Volume 18 Number 95 Produced: Wed Mar 22 9:13:01 1995 Subjects Discussed In This Issue: The two Mathematical Code Systems [Sylvain Cappell] Uncertainty Principle, Etc. [Harold Gans] ---------------------------------------------------------------------- From: <cappell@...> (Sylvain Cappell) Date: Fri, 24 Feb 95 00:48:25 EST Subject: The two Mathematical Code Systems Subsequent to my posting refering to the two new different systems of mathematical codes in texts, there have been many postings and I have also received curiously analogous emails from afficanados of both the "topological codes" and the "statistical codes," generally arguing that their own distinctive way of creating an innovative approach to religion and text is based on a valuable use of higher mathematics, while the other is devoid of scientific interest. While I had not disputed, analyzed or compared the contrasting claims of each of these systems of mathematical religious codes, I am afraid that I really am not yet able to see all the sharp contrasts between the "topolgical codes" and "statistical codes" that both groups seem to wish to draw. Indeed, enthusiasts for opposed escoteric systems are often prepared to explain how their particular novel methodology merits special consideration and is to be totally and absolutely distinguished from what they view as the other's pseudoscience, whose fallacies are all too evident to them. Both code methods, while making some references to historical Rabbinic Judaism, do in fact share being based upon radically new departures in religious epistomolgy, in both cases based on mathematical inspired methodologies or languages which may, at least in principle, be applied or adapted to the texts of many religions. In both the "topolgical codes" and "statistical codes" groups I indeed have some good and deeply valued mathematical friends who may be involved, or more precisely, are perhaps just intruiged or attracted by the astonishing vast claims being asserted for the power or novelty of their respective speculative mathematically based approaches to religion and texts. Indeed, in the case of the "topological codes" ( which I have looked at further and which despite being a researcher in topology still can not personally understand anything of ) there has been some interest expressed by a mathematical friend who is a recognized expert in topology. However, supporters of the "statistical codes" write that in assessing scientifically the claims of the "topological codes" this is perhaps not really relevant, as in the final analysis, apparently it was not in any case argued that these notions of geometrically reading novel meanings into religious texts bear any direct relation to conventional topology as commonly practiced by mathematicians. The "statistical code" novelties, on the other hand, while it has intruiged several fine pure mathematical friends, has not apparently seriously interested any leader in statistical research, a subject deservedly famous for having all too often trapped even distinguished nonspecialist scientists, and the only very distinguished and disinterested academic expert on statistics that I know of who has examined this material gives it no credit. Some writers referred to the publication of a paper in a peer-reviewed journal as demonstrating the absolutely superior claim of "statistical codes" to be a scientifically based approach to religion, unlike the "topological codes". This doesn't really seem quite fair as it is commonly known to all serious scientists, that the mere publication of a paper in one of the several hundred thousand peer-reviewed scientific journals currently in print does not imply that the paper is correct or that it represents even the presumptive currently accepted scientific consensus. ( As a particularily widely discussed example of this commonplace, recall the controversy a few years back when the editor of Nature, one of the great journals of science, published a paper on th claims of the pseudoscience of homeopathy. ) Some colleagues doing research in statistics have said to me that, alas, that is notoriously true of some papers that appear in the journal containing the paper on which the adepts of the "statistical codes" base their claim to have a more scientificly based approach to religious texts. In any case, to be fair, the proponents of the "topological codes" may analogously also come to seek the "confirmation" of trying to get a scientific publication. There are of course important epistomological differences immediately apparent between the two schools of applying codework to religion. To the perhaps mystically inclined devotees of the "topological codes," it may seem to offer practioners novel cosmic meanings ( perhaps related to those some have usually sought in some other Eastern religions and religious traditions ), however alien to both conventional Judaism and to standard science. The "statistical codes" approach, on the other hand, by its nature tends rather to in effect deprecate the traditional centrality of meaning in Jewish texts. ( In this connection, some submitters expressed concerns about what may ensue when "statistical codes" come to be invoked by propagandists for some other religions, who perhaps as they may have greater funding, will use even bigger computers in developing statistical religious points. Indeed, I have been told by Russian colleagues that statistical "proofs" had earlier been used by Russian Orthodox Christian mathematical mystics in the former Soviet Union, though at the time they did not have access to poweful computers. Happily, it should not prove necessary to invest in ever bigger computers to defend Judaism from any "statistical attacks"; the power of Jewish humor should generate an adequate defence. ) Both these novel approaches to applying mathematics to religion and texts do, in fact, raise some perplexing and deeply disturbing sociological questions. Some of these difficult sociological problems will, in the Jewish context, no doubt be the focus of some serious academic researches: Why are some people apparently at this particular time unfulfilled by the traditional Jewish approaches to text and why in favor of novel methodologies that some traditionalists will view as more radical than any of those proposed by, say, the early nineteenth century Reformers ? Why have some people apparently no longer drawn meaning and satisfaction in traditional ways from the texts and so may be reduced to viewing them as formal or mathematical cribs ? From whence the novel feeling that the texts are somehow in need of scientific endorsements or expansion in outlook or could gain "prestige" from invoking fancy sounding mathematical language ? Why is there so little concern that intelligent, well-educated and sensitive Jews sadly unfamiliar with Jewish texts may be repelled from even looking at them when turned off by what they may view as formalistic, boring, puerile or profoundly nihilistic presentations ? Of course, conventional mathematics is hardly likely to be damaged by such happenings or disputes or even to ever take notice. Some outside the groups of each of the opposed system of codes, however, may be concerned about a potential for damage to the general public standing of Judaism. On a personal note, let me ask again, as none of the many replies and postings responded to this: Why shouldn't we be confident that the reasons for becoming interested in Jewsh texts can be drawn, as always, from their uniquely profound and exciting ideas, legal codes, traditions, history, stories, poetry, wisdom and values ? Those are all things that mathematics, wonderful and beautiful as it is, can make no claims of providing. Professor Sylvain Edward Cappell Courant Institute of Mathematical Sciences, New York University 251 Mercer Street New York, N.Y., 10012 <cappell@...> ---------------------------------------------------------------------- From: <AishNY@...> (Harold Gans) Date: Mon, 20 Mar 1995 20:40:26 -0500 Subject: Uncertainty Principle, Etc. In MJ issue of 2/20/95, Moshe Koppel says "Harold Gans claims to be in possession of a proof which invokes the Uncertainty Principle, the Incompleteness Theorem, and Chaos Theory. I've seen many 'proofs' which are uncertain, incomplete and chaotic, but I've never seen a real proof which depends on all those heavy duty tools. Tell us more." I shall attempt to answer your request as best I can given that the subject is a complex one and I really do not have time to do it justice. First, I must point out that I do not claim to have a "proof." I use the term "proof" in a very technical way. To me, as a mathematician, it means nothing more or less than a sequence of well formed formulae (i.e. propositions) in some formal system in which each element of the sequence is either an axiom in the system or else can be deduced from previous elements in the sequence using the rules of formal logic. The word "proof" therefore does not apply to anything other than the world of formal mathematics. What I will present is a demonstration, or argument, which shows (but does not prove in the formal sense) that precise, detailed prediction of far future events, such as we find in the codes of the Torah, is physically impossible. The Uncertainty Principle of Quantum Mechanics was discovered by Verner Heisenberg in 1927. It states that the product of the error in measuring any one dimensional component of the position of a particle and the error in measuring the same directional component of the particle's momentum is always greater than or equal to a small positive constant (Planck's constant, approximately 6.6E-27 ERG-SEC. divided by 2 pi). This implies that neither error can ever be zero. This lower bound on these errors is not a result of the limitations of our measuring equipment; it is the consequence of the quantum nature of reality. Now Planck's constant is very small so it would be natural to assume that the Uncertainty Principle has no practical effect in the world of large objects that we normally relate to. This is, however, not so. Chaos Theory, developed over the last few decades, has shown that virtually all meaningful systems in the real world (technically known as dynamic or nonlinear systems) are chaotic. This has a precise mathematical meaning. It means that the evolution of the system is very dependent on initial conditions. Thus, exceedingly small errors in determining the initial conditions of a system can result in total unpredictability of the status of the system at some future point. This point is determined by where the possible evolutionary tracks of the system diverge, and is a function of the nature of the system and the actual precision of the initial measurements. For weather, which is chaotic, the point of significant divergence is reached within several months; for the orbit of Pluto, which is also chaotic, it is millions of years. Since the Uncertainty Principle guarantees that all measurements will be inaccurate, Chaos Theory guarantees that we can never predict precise future events in any dynamic system. (Incidentally, the word "dynamic" excludes very simple systems such as a periodically swinging pendulum, or a rolling ball on a smooth constant incline. Virtually all "real life" systems, particularly systems with living components, are dynamic and therefore chaotic.) A deeper form of chaos is based on the Incompleteness Theorem, discovered by Kurt Godel in 1930. There are actually several incompleteness theorems; we are interested in the one for arithmetic. This theorem states that any mathematical system which includes the five axioms of arithmetic is either incomplete or inconsistent. Incompleteness for a formal mathematical system means that there are statements that are true in that system (i.e., there are no counter examples) but that can not be proven in the system. Here, I use "proof" in the formal sense as I defined it earlier. Since the rules of arithmetic are used in solving equations of physics, the Godel Incompleteness theorem can, under certain conditions, also imply nonpredictability of physical events. One example of this phenomenon is recorded in the article "Chaotic Chaos in Linked Electrical Circuits," Science News, January 14, 1995, where it says "Mathematicians have pinpointed how certain features in equations, including some of those used to describe physical phenomena such as fluid flow, lead to an extreme kind of unpredicability in the solution to those equations." Another relatively nontechnical reference on this subject is an article, "Everywhere You Look Everything is Chaotic," Science, Vol. 245, July 7, 1989, page 28. If you are interested in a slightly more technical exposition of the implications of the Godel theorem to predictability in the physical world, see "Randomness in Arithmetic" by Gregory J. Chiatin, Scientific American, July 1988. One of the best references on the interaction of the Uncertainty Principle, the Incompleteness Theorem and Chaos Theory is "Classical Chaos" by Roderick Jensen, American Scientist, Vol. 75, March/April 1987. I hope this answers your query satisfactorily. Thank you for your interest. ----------------------------------------------------------------------

End of Volume 18 Issue 95