The Sleepwalkers Read Online Free Page B
Author: Arthur Koestler
senses – which is how the divine mind must be supposed to operate. The ecstatic contemplation of geometrical forms and mathematical laws is therefore the most effective means of purging the soul of earthly passion, and the principal link between man and divinity.
The Ionian philosophers had been materialists in the sense that the chief accent of their inquiry was on the stuff from which the universe was made; the Pythagoreans' chief accent was on form, proportion and pattern; on the eidos and schema , on the relation, not on the relata. Pythagoras is to Thales what Gestalt philosophy is to the materialism of the nineteenth century. The pendulum has been set swinging; its ticking will be heard through the entire course of history, as the blob alternates between the extreme positions of "all is body", "all is mind"; as the emphasis shifts from "substance" to "form", from "structure" to "function", from "atoms" to "patterns", from "corpuscles" to "waves", and back again.
The line connecting music with numbers became the axis of the Pythagorean system. This axis was then extended in both directions: towards the stars on one side, the body and soul of man on the other. The bearings, on which the axis and the whole system turned, were the basic concepts of armonia : harmony, and katharsis : purge, purification.
The Pythagoreans were, among other things, healers; we are told that "they used medicine to purge the body, and music to purge the soul". 2 One of the oldest forms, indeed, of psychotherapy consists in inducing the patient, by wild pipe music or drums, to dance himself into a frenzy followed by exhaustion and a trance-like, curative sleep – the ancestral version of shock treatment and abreaction therapy. But such violent measures were only needed where the patient's soul-strings were out of tune – overstrung or limp. This is to be taken literally, for the Pythagoreans regarded the body as a kind of musical instrument where each string must have the right tension and the correct balance between opposites such as "high" and "low", "hot" and "cold", "wet" and "dry". The metaphors borrowed from music which we still apply in medicine – "tone", "tonic", "well-tempered", "temperance", are also part of our Pythagorean heritage.
However, the concept armonia did not have quite the same meaning that we lend to "harmony". It is not the pleasing effect of simultaneously-sounded concordant strings – "harmony" in that sense was absent from classical Greek music – but something more austere: armonia is simply the attunement of the strings to the intervals in the scale, and the pattern of the scale itself. It means that balance and order, not sweet pleasure, are the law of the world.
Sweetness does not enter the Pythagorean universe. But it contains one of the most powerful tonics ever administered to the human brain. It lies in the Pythagorean tenets that "philosophy is the highest music", and that the highest form of philosophy is concerned with numbers: for ultimately "all things are numbers". The meaning of this oft-quoted saying may perhaps be paraphrased thus: "all things have form, all things are form; and all forms can be defined by numbers". Thus the form of the square corresponds to a "square number", i.e. 16=4×4, whereas 12 is an oblong number, and 6 a triangular number:
Numbers were regarded by the Pythagoreans as patterns of dots which form characteristic figures, as on the sides of a dice; and though we use arabic symbols, which have no resemblance to these dot-patterns, we still call numbers "figures", i.e. shapes.
Between these number-shapes unexpected and marvellous relations were found to exist. For instance, the series of "square numbers" was formed simply by the addition of successive odd numbers:
and
so forth:
The addition of even numbers formed "oblong numbers", where the ratio of the sides represented exactly the concordant intervals of the musical octave:
2 (2 : 1, octave) + 4 = 6 (3 : 2,
The Ionian philosophers had been materialists in the sense that the chief accent of their inquiry was on the stuff from which the universe was made; the Pythagoreans' chief accent was on form, proportion and pattern; on the eidos and schema , on the relation, not on the relata. Pythagoras is to Thales what Gestalt philosophy is to the materialism of the nineteenth century. The pendulum has been set swinging; its ticking will be heard through the entire course of history, as the blob alternates between the extreme positions of "all is body", "all is mind"; as the emphasis shifts from "substance" to "form", from "structure" to "function", from "atoms" to "patterns", from "corpuscles" to "waves", and back again.
The line connecting music with numbers became the axis of the Pythagorean system. This axis was then extended in both directions: towards the stars on one side, the body and soul of man on the other. The bearings, on which the axis and the whole system turned, were the basic concepts of armonia : harmony, and katharsis : purge, purification.
The Pythagoreans were, among other things, healers; we are told that "they used medicine to purge the body, and music to purge the soul". 2 One of the oldest forms, indeed, of psychotherapy consists in inducing the patient, by wild pipe music or drums, to dance himself into a frenzy followed by exhaustion and a trance-like, curative sleep – the ancestral version of shock treatment and abreaction therapy. But such violent measures were only needed where the patient's soul-strings were out of tune – overstrung or limp. This is to be taken literally, for the Pythagoreans regarded the body as a kind of musical instrument where each string must have the right tension and the correct balance between opposites such as "high" and "low", "hot" and "cold", "wet" and "dry". The metaphors borrowed from music which we still apply in medicine – "tone", "tonic", "well-tempered", "temperance", are also part of our Pythagorean heritage.
However, the concept armonia did not have quite the same meaning that we lend to "harmony". It is not the pleasing effect of simultaneously-sounded concordant strings – "harmony" in that sense was absent from classical Greek music – but something more austere: armonia is simply the attunement of the strings to the intervals in the scale, and the pattern of the scale itself. It means that balance and order, not sweet pleasure, are the law of the world.
Sweetness does not enter the Pythagorean universe. But it contains one of the most powerful tonics ever administered to the human brain. It lies in the Pythagorean tenets that "philosophy is the highest music", and that the highest form of philosophy is concerned with numbers: for ultimately "all things are numbers". The meaning of this oft-quoted saying may perhaps be paraphrased thus: "all things have form, all things are form; and all forms can be defined by numbers". Thus the form of the square corresponds to a "square number", i.e. 16=4×4, whereas 12 is an oblong number, and 6 a triangular number:
Numbers were regarded by the Pythagoreans as patterns of dots which form characteristic figures, as on the sides of a dice; and though we use arabic symbols, which have no resemblance to these dot-patterns, we still call numbers "figures", i.e. shapes.
Between these number-shapes unexpected and marvellous relations were found to exist. For instance, the series of "square numbers" was formed simply by the addition of successive odd numbers:
and
so forth:
The addition of even numbers formed "oblong numbers", where the ratio of the sides represented exactly the concordant intervals of the musical octave:
2 (2 : 1, octave) + 4 = 6 (3 : 2,
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