> [1] Gordon Fisher.
> Mr. Fisher seems to approve of the notion that it is mathematics
> if a (some? all?) mathematician recognizes it as mathematics. Then he
> identifies the presence of mathematics with the presence of numbers and
> their algebraical-logical treatment. (There are other layers to his
> response.)
> Since I was asking for a rule of thumb, it would be out of
> place to ask "which mathematician", etc. [...]
The position is somewhat circular, but such answers are sometimes
reasonable to cultural questions.
I think that Bruno LaTour, who has studied science laboratories as
anthropological objects, would agree that Mr. Tragresser's is a cultural
question, more like the question "How do I be courteous?" than like the
question "How do I make nitroglycerine?"
The follow-up question, though ought to be "What kinds of artifacts are
likely to be accepted by the community as mathematical?"
I follow Foucault in this, and say that acceptance of an artifact is
determined by the power of its advocates. I offer a few examples:
Notched bones are regarded as mathematical artifacts, despite the
speculative nature of their mathematical content, in part because of the
political power of those seeking a multicultural perspective on the history of
mathematics.
Mesopotamian mathematics are suffering a bit of a difficult decade,
partly because of the death and retirement respectively of two of its powerful
icons, Neugebauer and Aaboe, and partly because access to "new" artifacts has
been cut off by the political situation in Iraq.
Scholarship on Euler has waned since the fall of the Berlin Wall, since
some of the interest in his work was sustained by his role as a Cold War image
as an historical link between Russia and Germany.
Power in the scholarly community is usually gained by being right, so
usually, those artifacts identified by power blocs as mathematical will still
be accepted as mathematical by succeding generations. [I know of one
counterexample: Karpinsky identified the King of Spain's "Pragmatica sobre
los diez dias del anno" as mathematical because it dealt with the change in
the calendar, but I have doubts today.]
So, for a rule of thumb, an artifact will be accepted as mathematical
if its proponent can see in it ideas of number, shape or logic, and can
make enough other people see those ideas as well.
Ed Sandifer
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* Ed Sandifer * sandifer@wcsu.ctstateu.edu *
* Professor of Mathematics * *
* Western Connecticut State University* www.wcsu.ctstateu.edu/~SANDIFER/*
* Danbury, CT 06810 * *
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