Newsgroups: comp.ai.philosophy Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!caen!hellgate.utah.edu!fcom.cc.utah.edu!fcom.cc.utah.edu!dirish From: dirish@csc-sun.math.utah.edu (Dudley Irish) Subject: Re: how many distinct thoughts can a person have? In-Reply-To: thomas@ckgp.UUCP's message of 20 Jun 91 23:28:54 GMT Message-ID: Sender: news@fcom.cc.utah.edu Organization: Department of Mathematics, University of Utah References: <1991Jun19.033316.18773@athena.mit.edu> <1991Jun19.195149.19583@panix.uucp> <607@ckgp.UUCP> Distribution: usa Date: 21 Jun 91 07:41:38 I am sure that that you have all heard the old saw, "You can never step into the same river twice." I would similarly argue that you can never have the same thought twice. Thus, for as long as you live you are constantly having different thoughts. There are two questions here. First, does this sequence map to the integers or to the real numbers, in other words, is the sequence of brain states countably infinite or uncountably infinite. The other question is whether because people only live a finite time we want to accept that the sequence of thoughts has an end or whether we want to take a theoretical stance where we don't view the sequence as ending. Now, be careful. Remember the number of real numbers from zero to one is uncountably infinite. If you believe that thoughts map to the real numbers rather than the integers this still leaves you with an uncountable number of thoughts. Also, the number of rational numbers from zero to one is countably infinite. Thus if between every pair of thoughts there is another thought, then even if we take the sequence as ending, it still is countably infinite. So you simply must decide whether thoughts are continuous or not. I don't have a clue as to how to decide this issue. Now, before you think to flame me for a screwup in my understanding of cardinal number theory, I will warn you that my favorite mathematics professor taught a set theory class two quarters ago that I sat in on. I seriously believe that I remember all this stuff correctly. Though what it has to do with AI, I don't know. -- Dudley Irish / dirish@math.utah.edu / Manager Computer Operations Center for Scientific Computing, Dept of Mathematics, University of Utah The views expressed in this message do not reflect the views of the Dept of Mathematics, the University of Utah, or the State of Utah.