Thursday, September 4, 2014

Halloween Manifestos, 2013:

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

Here and at Catholics for Classical Education.

See also Tom Wolfe on manifestos —

Wolfe on manifestos in 'From Bauhaus to Our House'

— and part of an interesting Sept. 2, 2014, manifesto by
Common Core supporter Keith Devlin:

“Graduate students of mathematics are introduced to further
assumptions (about handling the infinite, and various other issues),
equally reasonable and useful, and in accord both with our everyday
intuitions (insofar as they are relevant) and with the rest of
mainstream mathematics. And on the basis of those assumptions,
you can prove that

1 + 2 + 3 + … = –1/12.

That’s right, the sum of all the natural numbers equals –1/12.

This result is so much in-your-face, that people whose mathematics
education stopped at the undergraduate level (if they got that far)
typically say it is wrong. It’s not. Just as with the 0.999… example,
where we had to construct a proper meaning for an infinite decimal
expansion before we could determine what its value is, so to we
have to define what that infinite sum means. ….”

For a correction to Devlin’s remarks, see a physics professor’s weblog post —

“From a strictly mathematical point of view,
the equation 1+2+3+4+ … = -1/12 is incorrect,
and involves confusing the Dirichlet series with
the zeta function.”  — Greg Gbur, May 25, 2010

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