Mathematical Inspiration from the Sea

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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.

In 1872, expedition vessel HMS Challenger set sail with very similar goals in mind to those of the census. Until 1876 it sailed over 100 000 kilometres, all the time sounding, sampling and probing the sea. The scientific outcome is summarised in the massive Report of the Scientific Results of the Exploring Voyage of H.M.S. Challenger During the Years 1873-76.

(Another reason at that time to get the measure of the bottom of the sea was to prepare the ground for the laying of undersea cables. This is another fascinating topic worked out in some detail in Neal Stephenson’s Wired article Mother Earth Mother Board.)

Hermann Weyl used illustrations from Ernst Haeckel’s Challenger Monograph in his beautiful book on symmetry to show polyhedral symmetry in nature. This is where I first saw illustrations of radiolaria and I cannot help but feel mathematics at work when I behold them.

I wonder just how many wonderful scientific illustrations are hidden between the covers of old (and new!) scientific books, only glimpsed by a few researchers in the respective fields. The Challenger Monograph and books like Hooke’s Micrographia and Vesalius’s De humani corporis fabrica libri septem are probably among the better known. Let me know of your favorite scientific illustrations in books with a small readership in the comments.

So what is interesting about radiolaria? They are small (0.1-0.2 mm) unicellular organisms living in the sea as part of the zooplankton. However, they are the knights among the zooplankton, covering themselves in an armour in the form of a mineral skeleton. They come in such a wonderful variety of shapes that you simply must see an excerpt of the animated documentary film Proteus – A Nineteenth Century Vision based on Haeckel’s drawings to get a first idea:

Now, the science of shape is mathematics, so to me it seems impossible not to be aroused mathematically by these organisms. As a layman in biology, I can only wonder: how much of the shape of the radiolaria’s skeleton is encoded in their genome and how? I am sure, however, that the path from radiolaria genomes to the shape of their skeletons is full of mathematics.