A spontaneous Haiku inspired by a pithy friend's analysis of our discussion:
/The Halting Problem//
//Pretty Girl; Cocktail Party//
//Knowing when to sto//p/
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").
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