Re: Quotation concerning rational arithmetic

[Guy.Steele at CMU-10A]

In reply to GJC's message of 7 Jan:
True, Stoutemeyer did not mention those (modular and Boolean arithmetic);
but on the other hand, the New Math has been for the most part a
resounding failure, I suspect because it was poorly organized and because
it really is more useful to most people just to be able to add than
to understand why it works.  New Math tried to produce a generation
of mathematicians instead of (human) computers; the trouble is, the
world needs computers.  Imagine the disaster if we had thousands of
hydraulic physicists and no plumbers.
End of tirade about New Math.  (Feel free to disagree.  But I feel lucky
to have barely missed it.  My brother got New Math, and it was awful.)

As for accommodating these arithmetics in LISP:
(2) Boolean arithmetic is provided by the LOGxxx functions, on either
single bits or on sets of unbounded size (one may use signed integers
as sets over a countably infinite universe provided that either the set
is finite or its complement is finite).
(1) Modular arithmetic would be nice -- some algorithms can be more clever
if it is known that the result need only be mod some number.  *But* it
is nice to be able to pick your own modulus, rather than having some single
arbitrary power-of-two imposed!
--Guy