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 DannyB on Tuesday February 14 2017, @09:00PM
fascinating: The act of attaching two objects together so they are permanently bonded.
English isn't screwed up. It just wasn't planned by someone having good mathematical or logical skillz. It doesn't help that partial merges were done with vocabularies from other languages.
The lower I set my standards the more accomplishments I have.
(Score: 2, Interesting) by Oakenshield on Tuesday February 14 2017, @09:51PM
(Score: 2) by NewNic on Tuesday February 14 2017, @11:57PM
I think that some of those examples of the "meaningless do" are cases where the use of "did" adds clarity. It's not useless because the use of "did" makes it clear that it is a question, not a statement.
lib·er·tar·i·an·ism ˌlibərˈterēənizəm/ noun: Magical thinking that useful idiots mistake for serious political theory