I don't think the beautiful woman would accept "go read the Wikipedia article" as am answer.
N -----Original Message----- From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of Joseph Spinden Sent: Wednesday, April 17, 2013 8:21 PM To: The Friday Morning Applied Complexity Coffee Group Subject: Re: [FRIAM] Isomorphism between computation and philosophy Owen is right that there are N! ways to map a set of N objects 1-1, onto another set of N objects. The first object can go to 1 of N objects, the next to 1 of N-1, etc. That's pretty standard. As to the Halting Problem, Why not start with the first few lines of the Wikipedia article ? That is simple and easy to understand. Joe On 4/17/13 7:32 PM, lrudo...@meganet.net wrote: > Nick asks Owen: > >> So, Owen, you meet a beautiful woman at a cocktail party. She seems >> intelligent, not a person to be fobbed off, but has no experience >> with either Maths or Computer Science. She looks deep into your >> eyes, and asks "And what, Mr. Densmore, is the halting problem?" You >> find yourself torn between two impulses. One is to use the language >> that would give you credibility in the world of your mentors and >> colleagues. But you realize that that language is going to be of >> absolutely no use to her, however ever much it might make you feel authoritative to use it. She expects an answer. >> Yet you hesitate. What language do you use? >> >> You would start, would you not, with the idea of a "problem." A >> problem is some sort of difficulty that needs to be surmounted. >> There is a goal and something that thwarts that goal. What are these elements in the halting >> PROBLEM? And why is HALTING a problem? > Nick, Owen may well disagree, but from my point of view you've already > staked a dubious claim, by assuming (defensably) that "problem" in the > MathEng phrase "Halting Problem" can and should be understood to be > the same word as "problem" in your dialect of English. But this is, I think, a false assumption. Now, at least, whatever the case was when the "Halting Problem" > got its original name (in MathGerman, I think), the meaning that > "Halting Problem" conveys in MathEng is the same (or nearly the same) > as that conveyed by "Halting Question". "Problem" is there for > historical reasons, just as, in geometric topology, a certain question > of considerable interest and importance (which has been answered for > fewer decades than has the "Halting Problem") is still called--even in MathEng!--"the Hauptvermutung". The framing in terms of "a goal" and "something that thwarts" is delusive. There is, rather, "a question" > and--if you must be florid--a "quest for an answer". Note, "*an* > answer". Of course, at an extreme level (I can't decide whether it's > the highest or the lowest: I *hate* "level" talk precisely for this > kind of reason) there is *the* answer ("no"). But that isn't, in > itself, very interesting (any more: of course it was before it was > known to be "the" answer). *How* you get to "no" is interesting, and > there are (by now) many different "hows" (for the "Halting Question", the Hauptvermutung, Poincare's Conjecture, and so forth and so on), each of which is *an* answer (as are many of the "not hows"). > > ============================================================ > FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe > at St. John's College to unsubscribe > http://redfish.com/mailman/listinfo/friam_redfish.com > -- "Sunlight is the best disinfectant." -- Supreme Court Justice Louis D. Brandeis, 1913. ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
