First notable extract (p3, footnote):
In modern medical terms, it's fairly clear that G.P.L.F. Cantor suffered from manic-depressive illness at a time [1800s] when nobody knew what this was, and that his polar cycles were aggravated by professional stresses and disappointments, of which Cantor had more than his share. Of course, this makes for less interesting flap copy than Genius Driven Mad By Attempts To Grapple With ∞. The truth, though, is that Cantor's work and it's context are so totally interesting and beautiful that there's no need for breathless Promethiusizing of the poor guy's life. The real irony is that the view of ∞ as some forbidden zone or road to insanity—which view was very old and powerful and haunted math for 2000+ years—is precisely what Cantor's work overturned. Saying that ∞ drove Cantor mad is like mourning St. George's loss to the dragon; it's not only wrong but insulting.
(Isn't that blazingly clear and refreshing writing?)
Second notable extract (p41):
The standard way [of dealing with the Paradox of Galileo] is to declare infinite sets the math equivalent of unicorns ... The other—which is revolutionary, both intellectually and psychologically—is to treat Galileo's paradoxical equivalence not as a contradiction but as a description of a certain new kind of mathematical entity [as G. Cantor did]... Except on the other hand such an attitude could not be revolutionary but merely insane. Rather like taking the fact that nobody's ever once seen a unicorn as claiming ... that unicorns constitute a whole new kind of animal with the property of invisibility. Here of course we get The Fine Line Between Brilliance and Madness that modern writers/filmmakers dine out on. The truth is that all manner of strange [concepts] originally entered math under the same sort of insanity/incoherence cloud but are now totally accepted, even essential.
There's lots more (ob-viously) and I haven't finished it yet but cool huh? And appropriate to the current topic in comments.
5 comments:
i love it i love it brilliance and madness and oh how glad i am to be a little loopy even though this sometimes leads me to fits of low self esteem when i feel as though i don't quite fit in or people look at me a little funny in a way that assume to mean she's a bit loopy isn't she. not that i am claiming any particular brilliance. that would be cocky. bye.
yes it is true, that is clear and refreshing writing!
And Cantor has reminded me of Boltzmann who was around at a similar time and would also have been diagnosed as a manic-depressive if he were about today, and also, despite that he made a massive imapact such that he now has his name repeated endlessly to undergraduate physics students!
yes it is cool. huh.
:-)
lise cool; and aww; and you are quite brilliant. bye!
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