Humanist Discussion Group, Vol. 13, No. 496.
Centre for Computing in the Humanities, King's College London
<http://www.princeton.edu/~mccarty/humanist/>
<http://www.kcl.ac.uk/humanities/cch/humanist/>
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.)
Osher
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