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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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