Re: Why does Cantor a target for cranks?


Larry Hammick wrote:
On Dec 9, 9:32 pm, "Andrew Usher" <k_over_hb...@xxxxxxxxx> wrote:
Why are there so many on this groups whose mathematical goal is to
disprove uncountability? I can't imagine, really, why it would be a
crank target.
Well, when Cantor himself was around, it wasn't just the cranks who had
their doubts about his stuff. Remember Kronecker and Poincaré, who
were far from cranks. Set theory, axioms of choice, cardinals, and all
that stuff, were hotly disputed for quite a few years.
A survey of this branch of crankology:

http://www.crank.net/cantor.html

Wilfrid Hodges's paper "An Editor Recalls Some Hopeless Papers" at this
website (
http://www.crank.net/cgi-bin/redirect.cgi?http://www.math.ucla.edu/~asl/bsl/0401/0401-001.ps
) is especially telling; on page 3, he states: "It's nothing more than
a guess, but I do guess that the problem with Can­tor's argument is as
follows. This argument is often the first mathematical argument that
people meet in which the conclusion bears no relation to any­thing in
their practical experience or their visual imagination."

I'll add a minor detail: Nowadays many people work on computers and
software and they acquire a variety of bad habits of thought in the
process. One example (putting it informally) is the notion that if no
amount of RAM will ever be enough to distinguish one infinite ordinal
from another, then there must be something objectionable about
comparing infinite ordinals. That's just an example.

N. J. Wildberger's rant about Set Theory (I think it's "Set Theory:
Should You Believe?") also springs to mind. He states that we should
never consider big numbers, because we have no way to represent them in
the Universe. My reaction was the question of why we should abandon
something just because it's beyond the grasp of one particular
individual (Wildberger). The fact that that particular individual
should know better just reinforces my "beliefs".

--- Christopher Heckman

.

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