A History of Mathematics by Orwin O'Dowd

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Evariste Galois was a brilliant young mathematician who was tragically killed in the civil disturbances of the Empire of Louis Napoleon. The whole of modern physics is indebted to his work, and remains accordingly incomplete.

Galois was also tutored by his mother, and thought at school to be merely pretending genius. In this he perhaps resembles Alan Turing, who also died young in tragic circumstances, after which his mother signed off on his scientific papers. The whole of computer science is indebted to Turing.

After the again tragic death of Pythagoras, we hear that his work was continued by his wife, taking a special interest in the Golden Ratio. The whole of classical physics is indebted to Pythagoras, and Hermann Weyl described Einstein's work as a synthesis of Pythagoras and Newton.

In the system of numbers known as continued fractions the Golden Ratio occupies pride of place as the simplest number in the full form of a continued fraction. In this it resembles Euler's constant e in the system of logarithms.

We know that Galois' first mathematical paper, which is lost, was on continued fractions.

His work also runs with that of Abel, a contemporary who also died young, and Gauss, who had access to the archives of Goettingen University. Recorded there was a long collaboration with the Scots, requested by the founder. Newton thought their ideas essential for understanding his physics, which he attributed to the Ancients!

We know that continued fractions were in use among ancient astronomers. To find the continued fraction for an ordinary ratio is a so-called inverse problem, asking after 'that which' satisfies given conditions. Newton could not solve the inverse problem of gravitation, and indeed derided it as an 'hypothesis'.

Hypotheses were also denigrated at the Academy of Plato, after which science was appended to theology in dependence on direct proof. After Newton, Euler solved the inverse problem using the calculus of variations, developed for the purpose.

Now ancient astronomers seeking continued fractions had to work that way, and evidently bought hypotheses to their work, despite Plato's attitude, for a yield reported by Newton, but not according to their method!

Newton followed Galileo, who took his cue from Plato! We also know that physicists who read Galois' work could not understand it. He did not follow their cannon of proof, but rather an intuitive or semantic process.

What can the Golden Ratio tell us about ancient astronomy and Pythagoras? The ratio appears in geometry as a fractal, a pattern that repeats at different scales. We hear from Aetius that Pythagoras viewed musical harmonies as 'symmetries' in just this sense!

There is actually a huge difference in scale between the orbits of Mercury and Venus, and those of the outer planets. Robert Fludd, a follower of Paracelsus, depicted them as two musical scales, mediated by the Sun as 'conductor' of the universal harmony.  So the terms microcosm and macrocosm find an astronomical meaning, and Paracelsus followed astronomy rather than astrology.

Leibniz spoke of a living universe in such terms, and we can now trace several steps in the chain: a social group notices a sick person; the individual a pain in an organ; organs get infected by fungi and bacteria; but these microbes suffer from phagues; and phagues carry viruses!

For all we know, viruses are disturbed by prions, and prions by radioactivity; radioactives by quark disorder, and quarks by gluon problems, but we can't see any further without Galois.

It would certainly be simpler to treat the whole fractal, but what can a healer do about gravity? Surprisingly, we have more than a few good answers to that hard question.

The obvious fact is that the spine mediates gravity, and that gives you the largest group of answers, as varied as the spine is complex: massage, Tantra, hatha yoga, cranio-sacral therapy, chiropractic, osteopathy, Alexander, Feldenkreis, dance... There are also more indirect answers, but they require some explanation, and another article.