Re: Cantor's circular "proof" that evens = integers

On 2007-05-12, in sci.logic, Herman Jurjus wrote:
Hm. Indeed this might work. I wonder why nobody has tried it yet?

Finding a way to explain mathematics, and related conceptual stuff, to
someone, in a way that connects with their understanding, requires considerable
effort; a necessary pre-requisite is also that the explainer himself
understands the results and concepts in sufficient detail to know which
technical details are relevant, which are not, to the confused person's
confusion, and so on. Such an understanding is not at all necessary for
doing ordinary mathematics, though it would be nice if textbook authors in
particular were more sensitive to such subtleties.

I made a few half-hearted attempts at this direction with Phil, but quickly
gave up. It just didn't seem interesting enough an exercise. Often people
who are knowledgeable in unrelated areas, and quite capable of thinking stuff
through on their own in their speciality, are remarkably disinclined to
suppose that when it comes to mathematics they are not in a much better
position than a beginning student. Sometimes this phenomenon is accompanied
by the bizarre idea that they, in fact, understand the mathematics in some
deeper way than the mathematicians themselves, having the benefit of a
special "outsider view". It's sporting to try and dissuade these people in
their fantasies, but rarely worth the effort. In contrast, many students of
mathematics are also confused about these issues -- for them there is hope,
and it is usually possible to make them see the light. The experience
also helps oneself to clarify the fundamental conceptual issues, or at least
provides good practice at mathematical pedagogy, getting closer to the
optimal way of conveying the mathematical understanding to a confused person
sharing the same sort of background, inclinations, natural ways of thinking,
and so on, as the one helped.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.

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