Have you heard of the Thompson Lamp, which turns itself on for one hour, then turns itself off for half an hour, then on again for 1/4 hour, off again for 1/8 hour, on for 1/16 hour, and on and on until the time has been exactly two hours since the beginning? No one knows whether the lamp is on or off after 2 hours.
(more…)

Since 1986, The Economist magazine has been running the light-hearted Big Mac Index to measure exchange rates. Based on the theory of purchasing-power parity (PPP), Burgernomics finds out how much a Big Mac costs in different countries, and thereby deduces whether and by how much a country’s currency is overvalued or undervalued.

The rational minds might object that the cost of a Big Mac cannot reflect exchange rates, as it is much influenced by number of KFCs, number of obese citizens, number of mad cows, or the existence of certain Monsieur Jose Bove. Nevertheless, Big Mac brings a vivid and fatty touch to the dismal science.

I imagine I lived in the ancient time, and was a hunter of deers and a forager of berries. I saw the direction of streams, the movements of stars, the shape of clouds in summers and winters, and the colours of trees in springs and autumns. The lawfulness of nature was apparent to me, although I could not decipher the details of its laws. What language must I invent to describe a generalization of nature? What system must I devise to bring together a list of abstract principles derived from observation and experience?

Reading I-Ching, the sweeping vision of nature and humanity in ancient times spreads before me. I-Ching, also known as the Book of Change, is a system said to be originated by Fu Hsi (~2800BC). Using a binary notation to denote an extraordinary set of symbols, it is a system to interpret the processes of nature, and thereby the affairs of man.
(more…)

Perhaps partly inspired by Hermann Hesse’s classic The Glass Bead Game, this remarkable book by Manfrend Eigen and which uses simple games to illustrate concepts from the natural world, such as equilibrium, selection, and growth. In particular, it shows how the interplay of rules and chance can generate the rich complexities in nature — as well as in society. It is a difficult yet delightful book, mingling the playfulness of games with the wonderments of nature.

Image above showing the dissipative patterns of Zhaboutinsky reaction discussed in the book.

A curiosity in the topological spaces, the Alexander Horned Sphere is formed by pushing out two horns from a sphere, twisting the horns together, pushing out two more horns from each horn, twisting the new horns, pushing out more horns, ad infinitum. Here is a monster that is topologically the same as a sphere, although its space outside is not topologically equivalent to that of a sphere.

Could it be some sort of Martian brocolli, or weird sponge in the sea? Or an Alexander Horned Croissant would be nice for breakfast, would it not?