Numbers, Measures, and Music

Just as we had Abraham for our example in astronomy, so we have the same Abraham in arithmetic. “When he heard that Lot had been taken captive, he counted his own household servants, born in his house — three hundred and eighteen”; and with them he beat a very large force of the enemy. Now some say that the letter that stands for three hundred is, in its very shape, a figure of the Lord’s sign, and that the iota and the eta point to the Savior’s name. So what was being indicated was that Abraham’s household were inside salvation: having fled to the Sign and the Name, they became masters of the captives, and of the very many unbelieving nations that came trailing after them. [a]

Three hundred is three times a hundred. Ten is agreed to be the perfect number. And eight is the first cube, equal in every dimension — length, width, and depth. “The days of men,” it says, “will be a hundred and twenty years.” And that total is what you get by adding up the numbers from one to fifteen. The moon, too, is full at fifteen days.

Looked at on another principle, a hundred and twenty is a triangular number, and it is made up of the equality of the number sixty-four — which is made up of eight of the odd numbers beginning with one — the adding of which one after another (1, 3, 5, 7, 9, 11, 13, 15) generates the squares; and of the inequality of the number fifty-six, made up of seven of the even numbers beginning with two (2, 4, 6, 8, 10, 12, 14), which produce the numbers that are not squares.

Again, indicated another way, the number a hundred and twenty is made up of four numbers: of one triangle, fifteen; of another, a square, twenty-five; of a third, a pentagon, thirty-five; and of a fourth, a hexagon, forty-five. The five is taken in the same ratio in each of these ways of counting. Among triangular numbers, five from one gives fifteen; among squares, twenty-five; and among those that follow, in proportion. Now twenty-five, which is the fifth number from one, is said to be the symbol of the tribe of Levi. And the number thirty-five depends on the arithmetic, geometric, and harmonic scale of doubles — 6, 8, 9, 12 — the adding of which makes thirty-five. In that many days, the Jews say, a child that comes at seven months takes shape. And the number forty-five depends on the scale of triples — 6, 9, 12, 18 — the adding of which makes forty-five; and in the same way they say that in that many days a child that comes at nine months takes shape.

That, then, is the style of the example taken from arithmetic. And for the witness of geometry, let it be the tabernacle that was set up and the ark that was made — both built in the most exact proportions, and by divine ideas, through the gift of understanding, which leads us up from the things of sense to the things the mind alone can reach, or rather from those to holy things, and to the holy of holies. For the squares of wood show that the square shape, which makes right angles, runs through the whole, and that it points to security. And the length of the structure was three hundred cubits, the width fifty, and the height thirty; and above, the ark ends in a single cubit, narrowing to a cubit from its broad base like a pyramid — the symbol of those who are purified and tested by fire. And this geometrical proportion has its place for the carrying of those holy dwellings, whose differences are indicated by the differences of the numbers set down below.

And the numbers brought in are sixfold, since three hundred is six times fifty; and tenfold, since three hundred is ten times thirty; and they hold one and two-thirds, since fifty is one and two-thirds of thirty. Now there are some who say that the three hundred cubits are the symbol of the Lord’s sign; that the fifty stands for hope and for the release given at Pentecost; and that the thirty — or, as some copies have it, twelve — points to the preaching, because the Lord preached in his thirtieth year and the apostles were twelve. And the structure’s ending in a single cubit is the symbol of the righteous advancing to oneness, and to “the unity of the faith.”

And the table that stood in the temple measured six cubits, and its four feet were about a cubit and a half. So they add these up to twelve cubits, matching the turning of the twelve months in the yearly circle, during which the earth brings everything forth and ripens it, fitting itself to the four seasons. And the table, in my opinion, presents an image of the earth, held up as it is on four feet — summer, autumn, spring, winter — on which the year travels. That is also why the table is said to have “wavy chains”: either because the universe turns in the circuits of time, or perhaps it was indicating the earth ringed about by the tide of ocean.

Further, as an example of music, let us bring forward David, who played and prophesied at once, praising God in melody. Now the enharmonic style suits the Dorian mode best, and the diatonic the Phrygian, as Aristoxenus says. So the mode of the foreign harp, which had a grave and weighty strain and is the most ancient of all, was surely the model for Terpander in the Dorian mode. He sings the praise of Zeus like this:

The lyre, in its first meaning, may be used by the psalmist as a figure for the Lord; in its second, for those who keep striking the strings of their souls under the lead of the choir-master, the Lord. And if the people who are saved are called the lyre, it will be understood to be because they give glory musically, by the breathing of the Word into them and the knowledge of God, being struck by the Word so as to sound out faith. You may take music in yet another way: as the church’s symphony of the law and the prophets at once, with the apostles alongside the good news, and as the harmony that held within each prophet, in his shifts from one speaker to another.

But it seems that most of those who are enrolled under the Name handle the word clumsily, like the companions of Odysseus: they sail past not the Sirens but the rhythm and the melody, stopping their ears with ignorance, since they know that once they have lent their ears to Greek studies they will never afterward be able to retrace their steps.

But the man who culls what is useful for the good of those under instruction — especially when they are Greeks, and “the earth is the Lord’s, and everything in it” — must not hold off from learning, like an animal without reason. He must gather as many aids as he can for his hearers. But he must by no means linger over these studies, except only for the advantage that comes from them, so that once he has grasped and secured that, he may be able to set off home to the true philosophy, which is a strong cable for the soul, keeping it safe from everything. Music, then, is to be taken up for the sake of shaping and settling our manners. At a banquet, for instance, we drink to one another while the music is playing, soothing the eagerness of our cravings with song, and giving glory to God for his lavish gift of human enjoyments, for his unfailing supply of the food our bodies and our souls need to grow. But we must refuse music that goes past what is needed, which unstrings men’s souls and drives them from one mood into another — now mournful, now loose and sensual, now frenzied and raving.

The same holds for astronomy. It treats of the description of the heavenly bodies, of the shape of the universe, of the turning of the heavens and the motion of the stars, and so leads the soul nearer to the creative power; and it teaches a man to be quick at reading the seasons of the year, the changes in the air, and the risings of the stars. Sailing and farming get much benefit from it, as building and architecture do from geometry. This branch of learning also makes the soul observant in the highest degree, able to perceive what is true and detect what is false, to discover correspondences and proportions, and so to hunt out likeness in things unlike; and it leads us to the discovery of length without width, and surface without thickness, and the point that cannot be divided, and carries us across from the things of sense to the things the mind alone can reach.

The studies that lead to philosophy, then, and philosophy itself, are aids in handling the truth. Take a cloak: it was once a fleece; then it was shorn, and became warp and weft; and then it was woven. In the same way the soul has to be prepared and put through many kinds of exercise if it is to become good in the highest degree. For in truth there is the element of knowing and the element of doing; and the second flows out of the first; and there is need of much practice, and training, and experience. But within the knowing, one part has to do with our neighbors and another with ourselves. So training ought to be shaped to fit both. The man, then, who has gained a competent acquaintance with the subjects that carry the principles leading to knowledge may stop there and stay quiet from then on, directing what he does in line with what he has seen. But for the good of his neighbors — in the case of men who have a bent for writing, and men who set themselves to deliver the word — other learning is useful as well, and reading the Lord’s Scriptures is necessary, in order to prove what is said, and especially if the hearers are converts from Greek culture.

Such is the church David describes: “The queen stood at your right hand, wrapped in a robe of gold, of many colors” — and, decked out with Greek and more than sufficient accomplishments, “clothed in many colors, in gold-fringed garments.” And the Truth says through the Lord: “For who would have known your plan, if you had not given wisdom and sent your Holy Spirit from on high? And so the ways of those on earth were set straight, and men learned what pleases you, and were saved by wisdom.” For the one who truly knows understands ancient things from the Scripture, and guesses at things to come. He understands the twists of words and the untying of riddles. He knows beforehand signs and wonders, and the outcomes of seasons and periods, as we have already said. Do you see the fountain of teaching that rises out of wisdom?

But there are those who object: what use is there in knowing the causes of the way the sun moves, for instance, or the rest of the heavenly bodies, or in having studied the theorems of geometry or of logic, or any of the other branches of study? These are no service in doing one’s duty, they say, and Greek philosophy is human wisdom, since it cannot teach the truth. To them the following has to be said. First, that they stumble over the highest matter of all — the mind’s free choice. “For those,” it says, “who keep holy things in a holy way will be made holy; and those who have been taught them will find a defense.” For the one who truly knows will alone do everything that has to be done in a holy way and according to reason, since he has learned it through the Lord’s teaching, received by way of men.

And again, on the other hand, we may hear: “For in his hand” — that is, in his power and wisdom — “are both we and our words, and all wisdom and skill in works; for God loves nothing but the man who lives with wisdom.” And again, they have not read what is said by Solomon; for, treating of the building of the temple, he says expressly, “And it was Wisdom, as craftsman, that framed it; and your providence, Father, governs the whole.” And how unreasonable it is to rank philosophy below architecture and shipbuilding! And the Lord fed the crowd who lay down on the grass across from Tiberias with the two fish and the five barley loaves, pointing to the preparatory training of the Greeks and of the Jews before the divine grain, which is the food the law cultivates. For barley is ripe for harvest sooner than wheat. And the fish stood for the Greek philosophy that came into being and moved about in the middle of the swell of the nations, given as they were for plentiful food to those lying on the ground — no longer growing, as the fragments of the loaves did, but having shared in the Lord’s blessing, and having a resurrection by divine power breathed into them through the working of the Word. But if you are curious, take one of the fish to be the ordinary course of study and the other the philosophy that comes on top of it. The gatherings point to the word of the Lord.

“And the choir of voiceless fish rushed toward it,” the Tragic Muse says somewhere.

“I must decrease,” said John the prophet, and the Word of the Lord alone, in whom the law comes to its end, must “increase.” Now understand for me the mystery of the truth, and grant me pardon if I shrink from going any further in setting it out, and announce this alone: “All things were made through him, and without him not even one thing was made.” Certainly he is called “the chief cornerstone, in whom the whole building, fitted together, grows into a holy temple of God,” as the divine apostle says.

For the present I pass over in silence the parable that says in the Gospel, “The kingdom of heaven is like a man who cast a net into the sea and, out of the great number of fish caught, picks out the better ones.”

And now the wisdom we possess announces the four virtues in such a way as to show that their sources were passed on to the Greeks by the Hebrews. This may be learned from the following: “And if anyone loves righteousness, her labors are virtues. For she teaches self-restraint and good sense, righteousness and courage; and there is nothing in life more useful than these to men.” Above all, this ought to be known: that by nature we are fitted for virtue — not so as to possess it from our birth, but so as to be fitted for acquiring it.