Part 8

VII. When Theon had done, I think it was Eustrophus of Athens who addressed us: ‘Do you see with what a will Theon backs Dialectic? He has only to put on the lion’s skin! Now then for you who put down under number all things in one mass, all natures and principles divine as well as human, and take it to be leader and lord in all that is beautiful and honourable! It is no time for you to keep quiet; offer to the God a first-fruits of your dear Mathematics, if you think that “E” rises above [Sidenote: F] the other letters, not in its own right by power or shape, or by its meaning as a word, but as the honoured symbol of an absolutely great and sovereign number, the “Pempad”, from which the Wise Men took their verb “to count”.’ Eustrophus was not jesting when he said this to us; he said it because I was at the time passionately devoted to Mathematics, though soon to find the value of the maxim, ‘NOTHING TOO MUCH‘, having joined the Academy.

VIII. So I said that Eustrophus’ solution of the problem by number was excellent. ‘For since,’ I continued, ‘when all number is divided into even and odd, unity alone is in its effect [Sidenote: 388] common to both, and therefore, if added to an odd number makes it even, and vice versa; and since even numbers start with two, odd numbers with three, and five is produced by combination of these, it has rightly received honour as the product of first principles, and it has further been called “Marriage”, because even resembles the female, odd the male. For when we divide the several numbers into equal segments, the even parts asunder perfectly, and leaves inside a sort of recipient principle or space; if the odd is treated in the same way, a middle part is always left [Sidenote: B] over, which is generative. Hence the odd is the more generative, and when brought into combination invariably prevails; in no combination does it give an even result, but in all cases an odd. Moreover, when each is applied to itself and added, the difference is shown. Even with even never gives odd, or passes out of its proper nature; it wants the strength to produce anything different. Odd numbers with odd yield even numbers in [Sidenote: C] plenty because of their unfailing fertility. The other powers of numbers and their distinctions cannot be now pursued in detail. However, the Pythagoreans called five “Marriage”, as produced by the union of the first male number and the first female. From another point of view it has been called “Nature”, because when multiplied into itself it ends at last in itself. For as Nature takes a grain of wheat, and in the intermediate stages of growth gives forms and shapes in abundance, through which she brings her work to perfection, and, after them all, shows us again a grain of wheat, thus restoring the beginning in the end of the whole process, so it is with numbers. When other numbers are multiplied into themselves, they end in different numbers after being squared; only those formed [Sidenote: D] of five or of six recover and preserve themselves every time. Thus six times six gives thirty-six, five times five twenty-five. And again, a number formed of six does this only once, in the single case of being squared. Five has the same property in multiplication, and also a special property of its own when added to itself; it produces alternately itself or ten, and that to infinity. For this number mimics the principle which orders all things. As Heraclitus[58] tells us that Nature successively produces the universe out of herself and herself out of the universe, bartering “fire for things and things for fire, as goods for gold [Sidenote: E] and gold for goods”, even so it is with the Pempad. In union with itself, it does not by its nature produce anything imperfect or foreign. All its changes are defined; it either produces itself or the Decad, either the homogeneous or the perfect.

IX. ‘Then if any one ask “What is all this to Apollo?”[59] Much, we will answer, not to Apollo only but also to Dionysus, who has no less to do with Delphi than has Apollo. Now we [Sidenote: F] hear theologians saying or singing, in poems or in plain prose, that the God subsists indestructible and eternal, and that, by force of some appointed plan and method, he passes through changes of his person; at one time he sets fire to Nature and so makes all like unto all, at another passes through all phases of difference—shapes, sufferings, powers—at the present time, for instance, he becomes “Cosmos”, and that is his most familiar name. The wiser people disguise from the vulgar the change [Sidenote: 389] into fire, and call him “Apollo[60]” from his isolation, “Phoebus[61]” from his undefiled purity. As for his passage and distribution into waves and water, and earth, and stars, and nascent plants and animals, they hint at the actual change undergone as a rending and dismemberment, but name the God himself Dionysus or Zagreus or Nyctelius or Isodaites. Deaths too and vanishings do they construct, passages out of life and new births, all riddles and tales to match the changes mentioned. So they sing to Dionysus dithyrambic strains, charged with sufferings and a change wherein are wanderings and dismemberment. [Sidenote: B]

_In mingled cries_ (says Aeschylus)[62] _the dithyramb should ring, With Dionysus revelling, its King._

‘But Apollo has the Paean, a set and sober music. Apollo is ever ageless and young; Dionysus has many forms and many shapes as represented in paintings and sculpture, which attribute to Apollo smoothness and order and a gravity with no admixture, to Dionysus a blend of sport and sauciness with seriousness and frenzy:

_God that sett’st maiden’s blood Dancing in frenzied mood, Blooming with pageantry! Evoe! we cry._

‘So do they summon him, rightly catching the character of either change. But since the periods of change are not equal, that [Sidenote: C] called “satiety” being longer, that of “stint” shorter, they here preserve a proportion, and use the Paean with their sacrifice for the rest of the year, but at the beginning of winter awake the dithyramb, and stop the Paean, and invoke this God instead of the other, supposing that this ratio of three to one is that of the “Arrangement” to the “Conflagration”.[63]

X. ‘But perhaps this has been drawn out at too great length for the present opportunity. This much is clear, that they do associate the Pempad with the God, as it now produces its own [Sidenote: D] self like fire, and again produces the Decad out of itself like the universe. Now take music, which the God favours so highly, are we not to suppose that this number has its share here?

‘Most of the science of harmonies, to put it in a word, is concerned with consonances. That these are five and no more is proved by reason, as against the man who is all for strings and holes, and wants to explore these points irrationally by the senses; they all have their origin in numerical ratios. The ratio of the fourth is four to three, of the fifth three to two, of the octave two to one, of the octave and fifth three to one, of the double octave four to one. The additional consonance which writers of [Sidenote: E] harmony introduce under the name of octave and fourth, does not merit admission, being extra-metrical; to admit it would be to indulge the irrational side of our sense of hearing, and to violate reason, or law. Passing by then five arrangements of tetrachords, and the first five “tones”, or “tropes”, or “harmonies”, whichever name is right, by variations of which, made higher or lower, the remaining scales, high and low, are produced, is it not true that, though intervals are many, indeed infinite, the principles of melody are five only, quarter tone, [Sidenote: F] half tone, tone, tone and a half, double tone? In sounds no other interval of high and low, be it smaller or greater, can be used for melody.

XI. ‘Passing over many similar points, I will’, I said, ‘produce Plato,[64] who, in discussing the question of a single universe, says that if there are others besides ours, and it is not alone, then the whole number of them is five and no more; not but that, if ours is the only universe in being, as Aristotle[65] also thinks, even this one is in a fashion composite and formed out of five; one of earth, one of water, a third of fire, and a fourth of air, [Sidenote: 390] while the fifth is called heaven or light or air, or by others “fifth substance”, to which alone of all bodies circular motion is natural, not due to force or other accidental cause. Therefore it is that Plato, observing the five perfect figures of Nature—Pyramid, Cube, Octahedron, Eicosahedron, and Dodecahedron—assigned them to the elements, each to each.

XII. ‘There are some who appropriate to the same elements our own senses, also five in number. Touch, as they see, is [Sidenote: B] resistent and earthy. Taste takes in properties by moisture in the things tasted. Air when struck becomes audible voice or sound. There remain two: smell, the object of our olfactory sense, is an exhalation engendered by heat, and so resembles fire; sight is akin to air and light, which give it a luminous passage, so there is a commixture of both which is sympathetic. Besides these, the animal has no other sense, and the universe no other substance, which is simple and not blended. A marvellous [Sidenote: C] apportionment of the five to the five!’

XIII. Here, I think, I paused, and after an interval I went on: ‘What has happened to us, Eustrophus? We have almost forgotten Homer,[66] as if he had not been the first to divide the universe into five parts, assigning the three in the middle to the three Gods, while he left common and unapportioned the two extremes, Olympus and earth, one the limit of what is below, the other of what is above. “We must cry back”, as Euripides says.[67] Now those who exalt the number four as the basis of the [Sidenote: D] genesis of every body, make out a fairly good case. For every solid body possesses length, breadth, and depth; but length presupposes a point as an unit; the line is called length without breadth, and is length; the movement of a line in breadth produces a plane surface, and that is three; add depth, and we get to a solid with four factors. Any one can see that the number four carries Nature up to this point, that is, to the formation of a complete body, which may be touched, weighed, or struck; there it has left her, wanting in what is greatest. [Sidenote: E] For that which has no soul is, in plain terms, orphaned and incomplete and fit for nothing, unless it be employed by soul. But the movement or disposition which sets soul therein—a change introducing a fifth factor—restores to Nature her completeness, its rational basis is as much more commanding than that of the Tetrad as the animal is above the inanimate. Further, the symmetry and potency of the whole five prevails, so as not to allow the animate to form classes without limit, but gives five types for all living things. There are Gods, we know, and [Sidenote: F] daemons, and heroes, and after these, fourth in all, the race of men: fifth, and last, the irrational order of brutes. Again, if you make a natural division of the soul itself, the first and least distinct principle is that of growth; second is that of sense, then comes appetite, then the spirited part; when it has reached the power of reasoning and perfected its nature, it stays at rest in the fifth stage as its upper limit.

XIV. ‘Now as this number five has powers so many and so great, its origin is also noble: not the process already described, out of the numbers two and three, but that given by the combination of the first principle of number with the first square. The first principle is unity, the first square is four; from these [Sidenote: 391] as from idea and limited substance, comes five. Or, if it be really correct, as some hold, to reckon unity as a square, being a power of itself and working out to itself, then the Pempad is formed out of the first two squares, and so has not missed noble birth and that the highest.

XV. ‘My most important point’, I went on, ‘may, I fear, bear hardly on Plato, just as he said that Anaxagoras “was hardly used by the name Selene”, when he had wished to appropriate the theory of her illumination, really a very old one. Are not [Sidenote: B] these Plato’s words, in the _Cratylus_?‘[68] ‘They certainly are,’ said Eustrophus, ‘but I fail to see the resemblance.’ ‘Very well then; you know, I suppose, that in the “_Sophist_”[69] he proves that the supreme principles are five: being, identity, difference, and after these, as fourth and fifth, movement and position. But in the _Philebus_[70] he divides on a different plan. He distinguishes the unlimited and the limited, from whose combination comes the origin of all being. The cause of combination he takes to be a fourth. The fifth, whereby things so mingled are again parted and distinguished, he has left to us to guess. I [Sidenote: C] conjecture that those on the one list are figures of those on the other; to being corresponds that which becomes, to motion the unlimited; to position the limited, to identity the combining principle, to difference that which distinguishes. But if the two sets are different, yet, on one view as on the other, there would be five classes, and five modes of difference. Some early inquirer, it will surely be said, saw into this before Plato, and consecrated two “E’s” to the God, as a manifestation and symbol of the number of all things. But further, having perceived that the good also takes shape under five heads, firstly [Sidenote: D] moderation, secondly symmetry, thirdly mind, fourthly the sciences and arts and true opinions which relate to soul, fifthly every pleasure which is pure and unmingled with what causes pain, he there leaves off, merely suggesting the Orphic verse,

_In the sixth order let the strain be stayed!_

XVI. ‘Having said so much’, I went on, ‘to you all, I will sing one short stave to Nicander and “his cunning men”.[71]

‘On the sixth day of the new moon, when the Pythia is introduced into the Prytaneum by one person, the first of your three castings of lot is a single one, namely the five: the three [Sidenote: E] against the two.’ ‘It is so,’ said Nicander, ‘but the reason may not be disclosed to others.’ ‘Then,’ I answered with a smile, ‘until such time as we become priests, and the God allows us to know the truth, this much and no more shall be added to what we have to say about the Pempad.’ Such, so far as I remember, was the end of our account of the arithmetical or mathematical reasons for extolling the letter ‘E’.

XVII. Ammonius, as one who himself gave Mathematics no mean place in Philosophy, was pleased at the course the conversation was taking, and said: ‘It is not worth our while to answer our young friends with too absolute accuracy on these points; I will only observe that any one of the numbers will provide not a few points for those who choose to sing its praises. [Sidenote: F] Why speak about the others? Apollo’s holy “Seven” will take up all one day before we have exhausted its powers. Are we then to show the Seven Wise Men at odds with common usage, and “the time which runs”[72], and to suppose that they ousted the “Seven” from its pre-eminence before the God, and consecrated the “Five” as perhaps more appropriate?

‘My own view is that the letter signifies neither number, nor [Sidenote: 392] order, nor conjunction, nor any other omitted part of speech; it is a complete and self-operating mode of addressing the God; the word once spoken brings the speaker into apprehension of his power. The God, as it were, addresses each of us, as he enters, with his “KNOW THYSELF”, which is at least as good as “Hail”. We answer the God back with “EI” (Thou Art), rendering to him the designation which is true and has no lie in it, and alone belongs to him, and to no other, that of BEING.

XVIII. ‘For we have, really, no part in real being; all mortal nature is in a middle state between becoming and perishing, and presents but an appearance, a faint unstable image, of itself. If you strain the intellect, and wish to grasp this, it [Sidenote: B] is as with water; compress it too much and force it violently into one space as it tries to flow through, and you destroy the enveloping substance; even so when the reason tries to follow out too closely the clear truth about each particular thing in a world of phase and change, it is foiled, and rests either on the becoming of that thing or on its perishing; it cannot apprehend anything which abides or really is. “It is impossible to go into the same river twice”, said Heraclitus;[73] no more can you grasp mortal being twice, so as to hold it. So sharp and so swift is change; it scatters and brings together again, nay not again, no nor afterwards; even while it is being formed it fails, [Sidenote: C] it approaches, and it is gone. Hence becoming never ends in being, for the process never leaves off, or is stayed. From seed it produces, in its constant changes, an embryo, then an infant, then a child; in due order a boy, a young man; then a man, an elderly man, an old man; it undoes the former becomings and the age which has been, to make those which come after. Yet we fear (how absurdly!) a single death, we who have died so many deaths, and yet are dying. For it is not only that, as Heraclitus[74] would say, “death of fire is birth of air”, and “death of air is birth of water”; the thing is much clearer in [Sidenote: D] our own selves. The man in his strength is destroyed when the old man comes into being, the young man was destroyed for the man in his strength to be, so the boy for the young man, the babe for the boy. He of yesterday has died into him of to-day; he of to-day is dying into him of to-morrow. No one abides, no one is; we that come into being are many, while matter is driven around, and then glides away, about some one appearance and a common mould. Else how is it, if we remain the same, that the things in which we find pleasure now are different from those of a former time; that we love, hate, admire, and censure [Sidenote: E] different things; that our words are different and our feelings; that our look, our bodily form, our intellect are not the same now as then? If a man does not change, these various conditions are unnatural; if he does change, he is not the same man. But if he is not the same man, he is not at all; his so-called being is simply change and new birth of man out of man. In our ignorance of what being is, sense falsely tells us that what appears is.

XIX. ‘What then really is? That which is eternal, was never brought into being, is never destroyed, to which no time ever brings change. Time is a thing which moves and takes the fashion of moving matter, which ever flows or is a sort of leaky vessel which holds destruction and becoming. Of time we use the words “afterwards”, “before”, “shall be”, and [Sidenote: F] “has been”, each on its face an avowal of not being. For, in this question of being, to say of a thing which has not yet come into being, or which has already ceased from being, that “it is”, is silly and absurd. When we strain to the uttermost our apprehension of time, and say “it is at hand”, “it is here”, or “now”, a rational development of the argument brings it all to nothing. “Now” is squeezed out into the future or into the past, as though we should try to see a point, which of necessity passes away to right or left. But if the case be the [Sidenote: 393] same with Nature, which is measured, as with time which measures, nothing in it abides or really is. All things are coming into being, or being destroyed, even while we measure them by time. Hence it is not permissible, even in speaking of that which is, to say that “it was”, or “it shall be”; these all are inclinations, transitions, passages, for of permanent being there is none in Nature.

XX. ‘But the God IS, we are bound to assert; he is, with reference to no time but to that age wherein is no movement, or time, or duration; to which nothing is prior or subsequent; no future, no past, no elder, no younger, which by one long “now” has made the “always” perfect. Only with reference to this that which really is, is; it has not come into being, it is [Sidenote: B] not yet to be, it did not begin, it will not cease. Thus then we ought to hail him in worship, and thus to address him as “Thou Art”, aye, or in the very words of some of the old people, “Ei Hen”, “Thou art one thing”.[75] For the Divine is not many things, in the sense in which each one of us is made up of ten thousand different and successive states, a scrap-heap of units, a mob of individuals. No, that which is must be one, as that which is one is. Variety, any difference in being, passes to one side to produce that which is not. Therefore the first [Sidenote: C] of the names of the God is right, and the second, and the third. “Apollo” (Not-many) denies plurality and excludes multitude. Ieïus means one and one only; Phoebus, we know, is a word by which the ancients expressed that which is clean and pure, even as to this day the Thessalians, when their priests pass their solemn days in strict seclusion outside the temple, apply to them a verb formed from Phoebus. Now The One is transparent and pure, pollution comes by commixture of this with that, just as Homer,[76] you remember, says of ivory dyed red that it is stained, and dyers say of mingled pigments that they are [Sidenote: D] destroyed, and call the process “destruction”. Therefore it is the property of that which is indestructible and pure to be one and without admixture.