Timaeus

Tim.

And for this reason the body acquired length, and, by God’s contriving, shot forth four limbs, extensible and flexible, to serve as instruments of transport, so that grasping with these and’ supported thereon it was enabled to travel through all places, bearing aloft the chamber of our most divine and holy part. In this wise and for these reasons were legs and hands attached to all men; and inasmuch as they demand the forepart superior to the hinder part in honor and dignity, the Gods gave us the most part of our going in this direction. Thus it was necessary that man should have the forepart of his body distinct and dissimilar. Wherefore, dealing first with the vessel of the head, they set the face in the front thereof and bound within it organs for all the forethought of the Soul; and they ordained that this, which is the natural front, should be the leading part. And of the organs they constructed first light-bearing eyes, and these they fixed in the face for the reason following. They contrived that all such fire as had the property not of burning but of giving a mild light should form a body akin to the light of every day.[*](There is a play here on the words ἥμερον (mild)... ἡμέρας (day); Cf. Cratyl. 418 C.) For they caused the pure fire within us, which is akin to that of day, to flow through the eyes in a smooth and dense stream; and they compressed the whole substance, and especially the center, of the eyes, so that they occluded all other fire that was coarser and allowed only this pure kind of fire to filter through. So whenever the stream of vision is surrounded by midday light, it flows out like unto like,[*](Vision is explained on the principle that like is known by like: a fire-stream issuing from the eye meets a fire-stream coming from the object of vision ( Cf. the view of Empedocles).) and coalescing therewith it forms one kindred substance along the path of the eyes’ vision, wheresoever the fire which streams from within collides with an obstructing object without. And this substance, having all become similar in its properties because of its similar nature, distributes the motions of every object it touches, or whereby it is touched, throughout all the body even unto the Soul, and brings about that sensation which we now term seeing. But when the kindred fire vanishes into night, the inner fire is cut off; for when it issues forth into what is dissimilar it becomes altered in itself and is quenched, seeing that it is no longer of like nature with the adjoining air, since that air is devoid of fire. Wherefore it leaves off seeing, and becomes also an inducement to sleep. For the eyelids —whose structure the Gods devised as a safeguard for the vision,—when they are shut close, curb the power of the inner fire; which power dissipates and allays the inward motions, and upon their allaying quiet ensues; and when this quiet has become intense there falls upon us a sleep that is well-nigh dreamless;

Tim.

but when some greater motions are still left behind, according to their nature and the positions they occupy such and so great are the images they produce, which images are copied within and are remembered by the sleepers when they awake out of the dream. And it is no longer difficult to perceive the truth about the formation of images in mirrors and in bright and smooth surfaces of every kind. It is from the combination with each other of the inner and the outer fires, every time that they unite on the smooth surface and are variously deflected, that all such reflections necessarily result, owing to the fire of the reflected face coalescing with the fire of the vision on the smooth and bright surface.[*](e.g.when a man looks at his own face reflected in a mirror. Cf. Soph.266 C.) And left appears as right, because contact takes place between opposite portions of the visual stream and opposite portions of the object, contrary to the regular mode of collision. Contrariwise, right appears as right and left as left whenever the fire changes sides on coalescing with the object wherewith it coalesces; and this occurs whenever the smooth surface of the mirrors, being elevated on this side and on that,[*](i.e., concave (and hemi-cylindrical).) repels the right portion of the visual stream to the left and the left to the right. And when this same mirror is turned lengthwise to the face it makes the whole face appear upside down, since it repels the bottom of the ray to the top, and conversely the top to the bottom. Now all these are among the auxiliary Causes[*](These causes are secondary, as contrasted with the primary or First Cause (which is also the final Cause), the Good; Cf. 29 E, 68 E,Phaedo99 B.) which God employs as his ministers in perfecting, so far as possible, the Form of the Most Good; but by the most of men[*](e.g. Anaxagoras and the Atomists.) they are supposed to be not auxiliary but primary causes of all things—cooling and heating, solidifying and dissolving, and producing all such effects. Yet they are incapable of possessing reason and thought for any purpose. For, as we must affirm, the one and only existing thing which has the property of acquiring thought is Soul; and Soul is invisible, whereas fire and water and earth and air are all visible bodies; and the lover of thought and knowledge must needs pursue first the causes which belong to the Intelligent Nature, and put second all such as are of the class of things which are moved by others, and themselves, in turn, move others because they cannot help it. And we also must act likewise. We must declare both kinds of Causes, but keep distinct those which, with the aid of thought, are artificers of things fair and good, and all those which are devoid of intelligence and produce always accidental and irregular effects.

Tim.

Now regarding the auxiliary causes which have helped the eyes to acquire the power which they now possess, let this statement suffice. Next we must declare the most important benefit effected by them, for the sake of which God bestowed them upon us. Vision, in my view, is the cause of the greatest benefit to us, inasmuch as none of the accounts now given concerning the Universe would ever have been given if men had not seen the stars or the sun or the heaven. But as it is, the vision of day and night and of months and circling years has created the art of number and has given us not only the notion of Time[*](Cf. 37 D ff.) but also means of research into the nature of the Universe. From these we have procured Philosophy in all its range, than which no greater boon ever has come or will come, by divine bestowal, unto the race of mortals.[*](Cf. Phileb. 16 C ff.) This I affirm to be the greatest good of eyesight. As for all the lesser goods, why should we celebrate them? He that is no philosopher when deprived of the sight thereof may utter vain lamentations But the cause and purpose of that best good, as we must maintain, is this,—that God devised and bestowed upon us vision to the end that we might behold the revolutions of Reason in the Heaven and use them for the revolvings of the reasoning that is within us, these being akin to those, the perturbable to the imperturbable; and that, through learning and sharing in calculations which are correct by their nature, by imitation of the absolutely unvarying revolutions of the God we might stabilize the variable revolutions within ourselves. Concerning sound also and hearing, once more we make the same declaration, that they were bestowed by the Gods with the same object and for the same reasons; for it was for these same purposes that speech was ordained, and it makes the greatest contribution thereto; music too, in so far as it uses audible sound, was bestowed for the sake of harmony.[*](For the importance of music in education Cf. Rep.401 D,Laws666 D ff.; also Tim.80 B.) And harmony, which has motions akin to the revolutions of the Soul within us, was given by the Muses to him who makes intelligent use of the Muses, not as an aid to irrational pleasure, as is now supposed, but as an auxiliary to the inner revolution of the Soul, when it has lost its harmony, to assist in restoring it to order and concord with itself. And because of the unmodulated condition, deficient in grace, which exists in most of us, Rhythm also was bestowed upon us to be our helper by the same deities and for the same ends. The foregoing part of our discourse, save for a small portion, has been an exposition of the operations of Reason; but we must also furnish an account of what comes into existence through Necessity.[*](i.e., the sphere of mechanical causation, physical and physiological processes and results.)

Tim.

For, in truth, this Cosmos in its origin was generated as a compound, from the combination of Necessity and Reason. And inasmuch as Reason was controlling Necessity by persuading her to conduct to the best end the most part of the things coming into existence, thus and thereby it came about, through Necessity yielding to intelligent persuasion, that this Universe of ours was being in this wise constructed at the beginning. Wherefore if one is to declare how it actually came into being on this wise, he must include also the form of the Errant Cause, in the way that it really acts. To this point, therefore, we must return, and taking once again a fresh starting point suitable to the matter we must make a fresh start in dealing therewith, just as we did with our previous subjects. We must gain a view of the real nature of fire and water, air and earth, as it was before the birth of Heaven, and the properties they had before that time; for at present no one has as yet declared their generation, but we assume that men know what fire is, and each of these things, and we call them principles and presume that they are elements[*](στοιχεῖα, here applied to physical elements, was the regular term for letters of the alphabet; Cf. Theaet. 203 B ff.,Rep.402 A ff.) of the Universe, although in truth they do not so much as deserve to be likened with any likelihood, by the man who has even a grain of sense, to the class of syllables. For the present, however, let our procedure be as follows. We shall not now expound the principle of all things—or their principles, or whatever term we use concerning them; and that solely for this reason, that it is difficult for us to explain our views while keeping to our present method of exposition.[*](i.e., a method which aims only at probability or likelihood: to attain to first principles we should need to employ the dialectic method.) You, therefore, ought not to suppose that I should expound them, while as for me—I should never be able to convince myself that I should be right in attempting to undertake so great a task. Strictly adhering, then, to what we previously affirmed, the import of the likely account, I will essay (as I did before) to give as likely an exposition as any other (nay, more so), regarding both particular things and the totality of things from the very beginning. And as before,[*](Cf. 27 C.) so now, at the commencement of our account, we must call upon God the Saviour to bring us safe through a novel and unwonted exposition to a conclusion based on likelihood, and thus begin our account once more. We must, however, in beginning our fresh account of the Universe make more distinctions than we did before; for whereas then we distinguished two Forms,[*](Cf. 28 A.) we must now declare another third kind.

Tim.

For our former exposition those two were sufficient, one of them being assumed as a Model Form, intelligible and ever uniformly existent, and the second as the model’s Copy, subject to becoming and visible. A third kind we did not at that time distinguish, considering that those two were sufficient; but now the argument seems to compel us to try to reveal by words a Form that is baffling and obscure. What essential property, then, are we to conceive it to possess? This in particular,—that it should be the receptacle, and as it were the nurse, of all Becoming. Yet true though this statement is, we must needs describe it more plainly. That, however, is a difficult task, especially because it is necessary, for its sake, to discuss first the problem of fire and its fellow elements. For in regard to these it is hard to say which particular element we ought really to term water rather than fire, and which we ought to term any one element rather than each and all of them, while still employing a terminology that is reliable and stable. How, then, shall we handle this problem, and what likely solution can we offer? First of all, we see that which we now call water becoming by condensation, as we believe, stones and earth; and again, this same substance, by dissolving and dilating, becoming breath and air; and air through combustion becoming fire; and conversely, fire when contracted and quenched returning back to the form of air and air once more uniting and condensing into cloud and mist; and issuing from these, when still further compressed, flowing water; and from water earth and stones again: thus we see the elements passing on to one another, as it would seem, in an unbroken circle the gift of birth. Accordingly, since no one of these ever remains identical in appearance, which of them shall a man definitely affirm to be any one particular element and no other without incurring ridicule? None such exists. On the contrary, by far the safest plan in treating of these elements is to proceed thus: Whatsoever object we perceive to be constantly changing from one state to another, like fire, that object, be it fire, we must never describe as this but as suchlike, nor should we ever call water this but suchlike nor should we describe any other element, as though it possessed stability, of all those which we indicate by using the terms this and that and suppose ourselves to refer to a definite object. For such an object shuns and eludes the names this and that and every name which indicates that they are stable. Thus we must not call the several elements these, but in regard to each of them and all together we must apply the term suchlike to represent what is always circling round: thus we shall call that which is constantly suchlike by the name of fire, and so with everything else that is generated.

Tim.

But that wherein they are always, in appearance, coming severally into existence, and wherefrom in turn they perish, in describing that and that alone should we employ the terms this and that; whereas, in describing what is suchlike—hot, for instance, or white, or any of the opposite qualities, or any compounds thereof—we ought never to apply to it any of these terms. But we must bestir ourselves to explain this matter again yet more clearly. Now imagine that a man were to model all possible figures out of gold, and were then to proceed without cessation to remodel each of these into every other, then, if someone were to point to one of the figures and ask what it is, by far the safest reply, in point of truth, would be that it is gold; but as for the triangle and all the other figures which were formed in it, one should never describe them as being seeing that they change even while one is mentioning them; rather one should be content if the figure admits of even the title suchlike being applied to it with any safety. And of the substance which receives all bodies the same account must be given. It must be called always by the same name; for from its own proper quality it never departs at all for while it is always receiving all things, nowhere and in no wise does it assume any shape similar to any of the things that enter into it. For it is laid down by nature as a molding-stuff for everything, being moved and marked by the entering figures, and because of them it appears different at different times. And the figures that enter and depart are copies of those that are always existent, being stamped from them in a fashion marvellous and hard to describe, which we shall investigate hereafter.[*](Cf. 53 C.) For the present, then, we must conceive of three kinds,—the Becoming, that Wherein it becomes, and the source Wherefrom the Becoming is copied and produced. Moreover, it is proper to liken the Recipient to the Mother, the Source to the Father, and what is engendered between these two to the Offspring; and also to perceive that, if the stamped copy is to assume diverse appearances of all sorts, that substance wherein it is set and stamped could not possibly be suited to its purpose unless it were itself devoid of all those forms which it is about to receive from any quarter. For were it similar to any of the entering forms, on receiving forms of an opposite or wholly different kind, as they arrived, it would copy them badly, through obtruding its own visible shape. Wherefore it is right that the substance which is to receive within itself all the kinds should be void of all forms; just as with all fragrant ointments, men bring about this condition by artistic contrivance and make the liquids which are to receive the odors as odorless as possible; and all who essay to mold figures in any soft material utterly refuse to allow any previous figure to remain visible therein, and begin by making it even and as smooth as possible before they execute the work.

Tim.

So likewise it is right that the substance which is to be fitted to receive frequently over its whole extent the copies of all things intelligible and eternal should itself, of its own nature, be void of all the forms. Wherefore, let us not speak of her that is the Mother and Receptacle of this generated world, which is perceptible by sight and all the senses, by the name of earth or air or fire or water, or any aggregates or constituents thereof: rather, if we describe her as a Kind invisible and unshaped, all-receptive, and in some most perplexing and most baffling way partaking of the intelligible, we shall describe her truly. In so far as it is possible to arrive at the nature of this kind from the foregoing account, one may state it most correctly in this way. That part of it which is made fiery appears each time as fire, that which has been liquefied as water; and it appears as earth and air in so far as it receives copies of these. But let us investigate the matter by more exact reasoning, and consider this question. Does there exist any self-subsisting fire or any of those other objects which we likewise term self-subsisting realities? Or is it only these things which we see, or otherwise perceive by means of bodily senses, that exist, possessed of sensible reality; beside which no other things exist anywhere or anyhow, and it is merely an idle assertion of ours that there always exists an intelligible Form of every object, whereas it is really nothing more than a verbal phrase? Now, on the one hand, it would be improper to dismiss the question before us without a trial and a verdict, and simply to asseverate that the fact is so; while, on the other hand, we ought not to burden a lengthy discourse with another subsidiary argument. If, however, it were possible to disclose briefly some main determining principle, that would best serve our purpose. This, then, is the view for which I, for my part, cast my vote. If Reason and True Opinion are two distinct Kinds, most certainly these self-subsisting Forms do exist, imperceptible by our senses, and objects of Reason only; whereas if, as appears to some, True Opinion differs in naught from Reason, then, on the contrary, all the things which we perceive by our bodily senses must be judged to be most stable. Now these two Kinds must be declared to be two, because they have come into existence separately and are unlike in condition. For the one of them arises in us by teaching, the other by persuasion; and the one is always in company with true reasoning, whereas the other is irrational; and the one is immovable by persuasion, whereas the other is alterable by persuasion; and of the one we must assert that every man partakes, but of Reason only the gods and but a small class of men.

Tim.

This being so, we must agree that One Kind is the self-identical Form, ungenerated and indestructible, neither receiving into itself any other from any quarter nor itself passing anywhither into another, invisible and in all ways imperceptible by sense, it being the object which it is the province of Reason to contemplate; and a second Kind is that which is named after the former and similar thereto, an object perceptible by sense, generated, ever carried about, becoming in a place and out of it again perishing, apprehensible by Opinion with the aid of Sensation; and a third Kind is ever-existing Place, which admits not of destruction, and provides room for all things that have birth, itself being apprehensible by a kind of bastard reasoning by the aid of non-sensation, barely an object of belief; for when we regard this we dimly dream and affirm that it is somehow necessary that all that exists should exist in some spot and occupying some place, and that that which is neither on earth nor anywhere in the Heaven is nothing. So because of all these and other kindred notions, we are unable also on waking up to distinguish clearly the unsleeping and truly subsisting substance, owing to our dreamy condition, or to state the truth—how that it belongs to a copy—seeing that it has not for its own even that substance for which it came into being, but fleets ever as a phantom of something else—to come into existence in some other thing, clinging to existence as best it may, on pain of being nothing at all; whereas to the aid of the really existent there comes the accurately true argument, that so long as one thing is one thing, and another something different, neither of the two will ever come to exist in the other so that the same thing becomes simultaneously both one and two. Let this, then, be, according to my verdict, a reasoned account of the matter summarily stated,—that Being and Place and Becoming were existing, three distinct things, even before the Heaven came into existence; and that the Nurse of Becoming, being liquefied and ignified and receiving also the forms of earth and of air, and submitting to all the other affections which accompany these, exhibits every variety of appearance; but owing to being filled with potencies that are neither similar nor balanced, in no part of herself is she equally balanced, but sways unevenly in every part, and is herself shaken by these forms and shakes them in turn as she is moved.

Tim.

And the forms, as they are moved, fly continually in various directions and are dissipated; just as the particles that are shaken and winnowed by the sieves and other instruments used for the cleansing of corn fall in one place if they are solid and heavy, but fly off and settle elsewhere if they are spongy and light. So it was also with the Four Kinds when shaken by the Recipient: her motion, like an instrument which causes shaking, was separating farthest from one another the dissimilar, and pushing most closely together the similar; wherefore also these Kinds occupied different places even before that the Universe was organized and generated out of them. Before that time, in truth, all these things were in a state devoid of reason or measure, but when the work of setting in order this Universe was being undertaken, fire and water and earth and air, although possessing some traces of their own nature, were yet so disposed as everything is likely to be in the absence of God; and inasmuch as this was then their natural condition, God began by first marking them out into shapes by means of forms and numbers. And that God constructed them, so far as He could, to be as fair and good as possible, whereas they had been otherwise,—this above all else must always be postulated in our account. Now, however, it is the disposition and origin of each of these Kinds which I must endeavor to explain to you in an exposition of an unusual type; yet, inasmuch as you have some acquaintance with the technical method which I must necessarily employ in my exposition, you will follow me. In the first place, then, it is plain I presume to everyone that fire and earth and water and air are solid bodies; and the form of a body, in every case, possesses depth also. Further, it is absolutely necessary that depth should be bounded by a plane surface; and the rectilinear plane is composed of triangles. Now all triangles derive their origin from two triangles, each having one angle right and the others acute[*](i.e., the rectangular isosceles triangle and the rectangular scalene; all other triangles can be built up from these two (e.g. see 54 E N.).); and the one of these triangles has on each side half a right angle marked off by equal sides, while the other has the right angle divided into unequal parts by unequal sides. These we lay down as the principles of fire and all the other bodies, proceeding according to a method in which the probable is combined with the necessary; but the principles which are still higher than these are known only to God and the man who is dear to God. We must now declare what will be the four fairest bodies, dissimilar to one another, but capable in part of being produced out of one another by means of dissolution; for if we succeed herein we shall grasp the truth concerning the generation of earth and fire and the mean proportionals. For to no one will we concede that fairer bodies than these, each distinct of its kind, are anywhere to be seen. Wherefore we must earnestly endeavor to frame together these four kinds of bodies which excel in beauty, and to maintain that we have apprehended their nature adequately.

Tim.

Now of the two triangles, the isosceles possesses one single nature, but the scalene an infinite number; and of these infinite natures we must select the fairest, if we mean to make a suitable beginning. If, then, anyone can claim that he has chosen one that is fairer for the construction of these bodies, he, as friend rather than foe, is the victor. We, however, shall pass over all the rest and postulate as the fairest of the triangles that triangle out of which, when two are conjoined, the equilateral triangle is constructed as a third.[*](i.e., the half of an equilateral triangle; e.g. if the triangle ABC is bisected by the line AD, we have two such triangles in ADB and ADC.) The reason why is a longer story; but should anyone refute us and discover that it is not so, we begrudge him not the prize. Accordingly, let these two triangles be selected as those wherefrom are contrived the bodies of fire and of the other elements,— one being the isosceles, and the other that which always has the square on its greater side three times the square on the lesser side.[*](i.e., in the triangle ADB (see last note) AB = 2Bsquared, and (AB)squared = (BD)squared + (AD)squared; therefore 4(BD)squared = (BD)squared + (AD)squared, and so 3(BD)squared = (AD)squared.) Moreover, a point about which our previous statement was obscure must now be defined more clearly. It appeared as if the four Kinds, in being generated, all passed through one another into one another, but this appearance was deceptive. For out of the triangles which we have selected four Kinds are generated, three of them out of that one triangle which has its sides unequal, and the fourth Kind alone composed of the isosceles triangle. Consequently, they are not all capable of being dissolved into one another so as to form a few large bodies composed of many small ones, or the converse; but three of them do admit of this process. For these three are all naturally compounded of one triangle, so that when the larger bodies are dissolved many small ones will form themselves from these same bodies, receiving the shapes that befit them; and conversely, when many small bodies are resolved into their triangles they will produce, when unified, one single large mass of another Kind. So let thus much be declared concerning their generation into one another. In the next place we have to explain the form in which each Kind has come to exist and the numbers from which it is compounded. First will come that form which is primary and has the smallest components, and the element thereof is that triangle which has its hypotenuse twice as long as its lesser side. And when a pair of such triangles are joined along the line of the hypotenuse, and this is done thrice, by drawing the hypotenuses and the short sides together as to a center, there is produced from those triangles, six in number, one equilateral triangle.[*](As in the figure the equilateral triangle ABC is divided into 6 triangles of unequal sides by joining the vertical points A, B, C to the points of bisection of the opposite sides, viz. D, E, F. Then the hypotenuse in each such triangle is double the shortest side (e.g. AO = 2FO). And FAO = 1/3 right angle; while FOA = 2/3 right angle. The three plane edges are thus of 60 degrees each = 180 degrees = the most obtuse plane angle; so that the solid angle is one degree less, i.e., 179 degrees.)

Tim.

And when four equilateral triangles are combined so that three plane angles meet in a point, they form one solid angle, which comes next in order to the most obtuse of the plane angles. And when four such angles are produced, the first solid figure[*](i.e., the tetrahedron or pyramid (molecule of fire).) is constructed, which divides the whole of the circumscribed sphere into equal and similar parts. And the second solid[*](i.e., the octahedron (molecule of air).) is formed from the same triangles, but constructed out of eight equilateral triangles, which produce one solid angle out of four planes; and when six such solid angles have been formed, the second body in turn is completed. And the third solid[*](i.e., the icosahedron (molecule of water).) is composed of twice sixty of the elemental triangles conjoined, and of twelve solid angles, each contained by five plane equilateral triangles, and it has, by its production, twenty equilateral triangular bases. Now the first of the elemental triangles ceased acting when it had generated these three solids, the substance of the fourth Kind[*](i.e., the cube, composed of 6x4 rectangular isosceles triangles (molecule of earth).) being generated by the isosceles triangle. Four of these combined, with their right angles drawn together to the center, produced one equilateral quadrangle; and six such quadrangles, when joined together, formed eight solid angles, each composed of three plane right angles; and the shape of the body thus constructed was cubic, having six plane equilateral quadrangular bases. And seeing that there still remained one other compound figure, the fifth,[*](i.e., the dodecahedron. How God used it up is obscure: the reference may be to the 12 signs of the Zodiac.) God used it up for the Universe in his decoration thereof. Now in reasoning about all these things, a man might question whether he ought to affirm the existence of an infinite diversity of Universes or a limited number; and if he questioned aright he would conclude that the doctrine of an infinite diversity is that of a man unversed[*](There is a play here on the two senses of ἄπειρος, unlimited and unskilled; Cf. Phileb. 17 E. The doctrine of an infinite number of worlds was held by the Atomists.) in matters wherein he ought to be versed; but the question whether they ought really to be described as one Universe or five is one which might with more reason give us pause. Now our view declares the Universe to be essentially one, in accordance with the probable account; but another man, considering other facts, will hold a different opinion. Him, however, we must let pass. But as for the Kinds which have now been generated by our argument, let us assign them severally to fire and earth and water and air. To earth let us give the cubic form; for of the four Kinds earth is the most immobile and the most plastic body, and of necessity the body which has the most stable bases must be pre-eminently of this character. Now of the triangles we originally assumed, the basis formed by equal sides is of its nature more stable than that formed by unequal sides; and of the plane surfaces which are compounded of these several triangles, the equilateral quadrangle, both in its parts and as a whole, has a more stable base than the equilateral triangle.

Tim.

Wherefore, we are preserving the probable account when we assign this figure to earth, and of the remaining figures the least mobile to water, and the most mobile to fire, and the intermediate figure to air; and, further, when we assign the smallest body to fire, and the greatest to water, and the intermediate to air; and again, the first in point of sharpness to fire, the second to air, and the third to water. As regards all these forms, that which has the fewest bases must necessarily be the most mobile, since it is in all ways the sharpest and most acute of all; and it must also be the lightest, since it is composed of the fewest identical parts; and the second comes second in point of these same qualities, and the third third. Thus, in accordance with the right account and the probable, that solid which has taken the form of a pyramid shall be the element and seed of fire; the second in order of generation we shall affirm to be air, and the third water. Now one must conceive all these to be so small that none of them, when taken singly each in its several kind, is seen by us, but when many are collected together their masses are seen. And, moreover, as regards the numerical proportions which govern their masses and motions and their other qualities, we must conceive that God realized these everywhere with exactness, in so far as the nature of Necessity submitted voluntarily or under persuasion, and thus ordered all in harmonious proportion. From all that we have hitherto said about these Kinds, they will, in all likelihood, behave themselves as follows. Earth will keep moving when it happens to meet with fire and has been dissolved by its acuteness, whether this dissolution takes place in pure fire or in a mass of air or of water; and this motion will continue until the particles of earth happen to meet together somewhere and reunite one with another, when they become earth again; for assuredly earth will never change into another form. But water, when broken up by fire or even by air, is capable of becoming a compound of one corpuscle of fire with two of air; and the fractions of air which come from the dissolving of one particle will form two corpuscles of fire. And again, when a small quantity of fire is enclosed by a large quantity of air and water, or of earth, and moves within them as they rush along, and is defeated in its struggle and broken up, then two corpuscles of fire unite to make one form of air. And when air is defeated and disintegrated, from two whole forms of air and a half, one whole form of water will be compounded.

Tim.

Once again let us reason out their character in this way. Whenever any of the other Kinds is caught within fire it is cut up thereby, owing to the acuteness of its angles and of the line of its sides, but when it has been re-composed into the substance of fire it ceases to be cut; for the Kind that is similar and uniform is in no case able either to cause any change in, or to suffer any affection from, a Kind which is in a uniform and similar state[*](The affinity of like to like was an axiom in early Greek thought; Cf. Lysis215 C ff.,Sympos. 186 A ff.); but so long as, in the course of its passage into another form, it is a weaker body fighting against a stronger, it is continually being dissolved. And again, whenever a few of the smaller corpuscles, being caught within a great number of larger corpuscles, are broken up and quenched, then, if they consent to be re-compounded into the shape of the victorious Kind, they cease to be quenched, and air is produced out of fire, and out of air water; but if they fight against combining with these or with any of the other Kinds, they do not cease from dissolution until either they are driven out to their own kindred, by means of this impact and dissolution, or else they are defeated and, instead of many forms, assume one form similar to the victorious Kind, and continue dwelling therewith as a united family. Moreover, it is owing to these affections that they all interchange their places; for while the bulk of each Kind keeps apart in a region of its own[*](The elements are conceived as having their proper abodes in concentric strata of space, one above another—earth in the center, water next, then air, and fire at the circumference of the World-Sphere.) because of the motion of the Recipient, yet those corpuscles which from time to time become dissimilar to themselves and similar to others are carried, because of the shaking, towards the region which belongs to those corpuscles whereto they have been assimilated. Such are the causes which account for the generation of all the unmixed and primary bodies. But within these four Kinds other classes exist, whereof the cause must be sought in the construction of each of the two elemental triangles, each such construction having originally produced not merely a triangle of one definite size, but larger and smaller triangles of sizes as numerous as are the classes within the Kinds. Consequently, when these are combined amongst themselves and with one another they are infinite in their variety; and this variety must be kept in view by those who purpose to employ probable reasoning concerning Nature. Now, unless we can arrive at some agreed conclusion concerning Motion and Rest, as to how and under what conditions they come about, our subsequent argument will be greatly hampered. The facts about them have already been stated in part; but in addition thereto we must state further that motion never consents to exist within uniformity. For it is difficult, or rather impossible, for that which is to be moved to exist without that which is to move, or that which is to move without that which is to be moved; but in the absence of these there is no motion, and that these should ever be uniform is a thing impossible.

Tim.

Accordingly, we must always place rest in uniformity, and motion in non-uniformity; and the cause of the non-uniform nature lies in inequality. Now we have explained the origin of inequality[*](Cf. 53 C ff.: the varying shapes and sizes of the primary triangles account for the inequality.); but we have not declared how it is that these bodies are not separated according to their several Kinds, and cease not from their motion and passage one through another. Wherefore, we shall once more expound the matter as follows. The revolution of the All, since it comprehends the Kinds, compresses them all, seeing that it is circular and tends naturally to come together to itself[*](i.e., exerts a centripetal force. For this compression cf. Emped. Frag. 185 Τιτὰν ἠδʼ αἰθὴρ σφίγγων περὶ κύκλον ἅπαντα.); and thus it suffers no void place to be left. Wherefore, fire most of all has permeated all things, and in a second degree air, as it is by nature second in fineness; and so with the rest; for those that have the largest constituent parts have the largest void left in their construction, and those that have the smallest the least. Thus the tightening of the compression forces together the small bodies into the void intervals of the large. Therefore, when small bodies are placed beside large, and the smaller disintegrate the larger while the larger unite the smaller, they all shift up and down towards their own proper regions; for the change in their several sizes causes their position in space also to change. And since in this way and for these reasons the production of non-uniformity is perpetually maintained, it brings about unceasingly, both now and for the future, the perpetual motion of these bodies. In the next place, we must observe that there are many kinds of fire: for example, there is flame; and the kind issuing from flame, which does not burn but supplies light to the eyes; and the kind which, when the flame is quenched, is left behind among the embers. So likewise of air, there is the most translucent kind which is called by the name of aether, and the most opaque which is mist and darkness, and other species without a name, which are produced by reason of the inequality of the triangles. The kinds of water are, primarily, two, the one being the liquid, the other the fusible[*](i.e., metals are classes as water, cf. 59 B ff.) kind. Now the liquid kind, inasmuch as it partakes of those small particles of water which are unequal, is mobile both in itself and by external force owing to its non-uniformity and the shape of its figure. But the other kind, which is composed of large and uniform particles, is more stable than the first and is heavy, being solidified by its uniformity; but when fire enters and dissolves it, this causes it to abandon its uniformity, and this being lost it partakes more largely in motion; and when it has become mobile it is pushed by the adjacent air and extended upon the earth; and for each of these modifications it has received a descriptive name—melting for the disintegration of its masses, and for its extension over the earth fluidity.

Tim.

Again, since the fire on issuing from the water does not pass into a void but presses on the adjacent air, this in turn compresses the liquid mass which is still mobile into the abodes of the fire and combines it with itself; and the mass, being this, is compressed and recovering again its uniformity, because of the departure of the fire, the author of its non-uniformity, returns to its state of self-identity. And this cessation of the fire is termed cooling, and the combination which follows on its departure solidification. Of all the kinds of water which we have termed fusible, the densest is produced from the finest and most uniform particles: this is a kind of unique form, tinged with a glittering and yellow hue, even that most precious of possessions, gold, which has been strained through stones and solidified. And the off-shoot of gold, which is very hard because of its density and black in color, is called adamant.[*](Perhaps haematite or platinum.) And the kind which closely resembles gold in its particles but has more forms than one, and in density is more dense than gold, and partakes of small and fine portions of earth so that it is harder, while it is also lighter owing to its having large interstices within it,—this particular kind of the bright and solid waters, being compounded thus, is termed bronze. And the portion of earth that is mixed therewith becomes distinct by itself, when both grow old and separate again-each from the other; and then it is named rust. And the rest of such phenomena it is no longer difficult to explain in full, if one aims at framing a description that is probable.[*](Cf. 29 B, D, 48 C, etc.) For as regards this, whenever for the sake of recreation a man lays aside arguments concerning eternal Realities and considers probable accounts of Becoming, gaining thereby a pleasure not to be repented of, he provides for his life a pastime that is both moderate and sensible. To this pastime let us now give free play, and proceed to expound in order the subsequent probabilities concerning these same phenomena in the following way. The water that is mixed with fire, which is fine and fluid, is termed fluid, owing to its motion and the way it rolls over the earth.[*](Alluding to a fanciful derivation of ὑγρόνfrom ὑπὲρ γῆν ῥέον.) Also it is soft owing to the fact that its bases, being less stable than those of earth, give way. When this kind is separated off from fire and air and isolated it becomes more uniform, but because of their outflow it is compressed upon itself; and when it is thus solidified, the part of it above the earth which is most affected by this process is termed hail, and the part upon the earth ice and the part which is less affected and is still only half-solid is called snow when it is above the earth, but when it is upon the earth and solidified out of dew it is called hoar-frost.

Tim.

Now as regards most forms of water that are intermingled one with another, the kind as a whole, consisting of water that has been strained through earth-grown plants, is called sap; but inasmuch as the several sorts have become dissimilar owing to intermixture, most of the kinds thus produced are unnamed. Four of these kinds, however, being fiery and specially conspicuous, have received names. Of these, that which is heating to the soul as well as the body is called wine; that which is smooth and divisive of the vision, and therefore bright to look upon and gleaming and glistening in appearance, is the species oil, including pitch and castor oil and olive oil itself and all the others that are of the same character; and all that kind which tends to expand the contracted parts of the mouth, so far as their nature allows, and by this property produces sweetness, has received as a general designation the name of honey; and the foamy kind, which tends to dissolve the flesh by burning, and is secreted from all the saps, is named verjuice.[*](Perhaps a kind of fig-juice.) Of the species of earth, that which is strained through water becomes a stony substance in the following way. When the water commingled therewith is divided in the process of mingling, it changes into the form of air; and when it has become air it rushes up to its own region; but because there was no void space above them, therefore it pressed against the adjacent air; and it, being heavy, when pressed and poured round the mass of earth, crushed it forcibly and compressed it into the spaces from which the new air was ascending. But when earth is thus compressed by the air so as to be indissoluble by water it forms stone; of which the fairer sort is that composed of equal and uniform parts and transparent, and the coarser sort the opposite. That kind from which all the moisture has been carried off by the rapidity of fire, and which is more brittle in its composition than the first kind, is the kind to which we have given the name of earthenware. But sometimes, when moisture is still left in the earth and it has been fused by fire and has cooled again, it forms the species which is black in hue. On the other hand there are two kinds, which, in exactly the same manner, are isolated after the mixture from much of their water, but are composed of finer parts of earth, and are saline: when these have become semi-solid and soluble again by water, one of them is purgative of oil and earth and forms the species called lye[*](i.e., potash or saltpeter.); and the other, which blends well with the combinations which affect the sensation of the mouth, is that substance which is customarily termed beloved of the gods,[*](Cf. Hom.Il. ix. 214 πάσσε δʼ ἁλὸς θείοιο.) namely salt. As regards the kinds which are a blend of these two, and are dissoluble by fire and not by water, their composition is due to the following cause. Fire and air do not melt masses of earth; for, inasmuch as their particles are smaller then the interstices of its structure, they have room to pass through without forcible effort and leave the earth undissolved, with the result that it remains unmelted; whereas the particles of water, being larger, must use force to make their way out, and consequently dissolve and melt the earth.