Boyer's Constant
mthayer@BIX.com
Date: 25 Apr 1993 22:44:11 -0400 (EDT)
From: mthayer@BIX.com
Subject: Boyer's Constant
To: qed@mcs.anl.gov
Message-Id: <9304252244.memo.3955@BIX.com> Sun, 25 Apr 1993 22:44:12 -0400 (EDT)
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Javier Thayer expresses his concern about the size of Boyer's
Constant, and says:
>Unfortunately, I do not have a clue how one would answer
>this question in a convincing way other than by
>experimentation -- which seems to go against the
>aprioristic program suggested earlier in this discussion
>by several contributors.
There is some evidence from the psychological literature
that
BC = 7^n
where the exponent n is the number of layers of abstraction
between the base language and the target mathematical
language. This is a good a priori estimate,which, coupled
with Javier's first concern that:
>then much of what we are talking about in this forum about
>"doing real mathematics" is highly speculative and may border
>on self-deception.
leads me to believe that experimentation is highly necessary,
or that the foundational leanings of many of the group MAY be
highly misplaced.
The alternative of doing various areas of mathematics in a
language and symbolism very close to that in current use
(as suggested by e.g. Victor Yodaiken) would leave
us with a (possibly) large number of little theories, each
expressed in their own terms. Supposing that the
substitutional apparatus of the base system is VERY strong,
its other logical resources could be more limited.
The advantage of this sort of mulit-lingual approach would
be that it
1) would be allow experimental determination of the size
of Boyer's Constant
2) would resemble the way in which mathematics is normally
done, while
3) allowing for the (possible) discovery of principles common
to all the little theories.
Michael Thayer
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