FOM: Re: Reuben Hersh: Mitteilungen der DMV (fwd)
rhersh at math.unm.edu
Sat Feb 28 20:32:01 EST 1998
On Fri, 27 Feb 1998, Ching-Tsun Chou wrote (excerpts):
> ...according to her calculation, if I squeeze a certain amount of a
> certain type of uranium in a certain way then there will be a gigantic
> explosion, I will take her much more seriously. Indeed, if I don't
> believe her assertion, she can dispel my doubts by demonstration. I
> don't think this kind of demonstration is available in most of the
> "social" constructs that Professor Hersh mentioned.
> It also seems to me that the line that Professor Hersh drew between
> things real and things unreal is somewhat arbitrary. >
> I guess Professor Hersh considers the five fingers on his left hand
> real, perhaps the number 5 too, but certainly not some very large
> numbers. But would he consider the electromagnetic field real?
> Indeed, I am rather doubtful whether my goldfish finds Beethoven's
> symphonies beautiful. However, if some beautiful theorem of Lagrange
> has some implications about the motion of my goldfish's body, I have
> very little doubt that it would indeed be the case. Similarly, I have
> very little doubt that many of the conclusions about the physical
> world that we can reach using the machinery of mathematics were true
> long before the rise of the humankind, are true now, and will continue
> to be true long after its demise. I wonder whether one can say the
> same about the beauty of Beethoven's symphonies.
Dear Dr. Chou,
Thank you for responding to my posting.
Yes, I think the e.m. field is real. And I think that the very
big number that I mentioned in my posting is real. The confusion is
about the word "real." We all understand about physical reality (what
we feel when we bang our heads on a low ceiling.)
But a traffic ticket or a layoff from our job or a suit for divorce are
also real! Only a different kind of reality. But definitely real!
The reason for my long list of social institutions and activities was
to convince you that social reality is really real! Like a jail sentence
or a draft notice, for instance. Real.
That was the first point. Social reality is really real.
It is not the same as physical reality. But it is real!
The second point was that math is real too, and it is
real as part of social reality. Including big, big numbers beyond the
size of any physical reality. More specifically, as the shared or
common thinking of certain people, including mathematicians and others.
You point out that math is different, it "works." Yes, math is
different from other aspects of social reality, and the other aspects are
different from each other. By saying math and religion are both
social realities I am certainly not saying math is religion or religion
The difficulty with identifying all math with the part that
has interpretations and applications in physics and engineering is
that you then have no explanation for the big part of math that
has no such interpretations or applications.
How about the undecidability of the axiom of
choice on the basis of the other Zermelo-Frankel axioms of set theory? What
does that say to your goldfish?
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