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Unfortunately, I'm still quite busy, so I don't have enough time to do this entry justice. I've been reading The Mystery of the Aleph by Amir D. Aczel. This is a book about how the mathematical concept of infinity was developed starting from its origins in ancient Judaism through today. Briefly, the Kabbalah was a secret society dedicated to the study of the Torah. The Kabbalists understood God as infinite in a very similar sense to how infinity had been previously described by the Greeks, such as Pythagoras. (Incidentally, when I showed my piano teacher this book, she showed me another book on the Kabbalah that listed Jesus as a Kabbalist, and described "walking on water" as part of the practice.)

The primary focus of the book is on the life and work of Georg Cantor, who proved that the integers and rational numbers were infinite sets that had the same cardinality (same number of elements), and that the real numbers, while also infinite, had a greater cardinality. However, he became depressed when he was unable to prove that the cardinality of power set (set of all subsets) of the integers was equal to the next highest cardinality. (This is known as the continuum hypothesis.) Quite possibly, his depression was worsened by his struggles with Kronecker, another mathematician who did not believe any of his theories and tried to discredit him.

Depression seems to be a common theme among those who studied concepts related to infinity. Several of the pioneers of algorithm theory (e.g. Gödel, Post) also seemed to suffer from some form of it. I don't think this is a coincidence. Actually, I have recognized, to some extent, my own depression in the difficulty of solving certain types of math problems, such as the puzzles and computability theory-related problems I've written about earlier. I think part of the problem is the paradoxical nature of such problems; I twist my mind into knots sometimes trying to solve them.


( 3 comments — Leave a comment )
Mar. 10th, 2005 12:07 pm (UTC)
my ex-girlfriend actually bought me that book as a gift. i read it on the way to the airport and generally enjoyed it.

i also remember enjoying 'innumeracy' or something...
Mar. 10th, 2005 09:21 pm (UTC)
I believe mathematics is as dependent upon creative interpretation for advancement as any art form. A relationship between science's and art's natures "in cognition" could explain a lot.

Your post reminds me of a book: Dr. Kay Redfield Jamison's Touched With Fire. She discusses genetic relationships between affective disorders (depression and bipolar disorder) in those with exceptionally high IQ's or creative abilities; my take on her views was there's potential that what cellular manifestations of expression of extremesis of any form we see in individuals may perhaps be forms of 'dialect' of the same genetic message which are sometimes expressed as genius, sometimes as illness. Kind of versions of high and low chemical tides, governed by something biochemically similar to the sleep cycle... & this is especially interesting in light of your observation on depression & mathematicians, if you consider high abilities of reason concomitant with the abilities of the sort Jamison considered for the book (& why wouldn't you, when you consider the intimacy of mathematics & music)...

Gifted=burdened? Perhaps by definition.
Mar. 10th, 2005 10:31 pm (UTC)
Aczel noted that Cantor's might've had bipolar disorder. Also, with regards to sleep, he touched on the life of Descartes, who was a sickly child, spent extra hours in bed thinking about math and philosophy until he felt well enough to get up. Descartes credited his success to being able to lie in bed and ponder.

( 3 comments — Leave a comment )