From: Marta Bunge <martabunge@hotmail.com>
To: <categories@mta.ca>
Cc: <joyal.andre@uqam.ca>
Subject: Re: Explanations
Date: Wed, 27 Apr 2011 09:20:36 -0400 [thread overview]
Message-ID: <E1QFPqG-0004T4-0Z@mlist.mta.ca> (raw)
In-Reply-To: <17617_1303861705_4DB759C9_17617_39_1_E1QEryD-0006dq-7k@mlist.mta.ca>
Dear Andre,
In connection with the current discussion on explanatory proofs, and more particularly about the difference between computer generated proofs and human ones, I have something to add to what you wrote --drawn from my own experience. Humans do not have either the speed or the ability to hold the enormous amounts of information that machines do. On the other hand, the only way to see the big picture is speed of reasoning coupled with intuition - naturally without checking the details at each step. That way, two things may happen to humans of which computers are free of: (1) errors are made, and (2) new ideas originate. Errors are not a good thing, of course, but they are a possible outcome from taking risks, without which no new ideas would ever surface. Working out the details of that first glimpse of the truth may be painful, but necessary. It may lead to truth (hardly ever), or to further glimpses. I agree with you that the sequence intuition --> computation---> intuition---> computation-->.... is the only available course of action for a good mathematician. With luck, the sequence terminates eventually, and it does in truth. But it must begin with intuition. Some of my collaborators have expressed surprise at my starting any investigation with a title and an abstract, when they would leave both for the end. Naturally, that title and abstract may very well change at the end of the investigation, but if I were incapable to see the big picture at first, I would not begin any work at all. A final trivial thought - computation alone is not mathematics, and neither is intuition alone. The former is typical of machines, whereas the latter is typical of artists.
Best regards,Marta
----------------------------------------
> Date: Mon, 25 Apr 2011 22:01:05 -0400
> Subject: categories: Re: Explanations
> From: joyal.andre@uqam.ca
> To: jds@math.upenn.edu; ronnie.profbrown@btinternet.com; graham@eecs.qmul.ac.uk
>
> Dear Jim,
>
> You are perfectly right!
> I am always amazed by the fact that a computation
> can yield a surprising result.
> It is as if the formal system knew more than me!
> Actually, I find a computation boring when the result is not surprising.
> Computing is probably the main vehicule by which we can move
> beyond a given body of intuitive knowledges.
> But after the initial surprise, we try hard to
> integrate the new result in a larger body,
> where it may become less surprising.
> It may even become obvious!
>
> The chain
>
> intuition--->computation---->intuition--->computation.....
>
> is probably more important than the chain
>
> proof--->method---->proof--->method.....
>
> André
>
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2011-04-27 13:20 UTC|newest]
Thread overview: 25+ messages / expand[flat|nested] mbox.gz Atom feed top
2011-04-22 13:55 Explanations Graham White
2011-04-23 20:27 ` Explanations David Yetter
2011-04-23 21:29 ` Explanations Ronnie Brown
2011-04-25 13:51 ` Explanations Joyal, André
2011-04-26 0:52 ` Explanations jim stasheff
2011-04-26 13:45 ` Explanations William Messing
[not found] ` <4DB6CC7D.40407@math.umn.edu>
2011-04-26 22:05 ` Explanations Ronnie Brown
2011-04-23 21:52 ` Explanations Dusko Pavlovic
2011-04-25 13:17 ` Explanations ClemsonSteve
2011-04-26 5:55 ` Explanations Timothy Porter
2011-04-27 7:53 ` Explanations Uli Fahrenberg
[not found] ` <17617_1303861705_4DB759C9_17617_39_1_E1QEryD-0006dq-7k@mlist.mta.ca>
2011-04-27 13:20 ` Marta Bunge [this message]
[not found] <654PeBPnq2496S01.1304350816@web01.cms.usa.net>
2011-05-02 18:22 ` Explanations peasthope
-- strict thread matches above, loose matches on Subject: below --
2011-05-01 21:27 Explanations peasthope
[not found] <609PDdViw1024S04.1304197762@web04.cms.usa.net>
2011-05-01 21:00 ` Explanations peasthope
2011-04-30 21:09 Explanations Fred E.J. Linton
[not found] <BANLkTi=XhOM=FKajXUA6pyOq575fm_N=PQ@mail.gmail.com>
2011-04-29 19:56 ` Explanations peasthope
2011-04-30 19:58 ` Explanations Charles Wells
2011-05-02 17:01 ` Explanations Clemson Steve
2011-05-01 12:50 ` Explanations F. William Lawvere
2011-04-28 13:12 Explanations Ellis D. Cooper
2011-04-27 8:16 Explanations Mattias Wikström
2011-04-20 17:22 Explanations Fred E.J. Linton
2011-04-21 19:09 ` Explanations peasthope
2011-04-19 23:37 Explanations Jean-Pierre Marquis
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=E1QFPqG-0004T4-0Z@mlist.mta.ca \
--to=martabunge@hotmail.com \
--cc=categories@mta.ca \
--cc=joyal.andre@uqam.ca \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).