pharmacist; he went to Paris in his twenties to study painting under Matisse, but soon moved into the study of theosophy and alchemy. He founded an ‘esoteric school’ called Suhalia near St Moritz, in Switzerland; after it broke up in 1929, he and his wife Isha moved to a large country mansion in Grasse, in the south of France, then in 1937 to Egypt, where he became fascinated by the temple of Luxor.
Schwaller came to believe that the Egyptians possessed a mode of thought that the modern world is almost incapable of grasping. In Alexandria he visited the tomb of Rameses IX,where he was fascinated by a painting that showed a right-angled triangle in which the hypotenuse was formed by the body of the pharaoh. The sides of the triangle formed the ratio 3:4:5, in other words, the triangle with which every schoolchild is taught Pythagoras’s theorem that the square on the hypotenuse is equal to the sum of the square of the other two sides. Schwaller was intrigued, since Rameses IX ruled around 1,100 BC, more than 500 years before Pythagoras. Since Schwaller had spent many years studying the architecture of the cathedrals of the Middle Ages, he was familiar with the story that the knowledge of the medieval masons came from ancient Egypt. He began a systematic study of Egyptian temples, and of Luxor in particular.
The first thing that strikes the tourist who looks at his map of Luxor is that the temple is ‘bent’, as if the courtyard that lies inside the entrance has been knocked slightly sideways by a blow from a giant mallet. Since the Egyptians were master builders, who could place blocks together so precisely that a razor blade cannot be inserted between them, there is obviously a reason for this anomaly. The marvellous harmony of the architecture leaves little doubt that it is part of some geometrical plan.
Schwaller set out to solve the riddle. The outcome was his masterwork,
The Temple of Man
(1957), 12 demonstrating that the Luxor temple is of immense geometrical complexity, and that it is a symbolic representation of a man – a kind of gigantic hieroglyph. Because the man is striding forward, like the striding colossus of Rameses II in its south-east corner, the courtyard representing the lower part of the leg has the shape of a square knocked sideways.
One of Schwaller’s main insights was that the temple also contains many examples of the geometrical proportion known as the ‘Golden Section’ (and called by the Greek letter phi). It sounds like an obscure definition from a geometry book, but it is a notion of profound importance, and it also plays a central part in the precise location of sacred sites.
Nature uses the Golden Section all the time. Your body is an example, with your navel acting as the division between the two parts. It can be found in the spirals of leaf arrangements, petals around the edge of a flower, leaves around a stem, pine cones, seeds in a sunflower head, seashells – even in the arms of spiral nebulae. Why is nature so fond of it? Because it is the best way of packing, of minimising wasted space. Artists also discovered it at a fairly early stage, because this way of dividing a picture is oddly pleasing to the eye, in exactly the same way that musical harmonies are pleasant to the ear.
Obviously, there is something very important about this simple-looking number. It is, in fact, 0.618034…, going on to infinity, non-recurring, as some decimals do.
Another form of phi is 1.618. If you wish to extend a line a phi distance, you simply multiply it by 1.618.
Another piece of mathematics is significant: a sequence of numbers discovered by the mathematician Fibonacci, inwhich each number is the sum of the preceding two numbers. If you begin with 0 and the next number is 1, 0 + 1 equals 1. And that 1 plus the previous 1 equals 2. And that 2 plus the preceding 1 equals 3. And so on: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…
If you take any two Fibonacci numbers, and divide each one by