more widely, for so called cognitive science). Instead, >>these true believers cling to an anachronistic (veiled mono or >>pluralistic deistic metaphysics whilst clearly demonstrating that >>they simply don't understand what they're objecting to. This ignorance >>has been empirically demonstrated time after time with each and every >>one of them, usually to no avail. Which is why I begin Fragments >>with the three quotes that I do (and why one of the living luminaries >>in the field was awarded a Nobel a couple of years ago). The facts >>are there for all to see. These folk just ignore them and keep >>deluding themselves, solipsistically denigrating precisely what they >>should be trying to come to grips with - namely, how epistemology or >>the theory of science has been naturalised as radical, or evidential >>behaviourism. The last century will, I predict be looked back upon by >>future generations with some consternation, as they will see how, >>especially in its latter part, hoards of apparently educated folk, got >>the temporal order of cognitivism and behaviourism completely the >>wrong way round, not for rational reasons, but for entirely irrational politically correct reasons. >Your bombastic message might have had more impact here had it addressed >the topic of computer assisted proofs in some slight measure. Your >message leaves the pertinent question of what the extensional stance >has to say relevant to computer assisted proofs open for us to guess. >In other words you are perversely pandering to the inscrutability of >reference of what you refer to as this. Shame on you ! >patty I don't expect my message to have anything but the effect that it clearly does on you metaphysical solipsists (who delude yourselves that you're methodological solipsists). This is an occupational hazard or disposition which computer folk and mathematicians appear to be especially prone or attracted to. I therefore don't expect what I say to do much more than annoy or confuse you (to have any other effect you'd have to practically (and demonstrably) do something in response to what has been said other than just whine about it). But beware, you *will* reinforce this behaviour in others, here and elsewhere, and you perhaps ought to wonder just how good a role model that is. If you'd done as directed and looked into what I have directed folk to look into (through recent links) you might have picked up how extensive this problem is and why. I count of the fact that you can't, or don't grasp what the referents are even though they're explicitly stated and left for you to put together. As with other examples (e.g. said that, remembered that, believed that etc) I'm illustrating something, not trying to recruit or persuade. That's your assumption/misconception. You simply don't know the practical difference between methodology and metaphysics. To appreciate the difference you'd have to know something about the merits of the science of behaviour over our natural common-sense folk psychology. You'd also have to appreciate why so much of philosophy is now no more than highbrow (largely male) romantic literature. -- David Longley http://www.longley.demon.co.uk === Subject: Re: Turing Machines and Physical Computation http://mygate.mailgate.org/mynews/comp/comp.theory/fc36fa654d334db067c1ea94c 6 e85614.48257%40mygate.mailgate.org > Your bombastic message might have had more impact > here had it addressed the topic of computer > assisted proofs in some slight measure. David Longley is profoundly mentally ill. No matter what the subject matter, his reply always concerns _his_ obsessions, the opaque inanities over which he has wasted his days, let his life tend to rot and decay, the antique (mis)understandings of his youth, never the material under discussion by other participants. It is for such persons that killfiles were first invented. As he has no intention to reform his boorish ways, to learn and to practice dialog instead of monolog, to return himself to being a participating, contributing member of the human species, rather than remain only an obstacle to the contributions of others, the only remaining recourse is to ignore him completely. I suggest this recourse be widely taken, in the interest of conserving bandwidth and memewidth so that others can carry on their attempts to enlarge human knowledge without his constant disruptions. HTH xanthian. -- === Subject: Re: Turing Machines and Physical Computation <41a38073$0$564$b45e6eb0@senator-bedfellow.mit.edu> <41a3ef28$0$576$b45e6eb0@senator-bedfellow.mit.edu> Your bombastic message might have had more impact >> here had it addressed the topic of computer >> assisted proofs in some slight measure. >David Longley is profoundly mentally ill. No matter >what the subject matter, his reply always concerns >_his_ obsessions, the opaque inanities over which he >has wasted his days, let his life tend to rot and >decay, the antique (mis)understandings of his youth, >never the material under discussion by other >participants. >It is for such persons that killfiles were first >invented. As he has no intention to reform his >boorish ways, to learn and to practice dialog >instead of monolog, to return himself to being a >participating, contributing member of the human >species, rather than remain only an obstacle to the >contributions of others, the only remaining recourse >is to ignore him completely. >I suggest this recourse be widely taken, in the >interest of conserving bandwidth and memewidth so >that others can carry on their attempts to enlarge >human knowledge without his constant disruptions. >HTH >xanthian. Let's get something clear. You insist on telling everyone that you suffer from an affective disorder, and yet you also tell everyone that this does not affect your judgement. What do the affective disorders affect do you think, and would you be in a position to soundly judge? As if that were not revealing enough, you now have the temerity to assert that I am profoundly mentally ill. Is that supposed to affect my judgement or behaviour? You tell others you have a debilitating problem in order to give expression to your pathology with impunity. This is deplorable - and it needs to be publicly stated so others who don't see what you're doing aren't misled or hurt by it. I've said before that you really need to think things like this through or you'll just end up sounding irrational, abusive and be punished for it. You're behaving like your behavioural brakes are off, and it will just reinforce your problems not help ameliorate them. Working on hard problems won't help either I suspect. Psychologists use those sorts of paradigms to *induce* experimental depression (in order to test treatments for alleviating it!). I've also suggested before that you don't have much awareness of the consequences of your behaviour - ie that you lack insight and impulse control. You have also failed to pick up on a number of other salient points made here, which might account for the fact that you don't understand what I have been saying (it might be even more referentially opaque to you than it is to others simply because you don't/can't look very far). None of this is surprising given what I have said above. You are behaving abusively, and pathologically so in my view. It's ironic and you don't seem to appreciate the extent to which you are, indirectly, really just abusing yourself. It certainly won't help you out of your predicament, and it will very probably just make matters worse, as most folk won't be as even handed or helpful as I. -- David Longley http://www.longley.demon.co.uk === Subject: Re: Turing Machines and Physical Computation > [Re: distrust of computer-assisted proofs] >>I thought there were cases of theorems considered to be proven that >>were later discovered not to be proven, because the computer was >>programmed in error? So how do you know for sure. > There are also cases of theorems considered to be proven that were later > discovered to have erroneous proofs, where no computer was involved, and > the only error involved was human error. Yes, this is true. > The attitude of most mathematicians nowadays is that every proof has some > risk of being wrong. The computer-assisted part of a proof, if properly > managed, tends to be *less* likely to have errors than the human part. > (Not that everyone properly manages their computer-assisted proofs. > Then again, not everyone properly manages their non-computer-assisted > proofs either.) I read back issues of the FOM mailing list because it is free and fascinating. Your contributions have been noted. My second favor author is Joe Shipman who I notice expresses his reservations mildly, we can not have the same type of certainty whereas I used the cruder distrust. There is alway some distrust of computer aided proofs. http://www.cs.nyu.edu/pipermail/fom/1998-August/002076.html Joe Shipman: In the absence of rigorous proofs of the correctness of computer systems (including chip design, programming language, compiler, and operating system), we can not have the same type of certainty about the correctness of a computer-aided proof as we can of a humanly surveyable proof. But we can attain moral certainty if we follow Nicely's recipe with sufficient thoroughness (I would demand more than two verifications in which all the components of the system were independent for an important result like 4CT or the Kepler conjecture). [SH: Shipman supports your point in this paragraph.] Conventional proofs are not always more certain than this. Three illustrations: 1) Smale's paper on Problems for the 21st Century in the Spring 1998 Mathematical Intelligencer (which I recommended to FOM a few months ago) mentions in passing a shockingly large number of incorrect theorems which were originally accepted and took years to be recognized as not really proved 2) Hsiang's 1990 proof of the Kepler conjecture, a consensus against which was obtained only several years later (the paper still has not been withdrawn) 3) The classification of finite simple groups is said to be several thousand pages long and I do not believe any single mathematician has carefully checked the entire thing; thus no one can have the confidence that this theorem is true that they can have about a proof they have personally checked, everyone can have only the confidence attainable from accepting the authority of other mathematicians, which is less. (I'm not even sure every piece of the proof of the Classification has been validated by several referees yet -- does anyone know if this has yet occurred?) For example, I have personally verified proofs of the Prime Number Theorem and Godel's Incompleteness Theorem; I depend on the authority of other mathematicians for my belief in Wiles's (Fermat's Last) Theorem and Friedman's latest independence results, though I look forward to one day personally verifying them. --------------------------------------------------------------------- > The dissatisfaction with computer-assisted proofs stems mostly from the > feeling that they don't give a lot of insight. SH: Harvey Friedman, my favorite FOM author agrees with you. http://www.cs.nyu.edu/pipermail/fom/1998-September/002210.html Harvey Friedman But the deep foundational question is, not whether it is true, but what does it mean? > -- Again, I appreciate the correction about the 1928 date and challenge. It certainly makes more sense that way! Stephen === Subject: Re: Turing Machines and Physical Computation Originator: tchow@lagrange.mit.edu.mit.edu (Timothy Chow) >Your contributions have been noted. My second favor author is Joe Shipman >who I notice expresses his reservations mildly, we can not have the same >type of certainty whereas I used the cruder distrust. There is alway >some distrust of computer aided proofs. >http://www.cs.nyu.edu/pipermail/fom/1998-August/002076.html Joe Shipman: >In the absence of rigorous proofs of the correctness of computer systems >(including chip design, programming language, compiler, and operating >system), >we can not have the same type of certainty about the correctness of a >computer-aided proof as we can of a humanly surveyable proof. But Shipman isn't even saying here that we can't have the same kind of certainty, only that we need proofs of correctness of the computer systems in question. By the way, I suspect that Shipman's objection is a minority objection, although admittedly I have only anecdotal evidence. I have problems with his objection myself: 1. Implicitly, Shipman seems to regard processing each step of a proof in my brain in the conventional way as being the gold standard. I don't see why this should be true. If the goal is certainty that there is no error, then I might do better by relying on someone or something else that has a lower error rate than I have. And then the distinction between computer-assisted and conventional proofs blurs. 2. But maybe I've misinterpreted Shipman, and he accepts that processing a proof in my brain isn't the only gold standard. After all, he doesn't say that the certainty of computer-aided proofs is *inferior*, only that it is *not the same type*. And he also refers to the surrogate process of checking proofs of correctness of computer systems. In that case, he and I are mostly in agreement, except that I don't quite agree with the implicit suggestion that proofs of correctness of computer systems would give the same type of certainty as conventional proofs. (Shipman doesn't state this explicitly; he only states the converse, but I think it's implicit.) The problem is that having a proof of correctness doesn't guarantee that the physical execution of a computer won't be corrupted by a stray cosmic ray, or more generally that the physical computer actually behaves as designed on paper. Note also that we never demand proofs of correctness of our brains. So proofs of correctness aren't sufficient or necessary to achieve the same type of certainty. --- Incidentally, computer-assisted proofs are gradually evolving from the type in which a large computation is delegated to the computer to the type where the *entire proof* is encoded in a data file governed by simple syntactical rules. So to check the correctness of the proof, you just have to write a short program of your own to verify that the certificate has the advertised syntax. Instead of having to worry about whether, say, a complex piece of software like Mathematica has some subtle bug in it that affects the correctness of your computation, you only have to worry that a very short piece of code that you can write yourself is executing as intended. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Turing Machines and Physical Computation > By the way, I suspect that Shipman's objection is a minority objection, > although admittedly I have only anecdotal evidence. I have problems with > his objection myself: > 1. Implicitly, Shipman seems to regard processing each step of a proof in > my brain in the conventional way as being the gold standard. I don't http://www.cs.nyu.edu/pipermail/fom/1998-February/001121.html Nevertheless, Tymoczko's book contains several interesting essays, e.g. Tymoczko's own essay about the 4-color theorem, suggesting that we need to broaden the concept of mathematical proof to include computer-aided proof. I would frame this differently, as a question of distinguishing among various kinds of mathematical proof. Rigorous conceptual proof is the gold standard, but computer-aided proof can also be valuable. This reminds me of Aristotle's discussion of reasoning which is correct but not fully scientific. For Aristotle, scientific reasoning gives not only knowledge, but knowledge of the cause. [posted by Stephen G. Simpson] > see why this should be true. If the goal is certainty that there is > no error, then I might do better by relying on someone or something > else that has a lower error rate than I have. And then the distinction > between computer-assisted and conventional proofs blurs. === Subject: Re: Turing Machines and Physical Computation <41a3ef28$0$576$b45e6eb0@senator-bedfellow.mit.edu> <41a4a697$0$563$b45e6eb0@senator-bedfellow.mit.edu> The following are taken from a series of messages posted internally within a closed network back in 1990. I thought they might be worth citing once again (although without their original context for reasons which some of the more thoughtful here will understand). A lot has been said here since. Most folk here won't see a fraction of what it's all about for many reasons that I've already covered. Some might be wise to take their emotional responses as something to further act upon. ON THE COMPUTER METAPHOR 'It has always bothered me that models of psychological processing were thought to be inspired by our understanding of the computer. The statement has always been false. Indeed, the architecture of the modern digital computer - the so-called Von Neumann architecture - was heavily influenced by people's (naive) view of how the mind operated. Perhaps I had better document this. Simply read the work on cybernetics and thought in the 1940's and 1950's prior to the development of the digital computer. The group of workers included people from all disciplines: See the Macy Conferences on Cybernetics, or Her Majesty's Conference on Thought processes. Read the preface to Wiener's book on cybernetics. Everyone who was working together - engineers, physicists, mathematicians, psychologists, neuroscientists (not yet named) - consciously and deliberately claimed to be modelling brain processes.' Reflections on Cognition and Parallel Distributed Processing D.A. Norman (Ch 26, p534, Parallel Distributed Processing Volume 2) McClelland J and Rumelhart D 1986 'A trait is EFFECTIVE if there is a hard and fast routine by which we can check for it, without guesswork or imagination...It came to be appreciated, in the mid- thirties, that recursiveness affords a sharp explication of effectiveness. This has come to be called Church's Thesis....By its nature, Church's Thesis was not open to formal proof; for the thesis equated a precise property, recursiveness, with a property - effectiveness - that was to be rendered precise only by the thesis itself. But the thesis was supported by such instances as could be mustered, and soon it was pretty well clinched by Alan Turing's pioneer work in the abstract theory of computing machines. His formulation of mechanical computability, in terms of ideal mechanization, turned out to be equivalent to recursiveness. Mechanical computability, surely, is very much what our intuitive talk of effectiveness was aiming at all along; so Church's Thesis is well sustained.' - Quine (1987) Recursion 'The first three chapters actually grew out of two earlier papers. Those papers were, in part, polemics against the views of my good friend and student Jerry Fodor. Fodor I hasten to say, is not the main target of this book; but I have retained some of my polemic against what I call MIT mentalism... The main target of the present book is one H Putnam (one of my former selves) and those who have adopted his views. Or perhaps it would be more accurate to say that the present book doesn't have a main target; for its aim is not so much to refute one particular view as to establish the need for a different way of looking at problems about mental states. At any rate, the intended contribution of these three chapters to that end is to do two things: (1) to establish a close connection (discovered and emphasised throughout his career by W V Quine) between problems about meaning and problems about belief fixation, by showing that the holistic character of belief fixation in science bears deeply on the issue of individuation of meanings (or contents or intentions, as they are called by various philosophers; and (2) to argue that, in fact, thinking of meanings (or contents) as theoretical entities - as scientific objects, objects which can be isolated and which can play an explanatory role in scientific theory - is a mistake. In the course of the argument I defend the view that there is no criterion for sameness of meaning except actual interpretative practice - a view made famous by Quine and Davidson' H Putnam (1988) Representation and Reality 'We cannot individuate concepts and beliefs without reference to the ENVIRONMENT. Meanings aren't in the head. The upshot of our discussion for the philosophy of mind is that propositional attitudes, as philosophers call them - that is, such things as 'believing that snow is white' and 'feeling certain that the cat is on the mat' - are not states of the human brain and nervous system considered in isolation from the social and nonhuman environment. A fortiori they are not functional states - that is, states definable in terms of parameters which would enter into a software description of the organism. FUNCTIONALISM, CONSTRUED AS THE THESIS THAT PROPOSITIONAL ATTITUDES ARE JUST COMPUTATIONAL STATES OF THE BRAIN, CANNOT BE CORRECT'. The arguments I just summarised were, it might be pointed out in this connection, arguments against methodological solipsism. H. Putnam (1988) 'Representation and Reality' (Professor of Mathematical Logic Harvard) - 'I subscribe entirely to these sentences of Count Verri: On the Nature of Pleasure and Pain: The only moving principle of man is pain. Pain precedes every pleasure. Pleasure is not a positive state.' - Immanuel Kant 1781 - - 'Meanwhile our eager-beaver researcher, undismayed by logic-of-science considerations and relying blissfully on the exactitude of modern statistical hypothesis- testing, has produced a long publication list and been promoted to a full professorship. In terms of his contribution to the enduring body of psychological knowledge, he has done hardly anything. His true position is that of a potent-but-sterile intellectual rake, who leaves in his merry path a long train of ravished maidens but no scientific offspring.' - P. E. Meehl (1967) Theory Testing in Psychology and Physics Philosophy of Science pp 103-115 - - C56. - Naloxone enhances neophobia - J.F.W. DEAKIN & D.C. LONGLEY* (introduced by T.J. Crow) - National Institute for Medical Research, Mill Hill, London, NW7 1AA - Several studies report that naloxone, an opiate receptor antagonist, reduces deprivation induced eating and drinking. However, in the present study, naloxone (5mg/kg,i.p.) did not reduce food intake of rats maintained on a 22 h deprivation - 2 h feeding schedule. In contrast, naloxone (5 mg/kg,i.p.) progressively reduced water intake in deprived animals to 46% of saline treated controls. No effects of naloxone (1, 5 mg/kg) on established bar pressing for food or water were observed with either continuous or fixed ratio schedules of reinforcement. However, naloxone (5mg/kg) accelerated extinction of responding when food and water were no longer available. - Animals treated with naloxone (5mg/kg) during training of the bar-pressing ate only 26% of the pellets delivered whereas controls ate all pellets delivered. Since the animals had not previously experienced the pellets or the operant apparatus, the possibilities arose that naloxone effects were due to enhanced neophobic effects of the novel food pellets or novel apparatus cues, or were due to conditioned taste aversion. Therefore, food novelty, apparatus novelty and timing of injections were independently varied in different groups of 8-10 rats treated with saline or naloxone. Rats were maintained at 85% body weight with 12g lab chow per day. On experimental days 46 small pellets (Cambden instruments) were placed on a small petri dish in the home cage of some groups or released from a pellet dispenser in an operant box for other groups. The dependent variable was the number of pellets eaten over 15 minutes. - Naloxone (1,5 mg/kg i.p.) injected 5 or 20 min before test almost completely suppressed pellet eating if the animals had not been previously exposed to the pellets (p<0.01 't' test vs saline groups). This occurred independently of whether tests were carried out in the home cage or novel operant box. Naloxone induced suppression of pellet eating was almost completely abolished in either environment if animals had been exposed to the pellets for the five preceding days in the same or different environment. Naloxone (5mg/kg, i.p.) administered immediately after pellet eating tests failed to suppress subsequent pellet eating. - Thus, naloxone suppressed pellet eating if the pellets were novel and if naloxone was administered before eating tests. The results suggest naloxone enhances neophobic effects of novel foods and that suppression of novel pellet eating is not due to enhanced effects of novelty of apparatus cues or to conditioned taste aversion. - Reference - FRENK, H & ROGERS G.H. (1979) The suppressant effects of naloxone on food and water intake in the rat. Behav. Neural. Biol, 26, 23-40. - PROCEEDINGS OF THE BRITISH PHARMACOLOGICAL SOCIETY (BPS) 1-3 April 1981 (Also British J Pharmacology 1981) 'A word now about similarity: subjective similarity, which is crucial to the learning process. I don't think anyone has an innate notion of similarity. What one has incontestably is an innate subjective behavioral standard of similarity. It can be tested in people and other animals by conditioning. - It is unfortunate that my phrase 'standard of similarity' suggests judgment or deliberate co