Mathematical Inspiration from the Sea

The Census of Marine Life is one of the truly big scientific endeavours of our time. Together with loads of scientific results, it produced incredible images of an alien world, largely unknown and full of wonders.

The NOAA maintains a website with many quotes along the lines of the following:

» Man’s perpetual curiosity regarding the unknown has opened many frontiers. Among the last to yield to the advance of scientific exploration has been the ocean floor. Until recent years much more was known about the surface of the moon than about the vast areas that lie beneath three-fourths of the surface of our own planet. «

— In Submarine Geology (1948) by F. P. Shepard. p. 1.

The situation was not much different when the Census of Marine Life started and this is one of the reasons why life from the deep can still astonish and inspire us.

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The Dihedral Group

Snow flakes are one of nature’s beauties which are easy to appreciate even for the more mathematically or technically minded. Kenneth G. Libbrecht produces wonderful photographs of them; some are available online.

The symmetry of snow flakes is described by the dihedral group. This is one of the first groups described in Felix Klein’s book I have advertised before. Here is my illustration of how Klein described this group geometrically.

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Lectures on the Icosahedron

Some weeks ago, I was looking for examples giving me a quick overview on how to control transparency in the raytracer POV-Ray. This took me to the website of David Dumas who has beautiful illustrations of limit sets. (A very good and accessible introduction to the beauty of the Kleinian groups behind this is given by the book “Indra’s Pearls” [1].) What took me as even more beautiful were the pages from old mathematics books he is using as a background.

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Believers in the Axiom of Choice

There was a time back at the university, when pretty much any question about mathematics I came up with led to the axiom of choice. This seemingly innocuous and at first sight quite reasonable axiom leads to pretty strange conclusions such as the Banach–Tarski paradox. Roughly speaking, it requires that for any collection of non-empty sets it should be possible to construct an element of the Cartesian product.

Here are two of the questions I had at the time:

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Welcome

Every now and then, mathematics and the sciences allow us glimpses of a fascinating world. Here, I wish to share some of those glimpses which are particularly fascinating to me.

Stay tuned for my views on things I deem worth a look such as

Tilings,
Diatoms,
Virus capsides,
Radiolaria,
Soap bubbles,
Protein structure,
L-Systems,
Snow flakes,
Crystals,
Fractals,
Butterfly wings,
Swarms.

This blog gives my personal opinions and view of the world.
In my professional life, I am a computer scientist and you can learn more about this facet at LinkedIn, Google Scholar, and ResearchGate.