Timaeus

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.

Tim.

Thus earth when it is not forcibly condensed is dissolved only by water; and when it is condensed it is dissolved by fire only, since no entrance is left for anything save fire. Water, again, when most forcibly massed together is dissolved by fire only, but when massed less forcibly both by fire and air, the latter acting by way of the interstices, and the former by way of the triangles; but air when forcibly condensed is dissolved by nothing save by way of its elemental triangles, and when unforced it is melted down by fire only. As regards the classes of bodies which are compounds of earth and water, so long as the water occupies the interspaces of earth which are forcibly contracted, the portions of water which approach from without find no entrance, but flow round the whole mass and leave it undissolved. But when portions of fire enter into the interspaces of the water they produce the same effects on water as water does on earth; consequently, they are the sole causes why the compound substance is dissolved and flows. And of these substances those which contain less water than earth form the whole kind known as glass, and all the species of stone called fusible; while those which contain more water include all the solidified substances of the type of wax and frankincense. And now we have explained with some fullness the Four Kinds, which are thus variegated in their shapes and combinations and permutations; but we have still to try to elucidate the Causes which account for their affective qualities. Now, first of all, the quality of sense-perceptibility must always belong to the objects under discussion; but we have not as yet described the generation of flesh and the appurtenances of flesh, nor of that portion of Soul which is mortal. But, in truth, these last cannot be adequately explained apart from the subject of the sensible affections, nor the latter without the former; while to explain both simultaneously is hardly possible. Therefore, we must assume one of the two, to begin with, and return later to discuss our assumptions. In order, then, that the affective properties may be treated next after the kinds, let us presuppose the facts about body and soul. Firstly, then, let us consider how it is that we call fire hot by noticing the way it acts upon our bodies by dividing and cutting. That its property is one of sharpness we all, I suppose, perceive;

Tim.

but as regards the thinness of its sides and the acuteness of its angles and the smallness of its particles and the rapidity of its motion—owing to all which properties fire is intense and keen and sharply cuts whatever it encounters,—these properties we must explain by recalling the origin of its form, how that it above all others is the one substance which so divides our bodies and minces them up as to produce naturally both that affection which we call heat and its very name.[*](i.e., θερμόν (quasi κερμόν) is derived from κερματίζω (minced up or mint).) The opposite affection is evident, but none the less it must not lack description. When liquids with larger particles, which surround the body, enter into it they drive out the smaller particles; but as they cannot pass into their room they compress the moisture within us, so that in place of non-uniformity and motion they produce immobility and density, as a result of the uniformity and compression. But that which is being contracted contrary to nature fights, and, in accordance with its nature, thrusts itself away in the contrary direction. And to this fighting and shaking we give the names of trembling and shivering; while this affection as a whole, as well as the cause thereof, is termed cold. By the term hard we indicate all the things to which our flesh gives way; and by the term soft all those which give way to our flesh; and these terms are similarly used relatively to each other. Now a substance gives way when it has its base small; but when it is constructed of quadrangular bases, being very firmly based, it is a most inelastic form; and so too is everything which is of very dense composition and most rigid. The nature of heavy and light would be shown most clearly if, along with them, we examined also the nature of above and below, as they are called. That there really exist two distinct and totally opposite regions, each of which occupies one-half of the Universe—the one termed below, towards which move all things possessing any bodily mass, and the other above, towards which everything goes against its will,— this is a wholly erroneous supposition[*](The reference here is, probably to Democritus (Aristotle also speaks of τὸ ἄνω φύσει, Phys. 208 b 14).) For inasmuch as the whole Heaven is spherical, all its outermost parts, being equally distant from the center, must really be outermost in a similar degree; and one must conceive of the center, which is distant from all the outermost parts by the same measures, as being opposite to them all. Seeing, then, that the Cosmos is actually of this nature, which of the bodies mentioned can one set above or below without incurring justly the charge of applying a wholly unsuitable name? For its central region cannot rightly be termed either above or below, but just central; while its circumference neither is central nor has it any one part more divergent than another from the center or any of its opposite parts. But to that which is in all ways uniform, what opposite names can we suppose are rightly applicable, or in what sense?

Tim.

For suppose there were a solid body evenly-balanced at the center of the universe, it would never be carried away to the extremities because of their uniformity in all respects; nay, even were a man to travel round it in a circle he would often call the same part of it both above and below, according as he stood now at one pole, now at the opposite.[*](i.e., above and below are purely relative terms.) For seeing that the Whole is, as we said just now, spherical, the assertion that it has one region above and one below does not become a man of sense. Now the origin of these names and their true meaning which accounts for our habit of making these verbal distinctions even about the whole Heaven, we must determine on the basis of the following principles. Suppose that a man were to take his stand in that region of the Universe in which the substance of fire has its special abode, and where also that substance to which it flies is collected in largest bulk; and suppose that, having the power to do so, he were to separate portions of the fire and weigh them, putting them on scales and lifting the balance and pulling the fire by force into the dissimilar air, it is obvious that he will force the smaller mass more easily than the larger. For if two masses are lifted up simultaneously by a single effort, the smaller will necessarily yield more and the larger less, owing to its resistance, to the force exerted; and the large mass will be said to be heavy and moving down, the small light and moving up. Now this is just what we ought to detect ourselves doing in our region here. Standing on the earth and detaching various earthy substances, and sometimes pure earth, we pull them into the dissimilar air by force and against nature, since both these kinds cleave to their own kindred; and the smaller mass yields more easily, and follows first, as we force it into the dissimilar kind; wherefore we name it light, and the region to which we force it above; and the conditions opposite thereto we name heavy and below. Thus, these must necessarily differ in their mutual relations, because the main masses of the Kinds occupy regions opposite to one another; for when we compare what is light in one region with what is light in the opposite region, and the heavy with the heavy, the below with the below, and the” above with the above, we shall discover that these all become and are opposite and oblique and in every way different in their mutual relations. There is, however, this one fact to be noticed about them all, that it is the passage of each kind to its kindred mass which makes the moving body heavy, and the region to which such a body moves below; while the opposite conditions produce the contrary results.[*](i.e., the attraction takes different directions, therefore up and down are relative terms.) Let this, then, stand as our account of the causes of these conditions.

Tim.

Of smoothness and roughness anyone might be able to discern the causes and explain them also to others. For the cause of the latter is hardness combined with irregularity, and of the former regularity combined with density. In respect of the affections common to the whole body a very important point, which still remains, is the cause of the pleasures and pains attaching to the sense-affections we have been discussing; and the cause also of those affections which have become perceptible by means of the bodily parts and involve in themselves concomitant pains and pleasures. Let us, then, try to grasp the causes in connection with every perceptible and imperceptible affection in the following way, bearing in mind the distinction we previously drew[*](Cf. 54 B ff., 57 D, E.) between mobile and immobile substances; for it is in this way that we must track down all those facts that we intend to grasp. Whenever what is naturally mobile is impressed by even a small affection, it transmits it in a circle, the particles passing on to one another this identical impression until they reach the organ of intelligence and announce the quality of the agent. But a substance of the opposite kind, being stable and having no circular movement, is only affected in itself and does not move any other adjacent particle; consequently, since the particles do not transmit to one another the original affection, it fails to act upon the living creature as a whole, and the result is that the affected body is non-percipient. This is the case with the bones and the hair and all our other parts that are mainly earthy whereas the former character belongs especially to the organs of sight and of hearing, owing to the fact that they contain a very large quantity of fire and air. Now the nature of pleasure and pain we must conceive of in this way. When an affection which is against nature and violent occurs within us with intensity it is painful, whereas the return back to the natural condition, when intense, is pleasant[*](Cf. Rep. 583 C ff.,Phileb. 31 D ff.); and an affection which is mild and gradual is imperceptible, while the converse is of a contrary character. And the affection which, in its entirety, takes place with ease is eminently perceptible, but it does not involve pain or pleasure; such, for example, are the affections of the visual stream itself, which, as we said before,[*](Cf. 45 B.) becomes in the daylight a body substantially one with our own. For no pains are produced therein by cuttings or burnings or any other affections, nor does its reversion to its original form produce pleasures; but it has most intense and clear perceptions concerning every object that affects it, and every object also which it strikes against or touches; for force is wholly absent both from its dilation and from its contraction.