Pythagoras wrote nothing. And his teaching was esoteric, delivered under pledge of secrecy. The essence of the echoes that reach us amounts to this: that numbers and ratio are the soul of things; that the soul itself is a number and a harmony.
Is there any possible reading of this from which it might appear profoundly true and illuminating?
We sometimes estimate savage intelligence by the power of counting, of adding units. From one point of view the power does not seem to go very far with ourselves. We cannot in one act of perception count more than a very few dots irregularly placed on a sheet of paper. If more than that few they must have some arrangement. Nine must be perhaps in three threes, twelve in four threes or three fours. But even before twenty is reached, no arrangement will permit one act of perception to accomplish the numbering. There is merely a considerable number, and actual unitary counting—of units or groups—is necessary to know how large it is.
But now let there be a sufficient number of dots to suggest to the eye say a flower form or a frieze pattern, and let them be so arranged. Before that arrangement they were a mere horde of ones; in their definite arrangement they have a meaning, excite an idea, a state of consciousness. Is not the advent of this meaning, the perception of this form as a whole, a new and transcendental kind of counting? Number in this sense, is form; and the form is form and not inchoateness, chaos, just because of its meaning; that is, because of the state of consciousness it excites in us.
You can count the ticks of the clock—as ones. If they were four times as fast you could perhaps still count them. As they became more rapid than that they would pass beyond the power of counting. As they became still more rapid they would presently cease to be units at all and become a musical note. Now they excite what might be called an idea, a state of feeling peculiar to that number per second. Is not the perception of that number as a note a kind of counting? Let the number per second be now suddenly doubled. Are we aware of the ratio of this new number to the previous one? Yes, but as a rise of an octave in the note, not as a counted doubling. To this corresponds another state of feeling, partly due to the new note as it is, partly due to its relation to the old one. It is a perception of ratio appearing in consciousness as aesthetic feeling.
Set this clock to beat twice as fast again, and having listened a moment so as to get the sense of the new note, stop it. Set a second clock to beat five for the first one's four. Listen so as to get the sense of it and then stop that clock also. Set a third to beat six for the first one's four and do the same.
Now start them all at once. You cannot by counting ascertain that whilst one beats six the other two are respectively beating five and four. But your appreciation of the fact takes the form of hearing the musical chord do, mi, sol, c, e, g, the common chord in its first position. Is not the perception of that chord, the acceptation of that state of feeling, really a recognition of the ratio, a highly transcendental counting? In the feeling you have the meaning of the numbers and of the ratios between them. It is those numbers themselves viewed from a high standpoint.
The same might be said of every other chord. Listening to music is perceiving ratios of vibratory speed between the successive notes and chords, transcendental counting. The feelings aroused are what those ratios mean. The meaning, the feeling, of the composer gets out into expression through those numbers and ratios. Number in the ordinary one-plus-one sense is the body of music; number in the transcendental sense is its soul.
We cannot in the ordinary sense count ether-touches on the optic nerve. But when they reach a certain number of trillions per second we suddenly perceive the meaning of that number—which we call the color red or the sensation of redness. When the rapidity is seven-fourths as many we get the sensation violet. But there is more than a sensation; the colors have an aesthetic and emotional value. And when colors, that is rates, are juxtaposited in certain ways we get art and the value may become spiritual.
But no two people are affected in exactly the same way by the same piece of music or of art work, though the souls of both may be touched. Since, as we have seen, the highest aspect of number and ratio is spiritual meaning, we can already see something in the Pythagorean saying that the soul is a number and a ratio or harmony. In its self-consciousness it has a spiritual meaning for itself; it means something to itself; it understands itself. And so each soul, each with its own special nature or meaning, reacts a little differently to the spiritual meaning of numbers and ratios coming to it from without.