On Dec 29, 2006, at 1:32 PM, Fred Bone wrote:
On 29 Dec 2006 at 12:08, Devon McCormick said:
Someone I know once calculated that there should be a 4000-year
correction
as well, to whit: there is an exception (flip parity) to the
"divisible by
400" exception if the year is divisible by 4000.
Less than optimal.
The current setup is equivalent to a mean year of 365.2425 days. The
actual mean tropical year is 365.242199 days. The discrepancy is just
over 26 seconds a year, or 1 day every
%365.2425-365.242199
3322.259136
years.
Omitting a leap year every 4000 years under-corrects, giving a mean
year
of
365+-/%4 100 400 4000
365.24225
days, which is still too long by 1 day every
%365.24225-365.242199
19607.84314
years: you need to omit another leap year at about this interval (say,
every 20000 years).
A better match IMHO is to omit once every 3200 years. This gives a
mean
year length of
365+-/%4 100 400 3200
365.2421875
days, which is too short by one day in
%365.2421875-~365.242199
86956.52153
years, which doesn't seem to admit a neat adjustment (though putting a
leap year back every 86400 years has a certain attraction).
However, since any change to the current calendar requires agreement
among at least most of the world's governments, it probably won't get
dealt with any time soon.
I wrote the essay "How Long is a Year" in APL Quote Quad 7.4, Winter
1977. It shows how to determine whether a year is common or leap,
assuming that the corrections occur in every 4th year, but not every
100th year unless it is also divisible by 400. It speculates about
extending this to include not every 3200th year unless it is the
86400th year. Such a correction would be one day off in a little over
thirteen and a half million years.
The article points out that 86400 is also the number of seconds in a
day -- which caused a Danish woman to have an intellectual orgasm. It
also led Jeffrey Shallit to write a joint paper with Erdos, which,
since I had written a joint paper with Jeff, gave me the Erdos number 2.
Phrase 14.B.m11 helps answer the question Is Year Y a Leap Year or
Common.
Eugene
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