It would be stranger if one of the profoundest thinkers that ever lived, a teacher whose grandeur of character made him almost an object of worship to his pupils, had selected his symbols to "spare himself" the labor of clear conception (or had let them conceal from himself the confusion of his own thought). According to Hegel we must respectfully see philosophy in the Christian Trinity; in the Pythagorean Dekad, none. 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.