Re: language wars (results 13 September) last posting

[ken@coho.halcyon.com (Ken Pizzini)]

In article <528lab$6af@mill.gdls.com>, Art Schwarz <schwarza@gdls.com> wrote:
>Just to provide a basis for settling the discussion, why not contribute
>your procedure to generate the appropriate statistics and contribute a
>summary of the statistics. It seems that the conjecture that Friday the
>13th (or any other day) occurs more frequently / less frequently than
>anything is demonstrable, so demonstrate.
>
>To be more contentious, there have been 2 (?) postings of algorithms.
>Before questions are levied on implementation or language features,
>post an algorithm which demonstrates your case.

I'm not sure, but I suspect that this posting was prompted by my
ill-considered posting where I unfairly hinted at the possibility
that someone's Smalltalk implementation was flawed.  I was basing
my claim on a mathematical proof, which unfortunately depended on a
lemma which I failed to prove, and which turned out to be false.  I
canceled that article twice -- once shortly after posting, when I
realized my error, and again after someone re-posted my article in
an attempt to clean-up after a rogue canceler.

For the benifit of other mathematically inclined calendar watchers,
the lemma was that a 400-year interval had a number of days which
is not divisible by 7.  Other simple lemmata about the calendar and
a dash of group theory would then show that the 13th of a month
will be equidistributed across the days of the week over any
multiple of 2800 years.  (The "proof" I had would not rule out
shorter periods, but the existence of such a period was sufficient
for the question at hand.)  Unfortunately for my proof, the number
of days in any 400 year interval on the Gregorian calendar *is* a
multiple of 7, and thus some other form of analysis is required
to determine what the distribution of the days of the week that
the 13th of a month fall on is.

		--Ken Pizzini