Frogs, science and magic mirrors

Levitation without meditationThe IOP has just launched a podcast feed (hat tip Yan Feng). Their first post (mp3 here) is a 20 minutes interview with Michael Berry, of the eponymous phase fame, whose work on levitating frogs earned him an IgNobel Price in Physics in 2000. Professor Berry talks neither of his phase nor his frogs in the interview, but of his current research on optics (having to do with conical diffraction and the angular momentum of light), and the relationship between science and art (he is very fond of images representing optical phenomena, as you can see in this beautiful gallery). He has also a couple of things to say about the interplay between theoretical work and practical applications and the part played by science in our society. In this regard, his little piece Living with Physics (pdf) and his unpublished Night thoughts of a theoretical physicist (pdf) are very worth reading; for instance, here’s a quite inspiring musing on the unity of science:

From science come inspiring and magical connections between very different things. This observation counters one of our commonest criticisms: that by the reductionist disarticulation of the world into its parts, which are then studied separately, we lose the sense of the whole. My favourite example starts with the question: Why is matter hard? Atoms consist mostly of empty space, after all, so why doesn’t matter squash down, with all the electrons collapsing into their lowest quantum energy states near the nuclei? Because this is prevented by the Pauli exclusion principle: no two electrons can be in the same state. And where does that come from? It could well originate in a property of rotation in three-dimensional space4: holding a glass of wine, you can turn it completely twice (that is, through 720°) and find at the end of this contortion that your arm is untwisted (this does not work for a single turn). I find that `two into none’ connection, that totally unexpected association of microscopic hardness with geometry5, miraculous.

A Makyoh in action. Click for more pictures.By the end of the interview, Berry returns to his research and mentions a quite curious recent result of his, the explanation of the workings of the oriental magic mirrors called Makyoh. This bit caught my eye (well, i guess it was my ear) because i had never hear of those magic mirrors before. They’re quite amusing. These cast and polished bronze mirrors, manufactured in China and Japan since at least 500 BC have a pattern embossed on the back that magically appears in a patch of light reflected by the mirror face (which to the naked eye looks as smooth and polished as one can get, except for a bit convexity). You can see a Makyoh in action in the figure on the right (more here): the pattern in the reflected light patch is nowhere to be seen in the mirror’s surface, which reflects images as a regular, slightly convex mirror would do. Credit for explaining the trick usually goes to Ayrthon and Perry, but, according to this article of the 1911 edition of the Encyclopedia Britannica,

The true explanation of the magic mirror was first suggested by the French physicist Charles Cleophas Person in 1847, who observed that the reflecting surface of the mirrors was not uniformly convex, the portions opposite relief surfaces being plane. Therefore, as he says, ‘ the rays reflected from the convex portion diverge and give but a feebly illuminated image,while, on the contrary, the rays reflected from the plane portions of the mirror preserve their parallelism, and appear on the screen as an image by reason of their contrast with the feebler illumination of the rest of the disk. Such differences of plane in the mirror surface are accidental, being due to the manner in which it is prepared, a process explained by W. E. Ayrton and J. Perry (Prot. Roy. Soc., 1878, vol. xxviii.), by whom ample details of the history, process of manufacture and composition of Oriental mirrors have been published.

I haven’t found these original papers on-line, but you can learn more about the history of Ayrton and Perry’s discoveries in this page on magic mirrors from Grand Illusions. A more in-depth treatment of the optics involved is given in Michael Berry’s article Oriental magic mirrors and the Laplace image (pdf), where he explains how the Laplacian of the relief height function gives rise to the image in the reflected patch (see also this article for comments on Berry’s and a bit more on the history of Makyoh).

I find Professor Berry’s willingness to investigate funny, every-day problems refreshing, not to mention his concern on making the physicist’s world closer to outsiders, like, say, taxi drivers. Or, as Berry himself puts it:

A source of delight is uncovering down-to-earth or dramatic and sometimes beautiful  examples of abstract mathematical ideas: the arcane in the mundane.

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One Response to “Frogs, science and magic mirrors”

  1. JustCurious Says:

    Nice post…thanks!! It might be interesting check out http://suhasinigururaja.blogspot.com/2006/08/talks-contd-makyoh-images.html for some more interesting cool facts on this subject.

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