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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: 3, Informative) by VLM on Tuesday February 14 2017, @09:42PM
Two countries separated by a common language. Its just "UK speak" for mathematics. From what I've seen of them, they talk very generically in conversation like "maths class" which in the USA would mean they're special education students still learning arithmetic even if they're high school students, because in the USA usually you take "math class" until you learn how to divide, and then you never take a math class again, you very specifically take "geometry class" or "trigonometry class" (trig) or "calculus class" (calc). You only take "math class" at age 18 if you're still mastering that addition thing at 18.
Its not just a math thing either, USA kids literally take "science class" until they're about 14 or so, then they start taking named courses of study like "chemistry class" or whatever.
An analogy the USA people might understand better is when I was a kid I ran into a group of arithmetic learning kids who called addition "plussing" and multiplication "timesing" and so on. Being a little kid I was more abrasive than I am now, and more or less asked them if they grew up in a fucking barn, but they weren't dumb or uncultured, that's just the weird way they were taught, there is no such thing as addition, there's just plussing using the plus operator and so forth. Addition, what a peculiar name for plussing, I'm sure I sounded weird to them too. When I was a little older I wonder what they'd call a sine function. Signing? Sinning?