...a companion blog to "Math-Frolic," specifically for interviews, book reviews, weekly-linkfests, and longer posts or commentary than usually found at the Math-Frolic site.

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"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck

"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)

******************************************************************** Rob Gluck

Tuesday, October 13, 2015

Of Myths and Madness (...and Math)


In a wonderful post last weekend  Peter Rowlett talks about popular math myths and inaccuracies:
http://aperiodical.com/2015/10/mathematical-myths-legends-and-inaccuracies-some-examples/

My favorite, of those cited, is the idea of Cantor being driven mad by the Continuum Hypothesis, which is followed up on by Richard Zach here:
https://www.ucalgary.ca/rzach/blog/2009/09/logic-and-madness.html

While I'd certainly agree that the Continuum Hypothesis, by itself, didn't drive Cantor mad, it's easy to imagine his obsessive-grappling with the entire mind-blowing subject of infinity as an ingredient in the process.
Zach actually touches on the broader issue of whether contemplating deep logical paradoxes perhaps leads to mental breakdowns, with other examples besides Cantor. The matter sometimes seems reminiscent of the Bible's tale of the Tower of Babel, where God thwarts the tower-builders from entering his domain by bestowing them with different languages, frustrating communication.
So too several mathematicians who thought they were approaching the 'mind of God' with their exploration of deep logical quandaries, instead were thwarted and unable to complete the task at-hand. The human brain, both its capabilities and limits, is endlessly fascinating.

Such ideas even bleed over into the whole Platonist/non-Platonist debate in math. Is our brain simply creating as we go along, the mathematics that seems to work in our particular universe... or are we discovering the immutable essence of all there is (as Max Tegmark argues, is the universe composed entirely of nothing-but mathematics).  And if our brains are indeed approaching that latter Platonic realm, then is there ultimately a price paid for doing so? If we stare at the sun... we go blind. What happens when we contemplate the deepest, most profound reaches of mathematics (or are we merely manipulating tautologies in our brain)? Like the statement, "This sentence is false," does the recursion of mathematically-thinking about mathematics, at the highest levels, eventually result in an endless loop of no escape? Are language and logic, impediments (instead of facilitators), to endless breakthroughs?

[Worth noting that the vast majority of working mathematicians do NOT end up in asylums, nor under psychiatric care, even if some of the most interesting and famous genius-level mathematicians of the past do fall into that category.]

Anyway, go read the other diverse myths/legends Rowlett serves up for debunking.


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