From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6649 Path: news.gmane.org!not-for-mail From: Marta Bunge Newsgroups: gmane.science.mathematics.categories Subject: Re: Explanations Date: Wed, 27 Apr 2011 09:20:36 -0400 Message-ID: References: Reply-To: Marta Bunge NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1303992178 12201 80.91.229.12 (28 Apr 2011 12:02:58 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 28 Apr 2011 12:02:58 +0000 (UTC) Cc: To: Original-X-From: majordomo@mlist.mta.ca Thu Apr 28 14:02:52 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.4]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1QFPvn-0005hP-I2 for gsmc-categories@m.gmane.org; Thu, 28 Apr 2011 14:02:51 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:47413) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1QFPqJ-0001rH-1N; Thu, 28 Apr 2011 08:57:11 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QFPqG-0004T4-0Z for categories-list@mlist.mta.ca; Thu, 28 Apr 2011 08:57:08 -0300 In-Reply-To: <17617_1303861705_4DB759C9_17617_39_1_E1QEryD-0006dq-7k@mlist.mta.ca> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6649 Archived-At: Dear Andre=2C In connection with the current discussion on explanatory proofs=2C and more= particularly about the difference between computer generated proofs and hu= man ones=2C I have something to add to what you wrote --drawn from my own e= xperience.=A0Humans do not have either the speed or the ability to hold the= enormous amounts of information that machines do. On the other hand=2C the= only way to see the big picture is speed of reasoning coupled with intuiti= on - naturally without checking the details at each step. That way=2C two t= hings may happen to humans of which computers are free of: (1) errors are m= ade=2C and (2) new ideas originate. Errors are not a good thing=2C =A0of co= urse=2C but they are a possible outcome from taking risks=2C without which = no new ideas would ever surface. Working out the details of that first glim= pse of the truth may be painful=2C but necessary. =A0It may lead to truth (= hardly ever)=2C 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=2C the seque= nce terminates eventually=2C and it does in truth. But it must begin with i= ntuition. Some of my collaborators have expressed surprise at my starting a= ny investigation with a title and an abstract=2C when they would leave both= for the end. Naturally=2C that title and abstract may very well change at = the end of the investigation=2C but if I were incapable to see the big pict= ure at first=2C I would not begin any work at all. A final trivial thought = - computation alone is not mathematics=2C and neither is intuition alone. T= he former is typical of machines=2C whereas the latter is typical of artist= s.=A0 Best regards=2CMarta ---------------------------------------- > Date: Mon=2C 25 Apr 2011 22:01:05 -0400 > Subject: categories: Re: Explanations > From: joyal.andre@uqam.ca > To: jds@math.upenn.edu=3B ronnie.profbrown@btinternet.com=3B graham@eecs.= qmul.ac.uk > > Dear Jim=2C > > 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=2C 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=2C we try hard to > integrate the new result in a larger body=2C > 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..... > > Andr=E9 > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]