Pythagoras: The whole thing is a number

Michael Lahanas

Πυθαγόρας ο Σάμιος

The whole thing is a number
The beginning of all is unity (monas); unity is a cause of indefinite duality as a matter; both unity and indefinite duality are sources of the numbers; the points are proceeding from numbers; the lines - from the points; from the lines are plane figures; from plane are volumetric figures; from them - sensibly acceptable solids, in which four elements are - fire, water, earth, and air; moving and changing totally, they give rise to the universe - inspired, intelligent, spherical, in the middle of which is the earth; and the earth is also spherical and inhabited from all sides. Alexander Polyhistor about the Pythagoreans according to Diogenes Laertios

Travelling back in time, one notes the historic role of Pythagoras — in realizing that qualitative differences in sense perception are based on mathematical reasoning. Significantly Professor S. Chandrasekhar adverts to just the relationship derived from scientific exactitude and aesthetic meaning in his Lecture, "Shakespeare, Newton and Beethoven or Patterns of Creativity": "The discovery by Pythagoras that vibrating strings, under equal tension sound together harmoniously, if their lengths are in simple numerical ratios, established for the first time a profound connection between the intelligible and the beautiful. I think we may agree with Heisenberg that this ‘is one of the truly momentous discoveries of mankind’." A. Ranganathan, Transmutation from One Form to Another, The Interaction of Colour and the Elements, Some Scientific and Aesthetic Considerations

Pythagoras actually suggests that every truth can be expressed by mathematics and probably a majority of scientists today believe or at least hope this to be true. I. V. Volovich in his paper “Number theory as the ultimate physical theory” in the CERN theory preprint CERN-TH 4781/87 (1987) adopts Pythagoras view. As he says "at the Planck scale doubt us cast on the usual notion of space-time and one cannot think about elementary particles. Thus the fundamental entities of which we consider our Universe to be composed cannot be particles, fields or strings but numbers."

The first to devote themselves to mathematics and to make them progress were the so-called Pythagoreans. They, devoted to this study, believed that the principles of mathematics were also the principles of all things that be. Now, since the principles of mathematics are numbers, and they thought they found in numbers, more than in fire and earth and water, similarities with things that are and that become (they judged, for example, that justice was a particular property of numbers, the soul and mind another, opportunity another, and similarly, so to say, anything else), and since furthermore they saw expressed by numbers the properties and the ratios of harmony, since finally everything in nature appeared to them to be similar to numbers, and numbers appeared to be first among all there is in nature, they thought that the elements of numbers were the elements of all that there is, and that the whole world was harmony and number. And all the properties they could find in numbers and in musical chords, corresponding to properties and parts of the sky, and in general to the whole cosmic order, they gathered and adapted to it. And if something was missing, they made an effort to introduce it, so that their tractation be complete. To clarify with an example: since ten seems to be a perfect number and to contain in itself the whole nature of numbers, they said that the bodies that move in the sky are also ten: and since one can only see nine, they added as tenth the anti-Earth.