Humanist Discussion Group, Vol. 13, No. 406.
Centre for Computing in the Humanities, King's College London
<http://www.princeton.edu/~mccarty/humanist/>
<http://www.kcl.ac.uk/humanities/cch/humanist/>
[1] From: "Osher Doctorow" <osher@ix.netcom.com> (71)
Subject: Re 13.0391 decision-making alternatives and
[2] From: "Osher Doctorow" <osher@ix.netcom.com> (44)
Subject: Discrete versus Continuous and Computers
--[1]------------------------------------------------------------------
Date: Tue, 15 Feb 2000 19:54:10 +0000
From: "Osher Doctorow" <osher@ix.netcom.com>
Subject: Re 13.0391 decision-making alternatives and
Dear Francois and Willard:
Thanks to Francois' communication, I have begun reading the Analytic
Onomasticon Project at
<http://www.princeton.edu/~mccarty/Onomasticon>http://www.princeton.edu/~mcc
arty/Onomasticon, although it can also be accessed by a browser just by
inserting the name Onomasticon Project if the browser is user friendly.
This is fascinating and enjoyable reading. Although I am only a beginner,
several ideas almost immediately occur to me (perhaps naively). If the
Metamorphoses are as important as it appears, then they might just be works
of maximum (1 on a scale of 0 to 1) LBP influence. I can see this
occurring due to the genius of the poet Ovid, but it makes me wonder what
events in his life interacted with and contributed to this genius and in
turn how it affected those of his times. This may not be entirely lost to
us. When I think of the genius of Beethoven and the critical times of
Napoleon that gave background to them and with which Beethoven interacted
in opposition (not to mention Beethoven's alcoholic father), I am tempted
to ask whether there were similar events (even similar in a very wide
sense) in the time of Ovid. Even if we have no direct evidence of this,
could we explore scenarios which derive from the assumption that these
events exist somewhat as we do with the Onomasticon? Could the
Onomasticon be extended to include these events as metatext? Could we in
fact go further and postulate these events simultaneously for the times of
Beethoven, Mozart, Ovid, the Bible, Pythagoras, etc.?
At the opposite extreme, there is the remote possibility that the
Metamorphoses have no common thread or influence, and there are many
possibilities in between the two scenarios of maximum and zero
influence. This has given me the idea of further studying the logic-based
probability (LBP) of null sets/events. Null sets/events are a special
subcategory of zero probability events which do not and cannot occur, at
least within standard logic. Whether they can occur within multivalued
logic is a question that, e.g., the multivalued logic group at the
University of Vienna and the Technical University of Vienna might be able
to tell us, or their fuzzy logic group for an analogous situation in fuzzy
logic. However, there is plenty to study just within LBP. In fact, the
complementarity principle of Bohr and Heisenberg in quantum theory is just
such a null set/event which has now been discredited on empirical grounds
(not on logical grounds - physicists are not that well trained in
philosophy in general). These theorists would have had us believe in
contradictions, and because of their stature in the physics community
almost the entire community of physicists said: "Amen," until
recently. But there is more: in conducting a study of how contradictions
and null sets/events differ from rare events, we may hope to avoid some of
the future incorrect decisions of scientists which are even now in the making.
I have been unable to touch on the questions of continuity versus
discontinuity which permeate the Onomasticon. It might be enough to start
by realizing that this question is just as important and unanswered in the
physical and life and behavioral and social sciences. The current fad in
physics, string theory, a completely discrete theory, is close to becoming
the mainstream which it once opposed (though it is hard to find any genius
of the level of Beethoven or Mozart who actually began and developed the
school, except for one late joiner, the brilliant Nobel Laureate Stephen
Weinberg). The string theorists whom I have communicated with are usually
incredibly non-humanist in their outlooks and personalities. It may seem
that we could not possibly fall into that trap, but the computer itself has
a hidden danger in that it cannot calculate at present continuous equations
without making some finite discrete approximation, and the string theorists
and their allies the topological field theorists usually regard the
universe as a bunch of disconnected strings or knots in various stages of
(semi-) interaction and change.
I do not think at my present early stage of reading the Onomasticon that
Ovid believed that his work was continuous and eternal only in the sense of
being open ended and intended to be completed by others. The Aristotles
and Socrates and Beethovens and others (including Chopin, I might add),
were global continuous advocates. In the Judeo-Christian tradition, i
think that the notion of spiritual and conceptual unity which the Jews
introduced into the divided and discrete ancient world came partly from the
rare events of those times, of which I mention only one which I think is
critical: slavery. The Jews were slaves of the Egyptians. How this
affected them, how it made them unify rather than divide, is one of the
fascinating questions that may well be answered by projects such as the
Onomasticon.
--[2]------------------------------------------------------------------
Date: Tue, 15 Feb 2000 19:54:49 +0000
From: "Osher Doctorow" <osher@ix.netcom.com>
Subject: Discrete versus Continuous and Computers
Francois and Willard,
You are probably familiar with the fact that the digital computer basically
operates by discrete finite processes rather than continuous and/or
infinite processes, but in terms of the Onomasticon Project and also
physical science projects this does not represent a choice of discrete
models versus continuous models.
To understand how this comes about, it is perhaps best to view the computer
in terms of what it really is: a stupid machine which does only what you
tell it to. Of course, very wise things can be constructed by stupid
machines if they are given wise instructions and controlled very carefully.
If you tell the computer to imitate a continuous process as closely as it
can, it will come close enough to the continuous process in most cases so
that it is very hard to tell that the computer is only approximating. On
the other hand, if you create a discrete model of a continuous process,
which often is very different from the continous process, then the computer
will give you exact results fairly easily, especially if you make the model
computer-friendly (which is more easily done for discrete models). This
has led many computer programming scientists to create discretized models
of continuous processes and to forget the original continuous processes
entirely. For example, this has recently has been done with the
Schrodinger equation in quantum theory, which is somewhat amusing to
creative physicists and mathematicians because Schrodinger, like Einstein,
was a Mozart-level genius and was least likely of anybody to believe that
the world is discrete. Luckily, even string physicists do not usually
believe that the Schrodinger equation is discrete. His equation, the
Schrodinger equation, is probably the most influential equation in quantum
theory in its continuous form.
There is a way to "computerize" continuous processes in probability using
digital computers, and at some point humanists and scientists will probably
have to decide whether to use it. It can be illustrated at one of the
biggest trouble points, namely, at zero (nil, 0). A discrete digital
computer does not calculate zero exactly; it is in a sense too dumb, and
comes up with something like .0000001 instead (perhaps much smaller). Here
is where the decision has to be made for the computer to interact with a
human being, much to the dismay of some, or else to simply program the
computer to assign probability zero to a certain list of humanly
preassigned events, or to truncate very small decimals of certain size
determined by human beings into 0. This cannot be done with Bayesian
programs because they are based on division, and division by zero will
cause big trouble for the computer. It can, however, be done with
logic-based probability (LBP) programs.
The insertion of tagged text and metatext into the Onomasticon is a similar
human process of interacting with the computer, and the two problems are
part of one larger problem.
Osher Doctorow
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