mm-1959 === Subject: Re: Laplace transformation, Volterra Integral equation > I wonder whether anybody could tell me if the following equation has a > unique solution for f(s,t): > f(s,t) = g(s+t) - int_{0}^{t} f(s+x,t-x) dx - int_{0}^{s} f(s-y,t-y) > dy > with g(s+t) a given and f(s,t) the unknown. > I tried Laplace transformation (first for s and then for t) but What are the allowed values for s and t? The integrals would make sense> without success. > Could anybody supply me with a pointer of how to go about this? The answer to your question and the methods to use to get there depend on some details of your problem you have not given. for s and t real, but then Laplace transform would not be the transformation of choice. If you want s and t to be non-negative, how is one to interpret the second integral when s>t? Do you have any growth condition for f when s and t become large? e.g. should f be integrable, or bounded? Michael. -- &&&&&&&&&&&&&&&&#@#&&&&&&&&&&&&&&&& Dr. Michael Ulm FB Mathematik, Universitaet Rostock michael.ulm@mathematik.uni-rostock.de === Subject: Re: The sunset of the soul > And as far as I know, not too many people have doppelganngers out > there. You don't throw yourself out, seek yourself, and examine it as > a biological entity. If people talk this way, they are speaking > **metaphorically.** I do not understand what doppelganger means in this context. you realize that philosophical talk operates nearly 100% with figurative speech and metaphor, of course. === Subject: Re: The sunset of the soul >> And as far as I know, not too many people have doppelganngers out >> there. You don't throw yourself out, seek yourself, and examine it as >> a biological entity. If people talk this way, they are speaking >> **metaphorically.** >I do not understand what doppelganger means in this context. >you realize that philosophical talk operates nearly 100% with >figurative speech and metaphor, of course. That's very Spanish of you to say. And it's true, if the only philosopher who ever lived was named Cervantes. It's true if you limit philosophy to Spanish culture. -- Certain questions, which one frequently hears, are not philosophical queries, but psychological confessions. Ayn Rand in Check Your Premises. === Subject: Re: need help in understanding Torkel's ZFC comment > > It is indeed some of the most feeble and pathetic invective yet seen > on this group. >> >> It's not really feeble. sci.relativity is feeble. >> sci.math is set theory with a moron leadings >> the sets, a homesexual chemist rubbing the >> sets, and a number theorists doing something >> kind of four thingy, when they really do >> should buy a Webster's on-line dictionary rather >> than a history of stupid. >> Yup! Feeble and pathetic; also incoherent and bonkers. > It's not pathetic. Fermat's Last Theorem is pathetic. That comment is pathetic, feeble and bonkers (but surpisingly not incoherent ---- you're losing your touch!). -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html Lacan, Jacques, 79, 91-92; mistakes his penis for a square root, 88-9 Francis Wheen, _How Mumbo-Jumbo Conquered the World_ === Subject: My virus warning Hi! Yes, that virus does really exist. Sorry if it scared anyone or it was too harsh, but I wanted to get the word out before something bad happened to someone's PC. I've been getting that virus in my E-mail lately (some others have come in too like MyDoom and Netsky), and I just wanted to warn you folks that this threat is out there. For more info, check the link: http://securityresponse.symantec.com/avcenter/venc/data/w32.swen.a@mm.html === Subject: Re: My virus warning > Hi! > Yes, that virus does really exist. Sorry if it scared anyone or it was > too harsh, but I wanted to get the word out before something bad > happened to someone's PC. I've been getting that virus in my E-mail > lately (some others have come in too like MyDoom and Netsky), and I > just wanted to warn you folks that this threat is out there. > For more info, check the link: > http://securityresponse.symantec.com/avcenter/venc/data/w32.swen.a@mm.html the worm is over 7 months old, now (it started last september)... most people who would have gotten it already have... -- we're the first ones to starve, we're the first ones to die the first ones in line for that pie in the sky and we're always the last when the cream is shared out for the worker is working when the fat cat's about === Subject: Re: My virus warning >Hi! >Yes, that virus does really exist. Sorry if it scared anyone or it was >too harsh, but I wanted to get the word out before something bad >happened to someone's PC. I've been getting that virus in my E-mail >lately (some others have come in too like MyDoom and Netsky), and I >just wanted to warn you folks that this threat is out there. Uh, you might read the replies to your first post before repeating it like this. Nobody doubts that the problem is real - we've all known about the problem for many months. >For more info, check the link: >http://securityresponse.symantec.com/avcenter/venc/data/w32.swen.a@mm.html ************************ David C. Ullrich === Subject: Re: My virus warning > Hi! > Yes, that virus does really exist. Sorry if it scared anyone or it was > too harsh, but I wanted to get the word out before something bad > happened to someone's PC. I've been getting that virus in my E-mail > lately (some others have come in too like MyDoom and Netsky), and I > just wanted to warn you folks that this threat is out there. > For more info, check the link: > http://securityresponse.symantec.com/avcenter/venc/data/w32.swen.a@mm.html This has been around for months. We don't need warning. Gib === Subject: Kalman filtering Hi! I'm not sure if this is the most relevant newsgroup, but someone can maybe advice me otherwise.... I'm looking for formulas for making Kalman type filters, as realtime as possible... My objective is to have a library of formulas - or maybe I need just one which I can alter - which I can apply to different areas of use. My useage is realted to GPS-tracking, and I want to able to taylor the filtering according to what kind of object the GPS-sensor is mounted on. An intelligent filter will need to look different for, let's say; a formula 1 car, a hockey player and a sailboat. I picture a solution were I can enter the physical boundries/rules which imply for each instance: the maximum speed/acceleration, change of direction, etc. As far as I gather (I'm far from an expert) a Kalman type filter doesn't relay on averaging a high number of previous occurances. This is an important demand for me: the filtering can't resolve in a great delay. My data has to be as realtime as possible. Rune Fergestad === Subject: Re: Kalman filtering >Hi! >I'm not sure if this is the most relevant newsgroup, but someone can maybe >advice me otherwise.... >I'm looking for formulas for making Kalman type filters, as realtime as >possible... My objective is to have a library of formulas - or maybe I need >just one which I can alter - which I can apply to different areas of use. My >useage is realted to GPS-tracking, and I want to able to taylor the >filtering according to what kind of object the GPS-sensor is mounted on. An >intelligent filter will need to look different for, let's say; a formula 1 >car, a hockey player and a sailboat. I picture a solution were I can enter >the physical boundries/rules which imply for each instance: the maximum >speed/acceleration, change of direction, etc. As far as I gather (I'm far >from an expert) a Kalman type filter doesn't relay on averaging a high >number of previous occurances. This is an important demand for me: the >filtering can't resolve in a great delay. My data has to be as realtime as >possible. You might look for an electric engineering / digital signal processing group. -- Stephen J. Herschkorn herschko@rutcor.rutgers.edu === Subject: [humor] Misheard lyrics, Math style And so I screwed up Billy Joel because math was always nearer to me than cuisine: ...he works at Mr. Carath.8eodory's down on southernly street... It's Sullivan Street BTW, but I keep wondering (now that I know) how Chicken Carath.8eodory might taste. Especially if it's nowhere dense. Moving out, -- Hauke Reddmann <:-EX8 fc3a501@uni-hamburg.de als man ankam wollte man werden, die geschichte schreiben, die doofen sollen sterben, der plan als man damals nach hamburg kam (Kettcar) === Subject: Re: PROOF that numbers are countable > You (like other Phillites) are sorely confused about the difference between > Infinite items and Infinite SETS of finite items (e.g. natural numbers, > sequence of 3's). My concrete example was an attempt to show you that > difference in your own terms, but there are none so blind.... >> have you wondered why you're the only person left arguing Cantors theorem? >I have to say I'm sincerely impressed with the patience of >a few people here in re-trying once and again to achieve >the unachievable... It's not quite that saintly . Yes, patience is necessary, but there also needs to be some motivation to bother with the net.cranks in the first place, since after a couple of posts it's pretty clear when someone is impervious to reason. In my case, I have run into various students who had firmly entrenched dysfunctional knowledge (anti-knowledge, so to speak), and I have more often than not been unable to get past the surface confusion and into their underlying internal logic. On the too-rare occasions when I have managed it, I have been able thereby to help the student bootstrap their way from their anti-knowledge into an actual understanding of the topic at hand. So, I view Usenet as an opportunity to have extensive interaction with some holders of anti-knowledge in order to practice my diagnostic and treatment skills for when I encounter real students (who are almost never as aggressively ignorant as the net.cranks). >Refutating Cantor's diagonalization proof seems be the >ultimate manifestation point for potential net.cranks... I reckon that anything having to do with infinity is fertile ground for them. The original Phil (for whom the Phillites are named) just couldn't get it that each individual natural number is finite BUT that there is an endless set of them. Herc is the one on sci.logic who has been most recently active in promoting that view; and Tony Thomas was the one before him. >Unbelievable that there seem so many regulars here which >seem to have a good grasp of set theory and no important >theorems to prove. How sad for the mathematical world... As my namesake once said, Math ... is hard. It's one thing to be somewhat familiar with axiomatic set theory; it's quite another to prove a significant theorem. >Stephan -- --------------------------- | BBB b Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | | B B a a r b b | | BBB aa a r bbb | ----------------------------- === Subject: xmds solves complex problems simply and quickly xmds - the eXtensible Multi-Dimensional Simulator - is a program for solving equations - fast. It is an Open Source tool to simplify the computer modelling of various systems, and is currently being developed within the Australian Centre for Quantum-Atom Optics at the University of Queensland in Australia. There are many situations in many areas where a system of interest can be modelled by a differential equation or equations. Such areas include: physics, mathematics, engineering, physical and theoretical chemistry, theoretical and computational biology, finance, and economics. Modelling these systems involves writing a computer program to find a solution to the equations, which is not necessarily easy to do. This is where xmds comes in. The advantage of using xmds instead of doing the same job by means of conventional programming is the same as ordering a pizza as opposed to making one yourself. The only thing you have to learn to become an xmds user is How to order a pizza. There are a couple of important differences here though: normally you have to pay for the pizza, while xmds comes for free; and xmds is like a gourmet pizza outlet - one has the option of exotic things like solving stochastic equations, which the chain-brand pizza vendors don't offer! xmds therefore makes writing complex computer simulations simple. Another major advantage of xmds is that it is free. The source code and documentation can be freely downloaded from the xmds web site, http://www.xmds.org/. xmds runs on Linux, Unix (including MacOS X) and the Cygwin environment on Windows, help for installing xmds on these systems is available both from the web site and the xmds distribution. xmds is especially useful in solving complex problems requiring solving the problem over many different random parameters. Such problems can be parallelised (run on lots of computers at the same time) and xmds does this automatically with little user input, making the solution of these problems a breeze. Often writing a computer program to solve complex problems can be very difficult, time-consuming, and error-prone. This is where xmds excels. One merely needs to write a script in a high-level form which low-level code for you, producing code that is better for a computer. This makes the writing of a simulation program significantly easier, reducing the development time, and almost eliminating bugs since xmds has written the vast majority of the code for you and has used thoroughly tested code and techniques in the production of the as code hand-written by an expert, so one can has the best of both worlds: quick development time, and quick execution. You can find examples of the use of xmds for solving complex (and simple) problems in the examples page of the xmds web site: http://www.xmds.org/examples/. So, if you're trying to model a bunch of atoms bouncing around together, the diffusion of an electrolyte solution, the reaction of enzymes with a substrate, or the volatility of stock prices, then xmds is the simulation tool for you. For more information visit the web site http://www.xmds.org/. === Subject: Re: Ubiquitous Naturals, Infinity You might have to consider why infinity is itself, and zero, one, and/or negative one. If you don't, perhaps you haven't. Please do. I have a variety of problems where infinity takes on the value of one. I might have problems about infinity being zero or negative one. What do you think about that? Regardless of that, I establish a canonical ordering upon any non-ordering-sensitive set. There may be none. So does AC, Zorn, or the well-ordering principle. The empty set has no ordering. Explain why infinity is one. I have. Explain why infinity is one, zero, and/or negative one. I may. Ross === Subject: Re: Ubiquitous Naturals, Infinity > You might have to consider why infinity is itself, and zero, one, > and/or negative one. > If you don't, perhaps you haven't. Please do. > I have a variety of problems where infinity takes on the value of one. > I might have problems about infinity being zero or negative one. > What do you think about that? > Regardless of that, I establish a canonical ordering upon any > non-ordering-sensitive set. There may be none. So does AC, Zorn, or > the well-ordering principle. The empty set has no ordering. > Explain why infinity is one. I have. > Explain why infinity is one, zero, and/or negative one. I may. > Ross One has heard of monkey's typing Shakespeare, but from the above, they still have a way to go. === Subject: Re: functions that halt >You can write down some specifications (for reals) that >are uncomputable, but I think you can't decide whether the >real that fulfills that spec just might happen to be a >fraction of square roots or some such (precisely because >you can't compute it and so check). At least all the >examples I have seen were of that kind. > No: all the proofs of uncomputability I can think of prove > that a number really isn't computable. For example theÍ real > B defined as 0.bbbbb... where the n'th bit is 1 iff the > programme with G.9adel number n halts is not computable. If it > were, then one could use another programme that took > programmes as argument, G.9adel encoded them and indexed B as > a solution to the halting problem. Note that the proof says > nothing to specify the reason behind computing B; the > contradiction would arise if /any/ programme could compute B > in any fashion. So B isn't a fraction of the square root of > anything computable. I did not understand it this way. I think that B could well be a computable number, but you'd never know. Since you can't compute B as defined, you can't really tell whether it is equal to another computable number or not. This also means that if B happens to be equal to some computable number, you cannot use that fact, because you cannot ever know of it (with certainty). Thus there is no paradox; you would only have a contradiction if a program could compute the number B and *know* it has computed computed a number that fulfills the definition of B. Michael -- Feel the stare of my burning hamster and stop smoking! === Subject: Re: functions that halt >>You can write down some specifications (for reals) that >>are uncomputable, but I think you can't decide whether the >>real that fulfills that spec just might happen to be a >>fraction of square roots or some such (precisely because >>you can't compute it and so check). At least all the >>examples I have seen were of that kind. >> No: all the proofs of uncomputability I can think of prove >> that a number really isn't computable. For example theÍ real >> B defined as 0.bbbbb... where the n'th bit is 1 iff the >> programme with G.9adel number n halts is not computable. If it >> were, then one could use another programme that took >> programmes as argument, G.9adel encoded them and indexed B as >> a solution to the halting problem. Note that the proof says >> nothing to specify the reason behind computing B; the >> contradiction would arise if /any/ programme could compute B >> in any fashion. So B isn't a fraction of the square root of >> anything computable. >I did not understand it this way. >I think that B could well be a computable number, but you'd never know. >Since you can't compute B as defined, you can't really tell whether it >is equal to another computable number or not. >This also means that if B happens to be equal to some computable number, >you cannot use that fact, because you cannot ever know of it (with >certainty). Thus there is no paradox; you would only have a >contradiction if a program could compute the number B and *know* it has >computed computed a number that fulfills the definition of B. That's an interesting approach, but unfortunately it doesn't work. The key thing about Omega (the real number referred to as 'B' above) is that it proveably cannot be computed by *any* algorithm, since if it could be computed at all (by some algorithm A) then the halting problem would also be solved by A, which is impossible since *no* finite algorithm can solve the halting problem. It doesn't matter whether some algorithm C is intended to compute Omega or not; *no* algorithm, regardless of what it is intended to do, solves the halting problem / computes Omega. Thus Omega is necessarily different from every computable number. >Michael -- --------------------------- | BBB b Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | | B B a a r b b | | BBB aa a r bbb | ----------------------------- === Subject: Re: Queen puzzle I think there are really a heck of a lot of them Consider the points at distance sqrt(n) from (5,5). We can hit any >single one of those points, or no point. This is true for every n. Thus the number of possible paths is the product from 1 to 49 of >(1+the number of points at distance sqrt(n) from 5,5)=the product from >1 to 49 of (1+the number of ways of writing n as a sum of two >squares). > ?? > Pardon me, but I thought the original problem had the restriction that > any move had to be a legal queen's move, i.e. into one of the 8 directions, > but no restrictions on the length of the moves. > ?? > Jyrki Yeah, I somehow managed to miss that it was actually a Queen making those moves. Whoops! === Subject: question on Finite Euclidean Geometry I have a few question on 'Finite Euclidean Geometry'. Every finite geometry can be represented with an incidence table. For an euclidean geometry constructed by taking as points elements from GF(2^ms) which is an extension field over GF(2^s), how can such an incidence table be described (and constructed). Is exhaustive search the way to do it, or is there a better solution. One more basic question about finite eucldean geometry. I am not able to derive the expression for total number of lines as (2^ms - 1)(2^(m-1)s - 1). The expression for finite projective geometry is okay, and i thought that just adding 2^ms/2^s parallel lines to it i could get the expression for total lines in EG. But this does not work. Prasanna. === Subject: ALBERT EINSTEIN Plagiarist of the Century Interesting... === Subject: Re: basic finite field question > why is a finite field of characteristic p a vector space of finite > dimension over Fp? More generally, if field K is an extension of field F, then K is a vector space over F. === Subject: Re: More on the Catbert Matrix > Recall that the Patalan numbers of order p may be > defined by p_0 = 1, p_n = p_(n-1)*(p^2*n - p)/(n+1) > for n > 0 [2]. The Catalan numbers are the Patalan > numbers for p = 2. > A previous posting conjectured that the inverse of > the Hankel matrix P defined by > P_{i, j} = 1/(p_n*(p+1)) ... Oops! This should be P_{i, j} = 1/(p_(i + j)*(p+1)) === Subject: Re: Geometric interpretation of the trace of a matrix? >> That is not all that dissimilar from the geometric interpretation >> of trace for which I regularly proselytize in these precincts: [as 1/n the average Rayleigh quotient] >I agree with this but would say it slightly differently. The natural >quantity is not the trace of A but the trace of A divided by n. Right. >This is equal to the average of the eigenvalues of A >and also equal to the average value of |Au|, with the average >taken over all unit vectors. (Like the interpretation I gave, it has the unfortunate feature that it appears to require a metric, since it's phrased in terms of unit vectors; though of course calculation shows it doesn't actually depend on the metric. Perhaps there is an obviously metric-free rephrasing, in terms of a differential form?) >This for me is a nice natural geometric >interpretation of the trace. It also leads to other natural geometric >invariants of A, where you average how much A changes the area >of k-dimensional spheres (or cubes) over all k-planes. Presumably (going on what I know about the Rayleigh-quotient situtation) those other natural geometric invariants of A either are precisely, or can easily be massaged to be, the higher traces of A, i.e., the other coefficients of the characteristic polynomial of A (up to sign)? >> I suppose that by torturing this interpretation you might be able >> to come up with some unit vector u, depending (discontinuously and >> unnaturally) on A, such that the trace of A is the length of A(u), >> up to sign. Even if you could, I don't think it would be a good idea. >I don't see how this is possible (try A = I). Of course; I should have written trace/dim, not trace. >But it is clear that there >exists u such that |Au| = |(trace(A)/n) u|. The set of all such u can >vary in a complicated way, but it seems like a reasonable object of >study to me. You're right. I was wrongly dismissive of the idea. Lee Rudolph === Subject: Re: Geometric interpretation of the trace of a matrix? ... >>This [that is, trace/dim] >>is equal to the average of the eigenvalues of A >>and also equal to the average value of |Au|, with the average >>taken over all unit vectors. my regret for not having known that, on the grounds that I like not to know *too* many things that are false. The average value of |Au|, with the average taken over all unit vectors, is surely strictly positive for non-zero A, is it not? Lee Rudolph === Subject: Re: problem solving PDE === Subject: problem solving PDE >how to solve PDE 's of the following form: > d u(x,y) d u(x,y) > a(x,y) -------- + b(x,y) -------- = 0 > dx dy >u(x,y) is the solution to the equation: > dy b(x,y) > ---- = ------- > dx a(x,y) dy b(x,y) -- = - ------ dx a(x,y) Seems more likely. >Can someone please explain why this is, because I don' t really >understand. Neither do I. How can u(x,y) be the solution to an equation which makes no reference to it? When dy/dx = -b/a a.du/dx + b.du/dy = a.du/dy.dy/dx + b.du/dy = a.du/dy.(-b/a) + b.du/dy = 0 Conversely when a.du/dx + b.du/dy = 0 0 = a.du/dx + b.du/dy = a.du/dy.dy/dx + b.du/dy = du/dy.(a.dy/dx + b) Either du/dy = 0 or a.dy/dx + b = 0 dy/dx = -b/a When du/dy = 0 a = 0 or du/dx = 0 whence equation has vanished. Here's differentials a.du/dx + b.du/dy = 0 a.dy/du.du/dx + b.du/dy.dy/du = 0 a.dy/dx + b.du/du = 0 a.dy/dx + b = 0 ---- === Subject: Fw: are you m a r r i e d.. boundary=--32758675231490095973 by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with SMTP id i3RCFbv01115; ---------------------------------------------------------------------
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----32758675231490095973-- === Subject: Stability of the electron - solved Ark your remark shows the conflict between Bohr and Bohm. You and Bohr say EVERYTHING is BIT, with no IT. an IT that is guided by the BIT field you are talking about. The IT is a soliton structure in sense of Wheeler's Mass without mass in the guv field in Einstein's vision so the math you cite below is irrelevant to the problem for us Bohmians who do not believe BIT is the final reality with the miracle of collapse or now environmental decoherence to give the classical world of IT. Good point. Can you elaborate? What then is meant by size of the electron? A form factor? What is size of electron then in QED? and how does it compare to 2Gm/c^2 Is quantum size of electron h/mc from virtual cloud, but what then about deep inelastic electron scattering for the pointlike internal lepto-quarks ~ 10^-17 cm? Who sez so? square-integrable functions of x,y,z. Dirac delta is not square OK apply that to the one-electron state. What size do you get? How many cm? I need to know the precise formula and number. The statement: According to quantum field theory lepto-quarks are point problems with short range interactions. But these problems are deeper than just point ark from arXiv:physics/0012025 v3 17 Dec 2000 Did 20th century physics have the means to reveal the nature of inertia and gravitation? Vesselin Petkov Physics Department, Concordia University 1455 de Maisonneuve Boulevard West Montreal, Quebec H3G 1M8 vpetkov@alcor.concordia.ca (or vpetkov@sympatico.ca) 14 December 2000 The classical electromagnetic mass theory appears to have been gradually forgotten and now many physicists believe that physics cannot say anything about the origin of inertia, mass, or gravitation. Even scientists directly involved in the efforts to discover the Higgs boson as Claude Detraz, one of the two research directors at CERN , think that .8aMass is a very important property of matter, and we have nothing in our current theory that says even a word about it.8a. In what follows we will see whether this is really the case. Here we shall follow the tradition established by the classical electron theory (i.e. the classical electromagnetic mass theory) and will study the inertial and gravitational properties of the simplest charged classical electron is studied: (i) There is no quantum mechanical model of the electron -quantum mechanics describes only its state not the electron itself (later we will make an attempt to outline the basis of the quantum electrodynamical formulation of the electromagnetic mass theory), and (ii) It is quite natural to complete the classical electromagnetic mass theory first before making the transition to a quantum description of the electron inertial properties. This has never been done since the classical electromagnetic mass theory was virtually abandoned when the theory of relativity and quantum mechanics were formulated. To abandon a promising theory that has never been proven wrong is an unprecedented case in physics. This unforgivable neglect is truly beyond one.89s comprehension because the electromagnetic mass theory is even now the only theory that addresses the origin of inertia and inertial mass in accordance with the experimental evidence of the existence of electromagnetic inertia and of the electromagnetic origin of some of the theory predicted that the (electromagnetic) mass increases with the increase of velocity (yielding the correct expression) and that the relationship between energy and mass is E = mc2 (see [3]) all this before the theory of relativity. 2 Classical electromagnetic mass theory resistant to being accelerated than an otherwise identical neutral electromagnetism. Due mostly to the works of Heaviside [5], Searle [6], Lorentz [7], PoincarÇe [8], Abraham [9], Fermi [27], Mandel [11], Wilson [12], Pryce [13], Kwal [14], and Rohrlich [15] this conjecture was developed into a theory (the classical electromagnetic mass theory of the electron) in which inertia is a local phenomenon originating from the interaction of the electron charge with itself (i.e. with its own electromagnetic field) [16]. According to the classical model of the electron its charge is uniformly distributed on a spherical shell. Such a model, however, cannot explain why the electron is stable since the negatively charged spherical shell tends to blow up due to the mutual repulsion of the different .8aparts.8a of the charge. This difficulty, known as the stability problem of the electron, has two sides -computational and conceptual. I claim to have solved this problem on the conceptual level with w = -1 exotic vacuum zero point fluctuations of positive pressure giving induced strong gravity core holding the hidden variable charge together in a guv field soliton as Einstein wanted in sense of Wheeler's Mass without mass The effective G* is 10^40 G on scale of a fermi. This dark matter on scale of 1 fermi holds a single electron IT hidden variable soliton togerher, on a large scale it holds the stars in our galaxy together i.e. the dark halo. As Above, So Below === Subject: Re: Stability of the electron - solved Nope, that's not it. Try again. Cho Ituo AT mit DOT org > Ark your remark shows the conflict between Bohr and Bohm. > You and Bohr say EVERYTHING is BIT, with no IT. > an IT that is guided by the BIT field you are talking about. > The IT is a soliton structure in sense of Wheeler's Mass without mass > in the guv field in Einstein's vision so the math you cite below is > irrelevant to the problem for us Bohmians who do not believe BIT is the > final reality with the miracle of collapse or now environmental > decoherence to give the classical world of IT. > Good point. Can you elaborate? > What then is meant by size of the electron? > A form factor? > What is size of electron then in QED? and how does it compare to > 2Gm/c^2 > Is quantum size of electron h/mc from virtual cloud, but what then about > deep inelastic electron scattering for the pointlike internal > lepto-quarks ~ 10^-17 cm? > Who sez so? > square-integrable functions of x,y,z. Dirac delta is not square > OK apply that to the one-electron state. What size do you get? How > many cm? I need to know the precise formula and number. > The statement: According to quantum field theory lepto-quarks are point > problems with > short range interactions. But these problems are deeper than just point > ark > from > arXiv:physics/0012025 v3 17 Dec 2000 > Did 20th century physics have the means to reveal the nature of inertia > and gravitation? > Vesselin Petkov Physics Department, Concordia University 1455 de > Maisonneuve Boulevard West Montreal, Quebec H3G 1M8 > vpetkov@alcor.concordia.ca (or vpetkov@sympatico.ca) > 14 December 2000 > The classical electromagnetic mass theory appears to have been > gradually forgotten and now many physicists believe that physics cannot > say anything about the origin of inertia, mass, or gravitation. Even > scientists directly involved in the efforts to discover the Higgs boson > as Claude Detraz, one of the two research directors at CERN , think that > Mass is a very important property of matter, and we have nothing in our > current theory that says even a word about it. In what follows we will > see whether this is really the case. > Here we shall follow the tradition established by the classical electron > theory (i.e. the classical electromagnetic mass theory) and will study > the inertial and gravitational properties of the simplest charged > classical electron is studied: > (i) There is no quantum mechanical model of the electron > -quantum mechanics describes only its state not the electron itself > (later we will make an attempt to outline the basis of the quantum > electrodynamical formulation of the electromagnetic mass theory), and > (ii) It is quite natural to complete the classical electromagnetic mass > theory first before making the transition to a quantum description of the > electron inertial properties. This has never been done since the > classical electromagnetic mass theory was virtually abandoned when the > theory of relativity and quantum mechanics were formulated. To abandon a > promising theory that has never been proven wrong is an unprecedented > case in physics. This unforgivable neglect is truly beyond one's > comprehension because the electromagnetic mass theory is even now the > only theory that addresses the origin of inertia and inertial mass in > accordance with the experimental evidence of the existence of > electromagnetic inertia and of the electromagnetic origin of some of the > theory predicted that the (electromagnetic) mass increases with the > increase of velocity (yielding the correct expression) and that the > relationship between energy and mass is E = mc2 (see [3]) all this > before the theory of relativity. > 2 Classical electromagnetic mass theory > resistant to being accelerated than an otherwise identical neutral > electromagnetism. Due mostly to the works of Heaviside [5], Searle [6], > Lorentz [7], PoincarÇe [8], Abraham [9], Fermi [27], Mandel [11], Wilson > [12], Pryce [13], Kwal [14], and Rohrlich [15] this conjecture was > developed into a theory (the classical electromagnetic mass theory of > the electron) in which inertia is a local phenomenon originating from > the interaction of the electron charge with itself (i.e. with its own > electromagnetic field) [16]. > According to the classical model of the electron its charge is uniformly > distributed on a spherical shell. Such a model, however, cannot explain > why the electron is stable since the negatively charged spherical shell > tends to blow up due to the mutual repulsion of the different parts of > the charge. This difficulty, known as the stability problem of the > electron, has two sides -computational and conceptual. > I claim to have solved this problem on the conceptual level with w = -1 > exotic vacuum zero point fluctuations of positive pressure giving > induced strong gravity core holding the hidden variable charge together > in a guv field soliton as Einstein wanted in sense of Wheeler's Mass > without mass > The effective G* is 10^40 G on scale of a fermi. > This dark matter on scale of 1 fermi holds a single electron IT hidden > variable soliton togerher, on a large scale it holds the stars in our > galaxy together i.e. the dark halo. > As Above, So Below === Subject: Re: Analysis on Elliptic Curves? >On the complex torus C/L, where L is a lattice, there is a natural >metric induced by the differential form dz. As you have indicated, the >analytic map Phi maps C/L to an algebraic curve in projective space >which has an affine equation of the form > y^2 = 4x^3 + g2*x + g3. >On this algebraic curve, the differential form dx/y will induce the >metric that you want, since if you pull back that differential form to >C/L, you get Phi^*(dx/y) = dp(z)/p'(z) = dz. Joe Silverman > Wait a second... you're not _the_ Joe Silverman, are you? The one > currently at Brown, who published Rational Points on Elliptic Curves > and Modular Forms and Fermat's Last Theorem? > 'cid 'ooh Yep, that's me, at least insofar as being the one at Brown who's written a few books (not sure that I really rate that prestigious _the_ title, though). But I seem to have misinterpreted the original post and answered a different question, sorry about that. At least there were some other posters who were helpful. JS === Subject: Re: IBM BlueGene Super Computer > current record of 1,240,000,000,000 digits)? Its not a matter of if it can be done, it could be done right now. It would just take more memory and more disk space, and more time. To compute the 1.24 trillion digits took 400 hours. If you are willing to wait you could calculate and number of digits you want with current technology. Now it would be true a faster machine could find the digits quicker, but that was not your question. === Subject: Re: IBM BlueGene Super Computer === >Subject: IBM BlueGene Super Computer >Would it be possible to use IBM's Blue Gene supercomputer (when it's >built) to compute pi to 8,796,093,022,208 digits (over 7 times the >current record of 1,240,000,000,000 digits)? > Computing it is a doddle. The problem is trying to print it. It'll print on a stack of CD's. Try memorizing it. === Subject: Re: ALBERT EINSTEIN Plagiarist of the Century peace is of the pi, d8>D Google TEN: Secret Worlds: The Universe Within http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/ >water. The author says that Jules Henri Poincar.8e is the true originator of the >special theory of relativity, not Albert Einstein. > Poincar.8e's contributions are well known and discussed in the > literature. See e.g. the scientific biography of Einstein by > Abraham Pais, Subtle is the Lord. === Subject: Re: ALBERT EINSTEIN Plagiarist of the Century say.) Are the allegations that Einstein (unwittingly or conveniently?) plagerised possibly accurate? That's really what I want to know, if truth to it, in that regard? Not to slander or discredit Professor Einstein, who has surely earned his reputation, but just to get to the truth of the matter, if there is more to the history of science and math that possibly has been revised? The key issue is about Poincar.8e, I think. I guess it's true that whom history gives credit to this or that discovery, it should always be taken with a few grains of light. :) Or is salt really not a grain at all, but a collapsed wave of the sea? g! Maybe I have a salty sea bicuit of skepticism in my brain, even over the sanctity of historical accuracy. lol! Munch! Crunch! Crack! Ouch! It does seem that Jules Henri Poincar.8e should be given much more credit than is historically given to Albert Einstein in the key mathematical tools he used to formulate the ideas behind Relativity Theory. Are there any similarities at work as to who invented the radio? Nikolai Tesla or Guglielmo Marconi? Apparantly it was really Tesla. But most people assume it was Marconi. To the Smithsonian or Bust:The Scientific Legacy of Nikola Tesla by Zara Herskovits http://www.yale.edu/scimag/Archives/Vol71/tesla.html Could the same kind of historical inaccuracies today be present as to who really should be credited with the mathematical inventions (discoveries?) of Albert Einstein, in context of Relativity Theory etc. farther than others, it is because I was standing on the shoulders of giants. Some people think it was Albert Einstein who said that. Re: If I have seen farther... http://phrases.shu.ac.uk/bulletin_board/7/messages/721.html ---------------------------------------------------------------------------- ---- In Reply to: If I have seen farther than others, it is because I am surrounded by dwarves posted by Mike on February 01, 2001 at 04:01:46: : Has anyone ever heard of this variation of the famous quote by Lucan: A dwarf standing on the shoulders of a giant may see farther than the giant himself. I am not sure if it is supposed to be a No, I haven't heard it. But it's a keeper. The original versions Pigmies placed on the shoulders of giants see more than the giants themselves. Lucan (A.D. 39-65) from The Civil War, Ib. II, 10 (Didacus Stella). I say with Didacus Stella, a dwarf standing on the shoulders of a giant may see farther than a giant himself. Robert Burton (1577-1640)from The Anatomy of Melancholy (1621-51). If I have seen further (than you and Descartes) it is by standing upon the shoulders of giants. Sir Isaac Newton (1642-1727) from Letter to Robert Hooke, Feb. 5, 1675/76. The dwarf sees farther than the giant, when he has the giant's shoulder to mount on -- Coleridge, 'The Friend' (1828). If I have seen further than others, it is because I have stood on the shoulders of giants. (it has been pointed out to me by a couple of people that this is most often attributed to Issac Newton - however, I found it in a book of Einstein quotes and so it is included here) Albert Einstein Quotes (1879-1955) Physicist and mathematician Nobel Prize for Physics 1921 http://www.empyrean.ca/words/quotes/einstein.html Naturally, we're all microscopic pigmies standing on the precipice of Eternity compared to the macroscopic shoulders of the giants, especially the one's in our imaginative minds! :-) To Infinity and Beyond... -Buzz Lightyear Now did he really say that??? g! Perhaps all mathematical discovery and invention is best accredited to Buzz Lightyear. peace is of the pi, d8>D > Yes, the time was ripe for special relativity. Many of the results of SR > were known - or speculated to exist - prior to Einstein. Indeed, the > contraction of length under SR is known as the Fitzgerald-Lorenxz > contraction for that reason. > What Einstein did in SR was show how these different effects - length > contraction, mass increase, different clocks - were a result of invariance > of change of co-ordinates, and not kludges to explain the Michelson Morley > results etc. He built the whole thing from two simple rules - invariance of > the speed of light between different observers and impossibility of passing > information faster than light. Putting all of this together on a simple, > powerful, consistent framework was Einstein's contribution, and one which > mage him a great scientist. > Little of this applies to General Relativity. GR was before its time. If > Einstein hadn't discovered it, it may have taken years before it was > discovered by somebody else. This, and Einstein's contributions to the > foundations of Quantum Theory (for which he won his Nobel Prize) is the > reason that Einstein can lay credible claim to being the greatest scientist > of all time (to date, anyway). >water. >The author says that Jules Henri Poincar.8e is the true originator of the >special theory of relativity, not Albert Einstein. >ALBERT EINSTEIN >Plagiarist of the Century >Einstein plagiarised the work of several notable scientists in his 1905 >papers on special relativity and E = mc2, yet the physics community has >never bothered to set the record straight in the past century. > -------------------------------------------------------------------------- > -- >---- >PO Box 30, Mapleton Qld 4560 Australia. editor@nexusmagazine.com >Telephone: +61 (0)7 5442 9280; Fax: +61 (0)7 5442 9381 >777 Treadlemire Road >Berne, NY 12023 >USA >Email: Slmrea@aol.com > -------------------------------------------------------------------------- > -- >---- >Abstract >Proponents of Einstein have acted in a way that appears to corrupt the >historical record. Albert Einstein (1879-1955), Time Magazine's Person of >actually called On the Electrodynamics of Moving Bodies, 1905a), without >listing any references. Many of the key ideas it presented were known to >Lorentz (for example, the Lorentz transformation) and Poincar.8e before >As was typical of Einstein, he did not discover theories; he merely >commandeered them. He took an existing body of knowledge, picked and chose >the ideas he liked, then wove them into a tale about his contribution to >special relativity. This was done with the full knowledge and consent of >many of his peers, such as the editors at Annalen der Physik. >The most recognisable equation of all time is E = mc2. It is attributed by >convention to be the sole province of Albert Einstein (1905). However, the >conversion of matter into energy and energy into matter was known to Sir >Isaac Newton (Gross bodies and light are convertible into one > another..., >1704). The equation can be attributed to S. Tolver Preston (1875), to > Jules >Henri Poincar.8e (1900; according to Brown, 1967) and to Olinto De Pretto >(1904) before Einstein. Since Einstein never correctly derived E = mc2 >(Ives, 1952), there appears nothing to connect the equation with anything >original by Einstein. >Arthur Eddington's selective presentation of data from the 1919 Eclipse so >that it supposedly supported Einstein's general relativity theory is >surely one of the biggest scientific hoaxes of the 20th century. His > lavish >support of Einstein corrupted the course of history. Eddington was less >interested in testing a theory than he was in crowning Einstein the king > of >science. >The physics community, unwittingly perhaps, has engaged in a kind of fraud >and silent conspiracy; this is the byproduct of simply being bystanders as >the hyperinflation of Einstein's record and reputation took place. This >silence benefited anyone supporting Einstein. >Introduction >Science, by its very nature, is insular. In general, chemists read and > write >about chemistry, biologists read and write about biology, and physicists >read and write about physics. But they may all be competing for the same >research dollar (in its broadest sense). Thus, if scientists wanted more >money for themselves, they might decide to compete unfairly. The way they >can do this is convince the funding agencies that they are more important >than any other branch of science. If the funding agencies agree, it could >spell difficulty for the remaining sciences. One way to get more money is > to >create a superhero - a superhero like Einstein. >Einstein's standing is the product of the physics community, his followers >and the media. Each group benefits enormously by elevating Einstein to > icon >status. The physics community receives billions in research grants, >Einstein's supporters are handsomely rewarded, and media corporations like > T >ime Magazine get to sell millions of magazines by placing Einstein on the >cover as Person of the Century. >When the scandal breaks, the physics community, Einstein's supporters and >the media will attempt to downplay the negative news and put a positive > spin >on it. However, their efforts will be shown up when Einstein's paper, On >the Electrodynamics of Moving Bodies, is seen for what it is: the >consummate act of plagiarism in the 20th century. >Special Relativity >Jules Henri Poincar.8e (1854-1912) was a great scientist who made a >significant contribution to special relativity theory. The Internet >Encyclopedia of Philosophy website says that Poincar.8e: (1) sketched a >preliminary version of the special theory of relativity; (2) stated that >the velocity of light is a limit velocity (in his 1904 paper from the > Bull. >of Sci. Math. 28, Poincar.8e indicated a whole new mechanics, where the >inertia increasing with the velocity of light would become a limit and not >be exceeded); (3) suggested that mass depends on speed; (4) formulated >the principle of relativity, according to which no mechanical or >electromagnetic experiment can discriminate between a state of uniform >motion and a state of rest; and (5) derived the Lorentz transformation. >It is evident how deeply involved with special relativity Poincar.8e was. > Even >Keswani (1965) was prompted to say that As far back as 1895, Poincar.8e, > the >innovator, had conjectured that it is impossible to detect absolute > motion, >and that In 1900, he introduced 'the principle of relative motion' which > he >later called by the equivalent terms 'the law of relativity' and 'the >principle of relativity' in his book, Science and Hypothesis, published in >1902. Einstein acknowledged none of this preceding theoretical work when > he >In addition to having sketched the preliminary version of relativity, >Poincar.8e provided a critical part of the whole concept - namely, his >treatment of local time. He also originated the idea of clock >synchronisation, which is critical to special relativity. >Charles Nordman was prompted to write, They will show that the credit for >most of the things which are currently attributed to Einstein is, in >reality, due to Poincar.8e, and ...in the opinion of the Relativists it is >the measuring rods which create space, the clocks which create time. All >this was known by Poincar.8e and others long before the time of Einstein, > and >one does injustice to truth in ascribing the discovery to him. >Other scientists have not been quite as impressed with Einstein's > special >relativity theory as has the public. Another curious feature of the now >famous paper, Einstein, 1905, is the absence of any reference to Poincar.8e > or > the >impression of quite a new venture. But that is, of course, as I have tried >to explain, not true (Born, 1956). G. Burniston Brown (1967) noted, It >will be seen that, contrary to popular belief, Einstein played only a > minor >part in the derivation of the useful formulae in the restricted or special >relativity theory, and Whittaker called it the relativity theory of > Poincar.8e >and Lorentz.83 >Due to the fact that Einstein's special relativity theory was known in > some >circles as the relativity theory of Poincar.8e and Lorentz, one would think >that Poincar.8e and Lorentz might have had something to do with its > creation. >What is disturbing about the Einstein paper is that even though Poincar.8e > was >the world's leading expert on relativity, apparently Einstein had never >heard of him or thought he had done anything worth referencing! >Poincar.8e, in a public address delivered in September 1904, made some > notable > are >confirmed, would arise an entirely new mechanics.83would be, above all, >characterised by this fact that no velocity could surpass that of >light.83because bodies would oppose an increasing inertia to the causes, > which >would tend to accelerate their motion; and this inertia would become >infinite when one approached the velocity of lightNo more for an observer >carried along himself in a translation, he did not suspect any apparent >velocity could surpass that of light: and this would be then a >contradiction, if we recall that this observer would not use the same > clocks >as a fixed observer, but, indeed, clocks marking 'local time'. (Poincar.8e, >1905) >Einstein, the Plagiarist >It is now time to speak directly to the issue of what Einstein was: he was >first and foremost a plagiarist. He had few qualms about stealing the work >of others and submitting it as his own. That this was deliberate seems >obvious. >Take this passage from Ronald W. Clark, Einstein: The Life and Times > (there >are no references to Poincar.8e here; just a few meaningless quotes). This > is >how page 101 reads: 'On the Electrodynamics of Moving Bodies'...is in > many >ways one of the most remarkable scientific papers that had ever been >written. Even in form and style it was unusual, lacking the notes and >references which give weight to most serious expositions.83 (emphasis > added). >Why would Einstein, with his training as a patent clerk, not recognise the >think that Einstein, as a neophyte, would overreference rather than >underreference. >Wouldn't one also expect somewhat higher standards from an editor when > faced >with a long manuscript that had obviously not been credited? Apparently >there was no attempt at quality control when it was published in Annalen > der >Physik. Most competent editors would have rejected the paper without even >reading it. At the barest minimum, one would expect the editor to research >the literature to determine whether Einstein's claim of primacy was > correct. >Max Born stated, The striking point is that it contains not a single >reference to previous literature (emphasis added) (Born, 1956). He is >clearly indicating that the absence of references is abnormal and that, > even >by early 20th century standards, this is most peculiar, even > unprofessional. >Einstein twisted and turned to avoid plagiarism charges, but these were >transparent. >Einstein's explanation is a dimensional disguise for Lorentz'sThus >Einstein's theory is not a denial of, nor an alternative for, that of >Lorentz. It is only a duplicate and disguise for itEinstein continually >maintains that the theory of Lorentz is right, only he disagrees with his >'interpretation'. Is it not clear, therefore, that in this [case], as in >other cases, Einstein's theory is merely a disguise for Lorentz's, the >apparent disagreement about 'interpretation' being a matter of words > only? > claimed >he'd never read Poincar.8e's contributions to physics. >Yet many of Poincar.8e's ideas - for example, that the speed of light is a >limit and that mass increases with speed - wound up in Einstein's paper, > On >the Electrodynamics of Moving Bodies without being credited. >Einstein's act of stealing almost the entire body of literature by Lorentz >and Poincar.8e to write his document raised the bar for plagiarism. In the >information age, this kind of plagiarism could never be perpetrated >indefinitely, yet the physics community has still not set the record >straight. >In his 1907 paper, Einstein spelled out his views on plagiarism: It > appears >to me that it is the nature of the business that what follows has already >been partly solved by other authors. Despite that fact, since the issues > of >concern are here addressed from a new point of view, I am entitled to > leave >out a thoroughly pedantic survey of the literature... >With this statement, Einstein declared that plagiarism, suitably packaged, >is an acceptable research tool. >Here is the definition of to plagiarise from an unimpeachable source, >Webster's New International Dictionary of the English Language, Second >Edition, Unabridged, 1947, p. 1,878: To steal or purloin and pass off as >one's own (the ideas, words, artistic productions, etc. of one another); > to >use without due credit the ideas, expressions or productions of another. > To >commit plagiarism (emphasis added). Isn't this exactly what Einstein did? >Giving due credit involves two aspects: timeliness and appropriateness. >Telling the world that Lorentz provided the basis for special relativity > 30 >years after the fact is not timely (see below), is not appropriate and is > to >Lorentz's contributions alters the fundamental act of plagiarism. >The true nature of Einstein's plagiarism is set forth in his 1935 paper, >Elementary Derivation of the Equivalence of Mass and Energy, where, in a >those relations is a natural one because the Lorentz transformation, the >real basis of special relativity theory... (emphasis added). >So, Einstein even acknowledged that the Lorentz transformation was the > real >basis of his 1905 paper. Anyone who doubts that he was a plagiarist should >ask one simple question: What did Einstein know and when did he know it? >Einstein got away with premeditated plagiarism, not the incidental >plagiarism that is ubiquitous (Moody, 2001). >The History of E = mc2 >Who originated the concept of matter being transformed into energy and > vice >versa? It dates back at least to Sir Isaac Newton (1704). Brown (1967) > made >the following statement: Thus gradually arose the formula E = mc2, >suggested without general proof by Poincar.8e in 1900. >One thing we can say with certainty is that Einstein did not originate the >equation E = mc2. >Then the question becomes: Who did? >Bjerknes (2002) suggested as a possible candidate S. Tolver Preston, who >formulated atomic energy, the atom bomb and superconductivity back in the >1870s, based on the formula E = mc2. >In addition to Preston, a major player in the history of E = mc2 who >deserves a lot of credit is Olinto De Pretto (1904). What makes this > timing >so suspicious is that Einstein was fluent in Italian, he was reviewing >papers written by Italian physicists and his best friend was Michele > Besso, >a Swiss Italian. Clearly, Einstein (1905b) would have had access to the >literature and the competence to read it. In Einstein's E = mc2 'was >Italian's idea' (Carroll, 1999), we see clear evidence that De Pretto was >ahead of Einstein in terms of the formula E = mc2. >In terms of his understanding the vast amount of energy that could be >released with a small amount of mass, Preston (1875) can be credited with >knowing this before Einstein was born. Clearly, Preston was using the E = >mc2 formula in his work, because the value he determined - e.g., that one >grain could lift a 100,000-ton object up to a height of 1.9 miles - yields >the equation E = mc2. >According to Ives (1952), the derivation Einstein attempted of the formula > E >= mc2 was fatally flawed because Einstein set out to prove what he > assumed. >This is similar to the careless handling of the equations for radioactive >decay which Einstein derived. It turns out that Einstein mixed kinematics >and mechanics, and out popped the neutrino. The neutrino may be a mythical >choices with respect to neutrinos: there are at least 40 different types > or >there are zero types. Occam's razor rules here. >The Eclipse of 1919 >There can be no clearer definition of scientific fraud than what went on > in >the Tropics on May 29, 1919. What is particularly clear is that Eddington >fudged the solar eclipse data to make the results conform to Einstein's >work on general relativity. Poor (1930), Brown (1967), Clark (1984) and >McCausland (2001) all address the issues surrounding this eclipse. >What makes the expeditions to Sobral and Principe so suspect is > Eddington's >zealous support of Einstein, as can be seen in his statement, By standing >foremost in testing, and ultimately verifying the 'enemy' theory, our >national observatory kept alive the finest traditions of science... >(emphasis added) (Clark, 1984). In this instance, apparently Eddington was >not familiar with the basic tenets of science. His job was to collect > data - >not verify Einstein's theories. >Further evidence for the fraud can be deduced from Eddington's own >statements and the introduction to them provided by Clark (ibid., p. 285): >May 29 began with heavy rain, which stopped only about noon. Not until > 1.30 >pm when the eclipse had already begun did the party get its first glimpse > of >the sun: 'We had to carry out our programme of photographs on faith...' >(emphasis added). Eddington reveals his true prejudice: he was willing to > do >anything to see that Einstein was proved right. But Eddington was not to > be >deterred: It looked as though the effort, so far as the Principe > expedition >was concerned, might have been abortive; We developed the photographs, > two >each night for six nights after the eclipseThe cloudy weather upset my > plans >and I had to treat the measures in a different way from what I intended; >consequently I have not been able to make any preliminary announcement of >the result (emphasis added) (Clark, ibid.). >Actually, Eddington's words speak volumes about the result. As soon as he >found one shred of evidence that was consistent with Einstein's general >relativity theory, he immediately proclaimed it as proof of the theory. Is >this science? >Where were the astronomers when Eddington presented his findings? Did > anyone >besides Eddington actually look at the photographic plates? Poor did, and > he >completely repudiated the findings of Eddington. This should have given >pause to any ethical scientist. >Here are some quotes from Poor's summary: The mathematical formula, by >which Einstein calculated his deflection of 1.75 seconds for light rays >passing the edge of the sun, is a well known and simple formula of > physical >optics; Not a single one of the fundamental concepts of varying time, or >warped or twisted space, of simultaneity, or of the relativity of motion > is >in any way involved in Einstein's prediction of, or formulas for, the >deflection of light; The many and elaborate eclipse expeditions have, >therefore, been given a fictitious importance. Their results can neither >prove nor disprove the relativity theory.83 (emphasis added) (Poor, 1930). >the world community that Einstein's theory was confirmed. What Eddington >based this on was a premature assessment of the photographic plates. >Initially, stars did appear to bend as they should, as required by >Einstein, but then, according to Brown, the unexpected happened: several >stars were then observed to bend in a direction transverse to the expected >direction and still others to bend in a direction opposite to that > predicted >by relativity. >The absurdity of the data collected during the Eclipse of 1919 was >demonstrated by Poor (1930), who pointed out that 85% of the data were >discarded from the South American eclipse due to accidental error, i.e., >it contradicted Einstein's scale constant. By a strange coincidence, the > 15% >of the good data were consistent with Einstein's scale constant. > Somehow, >the stars that did not conform to Einstein's theories conveniently got >temporarily shelved - and the myth began. >So, based on a handful of ambiguous data points, 200 years of theory, >experimentation and observation were cast aside to make room for Einstein. >Yet the discredited experiment by Eddington is still quoted as gospel by >Stephen Hawking (1999). It is difficult to comprehend how Hawking could >comment that The new theory of curved space-time was called general >relativityIt was confirmed in spectacular fashion in 1919, when a British >expedition to West Africa observed a slight shift in the position of stars >near the sun during an eclipse. Their light, as Einstein had predicted, > was >bent as it passed the sun. Here was direct evidence that space and time > were >warped. Does Hawking honestly believe that a handful of data points, >massaged more thoroughly than a side of Kobe beef, constitutes the basis > for >overthrowing a paradigm that had survived over two centuries of acid >scrutiny? >The real question, though, is: Where was Einstein in all this? Surely, > by >The actual stellar displacements, if real, do not show the slightest >resemblance to the predicted Einstein deflections: they do not agree in >direction, in size, or the rate of decrease with distance from the sun. > Why >didn't he go on the record and address a paper that directly contradicted >his work? Why haven't the followers of Einstein tried to set the record >straight with respect to the bogus data of 1919? >What makes this so suspicious is that both the instruments and the > physical >conditions were not conducive to making measurements of great precision. > As >Physics, the cap cameras used in the expeditions were accurate to only >1/25th of a degree. This meant that just for the cap camera uncertainty >alone, Eddington was reading values over 200 times too precise. >McCausland (2001) quotes the former Editor of Nature, Sir John Maddox: > They >[Crommelin and Eddington] were bent on measuring the deflection of > light.83; >What is not so well documented is that the measurements in 1919 were not >particularly accurate; In spite of the fact that experimental evidence > for >relativity seems to have been very flimsy in 1919, Einstein's enormous > fame >has remained intact and his theory has ever since been held to be one of > the >highest achievements of human thought (emphasis added). >It is clear that from the outset Eddington was in no way interested in >testing Einstein's theory; he was only interested in confirming it. One > of >the motivating factors in Eddington's decision to promote Einstein was > that >both men shared a similar political persuasion: pacifism. To suggest that >politics played no role in Eddington's glowing support of Einstein, one > need >ask only one question: Would Eddington have been so quick to support >Einstein if Einstein had been a hawk? This is no idle observation. >Eddington took his role as the great peacemaker very seriously. He wanted > to >unite British and German scientists after World War I. What better way > than >to elevate the enemy theorist Einstein to exalted status? In his zeal to >become peacemaker, Eddington lost the fundamental objectivity that is the >essential demeanour of any true scientist. Eddington ceased to be a >scientist and, instead, became an advocate for Einstein. >The obvious fudging of the data by Eddington and others is a blatant >subversion of scientific process and may have misdirected scientific >research for the better part of a century. It probably surpasses the >Piltdown Man as the greatest hoax of 20th-century science. The BIPP asked, >Was this the hoax of the century? and exclaimed, Royal Society 1919 >Eclipse Relativity Report Duped World for 80 Years! McCausland stated > that >In the author's opinion, the confident announcement of the decisive >confirmation of Einstein's general theory in November 1919 was not a > triumph >of science, as it is often portrayed, but one of the most unfortunate >incidents in the history of 20th-century science. >It cannot be emphasised enough that the Eclipse of 1919 made Einstein, >Einstein. It propelled him to international fame overnight, despite the > fact >that the data were fabricated and there was no support for general >relativity whatsoever. This perversion of history has been known about for >over 80 years and is still supported by people like Stephen Hawking and >David Levy. >Summary and Conclusions >The general public tends to believe that scientists are the ultimate >defenders of ethics, that scientific rigour is the measure of truth. > Little >do people realise how science is conducted in the presence of personality. >It seems that Einstein believed he was above scientific protocol. He > thought >he could bend the rules to his own liking and get away with it; hang in >there long enough and his enemies would die off and his followers would > win >the day. In science, the last follower standing wins - and gets to write >history. In the case of Einstein, his blatant and repeated dalliance with >plagiarism is all but forgotten and his followers have borrowed repeatedly >from the discoveries of other scientists and used them to adorn Einstein's >halo. >Einstein's reputation is supported by a three-legged stool. One leg is >Einstein's alleged plagiarism. Was he a plagiarist? The second leg is the >physics community. What did they know about Einstein and when did they > know >it? The third leg is the media. Are they instruments of truth or deception >when it comes to Einstein? Only time will tell. >The physics community is also supported by a three-legged stool. The first >leg is Einstein's physics. The second leg is cold fusion. The third leg is >autodynamics. The overriding problem with a three-legged stool is that if >only one leg is sawed off, the stool collapses. There are at least three >very serious disciplines where it is predictable that physics may > collapse. >Science is a multi-legged stool. One leg is physics; a second leg is the >earth sciences; a third, biology; and a fourth, chemistry (e.g., cold >fusion). What will happen if, for the sake of argument, physics collapses? >Will science fall? > -------------------------------------------------------------------------- > -- >---- >Bjerknes, C.J. (2002), Albert Einstein: The Incorrigible Plagiarist, XTX >Inc., Dowers Grove. >Born, M. (1956), Physics in My Generation, Pergamon Press, London, p. 193. >Brown, G. Burniston (1967), What is wrong with relativity?, Bull. of the >Inst. of Physics and Physical Soc., pp. 71-77. >Carezani, R. (1999), Autodynamics: Fundamental Basis for a New > Relativistic >Mechanics, SAA, Society for the Advancement of Autodynamics. >Carroll, R., Einstein's E = mc2 'was Italian's idea', The Guardian, >November 11, 1999. >Clark, R.W. (1984), Einstein: The Life and Times, Avon Books, New York. >De Pretto, O. (1904), Ipotesi dell'etere nella vita dell'universo, Reale >Istituto Veneto di Scienze, Lettere ed Arti, Feb. 1904, tomo LXIII, parte >II, pp. 439-500. >Einstein, A. (1905a), Zur Elektrodynamik bewegter K.9arper (On the >Electrodynamics of Moving Bodies), Annalen der Physik 17:37-65. >Einstein, A. (1905b), Does the Inertia of a Body Depend on its Energy >Content?, Annalen der Physik 18:639-641. >Einstein, A. (1907), .86ber die vom Relativit.8atspringzip geforderte > Tr.8agheit >der Energie, Annalen der Physik 23(4):371-384 (quote on p. 373). >Einstein, A. (1935), Elementary Derivation of the Equivalence of Mass and >Energy, Bull. Amer. Math. Soc. 61:223-230 (first delivered as The > Eleventh >Josiah Willard Gibbs Lecture at a joint meeting of the American Physical >Society and Section A of the AAAS, Pittsburgh, December 28, 1934). >Hawking, S., Person of the Century, Time Magazine, December 31, 1999. >Ives, H.E. (1952), Derivation of the Mass-Energy Relation, J. Opt. Soc. >Amer. 42:540-543. >Keswani, G.H. (1965), Origin and Concept of Relativity, Brit. J. Phil. >Soc. 15:286-306. >Mackaye, J. (1931), The Dynamic Universe, Charles Scribner's Sons, New > York, >pp. 42-43. >Maddox, J. (1995), More Precise Solar-limb Light-bending, Nature 377:11. >Moody, R., Jr (2001), Plagiarism Personified, Mensa Bull. 442(Feb):5. >Newton, Sir Isaac (1704), Opticks, Dover Publications, Inc., New York, p. >cxv. >Nordman, C. (1921), Einstein et l'univers, translated by Joseph McCabe as >Einstein and the Universe, Henry Holt and Co., New York, pp. 10-11, 16 >(from Bjerknes, 2002). >Poincar.8e, J.H. (1905), The Principles of Mathematical Physics, The > Monist, >vol. XV, no. 1, January 1905; from an address delivered before the >International Congress of Arts and Sciences, St Louis, September 1904. >Poor, C.L. (1930), The Deflection of Light as Observed at Total Solar >Eclipses, J. Opt. Soc. Amer. 20:173-211. >The Internet Encyclopedia of Philosophy, Jules Henri Poincar.8e (1854-1912), >at http://www.utm.edu/research/iep/p/poincare.htm. >Webster, N. (1947), Webster's New International Dictionary of the English >Language, Second Edition, Unabridged, p. 1878. >About the Author: >Richard Moody, Jr, has a Master's Degree in Geology, is the author of > three >books on chess theory and has written for the Mensa Bulletin. For the past >four years, he has done intensive research into Albert Einstein. He can be >contacted by email at Slmrea@aol.com. >peace is of the pi, >d8>D >There was a young lady named bright, >Who's speed was much faster than light, >She departed one day, >In a relative way, >And returned on the previous... >Big, black hole of Night! === Subject: Re: ALBERT EINSTEIN Plagiarist of the Century > Yes, the time was ripe for special relativity. Many of the results of SR > were known - or speculated to exist - prior to Einstein. Indeed, the > contraction of length under SR is known as the Fitzgerald-Lorenxz > contraction for that reason. > What Einstein did in SR was show how these different effects - length > contraction, mass increase, different clocks - were a result of invariance > of change of co-ordinates, and not kludges to explain the Michelson Morley > results etc. He built the whole thing from two simple rules - invariance of > the speed of light between different observers and impossibility of passing > information faster than light. Putting all of this together on a simple, > powerful, consistent framework was Einstein's contribution, and one which > mage him a great scientist. > Little of this applies to General Relativity. GR was before its time. If > Einstein hadn't discovered it, it may have taken years before it was > discovered by somebody else. This, and Einstein's contributions to the > foundations of Quantum Theory (for which he won his Nobel Prize) is the > reason that Einstein can lay credible claim to being the greatest scientist > of all time (to date, anyway). As for the greatest sciecntist of all time, Newton would have to be considered. At least it seems to me he got farther relative to where he started than Einstein did. By the way, a good book on all this appeared recently: _Einstein's Clocks, Poincare's Maps_ by Peter Galison, published by W. W. Norton. === Subject: Re: ALBERT EINSTEIN Plagiarist of the Century How about Buzz Lightyear! peace is of the pi, d8>D ... > As for the greatest sciecntist of all time, Newton would have to be > considered. At least it seems to me he got farther relative to where > he started than Einstein did. ... === Subject: Re: ALBERT EINSTEIN Plagiarist of the Century E.T. Whittaker, in his Theories of the Aether and Electricity, takes a similar tack (that Poincare is largely the originator of special relativity). Close but no cigar, I'd say. John -- John T Lowry, PhD Flight Physics 5217 Old Spicewood Springs Rd, #312 Austin, Texas 78731 (512) 231-9391 jlowry100@earthlink.net > water. > The author says that Jules Henri Poincar.8e is the true originator of the > special theory of relativity, not Albert Einstein. > ALBERT EINSTEIN > Plagiarist of the Century > Einstein plagiarised the work of several notable scientists in his 1905 > papers on special relativity and E = mc2, yet the physics community has > never bothered to set the record straight in the past century. > -------------------------------------------------------------------------- -- > ---- > PO Box 30, Mapleton Qld 4560 Australia. editor@nexusmagazine.com > Telephone: +61 (0)7 5442 9280; Fax: +61 (0)7 5442 9381 > 777 Treadlemire Road > Berne, NY 12023 > USA > Email: Slmrea@aol.com > -------------------------------------------------------------------------- -- > ---- > Abstract > Proponents of Einstein have acted in a way that appears to corrupt the > historical record. Albert Einstein (1879-1955), Time Magazine's Person of > actually called On the Electrodynamics of Moving Bodies, 1905a), without > listing any references. Many of the key ideas it presented were known to > Lorentz (for example, the Lorentz transformation) and Poincar.8e before > As was typical of Einstein, he did not discover theories; he merely > commandeered them. He took an existing body of knowledge, picked and chose > the ideas he liked, then wove them into a tale about his contribution to > special relativity. This was done with the full knowledge and consent of > many of his peers, such as the editors at Annalen der Physik. > The most recognisable equation of all time is E = mc2. It is attributed by > convention to be the sole province of Albert Einstein (1905). However, the > conversion of matter into energy and energy into matter was known to Sir > Isaac Newton (Gross bodies and light are convertible into one another..., > 1704). The equation can be attributed to S. Tolver Preston (1875), to Jules > Henri Poincar.8e (1900; according to Brown, 1967) and to Olinto De Pretto > (1904) before Einstein. Since Einstein never correctly derived E = mc2 > (Ives, 1952), there appears nothing to connect the equation with anything > original by Einstein. > Arthur Eddington's selective presentation of data from the 1919 Eclipse so > that it supposedly supported Einstein's general relativity theory is > surely one of the biggest scientific hoaxes of the 20th century. His lavish > support of Einstein corrupted the course of history. Eddington was less > interested in testing a theory than he was in crowning Einstein the king of > science. > The physics community, unwittingly perhaps, has engaged in a kind of fraud > and silent conspiracy; this is the byproduct of simply being bystanders as > the hyperinflation of Einstein's record and reputation took place. This > silence benefited anyone supporting Einstein. > Introduction > Science, by its very nature, is insular. In general, chemists read and write > about chemistry, biologists read and write about biology, and physicists > read and write about physics. But they may all be competing for the same > research dollar (in its broadest sense). Thus, if scientists wanted more > money for themselves, they might decide to compete unfairly. The way they > can do this is convince the funding agencies that they are more important > than any other branch of science. If the funding agencies agree, it could > spell difficulty for the remaining sciences. One way to get more money is to > create a superhero - a superhero like Einstein. > Einstein's standing is the product of the physics community, his followers > and the media. Each group benefits enormously by elevating Einstein to icon > status. The physics community receives billions in research grants, > Einstein's supporters are handsomely rewarded, and media corporations like T > ime Magazine get to sell millions of magazines by placing Einstein on the > cover as Person of the Century. > When the scandal breaks, the physics community, Einstein's supporters and > the media will attempt to downplay the negative news and put a positive spin > on it. However, their efforts will be shown up when Einstein's paper, On > the Electrodynamics of Moving Bodies, is seen for what it is: the > consummate act of plagiarism in the 20th century. > Special Relativity > Jules Henri Poincar.8e (1854-1912) was a great scientist who made a > significant contribution to special relativity theory. The Internet > Encyclopedia of Philosophy website says that Poincar.8e: (1) sketched a > preliminary version of the special theory of relativity; (2) stated that > the velocity of light is a limit velocity (in his 1904 paper from the Bull. > of Sci. Math. 28, Poincar.8e indicated a whole new mechanics, where the > inertia increasing with the velocity of light would become a limit and not > be exceeded); (3) suggested that mass depends on speed; (4) formulated > the principle of relativity, according to which no mechanical or > electromagnetic experiment can discriminate between a state of uniform > motion and a state of rest; and (5) derived the Lorentz transformation. > It is evident how deeply involved with special relativity Poincar.8e was. Even > Keswani (1965) was prompted to say that As far back as 1895, Poincar.8e, the > innovator, had conjectured that it is impossible to detect absolute motion, > and that In 1900, he introduced 'the principle of relative motion' which he > later called by the equivalent terms 'the law of relativity' and 'the > principle of relativity' in his book, Science and Hypothesis, published in > 1902. Einstein acknowledged none of this preceding theoretical work when he > In addition to having sketched the preliminary version of relativity, > Poincar.8e provided a critical part of the whole concept - namely, his > treatment of local time. He also originated the idea of clock > synchronisation, which is critical to special relativity. > Charles Nordman was prompted to write, They will show that the credit for > most of the things which are currently attributed to Einstein is, in > reality, due to Poincar.8e, and ...in the opinion of the Relativists it is > the measuring rods which create space, the clocks which create time. All > this was known by Poincar.8e and others long before the time of Einstein, and > one does injustice to truth in ascribing the discovery to him. > Other scientists have not been quite as impressed with Einstein's special > relativity theory as has the public. Another curious feature of the now > famous paper, Einstein, 1905, is the absence of any reference to Poincar.8e or the > impression of quite a new venture. But that is, of course, as I have tried > to explain, not true (Born, 1956). G. Burniston Brown (1967) noted, It > will be seen that, contrary to popular belief, Einstein played only a minor > part in the derivation of the useful formulae in the restricted or special > relativity theory, and Whittaker called it the relativity theory of Poincar.8e > and Lorentz.83 > Due to the fact that Einstein's special relativity theory was known in some > circles as the relativity theory of Poincar.8e and Lorentz, one would think > that Poincar.8e and Lorentz might have had something to do with its creation. > What is disturbing about the Einstein paper is that even though Poincar.8e was > the world's leading expert on relativity, apparently Einstein had never > heard of him or thought he had done anything worth referencing! > Poincar.8e, in a public address delivered in September 1904, made some notable are > confirmed, would arise an entirely new mechanics.83would be, above all, > characterised by this fact that no velocity could surpass that of > light.83because bodies would oppose an increasing inertia to the causes, which > would tend to accelerate their motion; and this inertia would become > infinite when one approached the velocity of lightNo more for an observer > carried along himself in a translation, he did not suspect any apparent > velocity could surpass that of light: and this would be then a > contradiction, if we recall that this observer would not use the same clocks > as a fixed observer, but, indeed, clocks marking 'local time'. (Poincar.8e, > 1905) > Einstein, the Plagiarist > It is now time to speak directly to the issue of what Einstein was: he was > first and foremost a plagiarist. He had few qualms about stealing the work > of others and submitting it as his own. That this was deliberate seems > obvious. > Take this passage from Ronald W. Clark, Einstein: The Life and Times (there > are no references to Poincar.8e here; just a few meaningless quotes). This is > how page 101 reads: 'On the Electrodynamics of Moving Bodies'...is in many > ways one of the most remarkable scientific papers that had ever been > written. Even in form and style it was unusual, lacking the notes and > references which give weight to most serious expositions.83 (emphasis added). > Why would Einstein, with his training as a patent clerk, not recognise the > think that Einstein, as a neophyte, would overreference rather than > underreference. > Wouldn't one also expect somewhat higher standards from an editor when faced > with a long manuscript that had obviously not been credited? Apparently > there was no attempt at quality control when it was published in Annalen der > Physik. Most competent editors would have rejected the paper without even > reading it. At the barest minimum, one would expect the editor to research > the literature to determine whether Einstein's claim of primacy was correct. > Max Born stated, The striking point is that it contains not a single > reference to previous literature (emphasis added) (Born, 1956). He is > clearly indicating that the absence of references is abnormal and that, even > by early 20th century standards, this is most peculiar, even unprofessional. > Einstein twisted and turned to avoid plagiarism charges, but these were > transparent. > Einstein's explanation is a dimensional disguise for Lorentz'sThus > Einstein's theory is not a denial of, nor an alternative for, that of > Lorentz. It is only a duplicate and disguise for itEinstein continually > maintains that the theory of Lorentz is right, only he disagrees with his > 'interpretation'. Is it not clear, therefore, that in this [case], as in > other cases, Einstein's theory is merely a disguise for Lorentz's, the > apparent disagreement about 'interpretation' being a matter of words only? claimed > he'd never read Poincar.8e's contributions to physics. > Yet many of Poincar.8e's ideas - for example, that the speed of light is a > limit and that mass increases with speed - wound up in Einstein's paper, On > the Electrodynamics of Moving Bodies without being credited. > Einstein's act of stealing almost the entire body of literature by Lorentz > and Poincar.8e to write his document raised the bar for plagiarism. In the > information age, this kind of plagiarism could never be perpetrated > indefinitely, yet the physics community has still not set the record > straight. > In his 1907 paper, Einstein spelled out his views on plagiarism: It appears > to me that it is the nature of the business that what follows has already > been partly solved by other authors. Despite that fact, since the issues of > concern are here addressed from a new point of view, I am entitled to leave > out a thoroughly pedantic survey of the literature... > With this statement, Einstein declared that plagiarism, suitably packaged, > is an acceptable research tool. > Here is the definition of to plagiarise from an unimpeachable source, > Webster's New International Dictionary of the English Language, Second > Edition, Unabridged, 1947, p. 1,878: To steal or purloin and pass off as > one's own (the ideas, words, artistic productions, etc. of one another); to > use without due credit the ideas, expressions or productions of another. To > commit plagiarism (emphasis added). Isn't this exactly what Einstein did? > Giving due credit involves two aspects: timeliness and appropriateness. > Telling the world that Lorentz provided the basis for special relativity 30 > years after the fact is not timely (see below), is not appropriate and is to > Lorentz's contributions alters the fundamental act of plagiarism. > The true nature of Einstein's plagiarism is set forth in his 1935 paper, > Elementary Derivation of the Equivalence of Mass and Energy, where, in a > those relations is a natural one because the Lorentz transformation, the > real basis of special relativity theory... (emphasis added). > So, Einstein even acknowledged that the Lorentz transformation was the real > basis of his 1905 paper. Anyone who doubts that he was a plagiarist should > ask one simple question: What did Einstein know and when did he know it? > Einstein got away with premeditated plagiarism, not the incidental > plagiarism that is ubiquitous (Moody, 2001). > The History of E = mc2 > Who originated the concept of matter being transformed into energy and vice > versa? It dates back at least to Sir Isaac Newton (1704). Brown (1967) made > the following statement: Thus gradually arose the formula E = mc2, > suggested without general proof by Poincar.8e in 1900. > One thing we can say with certainty is that Einstein did not originate the > equation E = mc2. > Then the question becomes: Who did? > Bjerknes (2002) suggested as a possible candidate S. Tolver Preston, who > formulated atomic energy, the atom bomb and superconductivity back in the > 1870s, based on the formula E = mc2. > In addition to Preston, a major player in the history of E = mc2 who > deserves a lot of credit is Olinto De Pretto (1904). What makes this timing > so suspicious is that Einstein was fluent in Italian, he was reviewing > papers written by Italian physicists and his best friend was Michele Besso, > a Swiss Italian. Clearly, Einstein (1905b) would have had access to the > literature and the competence to read it. In Einstein's E = mc2 'was > Italian's idea' (Carroll, 1999), we see clear evidence that De Pretto was > ahead of Einstein in terms of the formula E = mc2. > In terms of his understanding the vast amount of energy that could be > released with a small amount of mass, Preston (1875) can be credited with > knowing this before Einstein was born. Clearly, Preston was using the E = > mc2 formula in his work, because the value he determined - e.g., that one > grain could lift a 100,000-ton object up to a height of 1.9 miles - yields > the equation E = mc2. > According to Ives (1952), the derivation Einstein attempted of the formula E > = mc2 was fatally flawed because Einstein set out to prove what he assumed. > This is similar to the careless handling of the equations for radioactive > decay which Einstein derived. It turns out that Einstein mixed kinematics > and mechanics, and out popped the neutrino. The neutrino may be a mythical > choices with respect to neutrinos: there are at least 40 different types or > there are zero types. Occam's razor rules here. > The Eclipse of 1919 > There can be no clearer definition of scientific fraud than what went on in > the Tropics on May 29, 1919. What is particularly clear is that Eddington > fudged the solar eclipse data to make the results conform to Einstein's > work on general relativity. Poor (1930), Brown (1967), Clark (1984) and > McCausland (2001) all address the issues surrounding this eclipse. > What makes the expeditions to Sobral and Principe so suspect is Eddington's > zealous support of Einstein, as can be seen in his statement, By standing > foremost in testing, and ultimately verifying the 'enemy' theory, our > national observatory kept alive the finest traditions of science... > (emphasis added) (Clark, 1984). In this instance, apparently Eddington was > not familiar with the basic tenets of science. His job was to collect data - > not verify Einstein's theories. > Further evidence for the fraud can be deduced from Eddington's own > statements and the introduction to them provided by Clark (ibid., p. 285): > May 29 began with heavy rain, which stopped only about noon. Not until 1.30 > pm when the eclipse had already begun did the party get its first glimpse of > the sun: 'We had to carry out our programme of photographs on faith...' > (emphasis added). Eddington reveals his true prejudice: he was willing to do > anything to see that Einstein was proved right. But Eddington was not to be > deterred: It looked as though the effort, so far as the Principe expedition > was concerned, might have been abortive; We developed the photographs, two > each night for six nights after the eclipseThe cloudy weather upset my plans > and I had to treat the measures in a different way from what I intended; > consequently I have not been able to make any preliminary announcement of > the result (emphasis added) (Clark, ibid.). > Actually, Eddington's words speak volumes about the result. As soon as he > found one shred of evidence that was consistent with Einstein's general > relativity theory, he immediately proclaimed it as proof of the theory. Is > this science? > Where were the astronomers when Eddington presented his findings? Did anyone > besides Eddington actually look at the photographic plates? Poor did, and he > completely repudiated the findings of Eddington. This should have given > pause to any ethical scientist. > Here are some quotes from Poor's summary: The mathematical formula, by > which Einstein calculated his deflection of 1.75 seconds for light rays > passing the edge of the sun, is a well known and simple formula of physical > optics; Not a single one of the fundamental concepts of varying time, or > warped or twisted space, of simultaneity, or of the relativity of motion is > in any way involved in Einstein's prediction of, or formulas for, the > deflection of light; The many and elaborate eclipse expeditions have, > therefore, been given a fictitious importance. Their results can neither > prove nor disprove the relativity theory.83 (emphasis added) (Poor, 1930). > the world community that Einstein's theory was confirmed. What Eddington > based this on was a premature assessment of the photographic plates. > Initially, stars did appear to bend as they should, as required by > Einstein, but then, according to Brown, the unexpected happened: several > stars were then observed to bend in a direction transverse to the expected > direction and still others to bend in a direction opposite to that predicted > by relativity. > The absurdity of the data collected during the Eclipse of 1919 was > demonstrated by Poor (1930), who pointed out that 85% of the data were > discarded from the South American eclipse due to accidental error, i.e., > it contradicted Einstein's scale constant. By a strange coincidence, the 15% > of the good data were consistent with Einstein's scale constant. Somehow, > the stars that did not conform to Einstein's theories conveniently got > temporarily shelved - and the myth began. > So, based on a handful of ambiguous data points, 200 years of theory, > experimentation and observation were cast aside to make room for Einstein. > Yet the discredited experiment by Eddington is still quoted as gospel by > Stephen Hawking (1999). It is difficult to comprehend how Hawking could > comment that The new theory of curved space-time was called general > relativityIt was confirmed in spectacular fashion in 1919, when a British > expedition to West Africa observed a slight shift in the position of stars > near the sun during an eclipse. Their light, as Einstein had predicted, was > bent as it passed the sun. Here was direct evidence that space and time were > warped. Does Hawking honestly believe that a handful of data points, > massaged more thoroughly than a side of Kobe beef, constitutes the basis for > overthrowing a paradigm that had survived over two centuries of acid > scrutiny? > The real question, though, is: Where was Einstein in all this? Surely, by > The actual stellar displacements, if real, do not show the slightest > resemblance to the predicted Einstein deflections: they do not agree in > direction, in size, or the rate of decrease with distance from the sun. Why > didn't he go on the record and address a paper that directly contradicted > his work? Why haven't the followers of Einstein tried to set the record > straight with respect to the bogus data of 1919? > What makes this so suspicious is that both the instruments and the physical > conditions were not conducive to making measurements of great precision. As > Physics, the cap cameras used in the expeditions were accurate to only > 1/25th of a degree. This meant that just for the cap camera uncertainty > alone, Eddington was reading values over 200 times too precise. > McCausland (2001) quotes the former Editor of Nature, Sir John Maddox: They > [Crommelin and Eddington] were bent on measuring the deflection of light.83; > What is not so well documented is that the measurements in 1919 were not > particularly accurate; In spite of the fact that experimental evidence for > relativity seems to have been very flimsy in 1919, Einstein's enormous fame > has remained intact and his theory has ever since been held to be one of the > highest achievements of human thought (emphasis added). > It is clear that from the outset Eddington was in no way interested in > testing Einstein's theory; he was only interested in confirming it. One of > the motivating factors in Eddington's decision to promote Einstein was that > both men shared a similar political persuasion: pacifism. To suggest that > politics played no role in Eddington's glowing support of Einstein, one need > ask only one question: Would Eddington have been so quick to support > Einstein if Einstein had been a hawk? This is no idle observation. > Eddington took his role as the great peacemaker very seriously. He wanted to > unite British and German scientists after World War I. What better way than > to elevate the enemy theorist Einstein to exalted status? In his zeal to > become peacemaker, Eddington lost the fundamental objectivity that is the > essential demeanour of any true scientist. Eddington ceased to be a > scientist and, instead, became an advocate for Einstein. > The obvious fudging of the data by Eddington and others is a blatant > subversion of scientific process and may have misdirected scientific > research for the better part of a century. It probably surpasses the > Piltdown Man as the greatest hoax of 20th-century science. The BIPP asked, > Was this the hoax of the century? and exclaimed, Royal Society 1919 > Eclipse Relativity Report Duped World for 80 Years! McCausland stated that > In the author's opinion, the confident announcement of the decisive > confirmation of Einstein's general theory in November 1919 was not a triumph > of science, as it is often portrayed, but one of the most unfortunate > incidents in the history of 20th-century science. > It cannot be emphasised enough that the Eclipse of 1919 made Einstein, > Einstein. It propelled him to international fame overnight, despite the fact > that the data were fabricated and there was no support for general > relativity whatsoever. This perversion of history has been known about for > over 80 years and is still supported by people like Stephen Hawking and > David Levy. > Summary and Conclusions > The general public tends to believe that scientists are the ultimate > defenders of ethics, that scientific rigour is the measure of truth. Little > do people realise how science is conducted in the presence of personality. > It seems that Einstein believed he was above scientific protocol. He thought > he could bend the rules to his own liking and get away with it; hang in > there long enough and his enemies would die off and his followers would win > the day. In science, the last follower standing wins - and gets to write > history. In the case of Einstein, his blatant and repeated dalliance with > plagiarism is all but forgotten and his followers have borrowed repeatedly > from the discoveries of other scientists and used them to adorn Einstein's > halo. > Einstein's reputation is supported by a three-legged stool. One leg is > Einstein's alleged plagiarism. Was he a plagiarist? The second leg is the > physics community. What did they know about Einstein and when did they know > it? The third leg is the media. Are they instruments of truth or deception > when it comes to Einstein? Only time will tell. > The physics community is also supported by a three-legged stool. The first > leg is Einstein's physics. The second leg is cold fusion. The third leg is > autodynamics. The overriding problem with a three-legged stool is that if > only one leg is sawed off, the stool collapses. There are at least three > very serious disciplines where it is predictable that physics may collapse. > Science is a multi-legged stool. One leg is physics; a second leg is the > earth sciences; a third, biology; and a fourth, chemistry (e.g., cold > fusion). What will happen if, for the sake of argument, physics collapses? > Will science fall? > -------------------------------------------------------------------------- -- > ---- > Bjerknes, C.J. (2002), Albert Einstein: The Incorrigible Plagiarist, XTX > Inc., Dowers Grove. > Born, M. (1956), Physics in My Generation, Pergamon Press, London, p. 193. > Brown, G. Burniston (1967), What is wrong with relativity?, Bull. of the > Inst. of Physics and Physical Soc., pp. 71-77. > Carezani, R. (1999), Autodynamics: Fundamental Basis for a New Relativistic > Mechanics, SAA, Society for the Advancement of Autodynamics. > Carroll, R., Einstein's E = mc2 'was Italian's idea', The Guardian, > November 11, 1999. > Clark, R.W. (1984), Einstein: The Life and Times, Avon Books, New York. > De Pretto, O. (1904), Ipotesi dell'etere nella vita dell'universo, Reale > Istituto Veneto di Scienze, Lettere ed Arti, Feb. 1904, tomo LXIII, parte > II, pp. 439-500. > Einstein, A. (1905a), Zur Elektrodynamik bewegter K.9arper (On the > Electrodynamics of Moving Bodies), Annalen der Physik 17:37-65. > Einstein, A. (1905b), Does the Inertia of a Body Depend on its Energy > Content?, Annalen der Physik 18:639-641. > Einstein, A. (1907), .86ber die vom Relativit.8atspringzip geforderte Tr.8agheit > der Energie, Annalen der Physik 23(4):371-384 (quote on p. 373). > Einstein, A. (1935), Elementary Derivation of the Equivalence of Mass and > Energy, Bull. Amer. Math. Soc. 61:223-230 (first delivered as The Eleventh > Josiah Willard Gibbs Lecture at a joint meeting of the American Physical > Society and Section A of the AAAS, Pittsburgh, December 28, 1934). > Hawking, S., Person of the Century, Time Magazine, December 31, 1999. > Ives, H.E. (1952), Derivation of the Mass-Energy Relation, J. Opt. Soc. > Amer. 42:540-543. > Keswani, G.H. (1965), Origin and Concept of Relativity, Brit. J. Phil. > Soc. 15:286-306. > Mackaye, J. (1931), The Dynamic Universe, Charles Scribner's Sons, New York, > pp. 42-43. > Maddox, J. (1995), More Precise Solar-limb Light-bending, Nature 377:11. > Moody, R., Jr (2001), Plagiarism Personified, Mensa Bull. 442(Feb):5. > Newton, Sir Isaac (1704), Opticks, Dover Publications, Inc., New York, p. > cxv. > Nordman, C. (1921), Einstein et l'univers, translated by Joseph McCabe as > Einstein and the Universe, Henry Holt and Co., New York, pp. 10-11, 16 > (from Bjerknes, 2002). > Poincar.8e, J.H. (1905), The Principles of Mathematical Physics, The Monist, > vol. XV, no. 1, January 1905; from an address delivered before the > International Congress of Arts and Sciences, St Louis, September 1904. > Poor, C.L. (1930), The Deflection of Light as Observed at Total Solar > Eclipses, J. Opt. Soc. Amer. 20:173-211. > The Internet Encyclopedia of Philosophy, Jules Henri Poincar.8e (1854-1912), > at http://www.utm.edu/research/iep/p/poincare.htm. > Webster, N. (1947), Webster's New International Dictionary of the English > Language, Second Edition, Unabridged, p. 1878. > About the Author: > Richard Moody, Jr, has a Master's Degree in Geology, is the author of three > books on chess theory and has written for the Mensa Bulletin. For the past > four years, he has done intensive research into Albert Einstein. He can be > contacted by email at Slmrea@aol.com. > peace is of the pi, > d8>D > There was a young lady named bright, > Who's speed was much faster than light, > She departed one day, > In a relative way, > And returned on the previous... > Big, black hole of Night! === Subject: Re: ALBERT EINSTEIN Plagiarist of the Century > E.T. Whittaker, in his Theories of the Aether and Electricity, takes a > similar tack (that Poincare is largely the originator of special > relativity). Close but no cigar, I'd say. Poincare' stated the principle of relativity correctly but did not work out all the consequences. Einstein did. If Poincare' were younger and in better health, he very well might have done what Einstein did. Bob Kolker === Subject: Re: Closed form for a sum? >>What do you mean by the terms where n l + c < m? > Taking liberties, he means 0 in those instances. Right. (With my particular constants which I didn't give here, nl+c>=m always.) -- Alex. PS. To email me, remove loeschedies from the email address given. === Subject: Need help with theorem-contraction mapping problem by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3RCWbP03822; I am an independent student doing math. I am student real analysis on my home. Here is a theorem that has been bugging me for years Let F(x) be a continuously differentiable function defined on the interval [a,b] s.ty F(a)<0,F(b)>0 and 0I am an independent student doing math. >I am student real analysis on my home. >Here is a theorem that has been bugging me for years >Let F(x) be a continuously differentiable function defined on the >interval [a,b] s.ty F(a)<0,F(b)>0 and > 0Find the unique root of F(x)=0 >hint introduce aux. equ. f(x)=x-kF(x) s.t it works for the >equivilant equation f(x)=x You see why x is a root of F if and only if x is a fixed point of f, right? So you only need to show that f is a (strict) contraction. This will not be true for every choice of k, but it's possible to choose k in such a way that there exists c < 1 such that |f'(x)| <= c for all x. >This problem comes from Real Analysis by Kolmovgrov and Fomin >Any help to solve it would be appreciated >Larry ************************ David C. Ullrich === Subject: Continuum-hypothesis for closed sets in R by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3RCWUE03517; I need to prove that any closed set in R without isolated points has the cardinality of continuum, without using continuum-hypothesis. I have used the following argument: since a closed set forms a complete metric space, it's a set of the second Baire category, therefore, it should either include an open set (thus having the cardinality of continuum), or be an uncountable union of non-dense sets (thus being at least uncountable). But how can I show that the cardinality in the second case is exactly continuum? === Subject: Re: Continuum-hypothesis for closed sets in R >I need to prove that any closed set in R without isolated points has >the cardinality of continuum, without using continuum-hypothesis. Probably you also want to assume the set is nonempty. >I have used the following argument: >since a closed set forms a complete metric space, it's a set of the >second Baire category, therefore, it should either include an open >set (thus having the cardinality of continuum), or be an uncountable >union of non-dense sets (thus being at least uncountable). >But how can I show that the cardinality in the second case is exactly >continuum? Forget all that and just prove it: First show that if A is closed , nonempty and has no isolated points then there exist two disjoint subsets A0 and A1, each of which is closed, nonempty and has no isolated points. Now apply this to get subsets A00 and A01 of A0 and subsets A10 and A11 of A1. Repeat infinitely many times. Jiggle things so each set at the n-th stage has diameter less than 1/n. Then for every sequence b of 0's and 1's the intersection of Ae1, Ae1e2, Ae1e2e3, ... is nonempty; so you have a 1-1 mapping of {0,1}^N into A. ************************ David C. Ullrich === Subject: Need help with theorem-contraction mapping problem by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3RCWc703838; I am an independent student doing math. I am student real analysis on my home. Here is a theorem that has been bugging me for years Let F(x) be a continuously differentiable function defined on the interval [a,b] s.ty F(a)<0,F(b)>0 and 0I have this problem. Given a circle and another circle totally >inside it. Can we get a polynomial curve that strts from >the big circle and end on the small circle. The polynomial >must have an increasing curvature. Do you want the curvature to increase from the point of intersection of the polynomial curve with the big circle to the point of intersectio of the polynomial curve with the small circle, or to decrease? Also, do you want the polynomial curve to be tangent to the two circles at its points of intersection with them? I suspect that you can do this with an arc of a parabola, but will wait for more details before thinking more about it. Why do you have this problem, anyway? Lee Rudolph === Subject: Cyclic groups. How? Which of the following groups are cyclic and why? 1) Z3 + Z225 2) Z27 +Z25 3) Z3 + Z9 + Z25 (where '+' indicates direct sum) /Jimmy === Subject: Re: Cyclic groups. How? Adjunct Assistant Professor at the University of Montana. >Which of the following groups are cyclic and why? >1) Z3 + Z225 No. >2) Z27 +Z25 Yes >3) Z3 + Z9 + Z25 No. Fundamental Theorem of Finite(ly) Generated Abelian Groups. Or easier: show that if C and D are finite cyclic groups, then C+D is cyclic if and only if the orders of C and D are coprime. (For the if, show that (1,1) generates; for the only if, show that C+D has more than one subgroup of a given order) -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu === Subject: Re: Cyclic groups. How? > Which of the following groups are cyclic and why? > 1) Z3 + Z225 > 2) Z27 +Z25 > 3) Z3 + Z9 + Z25 > (where '+' indicates direct sum) Good question :-) -Michael. === Subject: ALBERT EINSTEIN Plagiarist of the Century water. The author says that Jules Henri Poincar.8e is the true originator of the special theory of relativity, not Albert Einstein. ALBERT EINSTEIN Plagiarist of the Century Einstein plagiarised the work of several notable scientists in his 1905 papers on special relativity and E = mc2, yet the physics community has never bothered to set the record straight in the past century. ---------------------------------------------------------------------------- ---- PO Box 30, Mapleton Qld 4560 Australia. editor@nexusmagazine.com Telephone: +61 (0)7 5442 9280; Fax: +61 (0)7 5442 9381 777 Treadlemire Road Berne, NY 12023 USA Email: Slmrea@aol.com ---------------------------------------------------------------------------- ---- Abstract Proponents of Einstein have acted in a way that appears to corrupt the historical record. Albert Einstein (1879-1955), Time Magazine's Person of actually called On the Electrodynamics of Moving Bodies, 1905a), without listing any references. Many of the key ideas it presented were known to Lorentz (for example, the Lorentz transformation) and Poincar.8e before As was typical of Einstein, he did not discover theories; he merely commandeered them. He took an existing body of knowledge, picked and chose the ideas he liked, then wove them into a tale about his contribution to special relativity. This was done with the full knowledge and consent of many of his peers, such as the editors at Annalen der Physik. The most recognisable equation of all time is E = mc2. It is attributed by convention to be the sole province of Albert Einstein (1905). However, the conversion of matter into energy and energy into matter was known to Sir Isaac Newton (Gross bodies and light are convertible into one another..., 1704). The equation can be attributed to S. Tolver Preston (1875), to Jules Henri Poincar.8e (1900; according to Brown, 1967) and to Olinto De Pretto (1904) before Einstein. Since Einstein never correctly derived E = mc2 (Ives, 1952), there appears nothing to connect the equation with anything original by Einstein. Arthur Eddington's selective presentation of data from the 1919 Eclipse so that it supposedly supported Einstein's general relativity theory is surely one of the biggest scientific hoaxes of the 20th century. His lavish support of Einstein corrupted the course of history. Eddington was less interested in testing a theory than he was in crowning Einstein the king of science. The physics community, unwittingly perhaps, has engaged in a kind of fraud and silent conspiracy; this is the byproduct of simply being bystanders as the hyperinflation of Einstein's record and reputation took place. This silence benefited anyone supporting Einstein. Introduction Science, by its very nature, is insular. In general, chemists read and write about chemistry, biologists read and write about biology, and physicists read and write about physics. But they may all be competing for the same research dollar (in its broadest sense). Thus, if scientists wanted more money for themselves, they might decide to compete unfairly. The way they can do this is convince the funding agencies that they are more important than any other branch of science. If the funding agencies agree, it could spell difficulty for the remaining sciences. One way to get more money is to create a superhero - a superhero like Einstein. Einstein's standing is the product of the physics community, his followers and the media. Each group benefits enormously by elevating Einstein to icon status. The physics community receives billions in research grants, Einstein's supporters are handsomely rewarded, and media corporations like T ime Magazine get to sell millions of magazines by placing Einstein on the cover as Person of the Century. When the scandal breaks, the physics community, Einstein's supporters and the media will attempt to downplay the negative news and put a positive spin on it. However, their efforts will be shown up when Einstein's paper, On the Electrodynamics of Moving Bodies, is seen for what it is: the consummate act of plagiarism in the 20th century. Special Relativity Jules Henri Poincar.8e (1854-1912) was a great scientist who made a significant contribution to special relativity theory. The Internet Encyclopedia of Philosophy website says that Poincar.8e: (1) sketched a preliminary version of the special theory of relativity; (2) stated that the velocity of light is a limit velocity (in his 1904 paper from the Bull. of Sci. Math. 28, Poincar.8e indicated a whole new mechanics, where the inertia increasing with the velocity of light would become a limit and not be exceeded); (3) suggested that mass depends on speed; (4) formulated the principle of relativity, according to which no mechanical or electromagnetic experiment can discriminate between a state of uniform motion and a state of rest; and (5) derived the Lorentz transformation. It is evident how deeply involved with special relativity Poincar.8e was. Even Keswani (1965) was prompted to say that As far back as 1895, Poincar.8e, the innovator, had conjectured that it is impossible to detect absolute motion, and that In 1900, he introduced 'the principle of relative motion' which he later called by the equivalent terms 'the law of relativity' and 'the principle of relativity' in his book, Science and Hypothesis, published in 1902. Einstein acknowledged none of this preceding theoretical work when he In addition to having sketched the preliminary version of relativity, Poincar.8e provided a critical part of the whole concept - namely, his treatment of local time. He also originated the idea of clock synchronisation, which is critical to special relativity. Charles Nordman was prompted to write, They will show that the credit for most of the things which are currently attributed to Einstein is, in reality, due to Poincar.8e, and ...in the opinion of the Relativists it is the measuring rods which create space, the clocks which create time. All this was known by Poincar.8e and others long before the time of Einstein, and one does injustice to truth in ascribing the discovery to him. Other scientists have not been quite as impressed with Einstein's special relativity theory as has the public. Another curious feature of the now famous paper, Einstein, 1905, is the absence of any reference to Poincar.8e or impression of quite a new venture. But that is, of course, as I have tried to explain, not true (Born, 1956). G. Burniston Brown (1967) noted, It will be seen that, contrary to popular belief, Einstein played only a minor part in the derivation of the useful formulae in the restricted or special relativity theory, and Whittaker called it the relativity theory of Poincar.8e and Lorentz.83 Due to the fact that Einstein's special relativity theory was known in some circles as the relativity theory of Poincar.8e and Lorentz, one would think that Poincar.8e and Lorentz might have had something to do with its creation. What is disturbing about the Einstein paper is that even though Poincar.8e was the world's leading expert on relativity, apparently Einstein had never heard of him or thought he had done anything worth referencing! Poincar.8e, in a public address delivered in September 1904, made some notable confirmed, would arise an entirely new mechanics.83would be, above all, characterised by this fact that no velocity could surpass that of light.83because bodies would oppose an increasing inertia to the causes, which would tend to accelerate their motion; and this inertia would become infinite when one approached the velocity of lightNo more for an observer carried along himself in a translation, he did not suspect any apparent velocity could surpass that of light: and this would be then a contradiction, if we recall that this observer would not use the same clocks as a fixed observer, but, indeed, clocks marking 'local time'. (Poincar.8e, 1905) Einstein, the Plagiarist It is now time to speak directly to the issue of what Einstein was: he was first and foremost a plagiarist. He had few qualms about stealing the work of others and submitting it as his own. That this was deliberate seems obvious. Take this passage from Ronald W. Clark, Einstein: The Life and Times (there are no references to Poincar.8e here; just a few meaningless quotes). This is how page 101 reads: 'On the Electrodynamics of Moving Bodies'...is in many ways one of the most remarkable scientific papers that had ever been written. Even in form and style it was unusual, lacking the notes and references which give weight to most serious expositions.83 (emphasis added). Why would Einstein, with his training as a patent clerk, not recognise the think that Einstein, as a neophyte, would overreference rather than underreference. Wouldn't one also expect somewhat higher standards from an editor when faced with a long manuscript that had obviously not been credited? Apparently there was no attempt at quality control when it was published in Annalen der Physik. Most competent editors would have rejected the paper without even reading it. At the barest minimum, one would expect the editor to research the literature to determine whether Einstein's claim of primacy was correct. Max Born stated, The striking point is that it contains not a single reference to previous literature (emphasis added) (Born, 1956). He is clearly indicating that the absence of references is abnormal and that, even by early 20th century standards, this is most peculiar, even unprofessional. Einstein twisted and turned to avoid plagiarism charges, but these were transparent. Einstein's explanation is a dimensional disguise for Lorentz'sThus Einstein's theory is not a denial of, nor an alternative for, that of Lorentz. It is only a duplicate and disguise for itEinstein continually maintains that the theory of Lorentz is right, only he disagrees with his 'interpretation'. Is it not clear, therefore, that in this [case], as in other cases, Einstein's theory is merely a disguise for Lorentz's, the apparent disagreement about 'interpretation' being a matter of words only? he'd never read Poincar.8e's contributions to physics. Yet many of Poincar.8e's ideas - for example, that the speed of light is a limit and that mass increases with speed - wound up in Einstein's paper, On the Electrodynamics of Moving Bodies without being credited. Einstein's act of stealing almost the entire body of literature by Lorentz and Poincar.8e to write his document raised the bar for plagiarism. In the information age, this kind of plagiarism could never be perpetrated indefinitely, yet the physics community has still not set the record straight. In his 1907 paper, Einstein spelled out his views on plagiarism: It appears to me that it is the nature of the business that what follows has already been partly solved by other authors. Despite that fact, since the issues of concern are here addressed from a new point of view, I am entitled to leave out a thoroughly pedantic survey of the literature... With this statement, Einstein declared that plagiarism, suitably packaged, is an acceptable research tool. Here is the definition of to plagiarise from an unimpeachable source, Webster's New International Dictionary of the English Language, Second Edition, Unabridged, 1947, p. 1,878: To steal or purloin and pass off as one's own (the ideas, words, artistic productions, etc. of one another); to use without due credit the ideas, expressions or productions of another. To commit plagiarism (emphasis added). Isn't this exactly what Einstein did? Giving due credit involves two aspects: timeliness and appropriateness. Telling the world that Lorentz provided the basis for special relativity 30 years after the fact is not timely (see below), is not appropriate and is Lorentz's contributions alters the fundamental act of plagiarism. The true nature of Einstein's plagiarism is set forth in his 1935 paper, Elementary Derivation of the Equivalence of Mass and Energy, where, in a those relations is a natural one because the Lorentz transformation, the real basis of special relativity theory... (emphasis added). So, Einstein even acknowledged that the Lorentz transformation was the real basis of his 1905 paper. Anyone who doubts that he was a plagiarist should ask one simple question: What did Einstein know and when did he know it? Einstein got away with premeditated plagiarism, not the incidental plagiarism that is ubiquitous (Moody, 2001). The History of E = mc2 Who originated the concept of matter being transformed into energy and vice versa? It dates back at least to Sir Isaac Newton (1704). Brown (1967) made the following statement: Thus gradually arose the formula E = mc2, suggested without general proof by Poincar.8e in 1900. One thing we can say with certainty is that Einstein did not originate the equation E = mc2. Then the question becomes: Who did? Bjerknes (2002) suggested as a possible candidate S. Tolver Preston, who formulated atomic energy, the atom bomb and superconductivity back in the 1870s, based on the formula E = mc2. In addition to Preston, a major player in the history of E = mc2 who deserves a lot of credit is Olinto De Pretto (1904). What makes this timing so suspicious is that Einstein was fluent in Italian, he was reviewing papers written by Italian physicists and his best friend was Michele Besso, a Swiss Italian. Clearly, Einstein (1905b) would have had access to the literature and the competence to read it. In Einstein's E = mc2 'was Italian's idea' (Carroll, 1999), we see clear evidence that De Pretto was ahead of Einstein in terms of the formula E = mc2. In terms of his understanding the vast amount of energy that could be released with a small amount of mass, Preston (1875) can be credited with knowing this before Einstein was born. Clearly, Preston was using the E = mc2 formula in his work, because the value he determined - e.g., that one grain could lift a 100,000-ton object up to a height of 1.9 miles - yields the equation E = mc2. According to Ives (1952), the derivation Einstein attempted of the formula E = mc2 was fatally flawed because Einstein set out to prove what he assumed. This is similar to the careless handling of the equations for radioactive decay which Einstein derived. It turns out that Einstein mixed kinematics and mechanics, and out popped the neutrino. The neutrino may be a mythical choices with respect to neutrinos: there are at least 40 different types or there are zero types. Occam's razor rules here. The Eclipse of 1919 There can be no clearer definition of scientific fraud than what went on in the Tropics on May 29, 1919. What is particularly clear is that Eddington fudged the solar eclipse data to make the results conform to Einstein's work on general relativity. Poor (1930), Brown (1967), Clark (1984) and McCausland (2001) all address the issues surrounding this eclipse. What makes the expeditions to Sobral and Principe so suspect is Eddington's zealous support of Einstein, as can be seen in his statement, By standing foremost in testing, and ultimately verifying the 'enemy' theory, our national observatory kept alive the finest traditions of science... (emphasis added) (Clark, 1984). In this instance, apparently Eddington was not familiar with the basic tenets of science. His job was to collect data - not verify Einstein's theories. Further evidence for the fraud can be deduced from Eddington's own statements and the introduction to them provided by Clark (ibid., p. 285): May 29 began with heavy rain, which stopped only about noon. Not until 1.30 pm when the eclipse had already begun did the party get its first glimpse of the sun: 'We had to carry out our programme of photographs on faith...' (emphasis added). Eddington reveals his true prejudice: he was willing to do anything to see that Einstein was proved right. But Eddington was not to be deterred: It looked as though the effort, so far as the Principe expedition was concerned, might have been abortive; We developed the photographs, two each night for six nights after the eclipseThe cloudy weather upset my plans and I had to treat the measures in a different way from what I intended; consequently I have not been able to make any preliminary announcement of the result (emphasis added) (Clark, ibid.). Actually, Eddington's words speak volumes about the result. As soon as he found one shred of evidence that was consistent with Einstein's general relativity theory, he immediately proclaimed it as proof of the theory. Is this science? Where were the astronomers when Eddington presented his findings? Did anyone besides Eddington actually look at the photographic plates? Poor did, and he completely repudiated the findings of Eddington. This should have given pause to any ethical scientist. Here are some quotes from Poor's summary: The mathematical formula, by which Einstein calculated his deflection of 1.75 seconds for light rays passing the edge of the sun, is a well known and simple formula of physical optics; Not a single one of the fundamental concepts of varying time, or warped or twisted space, of simultaneity, or of the relativity of motion is in any way involved in Einstein's prediction of, or formulas for, the deflection of light; The many and elaborate eclipse expeditions have, therefore, been given a fictitious importance. Their results can neither prove nor disprove the relativity theory.83 (emphasis added) (Poor, 1930). the world community that Einstein's theory was confirmed. What Eddington based this on was a premature assessment of the photographic plates. Initially, stars did appear to bend as they should, as required by Einstein, but then, according to Brown, the unexpected happened: several stars were then observed to bend in a direction transverse to the expected direction and still others to bend in a direction opposite to that predicted by relativity. The absurdity of the data collected during the Eclipse of 1919 was demonstrated by Poor (1930), who pointed out that 85% of the data were discarded from the South American eclipse due to accidental error, i.e., it contradicted Einstein's scale constant. By a strange coincidence, the 15% of the good data were consistent with Einstein's scale constant. Somehow, the stars that did not conform to Einstein's theories conveniently got temporarily shelved - and the myth began. So, based on a handful of ambiguous data points, 200 years of theory, experimentation and observation were cast aside to make room for Einstein. Yet the discredited experiment by Eddington is still quoted as gospel by Stephen Hawking (1999). It is difficult to comprehend how Hawking could comment that The new theory of curved space-time was called general relativityIt was confirmed in spectacular fashion in 1919, when a British expedition to West Africa observed a slight shift in the position of stars near the sun during an eclipse. Their light, as Einstein had predicted, was bent as it passed the sun. Here was direct evidence that space and time were warped. Does Hawking honestly believe that a handful of data points, massaged more thoroughly than a side of Kobe beef, constitutes the basis for overthrowing a paradigm that had survived over two centuries of acid scrutiny? The real question, though, is: Where was Einstein in all this? Surely, by The actual stellar displacements, if real, do not show the slightest resemblance to the predicted Einstein deflections: they do not agree in direction, in size, or the rate of decrease with distance from the sun. Why didn't he go on the record and address a paper that directly contradicted his work? Why haven't the followers of Einstein tried to set the record straight with respect to the bogus data of 1919? What makes this so suspicious is that both the instruments and the physical conditions were not conducive to making measurements of great precision. As Physics, the cap cameras used in the expeditions were accurate to only 1/25th of a degree. This meant that just for the cap camera uncertainty alone, Eddington was reading values over 200 times too precise. McCausland (2001) quotes the former Editor of Nature, Sir John Maddox: They [Crommelin and Eddington] were bent on measuring the deflection of light.83; What is not so well documented is that the measurements in 1919 were not particularly accurate; In spite of the fact that experimental evidence for relativity seems to have been very flimsy in 1919, Einstein's enormous fame has remained intact and his theory has ever since been held to be one of the highest achievements of human thought (emphasis added). It is clear that from the outset Eddington was in no way interested in testing Einstein's theory; he was only interested in confirming it. One of the motivating factors in Eddington's decision to promote Einstein was that both men shared a similar political persuasion: pacifism. To suggest that politics played no role in Eddington's glowing support of Einstein, one need ask only one question: Would Eddington have been so quick to support Einstein if Einstein had been a hawk? This is no idle observation. Eddington took his role as the great peacemaker very seriously. He wanted to unite British and German scientists after World War I. What better way than to elevate the enemy theorist Einstein to exalted status? In his zeal to become peacemaker, Eddington lost the fundamental objectivity that is the essential demeanour of any true scientist. Eddington ceased to be a scientist and, instead, became an advocate for Einstein. The obvious fudging of the data by Eddington and others is a blatant subversion of scientific process and may have misdirected scientific research for the better part of a century. It probably surpasses the Piltdown Man as the greatest hoax of 20th-century science. The BIPP asked, Was this the hoax of the century? and exclaimed, Royal Society 1919 Eclipse Relativity Report Duped World for 80 Years! McCausland stated that In the author's opinion, the confident announcement of the decisive confirmation of Einstein's general theory in November 1919 was not a triumph of science, as it is often portrayed, but one of the most unfortunate incidents in the history of 20th-century science. It cannot be emphasised enough that the Eclipse of 1919 made Einstein, Einstein. It propelled him to international fame overnight, despite the fact that the data were fabricated and there was no support for general relativity whatsoever. This perversion of history has been known about for over 80 years and is still supported by people like Stephen Hawking and David Levy. Summary and Conclusions The general public tends to believe that scientists are the ultimate defenders of ethics, that scientific rigour is the measure of truth. Little do people realise how science is conducted in the presence of personality. It seems that Einstein believed he was above scientific protocol. He thought he could bend the rules to his own liking and get away with it; hang in there long enough and his enemies would die off and his followers would win the day. In science, the last follower standing wins - and gets to write history. In the case of Einstein, his blatant and repeated dalliance with plagiarism is all but forgotten and his followers have borrowed repeatedly from the discoveries of other scientists and used them to adorn Einstein's halo. Einstein's reputation is supported by a three-legged stool. One leg is Einstein's alleged plagiarism. Was he a plagiarist? The second leg is the physics community. What did they know about Einstein and when did they know it? The third leg is the media. Are they instruments of truth or deception when it comes to Einstein? Only time will tell. The physics community is also supported by a three-legged stool. The first leg is Einstein's physics. The second leg is cold fusion. The third leg is autodynamics. The overriding problem with a three-legged stool is that if only one leg is sawed off, the stool collapses. There are at least three very serious disciplines where it is predictable that physics may collapse. Science is a multi-legged stool. One leg is physics; a second leg is the earth sciences; a third, biology; and a fourth, chemistry (e.g., cold fusion). What will happen if, for the sake of argument, physics collapses? Will science fall? ---------------------------------------------------------------------------- ---- Bjerknes, C.J. (2002), Albert Einstein: The Incorrigible Plagiarist, XTX Inc., Dowers Grove. Born, M. (1956), Physics in My Generation, Pergamon Press, London, p. 193. Brown, G. Burniston (1967), What is wrong with relativity?, Bull. of the Inst. of Physics and Physical Soc., pp. 71-77. Carezani, R. (1999), Autodynamics: Fundamental Basis for a New Relativistic Mechanics, SAA, Society for the Advancement of Autodynamics. Carroll, R., Einstein's E = mc2 'was Italian's idea', The Guardian, November 11, 1999. Clark, R.W. (1984), Einstein: The Life and Times, Avon Books, New York. De Pretto, O. (1904), Ipotesi dell'etere nella vita dell'universo, Reale Istituto Veneto di Scienze, Lettere ed Arti, Feb. 1904, tomo LXIII, parte II, pp. 439-500. Einstein, A. (1905a), Zur Elektrodynamik bewegter K.9arper (On the Electrodynamics of Moving Bodies), Annalen der Physik 17:37-65. Einstein, A. (1905b), Does the Inertia of a Body Depend on its Energy Content?, Annalen der Physik 18:639-641. Einstein, A. (1907), .86ber die vom Relativit.8atspringzip geforderte Tr.8agheit der Energie, Annalen der Physik 23(4):371-384 (quote on p. 373). Einstein, A. (1935), Elementary Derivation of the Equivalence of Mass and Energy, Bull. Amer. Math. Soc. 61:223-230 (first delivered as The Eleventh Josiah Willard Gibbs Lecture at a joint meeting of the American Physical Society and Section A of the AAAS, Pittsburgh, December 28, 1934). Hawking, S., Person of the Century, Time Magazine, December 31, 1999. Ives, H.E. (1952), Derivation of the Mass-Energy Relation, J. Opt. Soc. Amer. 42:540-543. Keswani, G.H. (1965), Origin and Concept of Relativity, Brit. J. Phil. Soc. 15:286-306. Mackaye, J. (1931), The Dynamic Universe, Charles Scribner's Sons, New York, pp. 42-43. Maddox, J. (1995), More Precise Solar-limb Light-bending, Nature 377:11. Moody, R., Jr (2001), Plagiarism Personified, Mensa Bull. 442(Feb):5. Newton, Sir Isaac (1704), Opticks, Dover Publications, Inc., New York, p. cxv. Nordman, C. (1921), Einstein et l'univers, translated by Joseph McCabe as Einstein and the Universe, Henry Holt and Co., New York, pp. 10-11, 16 (from Bjerknes, 2002). Poincar.8e, J.H. (1905), The Principles of Mathematical Physics, The Monist, vol. XV, no. 1, January 1905; from an address delivered before the International Congress of Arts and Sciences, St Louis, September 1904. Poor, C.L. (1930), The Deflection of Light as Observed at Total Solar Eclipses, J. Opt. Soc. Amer. 20:173-211. The Internet Encyclopedia of Philosophy, Jules Henri Poincar.8e (1854-1912), at http://www.utm.edu/research/iep/p/poincare.htm. Webster, N. (1947), Webster's New International Dictionary of the English Language, Second Edition, Unabridged, p. 1878. About the Author: Richard Moody, Jr, has a Master's Degree in Geology, is the author of three books on chess theory and has written for the Mensa Bulletin. For the past four years, he has done intensive research into Albert Einstein. He can be contacted by email at Slmrea@aol.com. peace is of the pi, d8>D There was a young lady named bright, Who's speed was much faster than light, She departed one day, In a relative way, And returned on the previous... Big, black hole of Night! === Subject: Re: ALBERT EINSTEIN Plagiarist of the Century > water. I know that there are people who claim that the Italian Olinto De Pretto published a paper prior to Einstein's where he proposed the equation mentioned above. I had the opportunity to read the original paper by De Pretto (I have a copy of it). I am italian (born and living in Italy) and, moreover, I have a degree in Mathematics and a further education in Mathematical Physics. I think that it would be clear to anyone who is not looking for a sensational story that De Pretto's paper has no connection with relativity. It is quite clear that by mv^2 he meant forza viva which is the way (twice the) kinetic energy was (also) called at that time in Italian books. His considerations revolve about the idea that the of light) would acquire a huge kinetic energy. The whole paper has almost no equations or precisely defined concepts and it is clear that the framework of special relativity is entirely missing. I think that this whole story would be forgotten if more people could actually read De Pretto's paper. As for the very few Italian supporters of this idea I noticed that they never present precisely De Pretto's ideas (or the few things one can get from them) but just cite this formula which, by itself, doesn't mean much, out of context. The reason is that this whole story holds no water. Maurizio === Subject: Re: Orders of elements in a group Mail-To-News-Contact: abuse@dizum.com >>My algebra text (Landin) has the following exercise: >>Given a group, G, of order n, show that if p prime and p|n, then there >>exists an element of G with order p. >The usual way is: >(a) Prove it for cyclic groups. Okay, this I've done. It's nice to know that I at least started off on the right foot. >(b) Then prove it for abelian groups. I'll have to stew over this for another day or two to find an angle of attack. I might be back. >(c) Then prove it for p-groups (using the class equation to reduce it > to case (b)). >(d) Then prove it for arbitrary groups (using Sylow's Theorems to > reduce it to (c). I'm beginning to have my doubts about Landin as a text for this self-study. At the point where the subject exercise is, p-groups, class equation and Sylow's Theorems are unknown terms. He's beginning to seem like the authors that Knuth complained about in _The Art of Computer Programming_, when explaining why he put a difficulty rating next to each exercise. (I'd apologize for the inadvertent cross-post to irrelevant groups, except that I've trimmed them from this follow-up.) -- Michael F. Stemper #include Life's too important to take seriously. === Subject: Re: Orders of elements in a group Adjunct Assistant Professor at the University of Montana. >My algebra text (Landin) has the following exercise: >Given a group, G, of order n, show that if p prime and p|n, then there >exists an element of G with order p. >>The usual way is: >>(a) Prove it for cyclic groups. >Okay, this I've done. It's nice to know that I at least started off on >the right foot. >>(b) Then prove it for abelian groups. >I'll have to stew over this for another day or two to find an angle >of attack. I might be back. Someone suggested showing that if N is a normal subgroup of G, and G/N has an element of order p, then G has an element of order p. Assume you manage to prove that: then let N be any proper cyclic of G (unless G is of prime order, in which case it is cyclic and there is nothing to do). If G/N has elements of order p, you are done. This will follow inductively if the order of G/N is a multiple of p. Otherwise, since G had order a multiple of p but G/N does not, that means that the order of N is a multiple of p, and you can apply (a). So: can you prove that if G/N has an element of order p then so does G? >>(c) Then prove it for p-groups (using the class equation to reduce it >> to case (b)). >>(d) Then prove it for arbitrary groups (using Sylow's Theorems to >> reduce it to (c). >I'm beginning to have my doubts about Landin as a text for this self-study. >At the point where the subject exercise is, p-groups, class equation >and Sylow's Theorems are unknown terms. As someone pointed out, the route I traced is not necessarily the best way to go at it: it's just the route that goes through the usual landmarks of an undergraduate course in group theory. You can prove it more easily in other ways. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu === Subject: ALBERT EINSTEIN Plagiarist of the Century === Subject: Re: ALBERT EINSTEIN Plagiarist of the Century <408dfebb$0$12033$afc38c87@news.optusnet.com.au> say.) Are the allegations that Einstein (unwittingly or conveniently?) plagerised possibly accurate? That's really what I want to know, if truth to it, in that regard? Not to slander or discredit Professor Einstein, who has surely earned his reputation, but just to get to the truth of the matter, if there is more to the history of science and math that possibly has been revised? The key issue is about Poincar.8e, I think. I guess it's true that whom history gives credit to this or that discovery, it should always be taken with a few grains of light. :) Or is salt really not a grain at all, but a collapsed wave of the sea? g! Maybe I have a salty sea bicuit of skepticism in my brain, even over the sanctity of historical accuracy. lol! Munch! Crunch! Crack! Ouch! It does seem that Jules Henri Poincar.8e should be given much more credit than is historically given to Albert Einstein in the key mathematical tools he used to formulate the ideas behind Relativity Theory. Are there any similarities at work as to who invented the radio? Nikolai Tesla or Guglielmo Marconi? Apparantly it was really Tesla. But most people assume it was Marconi. To the Smithsonian or Bust:The Scientific Legacy of Nikola Tesla by Zara Herskovits http://www.yale.edu/scimag/Archives/Vol71/tesla.html Could the same kind of historical inaccuracies today be present as to who really should be credited with the mathematical inventions (discoveries?) of Albert Einstein, in context of Relativity Theory etc. farther than others, it is because I was standing on the shoulders of giants. Some people think it was Albert Einstein who said that. Re: If I have seen farther... http://phrases.shu.ac.uk/bulletin_board/7/messages/721.html ---------------------------------------------------------------------------- ---- In Reply to: If I have seen farther than others, it is because I am surrounded by dwarves posted by Mike on February 01, 2001 at 04:01:46: : Has anyone ever heard of this variation of the famous quote by Lucan: A dwarf standing on the shoulders of a giant may see farther than the giant himself. I am not sure if it is supposed to be a No, I haven't heard it. But it's a keeper. The original versions Pigmies placed on the shoulders of giants see more than the giants themselves. Lucan (A.D. 39-65) from The Civil War, Ib. II, 10 (Didacus Stella). I say with Didacus Stella, a dwarf standing on the shoulders of a giant may see farther than a giant himself. Robert Burton (1577-1640)from The Anatomy of Melancholy (1621-51). If I have seen further (than you and Descartes) it is by standing upon the shoulders of giants. Sir Isaac Newton (1642-1727) from Letter to Robert Hooke, Feb. 5, 1675/76. The dwarf sees farther than the giant, when he has the giant's shoulder to mount on -- Coleridge, 'The Friend' (1828). If I have seen further than others, it is because I have stood on the shoulders of giants. (it has been pointed out to me by a couple of people that this is most often attributed to Issac Newton - however, I found it in a book of Einstein quotes and so it is included here) Albert Einstein Quotes (1879-1955) Physicist and mathematician Nobel Prize for Physics 1921 http://www.empyrean.ca/words/quotes/einstein.html Naturally, we're all microscopic pigmies standing on the precipice of Eternity compared to the macroscopic shoulders of the giants, especially the one's in our imaginative minds! :-) To Infinity and Beyond... -Buzz Lightyear Now did he really say that??? g! Perhaps all mathematical discovery and invention is best accredited to Buzz Lightyear. peace is of the pi, d8>D > Yes, the time was ripe for special relativity. Many of the results of SR > were known - or speculated to exist - prior to Einstein. Indeed, the > contraction of length under SR is known as the Fitzgerald-Lorenxz > contraction for that reason. > What Einstein did in SR was show how these different effects - length > contraction, mass increase, different clocks - were a result of invariance > of change of co-ordinates, and not kludges to explain the Michelson Morley > results etc. He built the whole thing from two simple rules - invariance of > the speed of light between different observers and impossibility of passing > information faster than light. Putting all of this together on a simple, > powerful, consistent framework was Einstein's contribution, and one which > mage him a great scientist. > Little of this applies to General Relativity. GR was before its time. If > Einstein hadn't discovered it, it may have taken years before it was > discovered by somebody else. This, and Einstein's contributions to the > foundations of Quantum Theory (for which he won his Nobel Prize) is the > reason that Einstein can lay credible claim to being the greatest scientist > of all time (to date, anyway). >water. >The author says that Jules Henri Poincar.8e is the true originator of the >special theory of relativity, not Albert Einstein. >ALBERT EINSTEIN >Plagiarist of the Century >Einstein plagiarised the work of several notable scientists in his 1905 >papers on special relativity and E = mc2, yet the physics community has >never bothered to set the record straight in the past century. > -------------------------------------------------------------------------- > -- >---- >Extracted from Nexus Magazine, Volume 11, Number 1 (December-January >PO Box 30, Mapleton Qld 4560 Australia. editor@nexusmagazine.com >Telephone: +61 (0)7 5442 9280; Fax: +61 (0)7 5442 9381 >777 Treadlemire Road >Berne, NY 12023 >USA >Email: Slmrea@aol.com > -------------------------------------------------------------------------- > -- >---- >Abstract >Proponents of Einstein have acted in a way that appears to corrupt the >historical record. Albert Einstein (1879-1955), Time Magazine's Person of >actually called On the Electrodynamics of Moving Bodies, 1905a), without >listing any references. Many of the key ideas it presented were known to >Lorentz (for example, the Lorentz transformation) and Poincar.8e before >As was typical of Einstein, he did not discover theories; he merely >commandeered them. He took an existing body of knowledge, picked and chose >the ideas he liked, then wove them into a tale about his contribution to >special relativity. This was done with the full knowledge and consent of >many of his peers, such as the editors at Annalen der Physik. >The most recognisable equation of all time is E = mc2. It is attributed by >convention to be the sole province of Albert Einstein (1905). However, the >conversion of matter into energy and energy into matter was known to Sir >Isaac Newton (Gross bodies and light are convertible into one > another..., >1704). The equation can be attributed to S. Tolver Preston (1875), to > Jules >Henri Poincar.8e (1900; according to Brown, 1967) and to Olinto De Pretto >(1904) before Einstein. Since Einstein never correctly derived E = mc2 >(Ives, 1952), there appears nothing to connect the equation with anything >original by Einstein. >Arthur Eddington's selective presentation of data from the 1919 Eclipse so >that it supposedly supported Einstein's general relativity theory is >surely one of the biggest scientific hoaxes of the 20th century. His > lavish >support of Einstein corrupted the course of history. Eddington was less >interested in testing a theory than he was in crowning Einstein the king > of >science. >The physics community, unwittingly perhaps, has engaged in a kind of fraud >and silent conspiracy; this is the byproduct of simply being bystanders as >the hyperinflation of Einstein's record and reputation took place. This >silence benefited anyone supporting Einstein. >Introduction >Science, by its very nature, is insular. In general, chemists read and > write >about chemistry, biologists read and write about biology, and physicists >read and write about physics. But they may all be competing for the same >research dollar (in its broadest sense). Thus, if scientists wanted more >money for themselves, they might decide to compete unfairly. The way they >can do this is convince the funding agencies that they are more important >than any other branch of science. If the funding agencies agree, it could >spell difficulty for the remaining sciences. One way to get more money is > to >create a superhero - a superhero like Einstein. >Einstein's standing is the product of the physics community, his followers >and the media. Each group benefits enormously by elevating Einstein to > icon >status. The physics community receives billions in research grants, >Einstein's supporters are handsomely rewarded, and media corporations like > T >ime Magazine get to sell millions of magazines by placing Einstein on the >cover as Person of the Century. >When the scandal breaks, the physics community, Einstein's supporters and >the media will attempt to downplay the negative news and put a positive > spin >on it. However, their efforts will be shown up when Einstein's paper, On >the Electrodynamics of Moving Bodies, is seen for what it is: the >consummate act of plagiarism in the 20th century. >Special Relativity >Jules Henri Poincar.8e (1854-1912) was a great scientist who made a >significant contribution to special relativity theory. The Internet >Encyclopedia of Philosophy website says that Poincar.8e: (1) sketched a >preliminary version of the special theory of relativity; (2) stated that >the velocity of light is a limit velocity (in his 1904 paper from the > Bull. >of Sci. Math. 28, Poincar.8e indicated a whole new mechanics, where the >inertia increasing with the velocity of light would become a limit and not >be exceeded); (3) suggested that mass depends on speed; (4) formulated >the principle of relativity, according to which no mechanical or >electromagnetic experiment can discriminate between a state of uniform >motion and a state of rest; and (5) derived the Lorentz transformation. >It is evident how deeply involved with special relativity Poincar.8e was. > Even >Keswani (1965) was prompted to say that As far back as 1895, Poincar.8e, > the >innovator, had conjectured that it is impossible to detect absolute > motion, >and that In 1900, he introduced 'the principle of relative motion' which > he >later called by the equivalent terms 'the law of relativity' and 'the >principle of relativity' in his book, Science and Hypothesis, published in >1902. Einstein acknowledged none of this preceding theoretical work when > he >In addition to having sketched the preliminary version of relativity, >Poincar.8e provided a critical part of the whole concept - namely, his >treatment of local time. He also originated the idea of clock >synchronisation, which is critical to special relativity. >Charles Nordman was prompted to write, They will show that the credit for >most of the things which are currently attributed to Einstein is, in >reality, due to Poincar.8e, and ...in the opinion of the Relativists it is >the measuring rods which create space, the clocks which create time. All >this was known by Poincar.8e and others long before the time of Einstein, > and >one does injustice to truth in ascribing the discovery to him. >Other scientists have not been quite as impressed with Einstein's > special >relativity theory as has the public. Another curious feature of the now >famous paper, Einstein, 1905, is the absence of any reference to Poincar.8e > or > the >impression of quite a new venture. But that is, of course, as I have tried >to explain, not true (Born, 1956). G. Burniston Brown (1967) noted, It >will be seen that, contrary to popular belief, Einstein played only a > minor >part in the derivation of the useful formulae in the restricted or special >relativity theory, and Whittaker called it the relativity theory of > Poincar.8e >and Lorentz.83 >Due to the fact that Einstein's special relativity theory was known in > some >circles as the relativity theory of Poincar.8e and Lorentz, one would think >that Poincar.8e and Lorentz might have had something to do with its > creation. >What is disturbing about the Einstein paper is that even though Poincar.8e > was >the world's leading expert on relativity, apparently Einstein had never >heard of him or thought he had done anything worth referencing! >Poincar.8e, in a public address delivered in September 1904, made some > notable > are >confirmed, would arise an entirely new mechanics.83would be, above all, >characterised by this fact that no velocity could surpass that of >light.83because bodies would oppose an increasing inertia to the causes, > which >would tend to accelerate their motion; and this inertia would become >infinite when one approached the velocity of lightNo more for an observer >carried along himself in a translation, he did not suspect any apparent >velocity could surpass that of light: and this would be then a >contradiction, if we recall that this observer would not use the same > clocks >as a fixed observer, but, indeed, clocks marking 'local time'. (Poincar.8e, >1905) >Einstein, the Plagiarist >It is now time to speak directly to the issue of what Einstein was: he was >first and foremost a plagiarist. He had few qualms about stealing the work >of others and submitting it as his own. That this was deliberate seems >obvious. >Take this passage from Ronald W. Clark, Einstein: The Life and Times > (there >are no references to Poincar.8e here; just a few meaningless quotes). This > is >how page 101 reads: 'On the Electrodynamics of Moving Bodies'...is in > many >ways one of the most remarkable scientific papers that had ever been >written. Even in form and style it was unusual, lacking the notes and >references which give weight to most serious expositions.83 (emphasis > added). >Why would Einstein, with his training as a patent clerk, not recognise the >think that Einstein, as a neophyte, would overreference rather than >underreference. >Wouldn't one also expect somewhat higher standards from an editor when > faced >with a long manuscript that had obviously not been credited? Apparently >there was no attempt at quality control when it was published in Annalen > der >Physik. Most competent editors would have rejected the paper without even >reading it. At the barest minimum, one would expect the editor to research >the literature to determine whether Einstein's claim of primacy was > correct. >Max Born stated, The striking point is that it contains not a single >reference to previous literature (emphasis added) (Born, 1956). He is >clearly indicating that the absence of references is abnormal and that, > even >by early 20th century standards, this is most peculiar, even > unprofessional. >Einstein twisted and turned to avoid plagiarism charges, but these were >transparent. >Einstein's explanation is a dimensional disguise for Lorentz'sThus >Einstein's theory is not a denial of, nor an alternative for, that of >Lorentz. It is only a duplicate and disguise for itEinstein continually >maintains that the theory of Lorentz is right, only he disagrees with his >'interpretation'. Is it not clear, therefore, that in this [case], as in >other cases, Einstein's theory is merely a disguise for Lorentz's, the >apparent disagreement about 'interpretation' being a matter of words > only? and > claimed >he'd never read Poincar.8e's contributions to physics. >Yet many of Poincar.8e's ideas - for example, that the speed of light is a >limit and that mass increases with speed - wound up in Einstein's paper, > On >the Electrodynamics of Moving Bodies without being credited. >Einstein's act of stealing almost the entire body of literature by Lorentz >and Poincar.8e to write his document raised the bar for plagiarism. In the >information age, this kind of plagiarism could never be perpetrated >indefinitely, yet the physics community has still not set the record >straight. >In his 1907 paper, Einstein spelled out his views on plagiarism: It > appears >to me that it is the nature of the business that what follows has already >been partly solved by other authors. Despite that fact, since the issues > of >concern are here addressed from a new point of view, I am entitled to > leave >out a thoroughly pedantic survey of the literature... >With this statement, Einstein declared that plagiarism, suitably packaged, >is an acceptable research tool. >Here is the definition of to plagiarise from an unimpeachable source, >Webster's New International Dictionary of the English Language, Second >Edition, Unabridged, 1947, p. 1,878: To steal or purloin and pass off as >one's own (the ideas, words, artistic productions, etc. of one another); > to >use without due credit the ideas, expressions or productions of another. > To >commit plagiarism (emphasis added). Isn't this exactly what Einstein did? >Giving due credit involves two aspects: timeliness and appropriateness. >Telling the world that Lorentz provided the basis for special relativity > 30 >years after the fact is not timely (see below), is not appropriate and is > to >Lorentz's contributions alters the fundamental act of plagiarism. >The true nature of Einstein's plagiarism is set forth in his 1935 paper, >Elementary Derivation of the Equivalence of Mass and Energy, where, in a >those relations is a natural one because the Lorentz transformation, the >real basis of special relativity theory... (emphasis added). >So, Einstein even acknowledged that the Lorentz transformation was the > real >basis of his 1905 paper. Anyone who doubts that he was a plagiarist should >ask one simple question: What did Einstein know and when did he know it? >Einstein got away with premeditated plagiarism, not the incidental >plagiarism that is ubiquitous (Moody, 2001). >The History of E = mc2 >Who originated the concept of matter being transformed into energy and > vice >versa? It dates back at least to Sir Isaac Newton (1704). Brown (1967) > made >the following statement: Thus gradually arose the formula E = mc2, >suggested without general proof by Poincar.8e in 1900. >One thing we can say with certainty is that Einstein did not originate the >equation E = mc2. >Then the question becomes: Who did? >Bjerknes (2002) suggested as a possible candidate S. Tolver Preston, who >formulated atomic energy, the atom bomb and superconductivity back in the >1870s, based on the formula E = mc2. >In addition to Preston, a major player in the history of E = mc2 who >deserves a lot of credit is Olinto De Pretto (1904). What makes this > timing >so suspicious is that Einstein was fluent in Italian, he was reviewing >papers written by Italian physicists and his best friend was Michele > Besso, >a Swiss Italian. Clearly, Einstein (1905b) would have had access to the >literature and the competence to read it. In Einstein's E = mc2 'was >Italian's idea' (Carroll, 1999), we see clear evidence that De Pretto was >ahead of Einstein in terms of the formula E = mc2. >In terms of his understanding the vast amount of energy that could be >released with a small amount of mass, Preston (1875) can be credited with >knowing this before Einstein was born. Clearly, Preston was using the E = >mc2 formula in his work, because the value he determined - e.g., that one >grain could lift a 100,000-ton object up to a height of 1.9 miles - yields >the equation E = mc2. >According to Ives (1952), the derivation Einstein attempted of the formula > E >= mc2 was fatally flawed because Einstein set out to prove what he > assumed. >This is similar to the careless handling of the equations for radioactive >decay which Einstein derived. It turns out that Einstein mixed kinematics >and mechanics, and out popped the neutrino. The neutrino may be a mythical >choices with respect to neutrinos: there are at least 40 different types > or >there are zero types. Occam's razor rules here. >The Eclipse of 1919 >There can be no clearer definition of scientific fraud than what went on > in >the Tropics on May 29, 1919. What is particularly clear is that Eddington >fudged the solar eclipse data to make the results conform to Einstein's >work on general relativity. Poor (1930), Brown (1967), Clark (1984) and >McCausland (2001) all address the issues surrounding this eclipse. >What makes the expeditions to Sobral and Principe so suspect is > Eddington's >zealous support of Einstein, as can be seen in his statement, By standing >foremost in testing, and ultimately verifying the 'enemy' theory, our >national observatory kept alive the finest traditions of science... >(emphasis added) (Clark, 1984). In this instance, apparently Eddington was >not familiar with the basic tenets of science. His job was to collect > data - >not verify Einstein's theories. >Further evidence for the fraud can be deduced from Eddington's own >statements and the introduction to them provided by Clark (ibid., p. 285): >May 29 began with heavy rain, which stopped only about noon. Not until > 1.30 >pm when the eclipse had already begun did the party get its first glimpse > of >the sun: 'We had to carry out our programme of photographs on faith...' >(emphasis added). Eddington reveals his true prejudice: he was willing to > do >anything to see that Einstein was proved right. But Eddington was not to > be >deterred: It looked as though the effort, so far as the Principe > expedition >was concerned, might have been abortive; We developed the photographs, > two >each night for six nights after the eclipseThe cloudy weather upset my > plans >and I had to treat the measures in a different way from what I intended; >consequently I have not been able to make any preliminary announcement of >the result (emphasis added) (Clark, ibid.). >Actually, Eddington's words speak volumes about the result. As soon as he >found one shred of evidence that was consistent with Einstein's general >relativity theory, he immediately proclaimed it as proof of the theory. Is >this science? >Where were the astronomers when Eddington presented his findings? Did > anyone >besides Eddington actually look at the photographic plates? Poor did, and > he >completely repudiated the findings of Eddington. This should have given >pause to any ethical scientist. >Here are some quotes from Poor's summary: The mathematical formula, by >which Einstein calculated his deflection of 1.75 seconds for light rays >passing the edge of the sun, is a well known and simple formula of > physical >optics; Not a single one of the fundamental concepts of varying time, or >warped or twisted space, of simultaneity, or of the relativity of motion > is >in any way involved in Einstein's prediction of, or formulas for, the >deflection of light; The many and elaborate eclipse expeditions have, >therefore, been given a fictitious importance. Their results can neither >prove nor disprove the relativity theory.83 (emphasis added) (Poor, 1930). to >the world community that Einstein's theory was confirmed. What Eddington >based this on was a premature assessment of the photographic plates. >Initially, stars did appear to bend as they should, as required by >Einstein, but then, according to Brown, the unexpected happened: several >stars were then observed to bend in a direction transverse to the expected >direction and still others to bend in a direction opposite to that > predicted >by relativity. >The absurdity of the data collected during the Eclipse of 1919 was >demonstrated by Poor (1930), who pointed out that 85% of the data were >discarded from the South American eclipse due to accidental error, i.e., >it contradicted Einstein's scale constant. By a strange coincidence, the > 15% >of the good data were consistent with Einstein's scale constant. > Somehow, >the stars that did not conform to Einstein's theories conveniently got >temporarily shelved - and the myth began. >So, based on a handful of ambiguous data points, 200 years of theory, >experimentation and observation were cast aside to make room for Einstein. >Yet the discredited experiment by Eddington is still quoted as gospel by >Stephen Hawking (1999). It is difficult to comprehend how Hawking could >comment that The new theory of curved space-time was called general >relativityIt was confirmed in spectacular fashion in 1919, when a British >expedition to West Africa observed a slight shift in the position of stars >near the sun during an eclipse. Their light, as Einstein had predicted, > was >bent as it passed the sun. Here was direct evidence that space and time > were >warped. Does Hawking honestly believe that a handful of data points, >massaged more thoroughly than a side of Kobe beef, constitutes the basis > for >overthrowing a paradigm that had survived over two centuries of acid >scrutiny? >The real question, though, is: Where was Einstein in all this? Surely, > by Poor: >The actual stellar displacements, if real, do not show the slightest >resemblance to the predicted Einstein deflections: they do not agree in >direction, in size, or the rate of decrease with distance from the sun. > Why >didn't he go on the record and address a paper that directly contradicted >his work? Why haven't the followers of Einstein tried to set the record >straight with respect to the bogus data of 1919? >What makes this so suspicious is that both the instruments and the > physical >conditions were not conducive to making measurements of great precision. > As Precise >Physics, the cap cameras used in the expeditions were accurate to only >1/25th of a degree. This meant that just for the cap camera uncertainty >alone, Eddington was reading values over 200 times too precise. >McCausland (2001) quotes the former Editor of Nature, Sir John Maddox: > They >[Crommelin and Eddington] were bent on measuring the deflection of > light.83; >What is not so well documented is that the measurements in 1919 were not >particularly accurate; In spite of the fact that experimental evidence > for >relativity seems to have been very flimsy in 1919, Einstein's enormous > fame >has remained intact and his theory has ever since been held to be one of > the >highest achievements of human thought (emphasis added). >It is clear that from the outset Eddington was in no way interested in >testing Einstein's theory; he was only interested in confirming it. One > of >the motivating factors in Eddington's decision to promote Einstein was > that >both men shared a similar political persuasion: pacifism. To suggest that >politics played no role in Eddington's glowing support of Einstein, one > need >ask only one question: Would Eddington have been so quick to support >Einstein if Einstein had been a hawk? This is no idle observation. >Eddington took his role as the great peacemaker very seriously. He wanted > to >unite British and German scientists after World War I. What better way > than >to elevate the enemy theorist Einstein to exalted status? In his zeal to >become peacemaker, Eddington lost the fundamental objectivity that is the >essential demeanour of any true scientist. Eddington ceased to be a >scientist and, instead, became an advocate for Einstein. >The obvious fudging of the data by Eddington and others is a blatant >subversion of scientific process and may have misdirected scientific >research for the better part of a century. It probably surpasses the >Piltdown Man as the greatest hoax of 20th-century science. The BIPP asked, >Was this the hoax of the century? and exclaimed, Royal Society 1919 >Eclipse Relativity Report Duped World for 80 Years! McCausland stated > that >In the author's opinion, the confident announcement of the decisive >confirmation of Einstein's general theory in November 1919 was not a > triumph >of science, as it is often portrayed, but one of the most unfortunate >incidents in the history of 20th-century science. >It cannot be emphasised enough that the Eclipse of 1919 made Einstein, >Einstein. It propelled him to international fame overnight, despite the > fact >that the data were fabricated and there was no support for general >relativity whatsoever. This perversion of history has been known about for >over 80 years and is still supported by people like Stephen Hawking and >David Levy. >Summary and Conclusions >The general public tends to believe that scientists are the ultimate >defenders of ethics, that scientific rigour is the measure of truth. > Little >do people realise how science is conducted in the presence of personality. >It seems that Einstein believed he was above scientific protocol. He > thought >he could bend the rules to his own liking and get away with it; hang in >there long enough and his enemies would die off and his followers would > win >the day. In science, the last follower standing wins - and gets to write >history. In the case of Einstein, his blatant and repeated dalliance with >plagiarism is all but forgotten and his followers have borrowed repeatedly >from the discoveries of other scientists and used them to adorn Einstein's >halo. >Einstein's reputation is supported by a three-legged stool. One leg is >Einstein's alleged plagiarism. Was he a plagiarist? The second leg is the >physics community. What did they know about Einstein and when did they > know >it? The third leg is the media. Are they instruments of truth or deception >when it comes to Einstein? Only time will tell. >The physics community is also supported by a three-legged stool. The first >leg is Einstein's physics. The second leg is cold fusion. The third leg is >autodynamics. The overriding problem with a three-legged stool is that if >only one leg is sawed off, the stool collapses. There are at least three >very serious disciplines where it is predictable that physics may > collapse. >Science is a multi-legged stool. One leg is physics; a second leg is the >earth sciences; a third, biology; and a fourth, chemistry (e.g., cold >fusion). What will happen if, for the sake of argument, physics collapses? >Will science fall? > -------------------------------------------------------------------------- > -- >---- >Bjerknes, C.J. (2002), Albert Einstein: The Incorrigible Plagiarist, XTX >Inc., Dowers Grove. >Born, M. (1956), Physics in My Generation, Pergamon Press, London, p. 193. >Brown, G. Burniston (1967), What is wrong with relativity?, Bull. of the >Inst. of Physics and Physical Soc., pp. 71-77. >Carezani, R. (1999), Autodynamics: Fundamental Basis for a New > Relativistic >Mechanics, SAA, Society for the Advancement of Autodynamics. >Carroll, R., Einstein's E = mc2 'was Italian's idea', The Guardian, >November 11, 1999. >Clark, R.W. (1984), Einstein: The Life and Times, Avon Books, New York. >De Pretto, O. (1904), Ipotesi dell'etere nella vita dell'universo, Reale >Istituto Veneto di Scienze, Lettere ed Arti, Feb. 1904, tomo LXIII, parte >II, pp. 439-500. >Einstein, A. (1905a), Zur Elektrodynamik bewegter K.9arper (On the >Electrodynamics of Moving Bodies), Annalen der Physik 17:37-65. >Einstein, A. (1905b), Does the Inertia of a Body Depend on its Energy >Content?, Annalen der Physik 18:639-641. >Einstein, A. (1907), .86ber die vom Relativit.8atspringzip geforderte > Tr.8agheit >der Energie, Annalen der Physik 23(4):371-384 (quote on p. 373). >Einstein, A. (1935), Elementary Derivation of the Equivalence of Mass and >Energy, Bull. Amer. Math. Soc. 61:223-230 (first delivered as The > Eleventh >Josiah Willard Gibbs Lecture at a joint meeting of the American Physical >Society and Section A of the AAAS, Pittsburgh, December 28, 1934). >Hawking, S., Person of the Century, Time Magazine, December 31, 1999. >Ives, H.E. (1952), Derivation of the Mass-Energy Relation, J. Opt. Soc. >Amer. 42:540-543. >Keswani, G.H. (1965), Origin and Concept of Relativity, Brit. J. Phil. >Soc. 15:286-306. >Mackaye, J. (1931), The Dynamic Universe, Charles Scribner's Sons, New > York, >pp. 42-43. >Maddox, J. (1995), More Precise Solar-limb Light-bending, Nature 377:11. >Moody, R., Jr (2001), Plagiarism Personified, Mensa Bull. 442(Feb):5. >Newton, Sir Isaac (1704), Opticks, Dover Publications, Inc., New York, p. >cxv. >Nordman, C. (1921), Einstein et l'univers, translated by Joseph McCabe as >Einstein and the Universe, Henry Holt and Co., New York, pp. 10-11, 16 >(from Bjerknes, 2002). >Poincar.8e, J.H. (1905), The Principles of Mathematical Physics, The > Monist, >vol. XV, no. 1, January 1905; from an address delivered before the >International Congress of Arts and Sciences, St Louis, September 1904. >Poor, C.L. (1930), The Deflection of Light as Observed at Total Solar >Eclipses, J. Opt. Soc. Amer. 20:173-211. >The Internet Encyclopedia of Philosophy, Jules Henri Poincar.8e (1854-1912), >at http://www.utm.edu/research/iep/p/poincare.htm. >Webster, N. (1947), Webster's New International Dictionary of the English >Language, Second Edition, Unabridged, p. 1878. >About the Author: >Richard Moody, Jr, has a Master's Degree in Geology, is the author of > three >books on chess theory and has written for the Mensa Bulletin. For the past >four years, he has done intensive research into Albert Einstein. He can be >contacted by email at Slmrea@aol.com. >peace is of the pi, >d8>D >There was a young lady named bright, >Who's speed was much faster than light, >She departed one day, >In a relative way, >And returned on the previous... >Big, black hole of Night! === Subject: SIMPLEX question Can I use the SIMPLEX method to solve the following type of problem: My variables in this case are restricted to integer elements from a small set: e.g. xi in { 1,2,3,5,7,9,11,13}. So instead of the normal terms used in SIMPLEX: e.g. ci*xi with c = constant and xi = real variable I replace it with 1*x1 + 2*x2 + 3*x3 + 5*x4 + 7*x5 + 9*x6 + 11*x7 + 13*x8 with additional constraints 0.0 <= xi <= 1.0 x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 = 1.0 My CONJECTURE is that SIMPLEX will always find optimization on constraint boundries, so all xi's will either be 0 or 1. My actual problem is NP-Complete, so I believe this approach will still be faster than a non-polynomial algorithm. James === Subject: Re: SIMPLEX question With the Simplex (for LP) method only the non-basic variables are at their bounds. The basic variables (there are m of them; where m is the number of constraints) are between their bounds. ---------------------------------------------------------------- Erwin Kalvelagen erwin@gams.com, http://www.gams.com/~erwin ---------------------------------------------------------------- === Subject: Cyclic group & isomorphism Can you show me an isomorphism between Z and the set / S={ |1-z -z | s.t. z in Z} | z 1+z| / ?? If no, can you show me a way to prove that S is cyclic ?? === Subject: Re: Cyclic group & isomorphism >Can you show me an isomorphism between Z and the set > / >S={ |1-z -z | s.t. z in Z} > | z 1+z| > / What is the product of two elements of S (say the one corresponding to z1 and the one corresponding to z2)? >If no, can you show me a way to prove that S is cyclic ?? ************************ David C. Ullrich === Subject: Re: Cyclic group & isomorphism > Can you show me an isomorphism between Z and the set > / > S={ |1-z -z | s.t. z in Z} > | z 1+z| > / > ?? You have not specified, what group structure you want to have for S. I assume, that you want to exhibit S as a subgroup of GL(2,Z) with multiplication. Calculate the product of two matrices from S. This should again give a matrix in S. Once you have done that, the desired isomorphism will be obvious to you. Of course, since you already described the matrices from S via some sort of parametrization / z --> |1-z -z | | z 1+z| / the map may already be obvious to you; still you need to check, that it is compatible with the group operations. Marc === Subject: Re: Cyclic group & isomorphism >Can you show me an isomorphism between Z and the set > / >S={ |1-z -z | s.t. z in Z} > | z 1+z| > / The _set_ Z and the set S are isomorphic (as sets) by construction: you have written down the isomorphism. >If no, can you show me a way to prove that S is cyclic ?? I don't know what you'd mean by a cyclic set (and I bet you don't, either). If you want to show that the set S (as you put it) is a cyclic _group_, then you should say what the group operation is. Then, if you have the wit to do so, you might try checking whether or not your given set isomorphism is a group isomorphism. Alternatively, you might just want to drop this course and take up another subject of study altogether. Lee Rudolph === Subject: Re: Cyclic group & isomorphism Lee Rudolph ha scritto nel messaggio >Can you show me an isomorphism between Z and the set > / >S={ |1-z -z | s.t. z in Z} > | z 1+z| > / >?? > The _set_ Z and the set S are isomorphic (as sets) by > construction: you have written down the isomorphism. / If you mean F:z in Z |---> |1-z -z | in S | z 1+z| / it isn't true that f(a+b)=F(a)*F(b) (if i consider S(*)) >If no, can you show me a way to prove that S is cyclic ?? > I don't know what you'd mean by a cyclic set (and I bet you > don't, either). If you want to show that the set S (as > you put it) is a cyclic _group_, then you should say what > the group operation is. Yes, I mean cyclic group. I think that the operation is *, the matrix product. === Subject: Re: Cyclic group & isomorphism fake ha scritto nel messaggio > Lee Rudolph ha scritto nel messaggio >>Can you show me an isomorphism between Z and the set >> / >>S={ |1-z -z | s.t. z in Z} >> | z 1+z| >> / >>?? >The _set_ Z and the set S are isomorphic (as sets) by >construction: you have written down the isomorphism. > / > If you mean F:z in Z |---> |1-z -z | in S > | z 1+z| > / > it isn't true that f(a+b)=F(a)*F(b) (if i consider S(*)) No, sorry. I was wrong. Sorry again. === Subject: Re: Cyclic group & isomorphism >[...] > / > If you mean F:z in Z |---> |1-z -z | in S > | z 1+z| > / > it isn't true that f(a+b)=F(a)*F(b) (if i consider S(*)) Sure? Marc === Subject: Why They R Not: CREEP in office in drag You'd think, the continuous fly on the ceiling coverage by Bob Strep Throat Woodward makes it fatuously plain, but Chairman George at Watergate (Ch.12) is the best expose of the one-party state. See http://tarpley.net for the '92 bio. (first-ever unauthorized). And, don't forget the Parrot Act, which is being promoted by cutesie lies, polls and statistics, in your local paper of record; is it not? about the MLM format of the party, which was apparently prototyped in 2002 .9a and it seems to have been used by Howie Troisieme; things that make y'go, Hm. It looks as if all of the vibrant pod-people are going to get a whole, GNU lease on life, liberty & property. Clearly, this newfound volunteerism with its huge slushfunds, combined with the funding of the Dems by Soros and company, there isn't much of an opposition, other than LaRouche (who's still #1, according to the FEC .-) --Give Earth a Trickier Dick Cheeny -- out of office after GIGA years! === Subject: Re: Factoring musings by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3RDeSF13204; n^2 - 1 = 0 mod M 1*(10^13) - 500 and 1*(10^13) in about 4 seconds on a 200 mhz PC. Next the >program outputs the primes between 1*(10^14) - 500 and 1*(10^14) in about 12 >seconds on a 200 mhz PC. Finally, the program (when extended) outputs the >primes between (1*(10^15)) - 500 and 1*(10^15) in about 36 seconds on a 200 >mhz PC. >So how would that time complexity be described ? Since you have not specified the algorithm, your question can not be answered. I will guess, however, that the algorithm is a simple sieve. Therefore, to find the primes in [x-A, x] has complexity 2 sqrt(x)/log(x) + A * loglog (2 sqrt(x)/log(x)). This is exponential in the size of the problem. === Subject: Re: How to get prime greather than given integer? |>The KBH shareware 'Primes from Composite Gaps' outputs the primes between |>1*(10^13) - 500 and 1*(10^13) in about 4 seconds on a 200 mhz PC. Next the |>program outputs the primes between 1*(10^14) - 500 and 1*(10^14) in about 12 |>seconds on a 200 mhz PC. Finally, the program (when extended) outputs the |>primes between (1*(10^15)) - 500 and 1*(10^15) in about 36 seconds on a 200 |>mhz PC. |>So how would that time complexity be described ? | Since you have not specified the algorithm, your question can not | be answered. I will guess, however, that the algorithm is a simple | sieve. Therefore, to find the primes in [x-A, x] has complexity | 2 sqrt(x)/log(x) + A * loglog (2 sqrt(x)/log(x)). This is | exponential in the size of the problem. A simple sieve? a (prime) sieve in the 10^14 range will require one quadtrillion bits. That's a hunka hunka storage (125 trillion bytes, or around 125Gb). There is no 200 mhz PC that has that kind of memory. Keeping the sieve on a harddrive somewhere will cause an inordinate amount of I/O when turning off the bits for composite numbers. I'd be interested in the algorithm in the prime generation. ________Gerard S. === Subject: Re: How to get prime greather than given integer? > The KBH shareware 'Primes from Composite Gaps' outputs the primes between > 1*(10^13) - 500 and 1*(10^13) in about 4 seconds on a 200 mhz PC. Next the > program outputs the primes between 1*(10^14) - 500 and 1*(10^14) in about 12 > seconds on a 200 mhz PC. Finally, the program (when extended) outputs the > primes between (1*(10^15)) - 500 and 1*(10^15) in about 36 seconds on a 200 > mhz PC. > So how would that time complexity be described ? I didn't see responses and was going to say that the time complexity appears to be O(N^2) and that a slower trial-division program also appears to be O(N^2) (but just a slower N^2)... The algorithm begins with 3 (as 'a' for instance) multiplying with each odd number greater than the lowerbound/3 until the current output is greater than the upperbound...then the overall process repeats with the next odd 'a'. Then no more 'a' are needed when 'a' is greater than the square root of the upperbound. Multiplication results (as composite numbers) are put into an array of 500 elements and unassigned odd locations of the array are prime numbers within the numerical range. And that's an approximate description of algorithm from recollection... Actually, the algorithm was developed and posted here in Sept 02 in response to someone else's subject idea. (They suggested a composite output to make a graphical structure and I was making the point that while it is okay to think in terms of a graphical structure that implementation should be in the form of a memory structure. I, of course, posted an algorithm not just an idea for an algorithm while the poser of the subject heading just posted an idea for an algorithm.) === Subject: Re: How to get prime greather than given integer? ||>The KBH shareware 'Primes from Composite Gaps' outputs the primes between ||>1*(10^13) - 500 and 1*(10^13) in about 4 seconds on a 200 mhz PC. Next the ||>program outputs the primes between 1*(10^14) - 500 and 1*(10^14) in about 12 ||>seconds on a 200 mhz PC. Finally, the program (when extended) outputs the ||>primes between (1*(10^15)) - 500 and 1*(10^15) in about 36 seconds on a 200 ||>mhz PC. ||>So how would that time complexity be described ? || Since you have not specified the algorithm, your question can not || be answered. I will guess, however, that the algorithm is a simple || sieve. Therefore, to find the primes in [x-A, x] has complexity || 2 sqrt(x)/log(x) + A * loglog (2 sqrt(x)/log(x)). This is || exponential in the size of the problem. | A simple sieve? a (prime) sieve in the 10^14 range will require | one quadtrillion bits. That's a hunka hunka storage (125 trillion | bytes, or around 125Gb). There is no 200 mhz PC that has that kind of | memory. Keeping the sieve on a harddrive somewhere will cause an | inordinate amount of I/O when turning off the bits for composite numbers. | I'd be interested in the algorithm in the prime generation. ________Gerard S. Oops, I forgot that the 125Gb number for the sieve can be halved by first still a hunka memory. ________________________________________________Gerard S. === Subject: Re: Four Color Theorem Proof Here is a proof of FCT and Hadwiger's Conjecture. http://arxiv.org/abs/math.GM/0311475 And the comments on the proof is here: http://caozx.100free.com/comment.pdf My idea is very simple. I just define a strange space on the adjacent relationship of neighbors and research the relation between the space and its cross-sections, the proof is shown. === Subject: Re: Exterior Dirichlet problem for unbounded regions by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3REghu20166; Did you find the suggested book (by Helms) helpful? I'm interested in a very similar problem. Juan >for the Laplace equation on bounded regions seems to be quite well >studied (Perron's construction, read about this in the book Harmonic >Function Theory by Axler/Bourdon/Ramey). >However, I was unable to find any information concerning solvability >of the external Dirichlet problem for unbounded regions. >Specifically, I have a flat circular disc in R^3, and I would like to >find a function harmonic on R^3 minus that compact set, continuous and >bounded on all of R^3, that has prescribed values on that disc. >I stumbled across this problem in Jackson's Classical >Electrodynamics (problem 3.3), and there seem to be some restrictions >on the boundary values that can yield a solution; in that book, the >boundary condition is a constant value (and 0 at infinity), and the >techniques in the book (expansion of the solution in a series >containing Legendre polynomials) yield contradictory results, so I >suspect this problem is not solvable at all. >Are there any results on this topic? Can anybody give me pointers to >literature? >-- >michael krause - 'raw style ^ farbrausch & lego' - www.soundtracker.org/raw/ > === Subject: @.@ Gaussian integer hello......doctor~ find the order and characteristic Z[i]/<1+i> ------------------------ each coset contains a representative of norm less than N(1+i) = 2 the only elements of Z[i] of norm less than 2 are 1,-1, i ,-i . since i = -1 + (1+i) and -i = 1 - (1+i) , we see that 1+<1+i> and -1+<1+i> are the only cosets. thus, the order of the ring is 2, and the characteristic is 2. ------------------------- um......i can't understand that characteristic is 2. help me......please~ thank you very much. === Subject: Re: @.@ Gaussian integer > hello......doctor~ > find the order and characteristic > Z[i]/<1+i ------------------------ > each coset contains a representative of norm > less than N(1+i) = 2 > the only elements of Z[i] of norm less than 2 > are 1,-1, i ,-i . No they aren't. > since i = -1 + (1+i) and -i = 1 - (1+i) , > we see that 1+<1+i> and -1+<1+i> are the only cosets. No they aren't. > thus, the order of the ring is 2, Actually it is but not by your argument. The characterstic is 2 since 1 =/= 0 in R but 2 = 0 in R, becuase (1+i) is a factor of 2 but not of 1 in Z[i] because.... -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html Lacan, Jacques, 79, 91-92; mistakes his penis for a square root, 88-9 Francis Wheen, _How Mumbo-Jumbo Conquered the World_ === Subject: Re: Suggestion: We should have a sci.math.discrete > Shall we have a specific place to discuss problems on discrete mathematics? Seems a very good idea to me. Felix. === Subject: Re: Virus Warning!! (THIS IS NOT A HOAX) > mike3 >>THIS IS REAL AND NOT A HOAX. For more information go to: >>http://securityresponse.symantec.com/avcenter/venc/data/w32.swen.a@mm.html >>If you get an email titled Microsoft Critical Patch or something >>similar, the attachment [buggers you up]. > I think this is the virus for which Microsoft has posted a 7-figure > reward, for info leading to conviction of the author. (I don't mean > me; I mean the author of the virus.) > If any bigtime professionals in programming are reading this, > they might consider bidding on this ambitious project: > http://www.darpa.mil/ato/programs/dqw.htm > about dynamic quarantine of worms or DQW. But it's Microsoft who are to blame, a lot of the time. The default security settings, in almost all of their software, are so ill-thought-out that they are almost begging for abuse. And as most people who know nothing about the underlying technology of the Internet (hence the btinternet.coms and the tiscali.*s in your list of gretatest hits) tend to use Microsoft products without question, the problem will remain with us for years. Even if Microsoft do bribe people into believing they're the heroes of the situation, there will still be so many people running half-decade-old copies of MS operating systems and Internet software, that we'll still be getting these childish viral worms for a long while to come. How many people on this maths usenet group (i.e. intelligent people outside of computing, not necessarily clued-up about computing) use exclusively Microsoft products? Windows XP / 2000; Outlook / Outlook Express; Internet Explorer; Windows Media Player; etc. There are so many good, alternative software options out there that deserve a chance. Anyone using Mozilla? Linux? FreeBSD? -- Bob London, UK echo Mail fefsensmrrjyaheeoceoq! | tr jefroq! @obe.uk === Subject: Re: Virus Warning!! (THIS IS NOT A HOAX) >>Hello all, >>This seems like a hoax - except that it's real. > Why would you say it looks like a hoax? 99% of viruses use deception to get > users to voluntarily install them. You are new in the Internet, right? (new being defined as you have been using it for less than 5 years) This can not be more exactly like the dozens (possibly hundreds?) of hoaxes that used to flood our mailboxes 6 to 10 years ago, using the chain letter mechanism to propagate. They all (and I mean ALL, quite possibly without a single exception) stated THIS IS NOT A HOAX -- THIS IS REAL... Typically, they continued saying that IBM, or Microsoft, or HP, or whatever big company in the IT world, had announced it; with very specific -- yet phony -- details; they would typically indicate a name for the spokesperson, and the name of a newspaper or an online place where the announcement was; sometimes you would even have a URL link -- if you bother to click on it, it would lead to a 404 error, but the point was that no-one would look at it -- it simply makes it look like it is really authentic, so people would not bother to go and read the news; they would immediately -- with all good intentions, and genuinely thinking that they were doing others a favor -- click on forward and send it to as many people as they knew; the virus succeded in propagating. So yes, if it weren't because I already know this virus (have received possibly more than a thousand copies of it over the past year or so -- and NO, I'm NOT exaggerating), I would have been willing to bet half my salary that it was a hoax. Carlos -- === Subject: Re: Virus Warning!! (THIS IS NOT A HOAX) >>Hello all, >>This seems like a hoax - except that it's real. >Why would you say it looks like a hoax? 99% of viruses use deception to get >users to voluntarily install them. > You are new in the Internet, right? (new being defined as > you have been using it for less than 5 years) > This can not be more exactly like the dozens (possibly hundreds?) > of hoaxes that used to flood our mailboxes 6 to 10 years ago, > using the chain letter mechanism to propagate. > They all (and I mean ALL, quite possibly without a single > exception) stated THIS IS NOT A HOAX -- THIS IS REAL... > Typically, they continued saying that IBM, or Microsoft, > or HP, or whatever big company in the IT world, had announced > it; with very specific -- yet phony -- details; they would > typically indicate a name for the spokesperson, and the name > of a newspaper or an online place where the announcement was; > sometimes you would even have a URL link -- if you bother to > click on it, it would lead to a 404 error, but the point was > that no-one would look at it -- it simply makes it look like > it is really authentic, so people would not bother to go and > read the news; they would immediately -- with all good > intentions, and genuinely thinking that they were doing others > a favor -- click on forward and send it to as many people as > they knew; the virus succeded in propagating. > So yes, if it weren't because I already know this virus > (have received possibly more than a thousand copies of it > over the past year or so -- and NO, I'm NOT exaggerating), > I would have been willing to bet half my salary that it was > a hoax. I'm not even sure what your point is. Fact is, I can't see how anyone would be surprised it was a real virus unless they had just started using email a few months ago or something. After your 50th message entitled Where were you last night? (or similar) with ads for viagra inside I think most people the truth. l8r, Mike N. Christoff === Subject: Re: Virus Warning!! (THIS IS NOT A HOAX) >>If you get an email like Microsoft Critical Patch or Microsoft >>Security Update, DO NOT OPEN THE ATTACHMENT! >>Microsoft does NOT send out patches via email. > And in other news, Francisco Franco is still dead. Well, you have to give it some credit. It is extremely remarkable the fact that some virus warning that says in capital letters THIS IS NOT A HOAX was indeed an actual, legitimate virus, as claimed by the message! I'm still deeply impressed by this!!! I'm still having a really hard time believing it!! :-) Carlos -- === Subject: Re: Virus Warning!! (THIS IS NOT A HOAX) >If you get an email like Microsoft Critical Patch or Microsoft >Security Update, DO NOT OPEN THE ATTACHMENT! >Microsoft does NOT send out patches via email. >> And in other news, Francisco Franco is still dead. >That's Generalissimo Francisco Franco to you. Typical mathematician, always looking for the greatest generality. Lee Rudolph === Subject: Re: Virus Warning!! (THIS IS NOT A HOAX) > THIS IS REAL AND NOT A HOAX. For more information go to: > http://securityresponse.symantec.com/avcenter/venc/data/w32.swen.a@mm.html > If you get an email titled Microsoft Critical Patch or something > similar, the attachment, upon opening, appears to be an install for a > legitimate patch. But it's not. It's a virus called W32.Swen.A@mm. > Once you open it, the only way to avoid getting infected is to turn > off your computer. Otherwise, if you click on any of the buttons, IT > WILL STILL INSTALL. It will then prompt for passwords and email > adresses using phony error mesage boxes and proceed to email more > copies to your friends. It will also disable anti-virus or firewall > software. > If you get an email like Microsoft Critical Patch or Microsoft > Security Update, DO NOT OPEN THE ATTACHMENT! It is a DANGEROUS virus > as it disables your security apps. I've been getting these in my email > and the scanner said it was a virus. Messages with subjects like > failure delivery notice may also contain it and it will infect your > computer by merely OPENING the message if you use Outlook or Outlook > Express for your email. This is NOT a hoax this is 100% real. > Microsoft does NOT send out patches via email. Bit late, aren't you? I've been getting that thing for more months than I care to remember. Does anyone know what virus creates the Undeliverable message emails that are about 142K, but have only a few words of text in them? Where is the rest of the data concealed? That one's been bugging me for about as long... === Subject: Re: Virus Warning!! (THIS IS NOT A HOAX) >THIS IS REAL AND NOT A HOAX. For more information go to: >http://securityresponse.symantec.com/avcenter/venc/data/w32.swen.a@mm.html >[...] >If you get an email like Microsoft Critical Patch or Microsoft >Security Update, DO NOT OPEN THE ATTACHMENT! It is a DANGEROUS virus >[...] Every once in a while the sysadmin in the math department sends out a warning about some new virus, giving details about exactly what we should not open. I usually reply all, suggesting that keeping a list in mind, don't open things if they have this subject line or whatever, is a bad idea. The only safe plan is to ignore _all_ executable attachments. (And make certain your email program also ignores them - that means avoid software that tries to be helpful by doing things for you before you ask, MS software in particular.) ************************ David C. Ullrich === Subject: Re: Virus Warning!! (THIS IS NOT A HOAX) says... > THIS IS REAL AND NOT A HOAX. For more information go to: > http://securityresponse.symantec.com/avcenter/venc/data/w32.swen.a@mm.html > If you get an email titled Microsoft Critical Patch or something > similar, the attachment, upon opening, appears to be an install for a > legitimate patch. But it's not. It's a virus called W32.Swen.A@mm. > Once you open it, the only way to avoid getting infected is to turn > off your computer. Otherwise, if you click on any of the buttons, IT > WILL STILL INSTALL. It will then prompt for passwords and email > adresses using phony error mesage boxes and proceed to email more > copies to your friends. It will also disable anti-virus or firewall > software. > If you get an email like Microsoft Critical Patch or Microsoft > Security Update, DO NOT OPEN THE ATTACHMENT! It is a DANGEROUS virus > as it disables your security apps. I've been getting these in my email > and the scanner said it was a virus. Messages with subjects like > failure delivery notice may also contain it and it will infect your > computer by merely OPENING the message if you use Outlook or Outlook > Express for your email. This is NOT a hoax this is 100% real. > Microsoft does NOT send out patches via email. Hmmm. I've been subscribed to this virus for a LONG time now, and now it seems like most e-mail services have installed anti-virus or Anyway, I'm using DrWeb's SpIDer mail, so instead of any virus I got such a message: --------------------------------- A message that was sent to you cannot be delivered. It was infected with Win32.HLLM.Gibe.2 virus. Message has been deleted. -- SpIDer Mail Anti-Virus (http://www.drweb.net, http://www.dials.ru) --------------------------------- Pity of course that the whole message is deleted, it could at least leave out the text. I'm also using The Bat!, and it's got its own HTML rendering engine with absolutely no Java/JS/whatever support - who needs those in e-mails anyway >:] But I was very amused by all the fake text the latest NetSky-based viruses put in the letters. While the first e-mail worms were simply putting see attached, the first NetSky was adding i found this document about you, here, the serials, you are a bad writer, etc. Now the latest variants come up with something like your paycheck or the letter could not be delivered, please open it from here: and eg. a link to the attached file, with the text www.yourmailserver.com/youraccount/inbox/message123.txt. Some even add some fake text about the message being checked by some anti-virus >:] Norton AntiVirus is a bunch of senseless code, it's got absolutely no heuristic virus recognition and it found only half of viriis from my virii folder. The large number of known viruses is achieved by adding programs like key-gens, cracks, patches and even some debuggers to the database. The best AV software is IMO Kaspersky's AVP and DrWeb (both developed by Russians), but AVP costs much (it's commercial IIRC). DrWeb also is updated daily, and its update takes seconds even on dial-up (in contrast to Norton). Although its scanning algorythm is slow and its monitor slows down the system. Also, registration keys that become public are always disabled in the next version >:] I also heard that the Romanians developed a nice anti-virus (RAV). -- Knowledge belongs to the World. That's why I'm here for. http://wercorporation.da.ru/ === Subject: How to generate a covariance matrix S uniformly on det(S) = 1? Does anyone know how to generate a covariance matrix S uniformly on det(S) = 1? Any help is appreciated. Mike === Subject: Re: How to generate a covariance matrix S uniformly on det(S) = 1? >Does anyone know how to generate a covariance matrix S uniformly on >det(S) = 1? Any help is appreciated. Covariance matrices are positive semidefinite, and are definite with probability 1 if there are as many degrees of freedom as the size. I have no idea what a uniform distribution could possibly be on these. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: mass density >Does everyone know the SI unit, symbol and name for mass density, and >what it is the density of? It is mass per unit volume, in SI units kg/m^3, usually called simply the density. -- When the fool walks through the street, in his lack of understanding he calls everything foolish. -- Ecclesiastes 10:3, New American Bible === Subject: Re: mass density > In sci.physics, Donald G. Shead > what it is the density of? > There is none. A derived unit might be kg/m^3. > I'd have to look regarding the name thereof. Good Heavens; don't do anything drastic. I was just wondering what the kg/m^3, SI mass density applied to: Like would it be the mass density of platinum or lead or something? Nobody seems willing or able to answer so I guess I'll just have to write to the people who know: Like NIST, the U S Metric Association, or maybe the archives at Sevres France. Think they know(;^? === Subject: Re: mass density W++ N+++ o+ K+++ w--- O? M+ V? PS+ PE++ Y+ PGP+ t++@* 5++ X++ R tv+ b++++ DI+ D+ G++ e>++++ h!>++ !r !y NFb(%f3xP0Q'p9!&!.hjA9Si:6MnDUkP%E&>u]_Q7J&v G. Shead teithant i thiw hin: > I was just wondering what the kg/m^3, SI mass density applied to: Like > would it be the mass density of platinum or lead or something? It applies to any substance with mass and volume. Why are you having so much trouble with grade-school physics concepts? -- Xaonon, EAC Chief of Mad Scientists and informal BAAWA, aa #1821, Kibo #: 1 http://xaonon.dyndns.org/ Guaranteed content-free since 1999. No refunds. This feels great! I never knew the Stockholm Syndrome could be so enjoyable, and (bzzt) YAAAAAAAAAAAAGGGGHHHH!!!!!! -- Spot === Subject: Re: mass density >In sci.physics, Donald G. Shead > Does everyone know the SI unit, symbol and name for mass density, and >> what it is the density of? >There is none. A derived unit might be kg/m^3. >I'd have to look regarding the name thereof. > Good Heavens; don't do anything drastic. > I was just wondering what the kg/m^3, SI mass density applied to: Like > would it be the mass density of platinum or lead or something? Nobody > seems willing or able to answer so I guess I'll just have to write to > the people who know: Like NIST, the U S Metric Association, or maybe > the archives at Sevres France. Think they know(;^? Dumb Donny Head, you are a terrible idiot. Contract for a seat in public school physics. Density is intensively covered around 4th grade. Archimedes correctly worked it through his head in ~240 BC. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) Quis custodiet ipsos custodes? The Net! === Subject: Re: mass density Cut< you are a terrible idiot. Contract for a seat in > public school physics. Density is intensively covered around 4th > grade. Archimedes correctly worked it through his head in ~240 BC. You are a chemist Uncle Ducaca: Surely you must know what the kg/m^3, SI mass density applies to: Like how does it compare to the density of pure water; which I always thought was the standard of density - One pound divided by one foot per second^2 = one dyne divided by one centimeter per second^2 = one newton divided by one meter per second ^2 - which is the density to which the density of platinum; lead, and other things is compared to get their density relative to it: Isn't that the basis of the hydometer? Wouldn't a kg/m^3 be about the lightest of all substances? Wouldn't it not only float on water, but also on the thinest of air? Or have I got that backwards? === Subject: Re: convexity question >Let E be a convex set in R^n and let U be the set of all x in R^(n-1) >such that (x, y) is in E for some y in R^1. How can we construct a C' >function alpha from U into R^1 such that (x, alpha(x)) is in E for all >x in U? > We can't, not even if E is compact. Consider the case n=3 where E > is the convex hull of one turn of a helix > {(cos(t), sin(t), t): 0 <= t <= 2 pi}. Then U is the disk > {(x,y): x^2 + y^2 <= 1}. For 0 < t < 2 pi, > (cos(t), sin(t), t) is the only point of E that projects down to > (cos(t),sin(t)), so we'd need alpha(cos(t), sin(t)) = t. But of course > this is not continuous at (1,0). > Robert Israel israel@math.ubc.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia > Vancouver, BC, Canada V6T 1Z2 I'm sorry. I forgot to add that E is open. === Subject: Re: convexity question >>Let E be a convex set in R^n and let U be the set of all x in R^(n-1) >>such that (x, y) is in E for some y in R^1. How can we construct a C' >>function alpha from U into R^1 such that (x, alpha(x)) is in E for all >>x in U? >I'm sorry. I forgot to add that E is open. For x in U, {y in R: (x,y) in E} is a nonempty open interval, say (a(x), b(x)). Note that a is convex and b is concave, so both are continuous on the convex open set U. Construct a smooth partition of unity in U, i.e. a sequence of smooth functions f_j such that sum_j f_j(x) = 1 for all x in U, each f_j has compact support K_j and each compact subset of U intersects only finitely many K_j. In addition we require that max_{x in K_j} a(x) < min_{x in K_j} b(x) for all j. Then taking c_j so max_{x in K_j} a(x) < c_j < min_{x in K_j} b(x) we let alpha(x) = sum_j c_j f_j(x). Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === Subject: Re: Definition of structure. > A structure is usually defined to be something like this: > because there is no single underlying set which all the functions are > defined on. > What's a better definition? Use a many-sorted structure, where the signature defines which sorts there are and which sorts are supposed to appear as which argument of functions/relations etc. Each sort is the represented by a separate set. Should be in any book on universal algebra. Stephan === Subject: Re: Definition of structure. >A structure is usually defined to be something like this: >because there is no single underlying set which all the functions are >defined on. >What's a better definition? > Use a many-sorted structure, where the signature defines which > sorts there are and which sorts are supposed to appear as > which argument of functions/relations etc. > Each sort is the represented by a separate set. That's what I thought, but other replies fancied another approach. > Should be in any book on universal algebra. > Stephan -- G.C. === Subject: Re: geophysics/math Ph.D. proposal, comments desired. > I'm currently editing my geophysics/applied math Ph.D. proposal > and would like comments back, At my proposal defense this morning I talked for 15 minutes and they asked not too tough questions. Then the examining committee talked for over an hour after I left and then my supervisor came and told me I had passed, but they expected more work out of me (I performed well from Sept02 to April03 but from May03 to March04 not as well, and reasonably well the last month). David http://www.nfld.com/~dalton === Subject: Re: analysis >>Let f(x) = e^(-1/x) if x >0 , 0 if x <=0. Using the definition of >>derivatives I need to find a formula for f ^(n) (x) for x >0 and prove that >>f ^(n) (0) = 0 for all positive integers n. The derivatives get messy real >>quickly, so what is the trick? >Start by showing that lim (x->0+)x^n*e^(-1/x) = 0 for *any* n>=0. Next Oops, that should be: lim (x->0+)(1/x)^n * e^(-1/x). This is equivalent to showing that lim (u->oo) u^n * e^(-u) = lim (u->oo) u^n / e^u = 0 for all n>=0. Maybe you see a l'Hospital lurking... >proceed inductively. Show that if f ^(n) (x) = P_n(x)*e^(-1/x) then f ^^^^^^ P_(n)(1/x) >^(n+1) = P_(n+1)(x)*e^(-1/x) whre P_(n+1) again is a polynomial. You ^^^^^^^ P_(n+1)(1/x) >*don't* have to calculate these Polynomials explicitly. Thomas === Subject: Re: analysis >Let f(x) = e^(-1/x) if x >0 , 0 if x <=0. Using the definition of >derivatives I need to find a formula for f ^(n) (x) for x >0 and prove that >f ^(n) (0) = 0 for all positive integers n. The derivatives get messy real >quickly, so what is the trick? This question has been coming up a lot lately... >Steve ************************ David C. Ullrich === Subject: Eventually-Prime Bump-then-Decrement Sequences [re-posted, with corrections] Goodstein sequences use hereditary base-b representations (http://mathworld.wolfram.com/HereditaryRepresentation.html http://mathworld.wolfram.com/GoodsteinSequence.html). I'm curious what sort of sequences result if we use a similar concept of hereditary prime factorization together with iteration of some suitable bump-then-decrement operation. (Unlike Goodstein sequences, these won't have the nice correspondence with ordinals in Cantor normal form.) Suppose we define the Hereditary Prime Factorization (HPF) of natural number n > 1 as follows: n = p_1^a_1 * p_2^a_2 * ... * p_k^a_k where p_1 < ... < p_k are primes *and* each a_i is expressed in this same form, and so on, until the entire expression on the righthand side contains only prime numbers. Example: 5184 = 2^6*3^4, so HPF(5184) = 2^(2*3)*3^(2^2). Now suppose we iterate a bump-then-decrement operation as follows, starting with natural number n > 1: (1) write the hereditary prime factorization of n; (2) for *every* prime p appearing in (1), replace p by p+1; (3) decrement by 1 the result of (2); (4) let n equal the result of (3) and repeat (1)-(4); *************** Such a sequence must either diverge (increase monotonically without bound), or converge to a prime. That is, if it does not diverge, it must eventually -- within a finite number of terms -- reach & fix on some prime, the primes being the fixed points of the bump-then-decrement operation.) Does every such sequence eventually reach a prime? *************** Examples: n = 4 = 2^2 (HPF) -> 3^3-1 = 2*13 (HPF) -> 3*14-1 = 41 (prime) n = 8 = 2^3 (HPF) -> 3^4-1 = 2^(2^2)*5 (HPF) -> 3^(3^3)*6-1 = 7*6536226415703 (HPF) -> 8*6536226415704-1 ... -> 132325733928959 (prime) n = 5184 = 2^(2*3)*3^(2^2) (HPF) -> 3^(3*4)*4^(3^3)-1 = 7*11*17*43*73*271*419*463*6553*6763 (HPF) -> 8*12*18*44*74*272*420*464*6554*6764-1 = 101*587*751*4283*69330903349 (HPF) -> 102*588*752*4284*69330903350-1 = 29*461927333701231901131 (HPF) -> 30*461927333701231901132-1 = 13857820011036957033959 (prime) Here are some results for small non-prime n (#terms is the number of terms up to and including the eventual prime): n #terms eventual prime -- -------- ---------------- 4 3 41 6 2 11 8 11 132325733928959 9 5 743 10 2 17 12 2 107 14 2 23 15 2 23 16 13 25547547504383 18 2 191 20 3 191 21 2 31 22 3 47 24 3 359 25 3 263 26 2 41 27 3 431 28 3 263 30 2 71 32 4 9311 ************** Does every n > 1 produce a sequence that's eventually prime? If not, what is the least exceptional n? ************** --r.e.s. === Subject: Re: Algebra vs. algebraic structure (request for clarification) > Neither algebra nore algebraic structure has any clearcut meaning > that is generally agreed. Terms with generally accepted meanings are > in order of expressiveness, equational strucutre (described by > operations and equations, such as groups), Horn structure (you are > also allowed inferences among equations, such as nx = 0 implies x = 0, > e.g. torsion free abelian groups), nearly equational (there are also > partial operations, but the domains must be describable in terms of > other operations or partial operations, e.g. categories in which the > domain of composition is source(g) = target(f) in order that fg be > defined), regular theory in which, in additional, existential > quantifiers are permitted (e.g. regular rings characterized by Ax,Ey > xyx = x) and first order theories (e.g. fields whose theory contains a > disjunction: x = 0 or x has an inverse). There are also higher order > theories, such as topological spaces in which you quantify over > subsets. By in order of expressiveness I presume you mean increasing order, with equational structure being least expressive. Is your list also a subset chain, so that (< here means subset): equational structures < Horn structures < nearly equational structures < regular theories < first order theories < higher order theories? Then algebra would refer to equational structure, and algebraic structure could refer to any of them, most generally to higher order theory but in typical usage more commonly to first order theory or regular theory, yes? === Subject: Re: Centroid or Centre of Gravity of a wire/arc >> The original poster was looking for a formula for the distance >> of the centroid from the center of the arc. I gave the required >> formula. Your calculations are correct as well, but are not >> directly relevant to the original inquiry. >was looking for... >However, would you be kind enough to show how you arrived at >2*R*SIN(theta * 0.5) / theta, theta * 0.5 >being the coordinates of the centroid relative to the centre of the >arc. The theta * 0.5 is the line of symmetry of the arc.... > I don't want to run the risk of doing someone else's homework problem > and short-circuiting their learning process. > If you state what you have attempted so far, I will be glad to > provide corrections and suggestion. Oh believe me I have tried numerous times but for some reason I am having a metal block on this. The closest I came to calculating the distance from the centre of the arc was 0.25 * R * (theta + sin(theta)) / sin (thetha * 0.5) I calculated this in the following way (I now know its wrong)... I made the wrong assumption that the centre of gravity of an arc(wire) can be found from the area of the arc. This area is the area under the arc if you draw a line from the start to the end of the arc (call this line SE). I assumed theta to be less than PI not to complicate matters. Once I had that area I divided it by the length SE to get the height of a rectangle with the same area. Call this distance H. I then added to this height the distance from the centre of the arc to the midpoint of SE to get the distance of the centroid from the centre of the arc. What I had calculated really was the centroid of a region bounded by the arc and SE not the centroid of the wire... I am still at a loss as to how to calculate the COG of a wire? This is not a homework assignment anyway but for programming purposes...:) === Subject: Re: Centroid or Centre of Gravity of a wire/arc However, would you be kind enough to show how you arrived at > 2*R*SIN(theta * 0.5) / theta, theta * 0.5 > being the coordinates of the centroid relative to the centre of the > arc. The theta * 0.5 is the line of symmetry of the arc.... Look up formula in mechanics of materials/elementary calculus books : (x or y)bar= integral((x or y) ds)/integral ds where s is arc length of wire. After this is over, proceed to find xbar,ybar for the sectorial area. === Subject: You can have him back Hello sci.math, Your resident kook has escaped. === Subject: Odd little factorization result I kept at the factoring idea, and this time I have checked, re-checked and double-checked my algebra, and I'm curious to know if any of you have ever seen anything like this before: (jk - Mk + M)(jk + Mk + M) = M^4 [...] Please, please, please, do take him back ;-) === Subject: Modular arithmetic on a sphere? Traditional arithmetic operates on a line. Modular arithmetic operates on a circle. ??? arithmetic operates on a sphere. That pretty much sums up my question, but in case you're confused, here's some elaboration: I'm interested in finding a better way to work with points on a sphere. Modular arithmetic is in a sense a ideal way work with points on a circle, since it contains at it's core the idea of circularity. Is there an arithmetic model that is build on the idea of sphericality? Would it be possible to develop one? Initially I thought using spherical coordinates with two modular angles might work. But there is a dependence between the two angles that should, I believe, be part of the model... Any ideas, complete or incomplete are welcome! Nathan === Subject: Re: Modular arithmetic on a sphere? >Traditional arithmetic operates on a line. >Modular arithmetic operates on a circle. >??? arithmetic operates on a sphere. Ix-nay on that. You can't define a continuous binary operation F : S x S ---> S under which the ordinary 2-sphere S becomes a topological group (using the usual topology for S). Oh, you could observe that S is isomorphic to the real line _as sets_ and use that to describe the set S as a group, but I don't think you are going to want that. By contrast, you CAN turn the 3-sphere (the one that sits naturally in R^4) into a topological group, by viewing it as the group of unit quaternions. The fact that you can't do what you want with the 2-sphere but you can do it if you jump up to the 3-sphere has caused at least one Irish bridge to be defaced by a graffiti artist. dave === Subject: Re: Modular arithmetic on a sphere? >Traditional arithmetic operates on a line. >Modular arithmetic operates on a circle. >??? arithmetic operates on a sphere. >That pretty much sums up my question, but in case you're confused, >here's some elaboration: >I'm interested in finding a better way to work with points on a sphere. >Modular arithmetic is in a sense a ideal way work with points on a >circle, since it contains at it's core the idea of circularity. Is there >an arithmetic model that is build on the idea of sphericality? Would it >be possible to develop one? You left out complex arithmetic operates in a plane. One of my HS math teachers had a diagram on his wall showing a coordinate system for the surface of a sphere which had (0,0) at one pole and (oo, oo) at the opposite. A consequence of this was that -oo = +oo, and hyperbolae actually became closed curves. If this coordinate system had a name, I don't remember. >Initially I thought using spherical coordinates with two modular angles >might work. But there is a dependence between the two angles that >should, I believe, be part of the model... What do you want to do with this? You can think of a sphere in terms of latitude and longitude determining a point, but that doesn't make it obvious that if you travel 2*pi*r in any direction you'll come back to your starting point. --Keith Lewis klewis {at} mitre.org The above may not (yet) represent the opinions of my employer. === Subject: Re: Modular arithmetic on a sphere? >Traditional arithmetic operates on a line. >Modular arithmetic operates on a circle. >??? arithmetic operates on a sphere. >That pretty much sums up my question, but in case you're confused, >here's some elaboration: >I'm interested in finding a better way to work with points on a sphere. >Modular arithmetic is in a sense a ideal way work with points on a >circle, since it contains at it's core the idea of circularity. Is there >an arithmetic model that is build on the idea of sphericality? Would it >be possible to develop one? > You left out complex arithmetic operates in a plane. > One of my HS math teachers had a diagram on his wall showing a coordinate > system for the surface of a sphere which had (0,0) at one pole and (oo, oo) > at the opposite. A consequence of this was that -oo = +oo, and hyperbolae > actually became closed curves. > If this coordinate system had a name, I don't remember. That's called the Riemann sphere. If you take the complex plane and then sit a sphere on top of it, with the south pole touching the origin of the plane, you correspond points by drawing a straight line from the north pole through the sphere to the plane. The points of intersection of the line with the sphere and the plane are the points that correspond to each other. You can see that the equator corresponds to the unit circle. As a point on the plane wanders off to infinity, plus or minus, the corresponding point on the sphere wanders off to the north pole. This makes sense, since there are no positive or negative complex numbers, therefore only one infinity. There are a lot more nice properties, which you can easily Google. The spherical representation of complex numbers is often used in math. === Subject: Definition of point. I believe that Euclid defined a point as that which has no size. Can any sense be made of this in modern terms? -- G.C. === Subject: Re: Definition of point. > I believe that Euclid defined a point as that which has no size. Can > any sense be made of this in modern terms? > -- > G.C. According to Professor Irwin Corey, the world's foremost authority: [After the Professor rambled aimlessly for a while] Merv Griffin: And what's the point, Professor? Professor: The point -- is the sharp end of a pencil. And seriously, a point is to me a postulated primitive in an axiomatic theory, along with lines, incidence relation etc. No mention about its size, mainly because some of these theories have models where, when illustrated, a point looks like a line, and a line looks like a point, and after an interpretation of axioms, everything fits together. In some (useful) spaces, a point looks like a function. And to make things worse, mathematicians also study pointless (seriously: point-free) geometries. See G. Gerla, R. Volpe, Geometry without points, The American Mathematical Monthly, 92 (1985) 707-711. and http://www.dmi.unisa.it/people/gerla/www/Down/grad_incl_pg.pdf And what's the point? :-)= === Subject: Re: Definition of point. > I believe that Euclid defined a point as that which has no size. Can > any sense be made of this in modern terms? A point is that which has no part. I.e. cannot be subdivided into smaller objects. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ === Subject: Re: Definition of point. >I believe that Euclid defined a point as that which has no size. Can >any sense be made of this in modern terms? > A point is that which has no part. I.e. cannot be subdivided into > smaller objects. -- G.C. === Subject: Re: How to get prime greather than given integer? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i3RIBZk11288; snip >|| Since you have not specified the algorithm, your question can not >|| be answered. I will guess, however, that the algorithm is a simple >|| sieve. Therefore, to find the primes in [x-A, x] has complexity >|| 2 sqrt(x)/log(x) + A * loglog (2 sqrt(x)/log(x)). This is >|| exponential in the size of the problem. >| A simple sieve? a (prime) sieve in the 10^14 range will require >| one quadtrillion bits. That's a hunka hunka storage (125 trillion >| bytes, or around 125Gb). snip No. Read the problem. You are not sieving from 2 to 10^14, you are sieving from 2^14-500 to 2^14. The sieve length is just 500 (variable A from above) You need the primes to sqrt(10^14). The time to sieve from 2 to y is y/log y using Schroeppel's sub-linear sieve. The time to create primes to sqrt(x) is therefore sqrt(x)/log(sqrt(x)) as stated. This requires only 10^7 bits of space. One merely sieves an interval of length A using primes up to sqrt(x). This takes the time I gave above. Furthermore, even if sieving from 2 to 10^14, you can do it in chunks of convenient size. i.e. sieve from 2 to 10^10, then from 10^10 to 2*10^10 etc. Large memory is not required. === Subject: Re: Richard Lloyd Morin - July 7th 1983 > Oh dear, hear Flip flip out, such anger. What > could have prompted such anger? insists upon going where no one wants him? But you already know what you are and why you're always unwelcome, Kabatoff. You just don't care. -- Wayne Brown (HPCC #1104) | When your tail's in a crack, you improvise fwbrown@bellsouth.net | if you're good enough. Otherwise you give | your pelt to the trapper. e^(i*pi) = -1 -- Euler | -- John Myers Myers, Silverlock === Subject: Re: @.@ topology~ >show that >A<=>every infinite subset of A has an accumulation point in A. >(<=) it's trivial~ right ?? Not without some assumptions, which might be part of the (=>) um.....if countable subset of A , trivial >because, sequentially compact => countably compact => has limit point >right ?? No need to bring countably compact into the picture. A limit of a convergent subsequence is a cluster point. >if uncountable subset of A, i can't prove~ >how to prove it ? Any infinite set has a countable subset. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === Subject: Re: @.@ topology~ >> A> <=>every infinite subset of A has an accumulation point in A. >Consider were A the rationals. How does that help? Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === Subject: Finite group acting on a lattice Adjunct Assistant Professor at the University of Montana. A friend asked a question which then led me to the following situation: Let G be a finite group, and let it act faithfully on a finite lattice L. We can think of the lattice as Z^n, with Z the infinite cyclic group and n>0 an integer, so G will be represented by n x n matrices with integer coefficients and determinant equal to 1 or -1. The group ring Z[G] naturally acts on Z^n as well; and the group algebra Q[G] will act on Q tensor Z^n = Q^n. Let u in Q[G] be such that u is an automorphism of Q^n, and maps lattice points to lattice points (so u maps Z^n to Z^n). QUESTION: Must u be an element of Z[G] multiplied by a nonzero rational? For example: say n=1. Then every element of G must act as either the identity or minus the identity. Since the action is faithful, that means that G is either trivial or cyclic of order 2. If G is trivial, then u in Q[G] maps the lattice to itself if and only if u in Z, so the answer is yes. If G is cyclic of order 2, then every element in Q[G] is of the form (a/b) + (c/d)g, and the action on an element q of Q is just multiplication by (a/b) - (c/d). If it sends Z into Z, then (a/b)-(c/d) must be an integer; invertibility yields that it is a nonzero integer. If we choose a,b,c,d so that gcd(a,b)=gcd(c,d)=1, b,d>0, then we must have b=d, so that u will be of the form u = (1/b)*(a+cg) with a,c in Z. Thus, it is a nonzero rational multiplied by an element of Z[G]. Is the answer always affirmative, or are there some well-known counterexamples? (I've asked that u be an automorphism because since G is finite, Z[G] and Q[G] will have lots of zero divisors, and those could lead to trouble, but maybe I don't have to ask that...) -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu === Subject: Re: Statistical question (discrete uniform sum distribution?) >Forgive my uselessness. It has been years since I last studied >probability and statistics. >I am trying to find a distribution that models the sum of >tabletop-gaming dice. For instance, 2D6 in tabletop-gaming terms means >the sum of two six-sided fair dice. >I'm trying to find a distribution that exactly models xDy - the sum of x >rolls of a y-sided fair die. >So far I've only found a continuous uniform sum distribution for the sum >of x results in the uniform range [0, 1]. Is there a distribution for >the sum of x results in the uniform discrete range 0, 1, 2, ..., y or am >I going to have to accept failure? (There is no way that I will have the >skill to actually work this out myself... I was rubbish at actually >proving mathematics. I was happiest applying it.) The simplest form is, I believe, due to Lagrange, both for the discrete as well as the continuous. It is a little easier to understand for the case where the die has faces numbered 0, ..., y-1. It helps to see the derivation. The generating function for one roll is (1/y)*(1-t^y)/(1-t), and so for x rolls it is the x'th power of this. The term 1/y^x is clear, and so the rest is (1-t^y)^x/(1-t)^x. Now 1/(1-t)^x = sum_0 C(-x, n)*(-t)^n, and putting in the other factor yields N(n) = sum (-1)^(k+n) C(x,k) C(-x, n-k*y) as the number of ways the sum can be n. The cumulative can be obtained similarly. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Statistical question (discrete uniform sum distribution?) What is the meaning of C(n,m) when n is negative? -- Stephen J. Herschkorn herschko@rutcor.rutgers.edu === Subject: Re: Algerbra number oddity >* katie_robertson_180@hotmail.com >> therefore .9999 recuring = 1. Now that just doesnt add up. It does add up. 0.999.. _is_ equal to 1. This subject has >recurrently appeared in sci.math over the years. > Was that a pun? > If a subject appears recurrently on sci.math, does that make it > a rational subject? No. Counterexample: James. Jason === Subject: Re: Algerbra number oddity First of all your proofs are not valid until you can prove that the arithmetic can be done with the infinite series. And the results are however the correct answers. 0.999 = 1 does add up for those who knows what it means. 0.999.... isn't a number. It is a symbol for an infinite series. An infinite series is, by definition, a sequence. The statement 0.999.... = 1 means that the sequence represented by the symbol on the left coinverges to the number represented by the numeral 1. That is a true statement and trivial to prove for those who understand convergence! >A question I have always wanted to ask but have never met anyone good >enough at maths to answer it. >The question involves rationalising forever recurring numbers. >for example x=0.8888 recuring,-> 10x = 8.88888 recuring, therefore >9x=8 (10x-x) >therefore 0.888 recuring = 8/9. >so that was easy enough and works all the time, except: >x=0.9999 recuring, 10x=9.9999 recuring, 9x=9 -> x=1 >therefore .9999 recuring = 1. Now that just doesnt add up. >The only thing I could see an error is the 9.9999-> - the 0.999-> = 9 >bit, but surely thats mathematically correct, plus it work in every >other example imaginable. (you can use the method for like >0.98989898->, just use 100x). >Can anyone help me understand this method always work (and was taught >in school) but doesnt work just for the 0.9-> example? >Katie x === Subject: Re: Path connectedness This is a followup to a discussion a couple of weeks ago about an elementary proof of the theorem that a path connected Hausdorff space is arc connected: >However I think a slight variation of your argument can be made to work. >Namely you can arrange that the images under f_n of the open intervals >](k-1)/2^n, k/2^n[ k=1,2,...,2^n are disjoint. Here's a link to a writeup of such a proof: https://webwork2.math.ohio-state.edu/moodle1_2/mod/resource/view.php?id=3298 &username=guest === Subject: Re: How to estimate this (Simple Linear Regression)? Mail-To-News-Contact: postmaster@nym.alias.net > Strictly speaking it is still non-linear because the errors are centred > on x not e^-x. Probably won't make a big difference though this can be considered a linear problem if a=0 === Subject: Re: How to estimate this (Simple Linear Regression)? :> Suppose you know that a process follows a function :> y(t) = a + b e^-x, t >= 0. :> ALso, suppose you have following data. :> t: { 0, 1, 2, 3 } :> y: { 2.2, 1.4, 0.87, 0.44 } :> How does one estimate the values of a and b? : This isn't a simple linear regression problem. It is a nonlinear : regression problem. There are a number of nonlinear regression programs : that can solve your problem for a and b. Here is such a program that I ran : through my NLREG program (http://www.nlreg.com) Yes, it is a simple linear regression problem: ordinary regression of y on e^-x. As the author of regression software, you should know better. Mike === Subject: Re: How to estimate this (Simple Linear Regression)? > : This isn't a simple linear regression problem. It is a nonlinear > : regression problem. There are a number of nonlinear regression programs > : that can solve your problem for a and b. Here is such a program that I > ran > : through my NLREG program (http://www.nlreg.com) > Yes, it is a simple linear regression problem: ordinary regression > of y on e^-x. As the author of regression software, you should know > better. I agree, by transforming the input variables this function is easily converted to a linear regression. But it can be handled more easily and properly as a nonlienar regression where no transformations are required. Remember that fitting a function to a transformed independent variable does not always yield the same fitting parameter results as fitting the function to the non-transformed input -- minimizing the sum of squared deviations for X is not the same as log(X) or sin(X). The difference can be significant. -- Phil Sherrod (phil.sherrod 'at' sandh.com) http://www.dtreg.com (decision tree modeling) http://www.nlreg.com (nonlinear regression) === Subject: Re: How to estimate this (Simple Linear Regression)? >> : This isn't a simple linear regression problem. It is a nonlinear >> : regression problem. There are a number of nonlinear regression programs >> : that can solve your problem for a and b. Here is such a program that I >> ran >> : through my NLREG program (http://www.nlreg.com) >> Yes, it is a simple linear regression problem: ordinary regression >> of y on e^-x. As the author of regression software, you should know >> better. >I agree, by transforming the input variables this function is easily >converted to a linear regression. But it can be handled more easily and >properly as a nonlienar regression where no transformations are required. ?? A linear regression is easier than a nonlinear regression, in general. For example, sometimes nonlinear regressions have multiple local optima. A linear regression has a single answer (except when there is perfect collinearity, which should be detected automatically). >Remember that fitting a function to a transformed independent variable does >not always yield the same fitting parameter results as fitting the function >to the non-transformed input -- minimizing the sum of squared deviations for >X is not the same as log(X) or sin(X). The difference can be significant. What you are saying here only makes sense if you believe there is some type of measurement error in X. If X is measured without error, then all you minimize is the sum of squared deviations in *Y*, not *X*. If X is measured with error, you will need additional information to identify the model. Namely, some information on the variance or relative variance of the errors in X. I didn't see any such suggestion or information in the original post. Clint Cummins (TSP International) === Subject: Order type of English names of natural numbers Originator: tchow@newton.mit.edu.mit.edu (Timothy Chow) Suppose we take the English name of every natural number and then alphabetize the names. What is the order type of the resulting total order? To make sense of this question, we need to have some system of naming numbers. One possibility is to use ordinary names of numbers up to (say) one trillion, and then to build larger numbers as illustrated by one hundred twenty-five billion fifty-three million one thousand four trillion trillion trillion trillion trillion trillion sixteen. When alphabetizing, one could assume that all spaces and punctuation are deleted. By order type I mean something like a copy of the natural numbers N followed by a million copies of the integers Z followed by a finite totally ordered set of fifteen elements. How sensitive is the answer to minor changes in the naming conventions? -- 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: Failing Linear Algebra: >I'm currently a math major and am taking linear algebra, but I'm in >serious danger of failing. I just don't get it! Is this newsgroup a >place to come to ask questions and get information about learning >math? Or is there somewhere more appropriate to go? I've always had >trouble with vectors, and I think I fell apart sort of right at the >beginning of linear algebra (although, I did manage to get a B- on the >very first exam). I've got another exam next week. What can I do? I >don't get all the terms, concepts, and jargon. Anyone know how to >make learning linear algebra easier and more practical? Anyone got >any practice problems? > I'd like to help you, but some specifics would be necessary. What > terminology are you having trouble with? anyone yet). I've made a few more posts, explaining my problems in more detail. > At any rate, this is the perfect opportunity to see if you have what > it takes to be a math major (or mathematician, if that's your goal). My goal is actually to go into either business or law. I'm a double major (economics/math). I wanted the economics major because I *was* always good at math in middle school and high school, and upper-level economics is nothing more than basic differentiation. But, my parents kind of pushed math since I've always been good at it, so I decided to do both, at least for the time being. Since I'll be a senior next year, I guess it'd make most sense just to stick with both majors. But, I'm not entirely sure math is for me anymore... Once I get a new math concept, I generally like doing problems on it and the problems come pretty easy. The same can maybe be said for proofs. For example, just this year (after having studied it in at least two other high school and college courses) I seemed to have mastered the concept of proof by induction, in algebraic structures; now, doing a proof by induction is a piece of cake for me. Maybe the same thing can happen with other styles of proof? But, I've definitely always had some trouble doing proofs, even since sophomore year of high school, when I first encountered them in geometry. Do you think I should just drop the math major, or is a math major supposed to be a challenge for most people? > You need to learn a method to go over the material quickly and > thoroughly. You need to learn how to come up with intuitive > representations of the concepts involved to guide your thinking. You > need to learn how to apply what you know to problem solving. > So, what I suggest is that you stick it out. Read the definitions > until your head hurts. I've been doing this. It's starting to stick, finally. Try to figure out exactly what the quantifiers > are telling you. Do problems until your head hurts more and you dream > about mathematical symbols. Don't let a problem intimidate you. I'd love to do this, but I can't necessarily find many problems about the type of stuff we're supposed to be studying. It really annoys me when a textbook that doesn't have a lot of exercises doesn't include ALL answers in the back of the book. The text book seems to have just too few examples that it's not quite possible to get any one type of problem without other sources, like Schaum's. > If this sounds appealling, you probably have what it takes. If not, I > would suggest another major--it's not going to get any easier after > linear algebra. It sounds appealing, I'd say. Will it get any *harder* after linear algebra? > 'cid 'ooh > (I'm not trying to scare you. I'm a student too, and I'm really > excited about facing new challenges in grad school. But I often have > to work for 48 hours straight to figure out a few measly problems. > Realistic expectations are important in any endeavor of this sort) Right. I've probably made the mistake of saving a few too many homework assignments till the last minute. === Subject: Re: Failing Linear Algebra: >>a significant role. They often stumble because (among other problems) >>they don't realize they need to _memorize_ definitions _precisely_. >Memorize? I can't remember ever memorizing anything. Better just to >practice until you understand. Discuss, ask questions, apply. That way >you memorize, of course, but that's just a side-effect. > No, for proof classes, which linear algebra is in many places, > it is crucial to *memorize* the definitions. This holds for > all the proof classes at higher levels also. There is simply no > way of giving rigorous proofs if you don't know the actual > definitions. All too often, students have some very vague ideas > of what is going on and then can't even get started on a proof > because they don't know the *exact* definiton used in the course. >>So you can do a little self-assessment here to figure out whether >>what you're missing is bits of topics or the core idea: can you, >>right this minute, define what a vector space is? >Hopefully not just as a one-to-one rendition of phrases from a >textbook... > The student should be able to give a rendition that is at least > equivalent to the one given in the book and that uses precise language. > If you can't say that a basis is an independent spanning set > then you don't know what a basis is. If you can't give the quantifiers > for the definition of independence, you won't be able to do a > proof using independence. > --Dan Grubb Let me try that one...independence means a group of vectors (in homogenous form???) such that if they all equal the zero vector, then the only possible way for that is the each coefficient of every vector has to equal 0 too. === Subject: Re: Failing Linear Algebra: >I'm currently a math major and am taking linear algebra, but I'm in >serious danger of failing. I just don't get it! Is this newsgroup a >place to come to ask questions and get information about learning >math? Or is there somewhere more appropriate to go? > The appropriate place to go is your teacher's office. Ask her to > take the time to go through a few problems with you & to suggest > what you ought to be doing to get a grip on the material. Oops, I also forgot to comment on office hours in my last post. Some friends have recommended this, but the way my schedule just so happens to be set up this semester, I'm almost always in other classes during my linear professor's assigned hours. On the days I'm not, there have always been other things going on that have prevented me from seeking help (I live in a triple room and my other two room mates have had severe problems with each other this semester; I've been caught in the middle and a lot of the time that I should have been using to study, read, do homework, and visit whatever office hours I'm free for has been taking up instead by talking to deans, my dorm's R.A.'s, etc--but this is a whole 'nother issue). When I've used office hours in the past, I've found that students generally need some kind of basic idea where their problem lies. With linear algebra, I'm not sure about that. I wouldn't want to waste the professor's time (or become even confused about the topics I thought I understood), especially since it's incredibly hard to find a time at a professor's office hours when they're free anyway. In the past, I've spent hours waiting and waiting outside a professor's office, just to go inside and not have any clue where my problem lies, and then leave the office hours feeling more confused than when I went in. So...I don't know what to do. I do want to meet with my professor when I'm free to do so on Thursday, before my last in-class exam on Friday (I'm not sure this will give me enough time to solve anything...) and perhaps again before my final exam in two weeks. I've come a long way in my understanding of linear algebra using the guides I have, but, like I've said, I'm still really unsure what my problem is. Something tells me I may just need a little more brushing up on a little more specific useage of the concepts, and I may be OK. Finding a way to solve proofs might be helpful too; this is something I generally suck at and not having all the concepts clearly seems to only make the proofs harder. === Subject: Re: Failing Linear Algebra: >I'm currently a math major and am taking linear algebra, but I'm in >serious danger of failing. I just don't get it! Is this newsgroup a >place to come to ask questions and get information about learning >math? Or is there somewhere more appropriate to go? I've always had >trouble with vectors, and I think I fell apart sort of right at the >beginning of linear algebra (although, I did manage to get a B- on the >very first exam). I've got another exam next week. What can I do? I >don't get all the terms, concepts, and jargon. Anyone know how to >make learning linear algebra easier and more practical? Anyone got >any practice problems? > I would bet that the single practice problem you need to work on is, > What is a vector space? > Our students do well on the very first exam because that's the part > of the course where we warm up with techniques for solving linear > systems of equations and such topics. But our LA course is also our > students' first course in which abstractions, axioms, and proofs play > a significant role. They often stumble because (among other problems) > they don't realize they need to _memorize_ definitions _precisely_. > So you can do a little self-assessment here to figure out whether > what you're missing is bits of topics or the core idea: can you, > right this minute, define what a vector space is? > dave Dave, this may be my problem. I did decent on the first exam because, like you said, it was solving linear systems, echelon form, linear dependences--easier stuff like that. I've always been a little confused with the concepts, but I think I may finally be getting a grip on what a vector space is: It's a group of vectors that can be multiplied by any scalar and/or added together in any way, and whatever possible combinations that can result is the vector space for that group of vectors. This is how I understand it. For vectors in R^2, a plane is formed (spanned???) by the vector space. For vectors in R^3, a solid area is formed by the vector space. It gets difficult for me to move into dimension 4. While I understand that the same concepts hold, there's no more physical picture I can use to visualize what's happening. Is my understanding of vector space sufficient enough? Am I missing anything? I know I am still struggling with the concepts of span and basis. The weird thing is that I'm alright with the more advanced stuff; matrices, determinants, eigenvalues, eigenvectors. I'm a little hazy with diagonalization because it's the newest thing we've done. I know it's got something to do with the eigenvalues of a special type of matrix. I guess I could also really use some help with understanding how a mapping gets converted into a matrix, and then how to solve it. I understand matrix multiplication and can do it well. But the concepts of image, kernel, and isomorphism and how they relate to the mappings/matrices seem to be lost on me. The odd thing is that I fully understand the definitions of kernel and image as they were applied in algebraic structures, but I don't get how they apply to linear really. Isomorphism is a concept I never understood in algebraic structures or linear algebra. about buying any other books. I already bought the text, the Cliff's and I even have an old 1968 version of Schaum's that my grandmother used when she majored in math. Cliff's has been helpful, but too basic. Schaum's seems almost too advanced; it's great that they solve all the problems, but sometimes the explanations are lacking. I find that I do much better at math problems if I can first figure out how to solve a certain type of problem and then go back and try to understand the concepts behind it, rather than the other way around. Schaum's examples don't allow for this, because they assume you've already read (and understood) the concepts behind how to solve certain problems. Maybe, if it isn't too much to ask, would anyone here be willing to post some problems relating to mappings/kernel/image/isomorphims and/or eigenvalues/eigenvectors, and I can attempt to solve them with your help? === Subject: Re: Failing Linear Algebra: >> Our students do well on the very first exam because that's the part >> of the course where we warm up with techniques for solving linear >> systems of equations and such topics. But our LA course is also our >> students' first course in which abstractions, axioms, and proofs play >> a significant role. They often stumble because (among other problems) >> they don't realize they need to _memorize_ definitions _precisely_. >> So you can do a little self-assessment here to figure out whether >> what you're missing is bits of topics or the core idea: can you, >> right this minute, define what a vector space is? >> dave >Dave, this may be my problem. I did decent on the first exam because, >like you said, it was solving linear systems, echelon form, linear >dependences--easier stuff like that. I've always been a little >confused with the concepts, but I think I may finally be getting a >grip on what a vector space is: That's familiar: You feel comfortable with specific examples but can't see the abstraction, the structure behind. In German there is a saying meaning roughly: You can't see the forest because of all the trees... As mathematics is the science of structures, you will have to get to this point. But it's a worthwhile goal to pursue because it's really uplifting if you finally reach that point - As the old greeks said: Heureka! I finally found! Thomas === Subject: Re: Failing Linear Algebra: >I think I may finally be getting a grip on what a vector space is: >It's a group of vectors that can be multiplied by any scalar and/or >added together in any way, and whatever possible combinations that can >result is the vector space for that group of vectors. Define vector. You can't really, since you haven't properly defined a vector space. Hint: axioms. >understand it. For vectors in R^2, a plane is formed (spanned???) >by the vector space. For vectors in R^3, a solid area is formed by >the vector space. Is span({0,0},{0,2}) a plane? Is span({0,0,0},{0,0,1},{0,0,2}) a solid area? -- I'm not interested in mathematics that might have anything to do with reality. -- Russell Easterly, in sci.math I am trying to do a simulation study on random vectors having multivariate normal distribution N(Mu, S). Suppose the generalized variance (the determinant of the covariance matrix det(S)) is 1. I am looking for a distribution of mean that would cover a wide range of applications and concentrate on the most important ones (maybe with the mean of |Mu| equaling to a specific number). Anyone has any idea Mike