elementary

Most people are probably aware that the ancient Greeks identified four ‘elements’—earth, fire, water and air—although these are not elements in the modern sense. The ancients will have been aware of the existence of gold, silver, iron, copper, tin and lead, but there is no evidence that they recognized them as fundamental. Of course, the Greek conception of elements is purely metaphysical, but it is preserved in English phrases such as ‘braving the elements’, which translates roughly as stepping outside in bad weather.

However, the Greeks had a problem. How many elements should there be? Plato had discovered that there are precisely five regular solids—tetrahedron, cube, octahedron, dodecahedron, icosahedron—and the prevailing wisdom was that by analogy, there must also be five elements. This is a false analogy, but it is the origin of the word quintessence (literally, ‘fifth essence’).

It is less well known that the ancient Chinese recognized a similar system of elements, one that is still in use today, especially in astrology and fung shui. They also identified five elements, although, unlike the Greeks, this was not by analogy with the five Platonic solids. The theoretical basis for Chinese astrology and fung shui is the lo shu square, two examples of which I present here:

The lo shu square is what Western mathematicians describe as a ‘magic square’, the fundamental property of which is that every row, column and diagonal adds up to the same total. This ‘magic square’ has other properties, the most obvious of which is that 5 must always go in the centre cell, and the four even numbers must occupy the four corners. In fact, once the starting condition has been defined, constructing a lo shu square becomes a forced process. And there are only two possible solutions, one of which is a mirror image of the other (see above).

The necessary presence of 5 in the centre cell seems to be why the Chinese decided that there must be five elements, each of which corresponds to one of the four corner cells or the central cell of the square.

So what did the Chinese decide were the five elements? Three—earth, fire and water—are the same as in the Greek classification, but the other two seem to me to be not even remotely elemental. Wood is a hybrid of earth and water, while metal is a hybrid of earth and fire. In this classification of elements, there is no way to explain the force exerted on the sails of a ship or a windmill, which is particularly mystifying given that the Chinese were the first to develop fore-and-aft sails, so they must have been aware of the force. Why did they fail to recognize air as a separate element?

Sound is another phenomenon that requires air for its explanation. It is a pressure wave that propagates through air, or another gaseous medium, and it is directional. It can also be transmitted through solids and liquids, but it does not exist in a vacuum. The earthquake-detection machine built by the Chinese more than 2,000 years ago could only have been designed by someone who understood that the shock waves from an earthquake are also directional, so why did they not make the connection? To be fair, there is no evidence that the ancient Greeks understood sound either, but at least they did have the means to explain it. Nothing in Chinese cosmology explains sound.

And there is another way to look at the Greek interpretation. You could argue that earth, water and air correspond to the three phases of matter: solid, liquid, gas. And there is a fourth phase! Plasma. The temperature at the heart of the Sun is so high that atoms no longer exist. Plasma is simply a fizzing soup of protons, electrons and other subatomic particles. That sounds like fire to me. And one hell of an insight for more than 2,000 years ago.

Meanwhile, perceiving some kind of esoteric magic in a lo shu square seems to me to be like believing in the healing power of crystals, the shapes of which are also the result of a forced process, one that depends solely on the relative size of their constituent atoms.