13.0406 statistical analysis & the Metamorphoses

From: Humanist Discussion Group (willard@lists.village.virginia.edu)
Date: Tue Feb 15 2000 - 20:02:51 CUT

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                   Humanist Discussion Group, Vol. 13, No. 406.
           Centre for Computing in the Humanities, King's College London

       [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

             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
    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

             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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