martillo@mit-athena.UUCP (Yakim Martillo) (07/29/85)
I would like to see Rosen prove that the universe can be described mathematically. This assumption is fundamental in all science and works well. But this is merely phenomenology and not proof. Also the assumption seems to break down in certain domains of physics and many mathematicians cringe at what the field theorists call proof. You may consult Shlomo Sternberg and Arthur Jaffe about this at Harvard. Further, the Hilbert, Bernays, Goedel formulation of mathematics fails in some sense because any mathematical system interesting enough to describe the universe is incomplete which is distressing if you believe math can provide a complete description of the universe (although Weinberg has a slightly different opinion - see Gravitation and cosmology). I have heard both Andrew Gleason and David Kazhdan at Harvard make this point.
sam@bu-cs.UUCP (Shelli Meyers) (07/30/85)
>I would like to see Rosen prove that the universe can be described >mathematically. Then, after proving all of the physical world mathematically, I would like to see him prove the divine in the same way.
jho@ihu1m.UUCP (Yosi Hoshen) (08/01/85)
>I would like to see Rosen prove that the universe can be described >mathematically. It is possible to describe the univrse mathematically. For example you could (conceptually) write a relativistic equation that describes every particle in the universee and its interactions with other particle. Such equation would be useless, because it cannot be solved. But conceptually it is possible to describe the universe mathematically. -- Yosi Hoshen, AT&T Bell Laboratories Naperville, Illinois, Mail: ihnp4!ihu1m!jho
david@fisher.UUCP (David Rubin) (08/05/85)
> I would like to see Rosen prove that the universe can be described > mathematically. This assumption is fundamental in all science and > works well. But this is merely phenomenology and not proof. Also > the assumption seems to break down in certain domains of physics and > many mathematicians cringe at what the field theorists call proof. > You may consult Shlomo Sternberg and Arthur Jaffe about this at > Harvard. Further, the Hilbert, Bernays, Goedel formulation of > mathematics fails in some sense because any mathematical system > interesting enough to describe the universe is incomplete which is > distressing if you believe math can provide a complete description of > the universe (although Weinberg has a slightly different opinion - > see Gravitation and cosmology). I have heard both Andrew Gleason and > David Kazhdan at Harvard make this point. I cannot answer whether Rosen indeed believes the universe can be so defined, but it appears to me that such criticisms confuse mathematics with science. The latter is fundamentally empirical, not logical, in nature; self-consistency (the standard of logical/mathematical systems) is given far less weight than consistency with observation. Mathematics is used by the scientist as a means, not an ends in itself, in an attempt to describe the pattern of all observations as compactly as possible. The scientist will often have many explanations that fit the data available to him, in which case he will favor the simplest one that does not conflict with the data and still remains "testable" (subject to refutation). Thus, the empiricist/scientist does not presume that there exists some explicit mathematical formulation of the laws of the universe, but rather that mathematical formulations may successfully approximate those laws to such an extent as to provide some mechanism to accurately predict future phenomena. For what is "understanding" of a system if not the ability to foresee its behavior? Science, in the end, PROVES nothing, for that is not its intent; it stands or falls on how well it DESCRIBES. As Martillo implies, religous endeavors can assume mathematical (i.e., logical) qualities; this is especially characteristic of Rabbinic Judaism, which proceeds from a set of assumptions (frequently disputed) to arrive at a conclusion. However, this does nothing to refute those who would approach cosmic matters empirically, rather than by religous doctrine or mathematical analysis. An overly simplified synthesis of how these differing approaches might influence dogma follows: the religous would declare that God exists, the logical might declare either way, depending upon their assumptions and the quality of their logic, and the empirical would not declare either way, save perhaps to declare the issue unresolvable (divine action being indistinguishable from other phenomena: is it God (however defined), or does our model merely need an overhaul?). David Rubin {allegra|astrovax|princeton}!fisher!david
wkp@lanl.ARPA (08/06/85)
> >I would like to see Rosen prove that the universe can be described > >mathematically. [MARTILLO] > > It is possible to describe the univrse mathematically. For example > you could (conceptually) write a relativistic equation that describes > every particle in the universee and its interactions with other particle. > [HOSHEN] This is untrue. Deterministic physics ended in the early part of the century with the advent of quantum mechanics. It is now known to be impossible to specify the exact position of ANY particle as long as its uncertainity in momentum is finite. This can be found in any sophomore physics book (e.g., Halliday and Resnick, or Feynman's lectures in physics.) -- bill peter ihnp4!lanl!wkp "Plasma physicist: a physicist standing too near a nuclear event."
jho@ihu1m.UUCP (Yosi Hoshen) (08/08/85)
> > It is possible to describe the univrse mathematically. For example > > you could (conceptually) write a relativistic equation that describes > > every particle in the universee and its interactions with other particle. > > [HOSHEN] > > > This is untrue. Deterministic physics ended in the early part of the > century with the advent of quantum mechanics. It is now known to be > impossible to specify the exact position of ANY particle as long as > its uncertainity in momentum is finite. This can be found in any > sophomore physics book (e.g., Halliday and Resnick, or Feynman's > lectures in physics.) > -- I didn't say that you can simultaneously determine the position and momentum of a particle. Quantum mechanics allows you to determine their expectation values. The issue is whether there is a mathematical model. I think mathematical model is possible. But such a model that considers all interactions is not solvable. > > bill peter ihnp4!lanl!wkp > > "Plasma physicist: a physicist standing too near a nuclear event." *** REPLACE THIS LINE WITH YOUR MESSAGE *** -- Yosi Hoshen, AT&T Bell Laboratories Naperville, Illinois, Mail: ihnp4!ihu1m!jho
wkp@lanl.ARPA (08/12/85)
In article <612@ihu1m.UUCP> Yosi Hoshen writes: > I didn't say that you can simultaneously determine the position and > momentum of a particle. Quantum mechanics allows you to determine > their expectation values. The issue is whether there is a mathematical > model. I think mathematical model is possible. But such a model that > considers all interactions is not solvable. The issue was whether or not it is possible to describe the universe mathematically. The laws of physics themselves decree that there exists a fundamental limitation to what is knowable. Hence, there are phenomena in physics which are inherently undecidable, and thus not describable by mathematics. In point of fact, mathematics is not even describable by itself. The famous Incompleteness Theorem states that: 1. It is not possible to prove the internal consistency of mathematics. 2. There are things that are true that can never be deduced from any finite set of axioms. The famous Halting Theorem in computer science is another example of a proven limitation to what is ultimately knowable. Of course, this has nothing to do with computational complexity. -- bill peter ihnp4!lanl!wkp "See how many hidden causes there are...hidden from the comprehension of human beings." --The Zohar
tan@ihlpg.UUCP (Bill Tanenbaum - AT&T Bell Labs - Naperville IL) (08/13/85)
> > [Yosi Hoshen] > > I didn't say that you can simultaneously determine the position and > > momentum of a particle. Quantum mechanics allows you to determine > > their expectation values. The issue is whether there is a mathematical > > model. I think mathematical model is possible. But such a model that > > considers all interactions is not solvable. > ------------------------------- > [Bill Peter] > The issue was whether or not it is possible to describe the universe > mathematically. The laws of physics themselves decree that > there exists a fundamental limitation to what is knowable. > Hence, there are phenomena in physics which are inherently > undecidable, and thus not describable by mathematics. --------------------------- The disagreement between Yosi Hoshen and Bill Peter is merely semantic, not substantive. Assume a mathematical equation which correctly models the behavior of the universe, but makes only statistical predictions. Yosi correctly states that we would have a mathematical model of the universe. Bill correctly states that such a model would not decide the result of specific experiments, and thus the universe is not completely describable by mathematics. End of discussion, I hope. If not, I suggest net.physics would be more appropriate. -- Bill Tanenbaum - AT&T Bell Labs - Naperville IL ihnp4!ihlpg!tan
rlr@pyuxd.UUCP (Rich Rosen) (08/14/85)
I hate to say this, but if MY articles were considered by some minority to be inappropriate for this group, I would think this Peter/Hoshen/Tanenbaum debate, though interesting, is not an n.r.j topic to be sure. Of course I could be wrong. -- "There! I've run rings 'round you logically!" "Oh, intercourse the penguin!" Rich Rosen ihnp4!pyuxd!rlr
martillo@csd2.UUCP (Joachim Martillo) (08/23/85)
I was not clear enough in my original posting. Rosen believes in science but not in God. My claim is that modern science rests on certain beliefs for which there is no logical basis and which must be taken on faith. The first is that "induction" (in a loose sense) works. That is we can take our few observations and generalize into physical laws. The next is that somehow mathematical equations can be used to model the universe. Now we know that there are fundamental problems with the Hilbert/Bernays/Goedel approach to mathematics. Also even without the problems in mathematics itself, many of the equations which we use tend to come up with embarrassing singularities. This is particulary a problem with the most empirically supported cosmological equations as t -> 0. There also may be some fundamental problems with mathematically modeling extremely small distance extremely high energy events. The last is repeatability. That is if I repeat an experiment N times and get some set of results and then if I repeat the experiment again at some unspecified time, I will get some results related in some rational way to the first set of results. Without these assumptions, there is no modern science. Modern science works well, but that does not prove these assumptions but rather shows they are good axioms. I am perfectly reasonable to take the efficacy of these axioms as possible evidence for the existence of a divinity stabilizing the universe in some sense.
rlr@pyuxd.UUCP (Rich Rosen) (08/25/85)
> Rosen believes in science but not in God. [MARTILLO] "Believes in science"? In the same sense that you believe in god? Or "believes that the methods of science provide the best (and often the only) means of acquiring solid knowledge". > My claim is that modern science rests on certain beliefs for which > there is no logical basis and which must be taken on faith. Which you use every day, especially when typing your words onto a keyboard and believing that when you strike the 'h' key, an 'h' will appear, and believing that when you edit a file or send an article or drive a car, the appropriate thing (as understood by scientific inquiry). > Without these assumptions, there is no modern science. Modern science > works well, but that does not prove these assumptions but rather shows > they are good axioms. I am perfectly reasonable to take the efficacy > of these axioms as possible evidence for the existence of a divinity > stabilizing the universe in some sense. It is only possible evidence in any reasonable sense if you have assumed your conclusion. -- "to be nobody but yourself in a world which is doing its best night and day to make you like everybody else means to fight the hardest battle any human being can fight and never stop fighting." - e. e. cummings Rich Rosen ihnp4!pyuxd!rlr
martillo@csd2.UUCP (Joachim Martillo) (08/30/85)
Well, if Rosen can suggest a reason why the axioms I listed have been so efficacious, I am willing to listen. Yehoyaqim Martillo
tan@ihlpg.UUCP (Bill Tanenbaum) (08/30/85)
> [Martillo] > My claim is that modern science rests on certain beliefs for which > there is no logical basis and which must be taken on faith. > [A list of assumptions upon which he says science depends] > Without these assumptions, there is no modern science. Modern science > works well, but that does not prove these assumptions but rather shows > they are good axioms. I am perfectly reasonable to take the efficacy > of these axioms as possible evidence for the existence of a divinity > stabilizing the universe in some sense. ------------------- Yes, science depends on assumptions. But assumptions are not the same thing as faith. The assumptions work, i. e. scientific theories have real predictive power, etc. When an assumption does not work, scientists discard it. This is not the same thing as religious faith. -- Bill Tanenbaum - AT&T Bell Labs - Naperville IL ihnp4!ihlpg!tan
martillo@csd2.UUCP (Joachim Martillo) (09/02/85)
I think Bill Tannenbaum is missing my point. I am not questioning the efficacy of the assumptions which science make. Also for my question the success of science as a method of relating to the universe is irrelevant. I want a answer why the assumptions which science makes are so efficacious. Who are what makes these good assumptions? I am asking a meta-scientific question and I consider at best a tautology the answer that these are good assumptions because they work. Now if Bill Tannenbaum is telling me there are some questions which I may ask and some which I may not, this sounds like some religions of which I have heard.
rlr@pyuxd.UUCP (Rich Rosen) (09/04/85)
> Well, if Rosen can suggest a reason why the axioms I listed have been > so efficacious, I am willing to listen. > > Yehoyaqim Martillo Because they work. Which particular axioms are you talking about? (You, Yakim, willing to listen? Don't make me laugh...) -- Life is complex. It has real and imaginary parts. Rich Rosen ihnp4!pyuxd!rlr
tan@ihlpg.UUCP (Bill Tanenbaum) (09/04/85)
> [Martillo] > I think Bill Tanenbaum is missing my point. I am not questioning the > efficacy of the assumptions which science make. Also for my question > the success of science as a method of relating to the universe is > irrelevant. I want a answer why the assumptions which science makes > are so efficacious. Who are what makes these good assumptions? I am > asking a meta-scientific question and I consider at best a tautology > the answer that these are good assumptions because they work. > > Now if Bill Tanenbaum is telling me there are some questions which I > may ask and some which I may not, this sounds like some religions of > which I have heard. ----- I thought that your [Martillo's] point was that science, like religion, rested on faith. I argued that the assumptions of science were accepted by scientists because they work, not because of faith. It does not require much faith on my part to believe that if I cut my finger, I will bleed. Belief in God does require faith. The question you ask above is irrelevent to this argument. It is of interest to theologians and philosophers, and certainly to this newsgroup. You may certainly ask. It IS a tautology or a definition to say that these (scientific) assumptions are good because they work. However, it is the reason I believe them. I can believe them without knowing why they work, or indeed, without knowing whether or not the why question is meaningful at all. -- Bill Tanenbaum - AT&T Bell Labs - Naperville IL ihnp4!ihlpg!tan