By soothing pow’r, and tame the wind,
not going on board themselves to share the peril, but appearing from above and delivering men; even so the Gods visit the worlds, now one and now another; drawn on by joy as they contemplate, and steering each in its natural course. |D| For the Zeus of Homer[[170]] had not very far to carry his eye from Troy to the parts of Thrace, and the wandering tribes about the Ister; but the real Zeus has beautiful passages and becoming to himself among worlds more than one, not looking out upon an infinite void, nor having his mind intent upon himself and nothing else (as was the view of some), but surveying many works of Gods and men, and movements and periodic orbits of stars. The divine nature is no foe to changes, but takes much delight in them, if we may judge from the bodies which |E| appear in the heavens, their changes and periods. Now Infinity is altogether without feeling or reason; it has no room to admit a God, all goes by chance and spontaneously. But the Providence which cares for worlds defined and limited in number appears to me to involve nothing less dignified or more laborious than that which has entered a single body, and attached itself thereto, to refashion or shape it anew in infinite particulars.’
XXXI. Having said so much, I paused. Philippus, after a short interval, went on: ‘Whether the truth about these |F| things be so, or not, I could not, for my own part, assert with confidence. But if we are to force the God outside one world, why make him the artificer of five worlds and no more; and what is the bearing of that number on the plurality of worlds? I would rather be informed on this point than as to the inner meaning of the consecration of the letter “E” in this place. That letter is neither triangle, nor square, nor “perfect”, nor cubic, nor has it any other apparent elegance for those who love and admire such things. The process out of the elements, at which the Master obscurely hinted, is hard to grasp |427| in every respect, and shows none of that probability which must have drawn him on to say that it is likely that out of five solid bodies having equal angles and equal faces and enclosed by figures of equal area, when set into matter, the same number of perfect worlds was at once produced.’
XXXII. ‘Yes,’ said I, ‘yet Theodorus of Soli seems to treat the argument very fairly, in expounding the Mathematics of Plato. This is his method: the Pyramid, the Octahedron, the Eicosahedron and the Dodecahedron, the solid figures which Plato ranks first, are all beautiful because of the symmetry and equality of their formulae; nothing better than these or equal to them has been left over for Nature to compose |B| or to frame. They have not, however, all been constructed on a single plan, nor have all a similar origin. The Pyramid is the finest and smallest, the largest and the one of most parts is the Dodecahedron; of the remaining two the Eicosahedron is more than double the Octahedron in number of triangles.[[171]] It follows that it is impossible for all to take their origin at once from one and the same matter. For those which are fine and small, and more simple in their structures, must be the first to obey him who stirs and fashions the mass; they must sooner cohere and be completed than those whose parts are abundant, and the figures complex, and their construction more laborious, |C| as the Dodecahedron. It follows that the Pyramid is the only primal body, and that none of the others is so; they are left behind by Nature in the becoming. For this strange result there is, however, a remedy, the division and distribution of matter into five worlds. Here the Pyramid (for it first formed substance), there the Octahedron, in a third world the Eicosahedron. But from the figure which first took substance in each the rest will take their origin, all change arising by concretion or dissolution of parts, as Plato himself shows.[[172]] He goes thoroughly into nearly all the cases, but for us a brief survey will suffice. Since air is formed when fire is extinguished, and when rarefied |D| again yields fire out of itself, we must observe what happens to the seeds of either element, and the changes. The seeds of fire[[173]] are the Pyramid with its twenty-four primary triangles; the seeds of air are the Octahedron with its forty-eight. Therefore one element of air is formed by the commixture and coherence of two of fire; and one of air is exchanged into two of |E| fire, or by close pressure into itself passes away into the form of water. Thus, universally, that which is first formed readily allows the others to come into being by transmutation. It is not the case that one is first; different elements in different structures give the initial and prerogative movement into being, yet the common name is kept throughout.’
XXXIII. ‘Bravo, Theodorus!’ said Ammonius; ‘he has worked out his task with spirit. Yet I shall be surprised if he is not found to be using assumptions which are mutually destructive. He wants to have it that all five solids do not attain their structure together, the finest and easiest of |F| composition always breaking first into being. Then, as though following upon this, and not conflicting with it, he lays it down that it is not all matter which admits the finest and simplest element first, but that sometimes the heavy and complex objects are the first to emerge out of matter. But to pass over this, whereas it is assumed that there are five primal bodies, and therefore an equal number of worlds, he makes out probability for four only; he has discarded the Cube as if playing at |428| counters, since Nature does not adapt it to pass into the others or them into itself, because the triangles are not of the same kind. In the other cases the basis of formation is the semi-(equilateral) triangle; to the Cube the right-angled isosceles is peculiar, which is incapable of converging towards the others or joining with them to form one solid angle. If then, there are five bodies and five worlds, and in each the primary belongs to some one, then where the Cube has been the first to come into being, the rest will be nowhere, for it is unable to change into any of them. I pass by the fact that they make the element of the Dodecahedron also a different thing from that scalene |B| out of which Plato constructs the Pyramid, the Octahedron, and the Eicosahedron. And so’, added Ammonius, with a laugh, ‘you must either resolve these difficulties, or give us something of your own about the common problem.’
XXXIV. ‘I have nothing more probable to offer, at least at the moment;’ I said, ‘yet perhaps it is better to show cause for one’s own view than for that of others. I say then, going back to the beginning, that if we assume two natures, one sensible, liable to changes of becoming and perishing, and to various movements at different times, the other essential, intellectual, always behaving alike under the same conditions, it is strange, friend, that the intellectual should admit of distinction and division within itself, while with regard to that which is bodily, and subject to affections, there should be trouble and |C| dissatisfaction if we refuse to leave it one, self-coherent and self-convergent, but separate and part it. Surely it is rather the permanent and divine which should hold together and shrink, as far as may be, from all dissection and analysis. Yet the force of “the Other” has gripped them, and has worked greater divergences than those of place in things intellectual, I mean those made by Reason and Idea. Hence Plato,[[174]] opposing those who make out the Whole to be one, tells us of Being, and the |D| Same, and the Different, and, besides all these, of Movement and Rest. Given then these five, it would not be wonderful if these five corporeal elements have been made by Nature copies and images of them severally, none free from admixture or transparent, but each element so far as it could best participate in each principle. Thus the Cube is clearly a body congenial to Rest, because of the stability and firmness of its surfaces. No one can fail to detect the fire-like, active character of the Pyramid in the fineness of its sides and the sharpness of its angles. The nature of the Dodecahedron, which embraces |E| the other figures, might well be taken for an image of Being in relation to all that is corporeal. Of the remaining two, the Eicosahedron is found most to partake of the idea of the Different, the Octahedron of that of the Same. Therefore the latter represented air, which holds all being in one constant form, the former water, which when mixed assumes new qualities the most numerous. If then Nature requires throughout equality before the law, it is probable that worlds have been created neither more nor less in number than the patterns, in order that each pattern in each world may hold that primacy and power which it has had in the composition of the elementary bodies.
|F| XXXV. ‘So much for that! May it reassure any one who is surprised at our dividing the natural processes of becoming and mutation into so many classes! Now comes another point, which I will ask you all to consider with me. Of the ultimate first principles, by which I mean unity and the undelimited two, the latter, as the element of all shapelessness and disorder, has been called Infinity; but unity by its nature limits and arrests what is void and irrational and undetermined in |429| Infinity, and imparts shape, and fits it to receive and endure that definition of things apprehended by the senses which is implied in counting. These principles appear first in connexion with number; but I would rather say, universally, that plurality is not number until unity supervenes, as form upon matter, and cuts off from undetermined Infinity, more on this side, less on that. For plurality in each case only becomes number when it is determined by unity. Again, if unity be struck off, the undetermined two throws all into a confusion without balance or limit or measure. Now since form is not a withdrawal |B| of underlying matter but is shape and order thereof, both principles must necessarily be found in number, and hence arises the first and greatest difference or dissimilarity. The undetermined principle is the constructive cause of the even, the better one of the odd. Two is the first of the even numbers, three of the odd; out of them comes five, in its composition common to both lists, in its effect, odd. For when the sensible and corporeal was to be divided into several parts, in virtue of the inherent cogency of the Other, their number must not be the first even nor yet the first odd, but the third, that formed out of these, so that it may take its origin from both |C| principles, that which constructs the even and that which constructs the odd; for neither could possibly be separated from the other; each possesses the nature and power of a principle. Both principles then being paired, the better one checked the indeterminate when it was dividing up the corporeal; and prevailed; when matter was being distributed between the two it set unity in the middle, and did not allow an equal division of the whole. So a plurality of worlds has been brought into being by the “Other” quality in the undetermined, and by difference; but that plurality is odd, made so by the operation of “the Same” and “the Determinate”, and odd in such a sense that Nature was not allowed to advance beyond what was best. For if the unity had been without admixture |D| and pure, matter would have been exempt from any breaking up whatever; but as it has been mingled with the discriminative power of the two, separation and division were so far accepted; but there it stopped, the even overcome by the odd.
XXXVI. ‘Hence again the ancients were accustomed to use the words “to take fives” for to count. I think, too, that the word for “all” (panta) has been logically formed as though from “five” (pente) because the number five is composed of the first numbers. For the others when multiplied by other numbers come out to a product different from themselves; but five if taken an even number of times gives a perfect ten, if an odd, it reproduces itself. I pass over the facts |E| that five is composed of the first two squares, one and four, and that its own square is equal to the sum of the two before it, forming with them the most beautiful of right-angled triangles, and that it is the first number to give sesquiplicate ratio. For perhaps they are not germane to the subject before us. This, however, is more germane, that the number five has a divisory virtue, and Nature divides most things by five. In |F| ourselves are five senses, and there are five parts of the soul, those of growth, sense, appetite, passion, reason. We have five fingers on each hand; seed is most fertile when it parts into five (no instance has been recorded of a woman bearing more than five at a birth); Rhea is said in Egyptian mythology to have given birth to five Gods,[[175]] a veiled reference to the production of the five worlds out of one matter. Turning to the universe, the surface of earth is divided into five zones, and the Heavens are divided by five circles, two Arctic, two |430| Tropic, one in the middle, the Equinoctial. Five are the orbits of the planets, if we take those of the sun and Venus and Mercury as one. Lastly, the universe has been composed in the Enharmonic Scale, just as our melody is made up of the arrangement of five Tetrachords, lowest, middle, conjunct, disjunct, highest. And the intervals are five: diesis, semitone, tone, tone and a half, double tone. Thus it seems that Nature loves to make all things on the principle of five, rather than, as Aristotle[[176]] used to say, of the Sphere.
XXXVII. ‘What is the real reason, some one will ask, why Plato[[177]] referred the number of five for his worlds to the five solid figures, saying that “God used the fifth formation on the universe to mark it out”? In the sequel, when he raises the |B| problem of plurality of worlds, whether we should properly speak of one or of five as naturally existing, he shows clearly that the suggestion came from the solids. If, then, we are to adjust what is actually probable to his conception, let us consider that difference in movement must in each case follow difference in the solids and their shapes, as Plato[[178]] himself teaches, when he |C| shows that what is rarefied or condensed suffers a change of place simultaneously with alteration of substance. If from air fire be formed, the Octahedron being resolved and broken up into Pyramids, or again if air from fire, when compressed and thrust into an Octahedron, it is impossible that either should remain where it was before; they fly off rapidly to another place, forcing a way out and battling with whatever resists and presses upon them. The result is shown still more clearly by an illustration from grain “tossed and winnowed by the fans and implements used for cleaning corn”; Plato[[179]] says that |D| in like manner the elements toss matter about and are tossed by it; like approaches like, different objects take different places, before the whole comes out finally marshalled. Thus then, matter being what any universe must be from which God is absent, the first five properties, each with its own tendency, at once began to move apart, not being entirely or purely separated, because, when all things were mixed up together, the vanquished particles always followed their conquerors, in despite of Nature. Hence they produced in the kinds of bodies, as they were borne in different directions, parts and divisions as many as themselves: one not of pure fire but |E| resembling fire, one not of unmixed air but resembling air, one not of earth simple and absolute but resembling earth. Most general was the association of air with water, because they passed out saturated with the many other classes. For God did not separate nor disperse being; but taking it up dispersed by its own operation and borne about in so many streams of disorder, he ordered and disposed it in symmetry and proportion. |F| Then he set reason in each to be a governor and guardian, and created as many worlds as there were kinds of primal bodies. Let so much then be inscribed to Plato for Ammonius’ sake. For myself, I could never speak with confidence as to the number of worlds and affirm that there are so many: but I think the view that there are more than one, yet not an indefinite but a limited number, as reasonable as either of the other views, when I see how scattered and divided matter naturally is, that it does not abide in one place, nor yet |431| is suffered by reason to pass into Infinity. Here, if anywhere, let us remember the Academy rule, and clear ourselves of excessive credulity, and treading on this slippery ground when reasoning about Infinity, only make sure that we keep our footing.’
XXXVIII. When I had finished, ‘Lamprias gives us sound advice’, said Demetrius. ‘The Gods by many forms—not “of sophistries”, as it is in Euripides,[[180]] but of things—deceive us, when we dare to pronounce opinions about these |B| great matters as if we knew. But “we must cry back”, to quote the same authority,[[181]] to the assumption from which our argument started. The statement that the oracles, when the daemons move off and desert them, lie idle and speechless, like musical instruments with none to play on them, raises another and a greater question as to the cause and power whereby they make the prophets and prophetesses subject to fits of inspiration and fancy. For it is impossible to allege the desertion as a cause of the silence unless we are first satisfied in what sense they preside and by their presence make the oracle active and vocal.’ ‘What?’ rejoined Ammonius, ‘do you suppose that the daemons are anything but souls which move around, as Hesiod[[182]] says “garmented in mist”? In my view, as man differs from man when he plays tragedy or |C| plays comedy, so soul differs from soul after it has fashioned for itself a body convenient to its present life. It is not then irrational or even wonderful that souls meeting souls should create within them fancies of that which is to be, just as we convey to one another, not only through voice, but often by written signs, by a touch, a glance, many intimations of things past, and forewarnings of things future. Or perhaps you have something different to tell us, Lamprias? For a rumour reached us lately that you had held a long discussion on these subjects with strangers at Lebadeia; but our informant |D| did not clearly remember any of it.’ ‘Do not be surprised at that,’ I said, ‘for there were many interruptions and much was going on, because it was a day of consultation and sacrifice, which made our conversation fragmentary and intermittent.’ ‘But now’, said Ammonius, ‘you have listeners with full leisure, and eager to inquire and to be told. There is no question of rivalry or faction, and you see what a frank full hearing has been accorded to every view.’