Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!ukma!tut.cis.ohio-state.edu!murthy From: murthy@tut.cis.ohio-state.edu (Murthy Gandikota) Newsgroups: comp.ai Subject: Re: Reasoning during dreams Message-ID: <40865@tut.cis.ohio-state.edu> Date: 28 Mar 89 20:37:54 GMT References: <2293@cps3xx.UUCP> Reply-To: Murthy Gandikota Organization: Ohio State University Computer Lines: 32 In article <2293@cps3xx.UUCP> hillman@cpsvax.cps.msu.edu (Thomas Hillman) describes a problem Herb Simon has posed: > Image a rectangular box. Now draw a line from one side of the box to >the other at the midpoint of the longest side. Next draw a line from >one corner to another. > Question: Do the two lines intersect? Can you imagine that they do? >Can you prove it on paper? > > --Tom- If the problem is as vague, then all I could do is guess or speculate even with my 3-d geometry background. But I am sure this problem can be solved using the line equations (3-d or 2-d depending on whether the two lines are on the same plane), if the meanings of "one side to the other" or "one corner to another" are made clear (mathematically or in some formal language). If someone doesn't want to give away the meanings, then all possible combinations of sides and corners can be considered. However, if the intent is to show that semantics of natural language are inadequate for certain kinds of proofs, I agree with a reservation. This should not be a case for mental visualization. Because if you change dimensions to 4-d I wonder what a "corner" means there...and what kind of visualization happens?...I suppose only symbols make sense. On the other hand if I've to visualize mentally "The Gardens of Eden" or "Hamlet's Physical Form" then you've a case. --murthy -- "What can the fiery sun do to a passing rain cloud, except to decorate it with a silver lining?" Surface mail: 65 E.18th Ave # A, Columbus, OH-43201; Tel: (614)297-7951