ON PYTHAGORAS

By: Giovanni Lombardo

(Part Two)

KNOWLEDGE AND DOGMA

The initiatory feature of knowledge made Pythagoreans think it could be gained only gradually and was not to be disclosed to who was not worthy of being made part of this knowledge. This rule had no exceptions. The episode of Hippasus of Metapontum is therefore emblematic.

Pythagoreans considered whole numbers to be their rulers and that all quantities could be explained by whole numbers and their ratios. An event would happen that would change the core of their beliefs.

According to the Pythagorean theorem, the square on the hypotenuse of an equilateral  triangle is equal to the sum of the squares on the two adjacent sides. Along came Hippasus who discovered the diagonal of a square, the side of which was one unit, could not be expressed as a whole number or a ratio. A number of this type is now called an irrational number. The proof that the square root of 2 is irrational was contrary to the long-held belief that every-thing was rational.

Another important consequence stems from the theorem. The leg and the diagonal have no common sub-multiple, therefore man calls them incommensurable. However, if man supposes that man gets a segment by drawing a finite series of points, it will result that one of them would be contained for a finite number of times in both the leg and the diagonal; then they would have a common sub-multiple, contradicting the theorem.

Man can so infer that incommensurability of physical quantities can be set up only by an infinity of points, not by a finite set of them. A further consequence consists in this, that discontinuity applies to arithmetic, not also to geometry, therefore it is not a feature of the whole mathematics.

Hippasus’s main fault was not only to upset the theorem, but to reveal the secret to “profanes”, thus breaking one of the most important dogmas of the Pythagorean School: the secrecy. He became so much hated by the other Pythagoreans, that not only did they cast him out of the community, but they also built a shrine for him as if he were dead, he who had once been their friend. Other legends report that he was drowned in the sea.

Was Hippasus a traitor? Or rather a hero, a real Prometheus who brought the light to his contemporaries ?

BODY AND SOUL

Cicero, in De Natura Deorumⁱ, refers to Pythagoras’s students debating, saying ipse dixit, that is, “he said it himself”, speaking of Pythagoras, whose authority they considered strong “even without reason”. Hence the accusation of dogmatism, that is false, in my opinion. To prove it, I have to say something about the relation body-soul.

 If, on the one hand, man imagined the soul as the body’s harmony, in the same way as man can speak either of harmony of sounds that are produced by a musical instrument, or of harmony resulting from a sculpture’s proportions; on the other hand man supported its immortal nature, contradicting numbers’ finite feature and body’s mortal nature: “Alcmæonⁱⁱ also seems to have held a similar view about soul; he says that it is immortal because it resembles ‘the immortals’, and that this immortality belongs to it in virtue of its ceaseless movement; for all the ‘things divine’, moon, sun, the planets, and the whole heavens, are in perpetual movement.”ⁱⁱⁱ

According to another hypothesis, Pythagoreans thought there were two souls: the mortal one, which is part of the psychic temperament and as such linked to the body; the other one, which an immortal principle set up and therefore is immortal itself.

The idea of an immortal soul stems from Orphism, that taught soul be a demon, therefore divine, but the body holds it in bondage. The soul has to pass through various reincarnations, to be purified and allowed to become reunite to the Divine, its true source.

Orphics thought purifications consisted in ascetic and ritual practices, while in Pythagoras’ opinion man could gain them by science, by the knowledge’s initiatory journey.

Pythagoras believed in metempsychosis (transmigration of the soul), that is the reincarnated demon gets in touch with the mortal soul and both can be purified if the latter walks the initiatory path, respecting however rules and practices of everyday life. Therefore he thought that eating meat was an abominable thing, saying that the souls of all animals enter different animals after death. He therefore forbade his pupils to eat meat. The prohibition was however compulsory only formathematikoi, not for akousmatikoi. It was an outcome of knowledge’s different levels, as we have already said.

The theory of different levels nullifies any idea of dogmatic teaching, allegedly grounded on the Master’s word. Dogma isan authoritative principle, belief, or statement of ideas or opinion, especially one considered to be absolutely true. There is no discussion. To the contrary, the Pythagorean knowledge is initiatory knowledge, to be gained by the efforts of any genuine researcher, in full conscience and absolute freedom. The contested ipse dixit is just a guide in the initiatory journey towards knowledge.

CONCLUSION

Man grounds Pythagorean School’s greatness on its intuitions, rather than on the scientific analysis which was necessarily limited within the cultural context of its époque.

The relationship between continuum and discontinuum is still today unresolved. The cosmos’s spherical conception, antecedent of the discovery of the curved space, anticipates the modern conception of the pulsating universe, in the centre of which there is a fire, to which the universe will become reunite one day, to be reborn once again. Last but not the least the relationship body-soul, which is of the utmost importance for the modern psychoanalysis. We still don’t know how many discoveries will come out from Pythagoras’s intuitions.

After 2500 years the Master is still speaking to us: let us hear him. He is saying that knowledge and initiation are two faces of the same coin and truths are not behind the veil, but within each human being, whose task is therefore to search after them, free from superstition and dogmas.

(The End)

1 1,5 2 Alcmæon (5th century BC) of Croton, in Magna Græcia, was one of the most eminent natural philosophers and medical theorists of antiquity.. He is said by some to have been a pupil of Pythagoras, and he may have been born around 510 BC. Although he wrote mostly on medical topics there is some suggestion that he was not a physician but a philosopher of science; he also indulged in astrology and meteorology. Nothing more is known of the events of his life. 3 Aristotle, On the Soul, I, 2 I, 5