Clement of Alexandria · a new plain-English translation from the original language
Just as, then, in the case of astronomy we have Abraham as our example, so too in the case of arithmetic we have that same Abraham. For when he heard that Lot had been taken captive, he numbered his own household servants — three hundred and eighteen — and, going out after them, overpowered a very great number of the enemy. Now they say that the shape of that three-hundredth letter typifies the Lord's emblem, while the iota and eta of the name mean "the one who saves"; whereby it is shown that Abraham's household belonged to salvation, since those who had taken refuge in that emblem and name became masters over their captors and over the very many faithless nations that followed them. Now the number three hundred is already a triad in the hundreds, and the decad is agreed to be perfect in every respect. And eight, the first cube, is equality in all its dimensions — length, breadth, and depth.
"And the days of man," it says, "shall be one hundred and twenty years." Now this number, reckoned by addition from unity, is the fifteenth, and the moon becomes full on the fifteenth day.
There is also another sense in which the number one hundred and twenty is triangular, and it is composed, on the side of equality, from sixty-four, whose successive partial sums produce the squares — one, three, five, seven, nine, eleven, thirteen, fifteen — and on the side of inequality, from fifty-six, the seven even numbers from two onward, which produce the oblong numbers — two, four, six, eight, ten, twelve, fourteen. According to yet another meaning, the number one hundred and twenty is composed of four numbers: one triangular, the fifteenth; another square, the twenty-fifth; a third pentagonal, the thirty-fifth; a fourth hexagonal, the forty-fifth. For by the same proportion the five is taken up in each kind: among the triangular numbers, reckoned from unity, the fifth is fifteen; among the squares, twenty-five; and so on proportionally for the rest. Indeed the number twenty-five, being the fifth from unity, is said to be a symbol of the tribe of Levi, and thirty-five likewise belongs to the diagram of doubled numbers — arithmetical, geometrical, and harmonic — of six, eight, nine, twelve, whose sum produces thirty-five; on these days, the Jews say, seven-month children are formed in the womb. And forty-five belongs to the diagram of tripled numbers, six, nine, twelve, eighteen, whose sum produces forty-five, and on these days likewise, they say, nine-month children are formed.
This, then, is the form of the arithmetical example. Let the tent that was built, and the chest that was fashioned, serve as witness for geometry — put together by certain most rational proportions, by divine designs, according to the giving of understanding, leading us from the things perceived by the senses to the things perceived by the mind, or rather from these to the holy things, and from the holy things to the holy of holies. For the square timbers, by the square figure standing firm in every direction and forming right angles, show forth stability. Its span measured three hundred cubits in length, fifty in breadth, thirty in depth; and above it was finished off to a single cubit, narrowing from its wide base after the manner of a pyramid — that chest standing as an emblem for those refined and proven through fire. This geometrical proportion supplies a means of conveying those holy unities, whose differences the differences of the subordinate numbers indicate.
The ratios involved are sixfold, as three hundred is to fifty; tenfold, since thirty taken ten times yields three hundred; and in the ratio of three to two, for fifty is one and a half times thirty. Some say that the three hundred cubits are a symbol of the Lord's emblem, and the fifty of hope and of the remission proclaimed at Pentecost, and the thirty — or, as in some accounts, twelve — they record as signifying the preaching, since it was in his thirtieth year that the Lord took up his preaching, and the apostles were twelve; and that the structure was completed to a single cubit, since the righteous man's advancement comes to an end in unity and in the oneness of faith.
Now the table set in the temple measured six cubits, and each of its four feet was a cubit and a half. Adding them all together one gets twelve cubits, matching the yearly circuit's turning through twelve months, in which the earth, adjusting to the four seasons, produces and brings to completion all things. The table, I think, signifies an image of the earth, resting upon four feet — summer, autumn, spring, winter — through which the year travels. This is why it is said that the table had twisted wreath-work, either because all things revolve in cycles of seasons, or perhaps because it also signified the earth encircled by Ocean.
Further, let David be set forth as the pattern of music, both singing psalms and prophesying at once, hymning God tunefully. Now the enharmonic genus, as Aristoxenus says, is especially suited to the Dorian mode, and the diatonic to the Phrygian. The harmony, then, of the barbarian psaltery, displaying the solemnity of its melody and being the most ancient of all, becomes an example especially for Terpander, who hymned Zeus to the Dorian mode in something like these words: "Zeus, beginning of all things, leader of all, Zeus, to you I send this beginning of hymns." The lyre might, allegorically, for the psalm-singer signify in its first sense the Lord, and in its second sense those who, near at hand, strike the strings of souls under the Lord as leader of the music. And even if the saved people is called a lyre, it is understood musically as glorifying God by the inspiration of the Word and by the knowledge of God, being struck into faith by the Word. One might also take, in another sense, the musical harmony of the church to be the concord of the law and the prophets together with the apostles, along with the gospel — the harmony that runs, in each prophet, according to the shifts of persons, in a subordinate register.
But, as it seems, the majority of those who bear the name, like the companions of Odysseus, approach the word crudely, dodging not the Sirens themselves but their cadence and tune, plugging their ears with ignorance, aware that once they let Greek learning reach their hearing they will afterward be unable to reach home. But for one who gathers out what is useful for the benefit of catechumens, especially since they are Greeks (for the whole earth belongs to the Lord, together with everything filling it), one must not abstain from the love of learning like an irrational animal, but rather must gather as many aids as possible for those who understand. Yet one must in no way linger over these things, except only for what is useful from them, so as, having taken and acquired this, to be able to return home to true philosophy, having procured for the soul a firm cable — the safety that comes from all things together.
Music, then, must be engaged for the ordering and composure of character.
Indeed, even over wine we sing to one another in our toasts, charming our desiring part and glorifying God for the ungrudging gift of human enjoyments — both the foods eternally supplied for the growth of the body and those for the growth of the soul. But excessive music, which softens souls and casts them into variety — now mournful, now licentious and voluptuous, now frenzied and maddening — must be spat out and rejected. The same reasoning applies also to astronomy; for this discipline, after the study of the heavenly bodies concerning the shape of the universe, the motion of heaven, and the movement of the stars, bringing the soul nearer to the creative power, teaches one to grasp keenly the year's turning seasons, the shifts of weather, and the risings of the stars; since both seafaring and farming are supplied by its usefulness, just as architecture and building are supplied by geometry. This branch of learning also prepares the soul, as far as possible, to be attentive, keen-sighted for truth and able to refute falsehood, discovering agreements and analogies, so as to track down the like among the unlike; and it leads us on to discover length without breadth, surface without depth, and the point without parts, and transposes us from the things of sense to the things of the mind.
The mathematical disciplines, then, are auxiliary to philosophy, and philosophy itself is auxiliary to grasping the truth. For instance, the cloak was at first fleece, then it was carded and became weft and warp, and only then was it woven. So too the soul must be prepared beforehand and worked upon in various ways, if it is to be fashioned in the best condition, since of truth one part is a matter of knowledge, another a matter of practice; it flows from the contemplative part, and requires much practice, joint training, and experience. But even of the contemplative part, one aspect concerns one's neighbors, another concerns oneself alone. For this reason education must be so equipped as to be fitted to both. It is enough, then, for one who has thoroughly learned the essentials of what leads to knowledge to remain at rest in quiet for the future, directing his actions toward contemplation; but for the benefit of one's neighbors — some being eager to write, others intent on handing down the teaching — both the rest of education generally and the reading of the Lord's scriptures are necessary, for the proof of what is said, especially if those who are learning have been led up from Greek education.
Such is the kind of church that David describes: "The queen stood at your right hand, clothed in gold-worked robes, arrayed in many colors" — including, indeed, both the Greek and the extraneous — "in golden fringes, arrayed in many colors." But the truth comes through the Lord. "For who has known your counsel," he says, "unless you have given wisdom and sent your holy spirit from on high? And so the paths of those on earth were made straight, and men were taught what pleases you, and rescued through wisdom." For the Gnostic, according to scripture, knows the ancient things and conjectures the things to come; he understands the turns of speech and the resolutions of riddles; he foreknows signs and wonders and the outcomes of seasons and times, as we have said before.
Do you see the fountain of the disciplines springing forth from wisdom? But to those who raise objections — for what use is it, they say, to know the causes of how the sun moves, for instance, and the rest of the stars, or to have examined the theorems of geometry, or the principles of dialectic, and each of the other disciplines, since these things are of no use for rendering our duties, and Greek philosophy is a merely human understanding — to those who say that truth is not something that can be taught, this must be said, first of all: that these people stumble even in the greatest of matters, that is, in the very direction of their mind. For, it says, "those who reverently observe the sacred things shall themselves be hallowed, and those instructed in them shall find recourse." For the Gnostic alone will reasonably do all that is to be done, piously, as he has learned according to the Lord's teaching, having received it through men. Again, one may hear it said: "since within his grasp — that is, within his strength and understanding — lie we ourselves and our sayings, and all comprehension and craft in what is made. For God loves nothing except the one who dwells together with wisdom." And further, have they not read what was said by Solomon? For, discoursing about the building of the temple, he says outright: "Wisdom, the craftswoman, built it; but your providence, Father, steers it."
And how is it not unreasonable to consider philosophy inferior to carpentry and shipbuilding? Perhaps, too, the Lord fed that multitude reclining on the grass opposite Tiberias with the two fish and the five barley loaves, hinting at the preliminary training of both Greeks and Jews prior to the divine wheat — the food cultivated according to the law; for barley ripens more readily than wheat, toward the season of summer. And the fish signified the Greek philosophy that is generated and carried about in the surge of the nations, given for abundant nourishment to those who still lay upon the ground; though it did not grow, unlike the fragments of the loaves, yet those who partook of the Lord's blessing were inspired, through the power of the Word, with the resurrection of divinity. But if you are curious, take one of the fish as signifying the encyclical learning, and the other as signifying that higher philosophy itself which has ascended beyond it — sounds in accord with the Lord's word; "a chorus of voiceless fish sounded around," as the tragic muse has said somewhere. "And I must decrease," while only the Lord's word must henceforth increase — the word into which the law comes to its end, as the prophet John has said.
Understand from me, then, the secret of the truth, granting pardon if I hesitate to proceed further with its elaboration, proclaiming only this: "all things came to be through him, and without him not one thing came to be." Indeed he is called the chief cornerstone, in whom every building, being fitted together, grows into a holy temple of God, according to the divine apostle. I say nothing for now of the gospel parable that says: "heaven's kingdom resembles a man who threw a net into the sea, and from the great haul of fish gathered picked out the better ones." And already our wisdom proclaims outright, in something like these words, the four virtues, so that even the sources of these were given to the Greeks from the Hebrews. One may learn this from the following: "and if one loves righteousness, her labors are virtues; for she teaches self-control and prudence, righteousness and courage, than which nothing is more useful to men in life." Above all, they ought also to have known this: that we have come to be by nature disposed toward virtue, yet not so as to possess it from birth, but rather fit to acquire it.
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