...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

Sunday, December 15, 2013

Of Dinosaurs and Mathematics... and Pathos



Anyone up for some philosophical reflection on a lazy Sunday morning...?

(image via Danny Cicchetti/WikimediaCommons)

Vocal math Platonist Martin Gardner famously wrote that if 2 dinosaurs met 2 other dinosaurs in a clearing, there would then be 4 dinosaurs present… whether or not there was any human mind around to appreciate the fact, and whether or not there existed any such words as "two" or "four," the relationship would still exist completely apart from human recognition of it. In fact, Gardner (who was actually more a philosopher than a mathematician) largely scoffed at the few professional mathematicians in his day who claimed that mathematics was merely some sort of human/cognitive creation. The case against Platonism has grown since then, with fewer, though still many adherents.

Non-Platonism comes in several different varieties and degrees, but Platonists tend to more uniformly feel that mathematics is a real, ubiquitous component of the Universe (or, in the case of Max Tegmark, they believe math is ALL there is -- it is ultimately the only component or structure of the Universe; p.s., Tegmark's new book "Our Mathematical Universe" will soon be out).

Much of this debate continues to seem semantic, hinging on what one means by words like "real," "existence," "component," and other words that simply can't be defined in terribly rigorous/consistent ways (even "mathematics" is not that easy to define). Is mathematics 'out there' in the Universe, apart from us and our existence, or is it only inside our heads, generated from neurochemical processes?

I bring all this up because recently Jason Rosenhouse broached the Platonist/Non-Platonist divide in this post where he addresses interview comments from Platonist/recent-author Ed Frenkel:

http://scienceblogs.com/evolutionblog/2013/12/13/in-what-sense-do-mathematical-objects-exist/

I tweeted a link to the above post when it first came out, but deliberately held off posting about it here right away, because I suspected it might lead to some engaging discussion in Jason's comment section… and, it has. Eventually, Ed Frenkel himself responded (twice), and all the discussion has been quite interesting... unless that is, you're in the camp that finds such philosophical debate sleep-inducing! ;-)

It certainly seems to me that if "science" has any reality in the Universe (and we're not just living in a simulation imposed by highly-advanced aliens) then there are elements of mathematics that must be real and integral to the Universe's operation -- if math ISN'T "real" in some sense, then "science" (which is based upon it) must also not be real, which implies that the Universe, rather than having 'order,' 'laws,' and causation as we perceive, is a rather hopelessly random/chaotic place (...which in turn assumes that "randomness" can truly exist!???)... but whether all of mathematics exists in some Platonic sense or only elements of it is more of a leap, and perhaps, as I say, more an argument over words and meaning, than mathematics itself... In any event, read Jason's take and the conversation that follows it.

....I wrote the above words yesterday for posting today, then this morning woke up to a tweet from Alexander Bogomolny linking to this quote on a discussion forum, from "Thelonious Mac," which somehow seems worth closing with:
"I just saw a television program in which a mathematician lost his daughter. Unable to express himself in the language of platitudes that most people use at such a time, he created a series of equations to represent her life, a work of art, expression, in math. Yes math is beautiful. There is absolutely no aspect of our lives for which you will not find math at its foundation. If I have a glass of clean water today, it is because of the math behind the engineering that brought it to me.
Math is the mother of all science. Without it, our lives would be incomprehensibly pathetic."

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