How to play mathematics

BOOK REVIEW

The Pearly Gates of Cyberspace, Author: Margaret Wertheim.
Physics on the Fringe, Author: Margaret Wertheim.
African Fractals: Modern Computing and Indigenous Design, Author: Ron Eglash.

(glasbergen.com)By Margaret Wertheim – 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 fibers 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.

Since at least the time of Pythagoras and Plato, there’s been a great deal of discussion in Western philosophy about how we can understand the fact that many physical systems have mathematical representations: the segmented arrangements in sunflowers, pine cones and pineapples (Fibonacci numbers); the curve of nautilus shells, elephant tusks and rams horns (logarithmic spiral); music (harmonic ratios and Fourier transforms); atoms, stars and galaxies, which all now have powerful mathematical descriptors; even the cosmos as a whole, now represented by the equations of general relativity.

The physicist Eugene Wigner has termed this startling fact ‘the unreasonable effectiveness of mathematics’.

Why does the real world actualize maths at all? And so much of it?

Even arcane parts of mathematics, such as abstract algebras and obscure bits of topology often turn out to be manifest somewhere in nature. more> https://goo.gl/ifKV2Z

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