Re: the hourglass problem

From	JohnF <john@please.see.sig.for.email.com>
Newsgroups	sci.logic, rec.puzzles, sci.math.num-analysis, comp.programming, sci.math
Subject	Re: the hourglass problem
Date	2012-01-06 04:40 +0000
Organization	PANIX Public Access Internet and UNIX, NYC
Message-ID	<je5u08$bgf$1@reader1.panix.com> (permalink)
References	(5 earlier) <EHcNq.74840$U16.69957@newsfe15.iad> <op.v7lvoebf1r0rdn@dell3100> <hPhNq.106017$Rz.25659@newsfe29.ams2> <M_2dnXXRr9HfUZjSnZ2dnUVZ_gydnZ2d@earthlink.com> <tenNq.66080$_H.8059@newsfe16.iad>

Cross-posted to 5 groups.

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In sci.math Daniel Pitts <newsgroup.nospam@virtualinfinity.net> wrote:
> [...] Hence my suggestion that the interesting problem is
> "using the fewest turns, how do you get 'n' minutes".

Not obvious that complexity theory (or accumulated error)
thrown into the "hourglass instruction set" really adds
anything of abstract interest. But it did originally seem
to me like the "language" might have interesting semantics
until someone pointed out you could measure four minutes
and then every minute after (and including) seven, with
just the 4- and 7-minute timers. So the "computable set"
of times is pretty trivial, being N\{1,2,3,5,6}.
    Is there any way to make it more interesting?
For example, suppose you're only allowed to reset the timer
after it runs out. Does that make the computable times
more interesting? Is there any way to make it more interesting?
    If so, then a question about the "algebra" occurred to me,
as follows. Suppose you have a set S1={k1,t1, k2,t2, ..., kn,tn}
meaning k1 hourglasses that time t1, ..., through kn that time tn.
And suppose that allows you to "compute" times T1={some set of times}.
Then T1 is the "semantics" of S1. And suppose you also have an
S2,T2. How do they (algebraically) combine? That is,
what's the T for S1\/S2 (the set-theoretic "or"), and
what's the T for S1/\S2 (the set-theoretic "and") of the S's?
And how do these T's relate to T1 and T2.
    Of course, you first need an instruction set that
gives rise to non-trivial T's (subsets of N) in the first place,
if that's possible. If not, is there some kind of
instruction set that does? I'd imagine so, but couldn't
figure out what to google.
-- 
John Forkosh  ( mailto:  j@f.com  where j=john and f=forkosh )

Thread

the hourglass problem RichD <r_delaney2001@yahoo.com> - 2011-12-31 18:03 -0800
  Re: the hourglass problem William Elliot <marsh@rdrop.com> - 2011-12-31 19:21 -0800
    Re: the hourglass problem Dave Dodson <dave_and_darla@Juno.com> - 2011-12-31 19:41 -0800
      Re: the hourglass problem William Elliot <marsh@rdrop.com> - 2012-01-01 19:48 -0800
        Re: the hourglass problem Patricia Shanahan <pats@acm.org> - 2012-01-01 20:44 -0800
          Re: the hourglass problem William Elliot <marsh@rdrop.com> - 2012-01-01 23:08 -0800
            Re: the hourglass problem Patricia Shanahan <pats@acm.org> - 2012-01-02 07:55 -0800
              Re: the hourglass problem Dr Nick <3-nospam@temporary-address.org.uk> - 2012-01-02 16:17 +0000
                Re: the hourglass problem Robert Wessel <robertwessel2@yahoo.com> - 2012-01-03 03:37 -0600
    Re: the hourglass problem Remysun <remysun2000@yahoo.com> - 2012-01-02 17:10 -0800
      Re: the hourglass problem "BartC" <bc@freeuk.com> - 2012-01-03 01:12 +0000
  Re: the hourglass problem root <NoEMail@home.org> - 2012-01-01 05:51 +0000
    Re: the hourglass problem William Elliot <marsh@rdrop.com> - 2012-01-01 20:04 -0800
      Re: the hourglass problem Duncan Booth <duncan.booth@invalid.invalid> - 2012-01-02 11:42 +0000
    Re: the hourglass problem RichD <r_delaney2001@yahoo.com> - 2012-01-03 15:05 -0800
      Re: the hourglass problem Daniel Pitts <newsgroup.nospam@virtualinfinity.net> - 2012-01-03 15:19 -0800
        Re: the hourglass problem PT <ptanenbaum@consultant.com> - 2012-01-04 12:28 -0800
          Re: the hourglass problem Daniel Pitts <newsgroup.nospam@virtualinfinity.net> - 2012-01-04 13:44 -0800
        Re: the hourglass problem Dave Dodson <dave_and_darla@Juno.com> - 2012-01-04 22:55 -0800
          Re: the hourglass problem Daniel Pitts <newsgroup.nospam@virtualinfinity.net> - 2012-01-04 23:55 -0800
            Re: the hourglass problem "Harry Vaderchi" <admin@127.0.0.1> - 2012-01-05 10:06 +0000
              Re: the hourglass problem "BartC" <bc@freeuk.com> - 2012-01-05 13:44 +0000
                Re: the hourglass problem Patricia Shanahan <pats@acm.org> - 2012-01-05 08:13 -0800
                Re: the hourglass problem Daniel Pitts <newsgroup.nospam@virtualinfinity.net> - 2012-01-05 11:55 -0800
                Re: the hourglass problem JohnF <john@please.see.sig.for.email.com> - 2012-01-06 04:40 +0000
            Re: the hourglass problem Dave <dave_and_darla@Juno.com> - 2012-01-05 15:37 -0800
              Re: the hourglass problem Daniel Pitts <newsgroup.nospam@virtualinfinity.net> - 2012-01-05 16:02 -0800
  Re: the hourglass problem Duncan Booth <duncan.booth@invalid.invalid> - 2012-01-02 11:50 +0000
  Re: the hourglass problem Frederick Williams <freddywilliams@btinternet.com> - 2012-01-02 17:18 +0000
    Re: the hourglass problem msb@vex.net (Mark Brader) - 2012-01-02 17:40 -0600
      Re: the hourglass problem RichD <r_delaney2001@yahoo.com> - 2012-01-02 17:37 -0800
        Re: the hourglass problem msb@vex.net (Mark Brader) - 2012-01-02 23:45 -0600
        Re: the hourglass problem "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2012-01-03 10:06 +0100
        Re: the hourglass problem Thomas Mlynarczyk <thomas@mlynarczyk-webdesign.de> - 2012-01-03 12:51 +0100
          Re: the hourglass problem Nicolas Neuss <lastname@scipolis.de> - 2012-01-03 18:07 +0100
            Re: the hourglass problem Thomas Mlynarczyk <thomas@mlynarczyk-webdesign.de> - 2012-01-03 21:58 +0100
        Re: the hourglass problem Frederick Williams <freddywilliams@btinternet.com> - 2012-01-03 13:22 +0000
      Re: the hourglass problem "BartC" <bc@freeuk.com> - 2012-01-03 12:59 +0000
    Re: the hourglass problem Thomas Mlynarczyk <thomas@mlynarczyk-webdesign.de> - 2012-01-03 12:47 +0100
  Re: the hourglass problem Frederick Williams <freddywilliams@btinternet.com> - 2012-01-05 14:09 +0000
    Re: the hourglass problem Patricia Shanahan <pats@acm.org> - 2012-01-05 08:17 -0800
      Re: the hourglass problem Frederick Williams <freddywilliams@btinternet.com> - 2012-01-05 16:27 +0000
      Re: the hourglass problem Daniel Pitts <newsgroup.nospam@virtualinfinity.net> - 2012-01-05 11:57 -0800
      Re: the hourglass problem JohnF <john@please.see.sig.for.email.com> - 2012-01-06 06:42 +0000

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