[FOM] Convincing math-blind people that math is different
Harvey Friedman
hmflogic at gmail.com
Wed Dec 24 09:05:08 EST 2014
I don't know if this is what Tim Chow is aiming at, but it does come
to mind when I read his message. Look at stuff at, e.g.,
http://en.wikipedia.org/wiki/Bridge_probabilities
"The most common bridge hand suit distribution is 4-4-3-2."
For math-blinds (Tim's phrase), this can only be tested statistically,
and that gets into a whole different set of issues.
So we want to cut this down as follows.
Look at suit distributions of less than 13 card hands. Use the biggest
number less than 13 such that brute force computer technology will
count the number of hands for each suit distribution.
Compare the mathematical theory with what the computer technology determines.
The main point here is that some seriously interesting mathematics can
be tested - even absolutely verified - by computers. This is not the
case outside mathematics. This whole scene strongly suggests that
there is something different about mathematical knowledge.
The issues become more subtle when we move to purely universal
statements over all integers, or bit sequences. We also need to go
into this more deeply for the original 13 card bridge hands, as there
are too many to count.
Harvey M. Friedman
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