In 1982, computer scientists Edward Fredkin and Tommaso Toffoli suggested that it might be possible to construct a computer out of bouncing billiard balls rather than electronic signals. Spherical balls bouncing frictionlessly between buffers and other balls could create circuits that execute logic, at least in principle.

In 2011, Yukio-Pegio Gunji and his colleagues at Kobe University extended this idea in an unexpected direction: They found that “swarms of soldier crabs can implement logical gates when placed in a geometrically constrained environment.” These crabs normally live in lagoons, but at low tide they emerge in swarms that behave in predictable ways. When placed in a corridor and menaced with a shadow representing a crab-eating bird, a swarm will travel forward, and if it encounters another swarm the two will merge and continue in a direction that’s the sum of their respective velocities.

Gunji et al. created a set of corridors that would act as logic gates, first in a simulation and then with groups of 40 real crabs. The OR gate, where two groups of crabs merge, worked well, but the AND gate, which requires the merged swarm to choose one of three paths, was less reliable. Still, the researchers think they can improve this result by making the environment more crab-friendly — which means that someday a working crab-powered computer may be possible.

(Yukio-Pegio Gunji, Yuta Nishiyama, and Andrew Adamatzky, “Robust Soldier Crab Ball Gate,” Complex Systems 20:2 [2011], 93–104.)

The historian Socrates tells us that the Emperor Tiberius, who was much given to astrology, used to put the masters of that art, whom he thought of consulting, to a severe test. He took them to the top of his house, and if he saw any reason to suspect their skill, threw them down the steep. Thither he took Thrasyllus, and after a long consultation with him, the emperor suddenly asked whether the astrologer had examined his own fate, and what was portended for him in the immediate future. Now the difficulty is this: If Thrasyllus says that nothing important is about to befall him, he will prove his lack of skill and lose his life besides. If, on the other hand, he says that he is soon to die, either the emperor will set him free, in which case the prophecy was false and he ought to have destroyed him; or Tiberius will destroy him, while he ought to have spared him as a true revealer of the future. Of course the solution is easy. Thrasyllus, after some observations and calculations, began to quake and tremble greatly, and said some great calamity seemed to be impending over him, whereupon the emperor embraced him and made him his chief astrologer.

— The Ladies’ Repository, July 1873

In his 1916 book The Science of Musical Sounds, Dayton Clarence Miller uses harmonic analysis to convert the line of a woman’s profile (left) into an equation of 18 terms. Then he uses this equation to reproduce the profile synthetically (right). “If mentality, beauty, and other characteristics can be considered as represented in a profile portrait,” he writes, “then it may be said that they are also expressed in the equation of the profile.”

He repeats the synthesized profile to produce a waveform:

“In this sense beauty of form may be likened to beauty of tone color, that is, to the beauty of a certain harmonious blending of sounds.”

In Noise, Water Meat: A History of Sound in the Arts, Douglas Kahn writes, “The simple beauty of the female expressed in the line thus becomes also the simple beauty of mathematics, graphic representation, and instrumentation, let alone mediation and reproduction, involved in the production of the equation and profile. Thus, we move beyond Lord Kelvin’s fascination with a beauty of mathematics to a fascination with a mathematics of beauty.”