Cantor Confusion
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From: David Marcus on 17 Oct 2006 22:14 imaginatorium(a)despammed.com wrote: > David Marcus wrote: > > stephen(a)nomail.com wrote: > > > What does it mean for a thing in the real world to be true? > > > How do you know if a thing in the real world is true? > > > > > > Consider the twin slit experiment. Is the fact that none of > > > the following accurately describe the situation an inconsistency? > > > a) the photon goes through one slit > > > b) the photon goes through both slits > > > c) the photon goes through neither slit > > > > In Bohmian Mechanics (and similar theories), the photon goes through > > only one slit. Physicists could learn something about logical thinking > > from mathematicians. > > But isn't it true that while "undoubtedly" going through one slit, it > interferes with itself "undoubtedly" not going through the other slit? "Interferes with itself"? I don't know what that means. Do you? The particle is guided by the wave. "Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored." J.S. BELL Speakable and Unspeakable in Quantum Mechanics http://www.math.rutgers.edu/~oldstein/quote.html -- David Marcus
From: David Marcus on 17 Oct 2006 22:19 mueckenh(a)rz.fh-augsburg.de wrote: > MoeBlee schrieb: > > mueckenh(a)rz.fh-augsburg.de wrote: > > > A good, if no the best source to learn about the different meanings of > > > infinity would be Cantor's collected works. > > > > Set theory has advanced since Cantor. The best source to learn about > > current set theoretic definitions of 'infinite' is not Cantor. > > There is no definition what infinity is and there is no definition what > a set is. Current set theory has forgotten about theoretic definitions > of the infinite at all and uses the notion "infinity" just as seems > necessary to avoid too obvious contradictions. "Infinity" most certainly is defined. As for sets, the axioms of set theory tell us how they behave and what properties they have. -- David Marcus
From: David Marcus on 17 Oct 2006 22:28 mueckenh(a)rz.fh-augsburg.de wrote: > > David Marcus schrieb: > > > stephen(a)nomail.com wrote: > > > > Consider the twin slit experiment. Is the fact that none of > > > the following accurately describe the situation an inconsistency? > > > a) the photon goes through one slit > > > b) the photon goes through both slits > > > c) the photon goes through neither slit > > > > In Bohmian Mechanics (and similar theories), the photon goes through > > only one slit. Physicists could learn something about logical thinking > > from mathematicians. > > LOL. Physicist know already that something which cannot be known does > not exist. Mathematicians have to learn it. Some will achieve it, but > certainly not all. > > Bohmian Mechanics allows for action at a distance. Without that > unrelativistic assumption case (b) is correct. But if no case were > correct, then no case would exist. That is the same as with actual > infinity. Bell's inequality shows that any theory that agrees with the predictions of quantum mechanics for a certain specific experimental setup must be non-local. So far, all experiments confirm this prediction of quantum mechanics. Hence, we are stuck with a non-local world. How this will be reconciled with Lorentz invariance remains to be seen. How physicists can deny that particles exist (or fields or something besides just the wave function) is a mystery. -- David Marcus
From: David Marcus on 18 Oct 2006 01:40 Virgil wrote: > In article <3832b$4534cd83$82a1e228$21528(a)news1.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > MoeBlee wrote: > > > Han.deBruijn(a)DTO.TUDelft.NL wrote: > > >>David Marcus schreef: > > >>>Han de Bruijn wrote: > > >>>>How can we know, heh? Can things in the real world be true AND false > > >>>>(: definition of inconsistency) at the same time? > > >>> > > >>>That is not the definition of "inconsistency" in Mathematics. On the > > >>>other hand, I don't know of any statements in Mathematics that are both > > >>>true and false. If you have one, please state it. > > >> > > >>What then is the precise definition of "inconsistency" in Mathematics? > > > > > > How many times does it have to be posted? > > > > > > G is inconsistent <-> G is a set of formulas such that there exists a > > > formula P such that P and its negation are both members of G. > > > > Isn't that exactly the same as: P is at the same time true AND false? No. -- David Marcus
From: David Marcus on 18 Oct 2006 01:51
mueckenh(a)rz.fh-augsburg.de wrote: > David Marcus schrieb: > > Are you now saying that you have a proof of > > > > lim_{t->infty} 9t = 0 > > > > in standard mathematics? If so, please give the proof (and just the > > proof). > > I prefer to hear what your result is, concerning the set of balls in > the vase at noon. If you give an answer, I will show you the > contradiction. > > > I gave my translation of the ball and vase problem. I don't see any > > contradictions that follow from it. If you say it implies two > > contradictory conclusions, please state them and your proof. > > What was the result of your translation? Are there balls in the vase at > noon or not? My translation produces a Calculus problem, so my answer is the same as any Calculus student would get. Are you asking me whether I know Calculus? I do. You said the problem leads to two different answers. Please show the second answer and its derivation. For your convenience, here is the problem again: Problem: For n = 1,2,..., define A_n = 12 - 1 / 2^(floor((n-1)/10)), R_n = 12 - 1 / 2^(n-1). For n = 1,2,..., define a function B_n by B_n(t) = 1 if A_n < t < R_n, 0 if t < A_n or t > R_n, undefined if t = A_n or t = R_n. Let V(t) = sum{n=1}^{infty} B_n(t). What is V(12)? -- David Marcus |