FOM: Answers to some of Gonzales Cabillon's questions
JOE SHIPMAN, BLOOMBERG/ SKILLMAN
jshipman at bloomberg.net
Wed Mar 18 15:18:02 EST 1998
1) Mathematics on other planets may be very different *BUT* the alien
mathematicians will *NOT* have any theorems formulable in the language of
arithmetic (equivalently in ZF without the axiom of infinity) which contradict
any of our theorems. They may well contradict our theorems about real numbers,
for example if they work from the Axiom of Determinacy instead of AC.
2) I would not argue with this as far as arithmetical statements are concerned.
3) Conway constructed the surreals; nobody knows who discovered pi.
4-5) Existence need not be localizable, space and time are physics not math;
even if I were an atheist it wouldn't bother me that there was no mind to think
about the mathematical concepts "before" we arrived.
6) The first is (subjectively) extremely high, the second very low; did you
7) I'm working on a posting on this; computers are practically very important
to mathematics, and will become increasingly important.
8) Math activity must be in principle communicable, it doesn't matter when. - JS
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