13.0496 a conjecture

From: Humanist Discussion Group (willard@lists.village.virginia.edu)
Date: Sat Mar 18 2000 - 08:49:56 CUT

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                   Humanist Discussion Group, Vol. 13, No. 496.
           Centre for Computing in the Humanities, King's College London

             Date: Sat, 18 Mar 2000 08:37:22 +0000
             From: "Osher Doctorow" <osher@ix.netcom.com>
             Subject: A Renaissance Conjecture

    Dear Colleagues:

    I have noticed that Willard McCarty asks fascinating questions without much
    of a pause, and this partly inspires me to suggest the following
    Renaissance Conjecture: A Renaissance occurs in the humanities and/or
    science when a society including its leaders repeatedly ("continually")
    distributes a list of open questions to the public. This conjecture has
    several subtle points that might not be immediately realized. For one
    thing, if it is true, then I am not sure that we are in a Renaissance,
    since I do not know of any leaders of any society who are distributing a
    list of open questions to the public. It is not fair to include indirect
    reference to issues or direct reference to goals, e.g., by politicians. A
    goal is not an open question. Secondly, I am not sure that the Italian
    Renaissance would qualify, but I suspect that it would because the Catholic
    Church at that time was in considerable open communication with the public
    and was leading the way. Thirdly, regardless of whether or not the
    "original Renaissance" qualifies by this conjecture, it is fascinating to
    notice that a few people do give lists of open questions to the public in
    every century. For example, early in the twentieth century, the pioneering
    German mathematician David Hilbert gave his list of open questions/problems
    to the public which have largely been the foundation of 20th century
    mathematics. Oddly enough, the eminent Swiss physicists C. Piron and Jauch
    made the greatest advances in classical quantum logic in the twentieth
    century by proving that "yes/no" answers/questions/experiments underlie
    classical quantum mechanics and have various mathematical properties. In
    modern times, number theory in mathematics has published lists of open
    questions, including the famous Fermat's last theorem which was recently
    solved by a Canadian. However, these are relatively rare. Even the
    Internet, which has so much capability for research, only rarely gives
    lists of open questions, usually in only a few fields.

    I will close this communication with a question which I asked my students
    when teaching mathematics and/or physics at Universities, High Schools,
    Middle Schools/Grammar Schools, and even Elementary schools: what are the
    20 main open questions in mathematics, or in physics, of the last 5
    years? Nobody had the slightest idea. I would recommend asking the same
    question in both sciences and humanities because it seems to me that if we
    do not know the questions, we cannot begin giving the answers. (Don't
    worry, I will eventually give you some of the questions. In particular, in
    mathematics, look under the topics non-smooth analysis and rare
    events/large deviations for a starting point.)


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