Programme

What makes equations correct? Are we looking for one super equation which describes the world around us, or is it not that simple? Why are we so hung on the fact that the laws of nature must have some sort of elegance and what are the criteria for this? During this talk about physics the aforementioned, and other, questions will be reviewed.

The wings of many birds, butterflies and beetles are strikingly patterned by colorful feathers and scales. Structural coloration occurs through the application of thin films, multilayers, or 3D-photonic crystals, sometimes in complex combinations and together with pigments. Thin films are widely applied in animal coloration. They are combined with pigmented multilayers in the breast feathers of the bird of paradise Lawes's Parotia (Parotia lawesii), allowing sudden changes from blue to green to golden colors. The silvery color of the nape feathers is due to regularly arranged melanin rodlets that create a reflective multilayer. The cortex of the feather barbs of the Common Kingfisher (Alcedo atthis) also acts as a thin film. In the orange breast feather barbs the cortex envelopes pigmented cells, but in the blue back feathers and the cyan tail feathers the cortex envelopes spongy cells, which act as quasi-ordered photonic crystals. Many butterflies use brightly reflecting multilayers, e.g. the famous Morphos and the common blues, but others employ gyroid photonic crystals, the optics of which is now well understood. The Diamond Weevil, Entimus imperialis, has large mono-crystalline photonic crystal domains in the single scales of diamond-type structure with distinct orientations in the scales cuticle. By applying microspectrophotometry, electron microscopy, imaging scatterometry, and finite-difference time-domain (FDTD) methods, the photonic response of the photonic crystals in the extremely colourful feathers and scales of birds, butterflies and beetles can now be understood in great detail. The colourful wings of the various animal species either play important roles in courtship display or rather in clever camouflage.

The person in the street (F/M) would probably not consider mathematics an art. Indeed, several parts of mathematical theory are of a dry and bookkeeping nature: verifications in the manner of an accountant. These necessary but dark branches of mathematics will stay in the dark today. The light will be on the artful construction of mathematical proof with elements that seem to come from the blue (as the light does). Theorems and proofs for all ages (of life) and from all ages (in history) will pass by. When not the mathematicians who completed these proofs will have been impressed by their own work, we will be!

In 1956, the Dutch graphic artist M.C. Escher made an unusual lithograph with the title 'Print Gallery'. It shows a young man viewing a print in an exhibition gallery. Amongst the buildings depicted on the print, he sees paradoxically the very same gallery that he is standing in. A lot is known about the way in which Escher made his lithograph. It is not nearly as well known that it contains a hidden 'Droste effect', or infinite repetition; but this is brought to light by a mathematical analysis of the studies used by Escher. On the basis of this discovery, a team of mathematicians at Leiden produced a series of hallucinating computer animations. These show, among others, what happens inside the mysterious spot in the middle of the lithograph that Escher left blank.

The idea that beauty is a sign of truth in science is intriguing and attractive. It recalls the ancient doctrine of the unity of the virtues, and it seems to promise scientists a route to identifying progress that does not depend on empirical tests. In this lecture, I will try to demystify the discussion by asking what we would need to establish in order to conclude that beauty is a sign of truth. We will see that the most plausible model of scientists’ aesthetic preferences suggests that there is a link of a particular sort between beauty and truth, and that scientists can use this link to pursue truths, but that the resulting practice is still based on empirical data.

Further reading:
James W. McAllister, Beauty and Revolution in Science. Ithaca, N.Y.: Cornell University Press, 1996.
James W. McAllister, “Is Beauty a Sign of Truth in Scientific Theories?”, American Scientist 86 (1998), pp. 174–183.