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

   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