APOLOGIA. 11

[...sen]sory Music, but one must philosophize more deeply, investigating with your Iamblichus A Neoplatonist philosopher who wrote on the divinity of numbers and music. why it happens that, for example, the intervals of the third, fourth, fifth, and octave delight us, while the second and seventh do not. Not only would you find me in agreement, but you would find nothing among the ancients to find fault with. For Ptolemy Claudius Ptolemy, the ancient astronomer and music theorist. had an excellent desire to extract this kernel; he even applied a sublime kind of philosophizing, which did not seem unworthy to Porphyry—the teacher of your Iamblichus—who wrote a commentary on it himself.

Yet none of the ancients dared to strip the inner essence of Harmony from quantities; rather, both they and Proclus, who followed them, raised the treasures of Geometry to the highest degree and hid them in the innermost essence of the Soul and even of divinity itself. In this regard, I have followed them vigorously, though I have corrected their dogmas according to the rule of Catholic doctrine; as I hope readers will recognize especially from the reading of the first four chapters of my fourth book. I decided to innovate in only this one area—indeed, I was driven to innovate by necessary proofs: that in place of the ancients' Numbers (a discrete quantity Individual units like 1, 2, 3, which the ancients used to describe musical ratios.), I have substituted the circle and Geometric figures (a continuous quantity Measurements that can be infinitely divided, like lines and shapes, which Kepler believed were the true source of harmony.).

If this ancient method of extracting the essence of Harmony were not distasteful to you; and if you did not relegate Mathematics to the mere husk or outer skin, or even label it a vain and frivolous shadow, but rather received it into the very Kernel itself: then truly no one among the truly philosophizing would fail to applaud you when you assert that the same harmony exists in man as in the World, the same in the Elements (if we understand elementary sounds) as in the Planets; and finally the same in those things as in the Archetypal World The "original blueprint" or divine idea of the universe in God's mind. itself, from which the Harmony of the whole Machine originally arose. For you see that I also assert the same things in almost the same words throughout my work, especially in Book III, folio 13, and Book IV, Chapters I, II, and III.

The word "Harmony" is ambiguous.

For we are compelled by grammatical right to admit this slight equivocation, since one person, following common usage, accepts Harmony only as that of Concord, which involves sound; another, following the original root of the word, accepts it for every kind of congruence of geometric things; while a third, walking the middle path, understands Geometric proportions—which are found in consonant voices—wherever else he finds them, as if they were abstracted from their subjects. In this latter sense, I use these words throughout almost my entire work.

But you, not content with these meanings, push the word further to include both the physical congruences of active and passive agents, and the hyperphysical congruences of the type and the Archetype. I do not blame you; I confess you have companions in this use of the word—distinguished philosophers while they play in their poems; among whom is Proclus, whose verse about Phoebus Apollo, the god of music and the sun. is here on my page 246:

original Greek: "ᾠδὰς δ' ὑπὸ θέσπελα μέλπων / ’Ευνάζει μέγα κῦμα βαρυφλοίσβοιο γενέθλης."
Singing divine songs, he calms the great wave of the loud-roaring generation.
This hints at a most sweet harmony between male and female in the act of generation; and this one about Paean Another name for Apollo, specifically as a healer.:
original Greek: "Πλήσας ἁρμονíης παναπήμονος εὐρέα κόσμον,"
Filling the wide world with all-healing harmony,
which I understand to refer to the various successful outcomes of natural motions.

I allow you, I say, to use words at your own discretion: however, I must necessarily warn you: hiding under this ambiguity, you stir up many disturbances everywhere, which are very easily calmed once the equivocation is detected. Or if it cannot be detected (as indeed in this very place more senses lie hidden in your Kernel of Harmony or marrow than my dullness can grasp), then we clash in vain efforts, like a panting wild beast seeking a little man wrapped and covered in an inexplicable breastplate, and leaves him unfound: the spectator is cheated of his pleasure; I say the reader gains no utility from a contest full of darkness.

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ON ANALYSIS X.

Because, I say, he indulges more in practice, and I in Theory; for him, pictures are convenient; for me, theorems. I have done you no wrong, Robert: I have fixed no mark of envy upon your work, but I have described the work to the reader by its own characteristic, so that he who has not yet bought it might know he will find what delights him, according to his own nature. For the printed book abounds in copperplate pictures, and you yourself just now reviewed in Analysis III which pictures you use instead of speech: the Temple, Columns, Hieroglyphics,