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Monday, February 20, 2012

"Does Math Really Exist"


"The bottom line is that human beings have brains capable of counting to high numbers and manipulating them, so we use mathematics as a useful tool to describe the world around us. But numbers and math themselves are no more real than the color blue – ‘blue’ is just what we tag a certain wavelength of light because of the way we perceive that wavelength. An alien intelligence that is blind has no use for the color blue. It might learn about light and the wavelengths of light and translate those concepts completely differently than we do."
The above comes from a Forbes magazine piece, of all places, that touches on (I think pretty weakly) the whole Platonist/Non-Platonist debate within mathematics... (does the human mind discover mathematics or create it?):

http://www.forbes.com/sites/alexknapp/2012/01/21/does-math-really-exist/

Long-term readers here know that I am fascinated with this very basic (philosophical) question of whether mathematics is a real part of the extant world, or merely a human cognitive construction. (see Web Platonism articles here or here.)

I have to believe that most of us with math inclinations grow up essentially as Platonists -- perceiving mathematics as real, whether or not any humans exist to explore it. But somewhere along the line, a lot of mathematicians step back to explore the question more openly, objectively, and casting biases aside, and end up swayed to the Non-Platonist side… I'm always impressed by some of these folks who not only see it that way, but seem to think it is rather obviously so (a mere human construction). While still leaning toward mathematical Platonism myself, each year I feel less certain of it. ...Circles, lines, prime numbers, etc. do not exist in the same sense that stars, hydrogen, or atoms do, but does that really make them less real than the latter??? -- they may not represent "real" things, but do they not represent real "relationships"?

One of the ideas that makes non-Platonism at least slightly more palatable is the notion, popular in many physics quarters these days, of a "Multiverse" -- the concept that the Universe we humans have long studied may be only one of many (or even an infinite number of) separate universes that exist. The "laws" and order we discover operating throughout 'our' universe, may simply not be operative in other unseen, separately-evolved universes (whose mathematics might therefore be hugely different). And then there is also (physicist) Max Tegmark's view that the entire Universe is nothing but mathematics ( “there is only mathematics; that is all that exists”).

The Platonist debate includes some purely semantic elements, and is less black-and-white than can be fleshed out here -- there are several possible non-Platonist stances, and the Platonist view itself comes in stronger and weaker forms -- certainly too complex an issue to ever resolve here... yet, a topic I'm continually drawn back to from time to time....

Lastly, a bit of an aside -- in the process of composing this post I chanced upon a couple of wonderful, past Martin Gardner (a well-known Platonist) book reviews bearing on the subject -- but you can read them for the sheer enjoyment of Gardner's prose apart from any philosophical content!:

http://www.newcriterion.com/articles.cfm/Larger-than-proof-2299

http://www.newcriterion.com/articles.cfm/Still-four-4349

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