FOM: An explanation of the method of thought experiments
rhersh at math.unm.edu
Sun Jan 4 13:00:24 EST 1998
The human race expires, and with it its culture including math, including
whatever we know about N.
Someplace else, some other race arises, attains consciousness in
some sense recognizable and even communicable to us (in imagination,
of course.) They live in an environment containing distinct, discrete,
reasonaly permanent, reasonably non-interacting objects. So they count,
and from their counting come in due time adding and so on.
Numbers are back! Are they the same numbers as befre, refuting
my statement that N disappeared with the human race?
Or are they a different N', even though possibly isomorphic to N?
Consider the daffodil in my front yard. After a certain passage of
time, it dies. No more stem, no more leaves, no more blossoms.
Then, perhaps years later, a new daffodil appears, in the same place.
Is it the same as the old one? No. Is it different? No, for it came
from the same bulb, which had the ability to generate a new daffodil.
What this question shows mainly is that the dichotomy new/old can
be simplistic and misleading. Sometimes we can only say that something
is new in one sense and old in another.
Since counting, and therefore arithmetic, arise from our interaction
with certain very general features of our environment, it is natural
to believe that if conscious life arose in a roughly comparable environment,
counting and arithmetic might reappear.
That wouldn't mean that N always existed Platonically, only that the
conditions for its appearance can reoccur here and there.
If any other culture element--art, music, politics--were to reappear
in another galaxy millions of years later, would you conclude that
art music and politics always existed Platonically? I hope not.
Thanks again for your very instructive letter.
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