Apsuvax.1010
net.games
utzoo!decvax!ucbvax!ARPAVAX:mhtsa!allegra!psuvax!sibley
Fri Dec 18 13:19:21 1981
Life
Conway's Game of Life has a property most people are not aware of
(and possibly not interested in, but here goes anyway). In the original
Martin Gardner column in Scientific American it was asked whether there
was a configuration which grew without limit. Later this was found to be
true, namely there is a (stable) 'cannon' which shoots 'gliders'.
Conway's interest in this stems from the fact that the positive
answer to this question allowed him to show that Life is a universal
machine, in the sense that any mathematical statement can be 'coded'
into an initial Life configuration which, when allowed to run, will
terminate with an empty configuration if and only if the statement is
provably true. The sequence of configurations can be 'decoded' into a
proof. Of course, as with most such things it is incredibly inefficient.
As far as I know Conway never published the details of his proof, but they
might be included in his next book. (Not his previous book
'On Numbers and Games')
Conway continually invents games for the amusement of graduate
students at Cambridge (the one in England) and has also devised a very
useful way of doing date-to-day-of-week conversions in ones head.
He calls it the Doomsday Method. Extensions to this allow him to
calculate things like phases of the moon and the date of Easter in his
head. I have the details of Doomsday and (somewhere, I think) phases
of the moon, if anyone is interested.
dave
psuvax!sibley
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