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Margaret Wertheim's wide-ranging essay on mathematics, "There’s more maths in slugs and corals than we can think of" covers how mathematics is implemented by humans, animals, or natural processes. It is clever and thought-provoking. Quite long, but well worth the read. Among other topics, the author touches on music, Fourier transforms, tiling, and coral reefs.
What does it mean to know mathematics? Since maths is something we teach using textbooks that demand years of training to decipher, you might think the sine qua non is intelligence – usually 'higher' levels of whatever we imagine that to be. At the very least, you might assume that knowing mathematics requires an ability to work with symbols and signs. But here's a conundrum suggesting that this line of reasoning might not be wholly adequate. Living in tropical coral reefs are species of sea slugs known as nudibranchs, adorned with flanges embodying hyperbolic geometry, an alternative to the Euclidean geometry that we learn about in school, and a form that, over hundreds of years, many great mathematical minds tried to prove impossible.
[...] The world is full of mundane, meek, unconscious things materially embodying fiendishly complex pieces of mathematics. How can we make sense of this? I'd like to propose that sea slugs and electrons, and many other modest natural systems, are engaged in what we might call the performance of mathematics. Rather than thinking about maths, they are doing it. In the fibres of their beings and the ongoing continuity of their growth and existence they enact mathematical relationships and become mathematicians-by-practice. By looking at nature this way, we are led into a consideration of mathematics itself not through the lens of its representational power but instead as a kind of transaction. Rather than being a remote abstraction, mathematics can be conceived of as something more like music or dancing; an activity that takes place not so much in the writing down as in the playing out.
(Score: 2) by maxwell demon on Wednesday February 15 2017, @08:14AM
OK, so now we know where the mathema comes from. But what is the origin of the tics?
The Tao of math: The numbers you can count are not the real numbers.
(Score: 3, Funny) by aristarchus on Wednesday February 15 2017, @08:50AM
Nervous reflex, no doubt. Those ὁι μαθηματικὸι tend to be a twitchy lot!
(Score: 2) by FatPhil on Thursday February 16 2017, @04:22PM
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 2) by aristarchus on Friday February 17 2017, @12:05AM
"Those ὁι ...", surely that can't be right?
Well, we have to distinguish between "Those ὁι ...", and "These ὁι ...", not to mention the hoi polloi. Demonstratives go fine with articles!
Now we need to get back to Sextus Empiricus' fine work, Adversus Mathematicos. Or consult St. Augustine, who wrote: "Unde concludit: Quapropter bono Christiano sive mathematici, sive quilibet impie divinantium, et maxime dicentes vera, cavendi sunt: ne consortio daemoniorum animam deceptam pacto quodam societatis irretiant." Or was that Aquinas?
(Score: 2) by FatPhil on Friday February 17 2017, @12:17PM
Anyway, thanks for the Greek clarification, I can't think of a construct that works quite the same way as the Greek in any language I am familiar with (and can't pretend to understand the full implications of the "hoi"). In some ways, it does justify the three word phrase you use above, because if neither these hoi polloi nor those hoi polloi are the real hoi polloi, then only the real hoi polloi are *the* hoi polloi?
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves