The Illustrated Timaeus

XVIII. Our new exposition of the universe then 

must be founded on a fuller classification than the former.

 

Then we distinguished two forms,

 but now a third kind must be disclosed.

 The two were indeed enough

 for our former discussion

 when we laid down 

one form

 as the

 pattern

intelligible and changeless

 the second as a copy of the pattern

 which comes into being and is visible.

 A third we did not then distinguish

 deeming that the two would suffice: but now

 it seems, by constraint of our discourse

 we must try to express and make manifest

 a form obscure and dim

 What power then must we conceive

 that nature has given it ?

 something like this "It"

 is the receptacle

 and as it were the nurse

 of all becoming

 This saying is true,

 but we must put "it"

 in clearer language

 and this is hard

 especially as for the sake of it

 we must needs inquire into fire

 and the substances that rank with fire

 For it is hard to say which

 of all these we ought to call water 

any more than fire

 or indeed which we ought to call

 by any given name

 rather than all and each severally

 in such a way as to employ any truthful

 and trustworthy mode of speech

 How then are we to deal with this point

 and what is the question that we should properly raise concerning it ? 

In the first place, what we now have named water

 by condensation as we suppose

 we see turning to stones and earth

 and by rarefying and expanding this same element

 becomes wind and air and air when inflamed

 becomes fire and conversely fire contracted and quenched

 returns again to the form of air

 also air concentrating and condensing becomes cloud and mist

 and from these yet further compressed comes flowing water

 and from water earth and stones once more

 and so, it appears, they hand on one to another the cycle of generation

 Thus then since these several bodies

 never assume one constant form

 which of them can we positively affirm to be really this

 and not another without being shamed in our own eyes?

 It cannot be: it is far the safest course

 when we make a statement concerning them 

to speak as follows. 

What we see in process of perpetual transmutation

 as for instance fire, we must not call this

 but such-like is the appellation we must confer on fire; 

nor must we call water "this" but always "such" 

 nor must we apply to anything

 as if it had any stability

 such predicates as we express

 by the use of the terms "this" and "that"

 and suppose that we signify something thereby

 For it flees and will not abide such terms as this and that

 and relative to this and every phrase which represents it as stable.

 The word "this" we must not use of any of them

 but "such" applying in the same sense to all their mutations

 we must predicate of each and all:

 fire we must call "that" which universally has "that" appearance

 and so must we name all things such as come into being

 That wherein they come to be severally 

and show themselves, and from whence again they perish

 in naming "that" alone must we use the words "that" and "this"

 but whatever has any quality, such as white or hot 

or any of two opposite attributes

 and all combinations of these

 we must denote by no such term

 But we must try to speak yet more clearly on this matter

 Suppose a man having moulded all kinds of figures out of gold

 should unceasingly remould them

 interchanging them all with one another

 it were much the safest thing in view of truth

 to say that it is gold

 but as to the triangles or any other shapes

 that were impressed on it, never to speak of them as existing

 seeing that they change even as we are in the act of defining them

 but if it will admit the term "such"

 with any tolerable security

 we must be content.

 The same language must be applied

 to the nature which receives into it all material things

 we must call it always the same

 for it never departs from its own function at all

 It ever receives all things into it

 and has nowhere any form in any wise

 like to aught of the shapes that enter into it

 For it is as the substance wherein 

all things are naturally moulded

 being stirred and informed by the entering shapes

 and owing to them it appears different from time to time

 But the shapes which pass in and out are 

likenesses of the eternal existences

 being copied from them in a fashion wondrous 

and hard to declare

 which we will follow up later on

 For the present however we must conceive three kinds

 first that which comes to be

 secondly that wherein it comes to be

 third that from which the becoming is copied when it is created

 And we may liken

 the recipient to a mother

 the model to a father

 and that which is between them to a child

 and we must remember

 that if a moulded copy is to present to view all varieties of form

 the matter in which it is moulded cannot be rightly prepared

 unless it be entirely bereft of all those

forms which it is about to receive from without.

 For were it like any one of the entering shapes

 whenever that of an opposite or

 entirely different nature came upon it

 it would in receiving it give the impression badly

 intruding its own form

 Wherefore that which shall receive all forms

 within itself must be utterly without share in any of the forms

just as in the making of sweet unguents

 men purposely contrive, as the beginning of the work

 to make the fluids that are to receive the perfumes perfectly scentless

 and those who set about moulding figures in any soft substance

 do not suffer any shape to show itself therein at the beginning

 but they first knead it smooth and make it as uniform as they can.

 In the same way it behoves

 that which is fitly to receive

 many times over its whole extent 

likenesses of all things

that is of all eternal existences

 to be itself naturally without part 

or lot in any of the forms

 Therefore the mother and recipient of creation

 which is visible and by any sense perceptible

 we must call neither earth nor air nor fire nor water

 nor the combinations of these 

nor the elements of which they are formed

 but we shall not err 

in affirming it to be a viewless nature and formless

 all-receiving in some manner most bewildering

 and hard to comprehend partaking of the intelligible

 But so far as from what has been said

 we may arrive at its nature

 this would be the most just account of it

 That part of it which is enkindled 

from time to time appears as fire

 and that which is made liquid as water

 and as earth and air such part of it 

as receives the likenesses of these 

But in our inquiry concerning these 

we must deliver a stricter statement

 Is there an absolute idea of fire?

 and do all those absolute ideas exist 

to which in every case we always 

ascribe absolute being? 

Or do those things which we actually see 

or perceive with any other bodily sense 

alone possess such reality ? 

and is it true that there are 

no manner of real existences beyond these at all?

 but we talk idly 

when we speak of an intelligible idea 

as actually existent whereas 

it was nothing but a conception ?

 Now it does not become us either

 to dismiss the present question

 unjudged and undecided

simply asserting that the ideas exist

 nor yet must we add to our already long discourse

 another as long which is subordinate

 But if we could see our way 

to a great definition couched in brief words

 that would be most seasonable for our present purpose

 Thus then do I give my own verdict

 if reason and true opinion are of two different kinds

 then the ideas do surely exist

 forms not perceptible by our senses

 the objects of thought alone

 but if, as some hold, true opinion 

differs nothing from reason

 then all that we apprehend by our bodily organs

 we must affirm to be the most real existence

 

Now we must declare them to be two

 because they are different in origin and uhlike in nature

 The one is engendered in us by

 instruction, the other by persuasion

 the one is ever accompanied by right understanding

 the other is without understanding

 the one is not to be moved by persuasion

 the other yields to persuasion

 true opinion we must admit is shared by all men

 but reason by the 

"gods" alone and a very small portion of mankind

 This being so, we must agree that there is first the unchanging idea

unbegotten and imperishable

 neither receiving aught into itself from without

 nor itself entering into aught else

 invisible nor in any wise perceptible 

even that whereof the contemplation 

belongs to thought

 Second is that which is named after it and is like to it

 sensible, created, ever in motion, coming to be

 in a certain place and again from thence perishing

 apprehensible by opinion with sensation

 And the third kind is space everlasting

 admitting not destruction

but affording place 

for all things 

that come into

 being

 itself apprehensible without sensation

 by a sort of bastard reasoning

 hardly matter of belief

 It is with this in view that dreaming

 we say that all which exists must be in some place

 and filling some space and that what is neither

 on earth nor in heaven anywhere is nought

 All these and many kindred fancies have we 

even concerning that unsleeping essence and truly existing

 for that by reason of this dreaming state

 we become impotent to arouse ourselves 

and affirm the truth namely

 that to an image it belongs

 seeing that it is not the very model of itself

 on which itself has been created

 but is ever the fleeting semblance of another

 in another to come into being

 clinging to existence as best it may

 on pain of being nothing at all

 but to the really existent essence 

reason in all exactness true comes as an ally

 declaring that so long as one thing is one

 and another thing is other

 neither of them shall come to be in the other

 so that the same becomes at once one and two

XIX. Such then is the statement 

for which I give my sentence

 as we have briefly reasoned it out

 that there are Being and Space and Becoming

 three in number with threefold nature

 even before the heavens were created

 And the nurse of becoming

 being made liquid 

and fiery and putting on the forms of earth and air

 and undergoing all the conditions that attend thereupon

 displays to view all manner of semblances

 and because she is filled with powers

 that are not similar nor equivalent

 she is at no part of her in even balance

 but being swayed in all directions unevenly

 she is herself shaken by the entering forms

 and by her motion shakes them again in turn

 and they, being thus stirred

 are carried in different directions and separated

 just as by sieves and instruments for Winnowing corn

 the grain is shaken and sifted

 and the dense and heavy parts go one way

 and the rare and light are carried to a different

place and settle there.

 Even so when the four kinds are shaken by the recipient

 which by the motion she has received acts as an instrument for shaking

 she separates the most dissimilar elements furthest apart from one another

 and the most similar she draws chiefly together

 for which cause these elements had different regions

 even before the universe was ordered out of them and created

 Before that came to pass 

all these things were 

without method or measure

 but when an essay was being made to order the universe

 first fire and water and earth and air

 which had certain vestiges of their own nature

 yet were altogether in such a condition as we should expect

 for everything when "God" is not in it

 being by nature in the state we have said

 were then first by the creator fashioned forth

 with forms and numbers

And that "God" formed them to be most fair and perfect

 not having been so heretofore must 

above all things be the foundation whereon our account is for ever based

 But now the disposition of each and their generation is what I must strive to make known to you in speech unwonted: but seeing ye are no strangers to the paths of learning, through which my sayings must be revealed to you, ye will follow me.

XX. In the first place

 that fire and earth and water and air

 are material bodies is evident to all

 Every form of body has depth

 and depth must be bounded by plane surfaces

 Now every rectilinear plane is composed of triangles

 And all triangles are derived from two triangles

 each having one right angle and the others acute

 and one triangle has on each side 

a moiety of a right angle marked off by equal sides

 the other has a moiety of a right angle divided into 

unequal parts by unequal sides

 These we conceive to be the basis

 of fire and the other bodies

 following up the probable account 

which is concerned with necessity

 but the principles yet more remote than these

 are known but to "God" and to whatsoever man is a friend of "God"

 Now we must declare what are the four 

fairest bodies that could be created

 unlike one another, but capable,

 some of themof being generated

 out of each other by their dissolution: 

for if we succeed in this

 we have come at the truth 

concerning earth and fire 

and the intermediate proportionals

 For we will concede to no one 

that there exist any visible bodies

 fairer than these, each after its own kind.

 We must do our diligence then 

to put together these four kinds of bodies 

most excellent in beauty, 

and so we shall say that we have

 a full comprehension

 of their nature.

 Now of the two triangles 

the isosceles has but one kind,

but the scalene an endless number.

 Out of this infinite multitude then

 we must choose the fairest

 if we are to begin upon our own principles. 

If then any man can tell of a fairer kind

 that he has selected for the composition of these bodies

 it is no enemy but a friend who vanquishes us

 however of all these triangles 

we declare one to be the fairest

 passing over the rest

that namely of which two conjoined 

form an equilateral triangle.

 The reason it were too long to tell

 but if any man convict us in this and find that it is not so

 the palm is ready for him with our right good will.

 Let then two triangles be chosen 

whereof the substance of fire 

and of the other elements 

has been wrought

the one isosceles, the other 

always having the square on the greater side

 three times the square on the lesser.

 And now we must more strictly define something 

which we expressed not quite clearly enough before.

 For it appeared as though all the four classes

 had generation through each other and into each other,

 but this appearance was delusive.

 For out of the triangles we have chosen 

arise four kinds, three from one of them,

 that which has unequal sides,

 and the fourth one alone composed of the isosceles triangle.

 It is not then possible for all of them

 by dissolution to pass one into another, 

a few large bodies being formed of many small,

 and the converse: but for three of them it is possible.

For since they all arise from one basis,

 when the larger bodies are broken up,

 a number of small ones will be formed

 from the same elements,

 putting on the shapes proper to them;

 and again when a number of small bodies 

are resolved into their triangles,

 they will become one in number 

and constitute a single large body 

of a different form. 

So much for their generation into one another: the next thing will be

 to say what is the form in which each has been created,

 and by the combination of what numbers. 

We will begin with the form 

which is simplest and smallest in its construction.

 Its element is the triangle which has the hypotenuse

 double of the shorter side in length.

 If a pair of these are put together so that their hypotenuses coincide,

 and this is done three times,

 in such a way that the hypotenuses 

and the shorter sides meet in one point as a centre,

 thus one equilateral triangle has been formed

 out of the other six triangles:

 and if four equilateral triangles are combined,

 so that three plane angles meet in a point, 

they make at each point one solid angle,

 that which comes immediately next 

to the most obtuse of plane angles;

 and when four such angles are produced

 there is formed the first solid figure,

 dividing its whole surface 

into four equal and similar parts.

 The second is formed of the same triangles 

in sets of eight equilateral triangles,

 bounding every single solid angle by four planes;

 and with the formation of six such solid angles 

the second figure is also complete.

 The third is composed of 120 

of the elementary triangles united,

 and of twelve solid angles, 

each contained by five plane equilateral triangles;

 and it has twenty equilateral surfaces.

 And the first element, 

when it had generated these figures,

 had done its part:

 the isosceles triangle generated the fourth,

 combined in sets of four, 

with the right angles meeting at the centre,

 thus forming a single square.

 Six of these squares joined together formed

 eight solid angles, each produced by three plane right angles: 

and the shape of the body thus formed was cubical,

 having six square planes for its surfaces.

 And whereas a fifth figure yet alone remained

"God" used it for the universe in embellishing it with signs

The Dodecahedron

  

e

The tetrahedron

The Tetrahedron

Fire

The Octahedron

Air

The Icosahedron

Water

The cube

Earth

The Dodecahedron

The aether

Now in reasoning about all these things

 someone would do so musically

 if he raised the following point

 perplexed as to whether he should say

 that there are indefinitely many cosmoses

 or that they’re finite in number

 he’d consider the former decree

 to be that of someone genuinely inexperienced

 in matters in which he should be experienced.

 But as to whether it’s appropriate to say that cosmoses are

 truly by nature one or five—if that’s the position he took

 then he’d be more suitably perplexed.

 So then, in keeping with the likely account

 our point of view discloses

 that the cosmos is by nature one "god"

 while someone else

 having looked elsewhere

 to different considerations

 will hold other opinions

 Let us dismiss him too

 and assign the kinds that 

have just now been born

 through our account 

to 

fire and water and air

 and earth

 To earth, then, let us give the cubic form

 for earth is the most immobile of the four kinds

 and the most malleable of bodies and it’s a necessity

 that the body having the most secure bases

 should be this sort of thing most of all.

 But among the triangles we hypothesized at the beginning

 the base of the one with equal sides 

is  by  nature   more  secure

 than that with unequal sides

 and 

the plane figure put together 

out of the former triangle

—the equilateral quadrangle—

is of necessity in its parts and as a whole

 more steadfastly based than the equilateral triangle

 That’s why, in assigning this form to earth,

 we are preserving the likely account

 and of the remaining forms in turn

 the least mobile form to water

 the most mobile to fire

 and the one in the middle to air

 and the smallest body to fire

 and the largest in turn to water

 and the one in the middle to air

 and again, the sharpest to fire

 the second in sharpness to air

 and the third to water.

 Now then, with respect to all these forms

 it’s a necessity for that which has 

the fewest bases to be by nature 

the most mobile

 being in every way the most cutting

 and sharpest of them all

 and furthermore it is the lightest

 having been constructed out of 

the fewest self-same parts

 and the second must have 

these same things

 to a second degree

 and the third third

 Now   in   keeping   with

 the correct and likely account

 let that solid which was born

 in the form of the pyramid 

be element and seed of fire

 and the second in order of birth

 let us call element and seed of air

 and the third of water

 Now one must think of all these as being so small

 that none of them, taken singly each in its own individual kind

 is seen by us because of their smallness

 but when many have been gathered together

 then we do see the masses of them

 And in particular

 with respect to the proportions

 concerning their quantities 

and their motions

 as well as

 their other 

powers

 one must think that 

when these had been perfected

 by the god with precision

 wherever the nature of necessity

—willingly and upon being persuaded—

yielded

 there 

he joined them together

 everywhere in due proportion

From all that we have already said 

in the matter of these four kinds

 the facts would seem to be as follows

 When earth meets with fire 

and is dissolved by the keenness of it

 it would drift about

 whether it were dissolved in fire itself

 or in some mass of air or water

 until the parts of it meeting and again 

being united became earth once more

 for it never could pass

into any other kind

But when water is divided by fire

or by Air it may be formed again

and become one particle of Fire

and two of air

and the divisions of air 

may become for every particle broken up

 two particles of fire

 And again when fire 

is caught in air or in waters or in earth

 a little in a great bulk

 moving amid a rushing body

 and contending with it 

is vanquished and broken up

 two particles of fire combine

 into one figure of air

 and when air is vanquished

 and broken small

 from two whole and one half particle

 one whole figure of water

will be composed

 Let us also reckon it once again thus

 when any of the other kinds is intercepted

 in fire and is divided by it 

through the sharpness 

of its angles

 and its sides

 if it forms into

 the shape of fire

 it at once ceases 

from being divided

 for a kind which is 

uniform and identical

 of whatever sort it be

 can neither be the cause of

 any change nor can it suffer

 any from that which is identical

 and uniform with itself

 but so long as passing into another kind

 a lesser bulk contends with the greater

 it ceases never from being broken

 And when the

smaller figures few in number

 are caught in a multitude of larger figures

 and are being broken in pieces and quenched

 if they consent to combine into the form of the stronger

 they then and there cease from being quenched

 and from fire arises air, from air water

 But if they assail the others

 and another sort meet and contend with them

 they cease not from being shattered until

being entirely repelled and dissolved

 they find refuge with some of their own kind

 or being overcome

 form from many of their own figures

 one similar to the victorious element

 and there remain and abide with it

 Moreover on account of these conditions 

they all are changing their places

 for the bulk of every kind are sorted

 into separate regions of their own

 through the motion of the recipient

 and those which are altered 

from their own nature 

and made like some other

 are carried by reason 

of this movement

 to the region proper to 

the element to which 

they are assimilated

 All unmixed and primary bodies

 have thus come into being

 through the causes we have described

 but for the fact that

 within the several classes

 different kinds exist

 we must assign

as its cause

 the structure of 

the elementary triangles

 it does not originally produce 

in each kind of triangle 

one and the same size only

 but some greater and some less

 and there are just so many sizes

 as there are kinds 

in the classes

 and when these

are mixed up with

 themselves

 or with one another

 an endless diversity arises

 which must be examined

 by those who would put forward

 a probable theory concerning nature.

Now concerning rest and motion

 how they arise and under what conditions

 we must come to an agreement

 else many difficulties will stand in the way

 of our argument that is to follow

This has been already in part set forth

 but we have yet to add that in uniformity

 no movement will ever exist

 For that what is to be moved

 should exist without that which is to move it

 or what is to move without that which is to be moved

 is difficult or rather impossible

 but without these there can be no motion

 and for these to be uniform is not possible

 So then let us always

 assign 

rest to uniformity 

and motion to its opposite

 Now the opposite of uniformity

 is caused by inequality

 and of inequality we have 

discussed the origin

 But how it comes to pass 

that all bodies are not sorted

 off into their several kinds

 and cease from passing through

 one another and changing their place

 this we have not explained

 Let us put it again in this way

 The revolution of the whole

 when it had embraced the four kinds

 being circular, with a natural tendency

 to return upon itself

 compresses everything and suffers

no vacant space to be left

 Therefore fire penetrates most of all

 through all things

 and in the second degree air

 since it is second in fineness

 and the rest in proportion

 For the substances which are formed

 of the largest parts have the most void

 left in their structure

 and those made of the smallest

 have the least

 Now the constriction of this

 contracting force 

thrusts the small particles

 into the interspaces

 between the larger

 so that when small

 are set side by side with great

 and the lesser particles divide the greater

 while the greater compress the smaller

 all things keep rushing backwards

 and forwards to their own region

 since in changing its bulk 

each changes its proper position in space

 Thus owing to these causes 

a perpetual disturbance of uniformity

 is always kept up and 

so preserves the perpetual

 motion of matter

 now and henceforth

 without cessation.

Next we must remember

 that of fire there are many kinds

for instance flame and that effluence from flame

 which burns not but gives light to the eyes

 and that which remains in the embers

 when the flame is out

 And so with air: the purest

is that which is called

 by the name of aether

 and the most turbid is mist and gloom

 and there are other kinds which have no name

 arising from the inequality of the triangles.

 Of water there are two primary divisions

 the liquid 

and the fusible kind.

 The liquid sort owes its nature 

to possessing the smaller kinds of watery atoms

 unequal in size

 and so it can readily either move of itself

 or be moved by something else

 owing to its lack of uniformity 

and the peculiar shape of its atoms

 But that which consists of larger

 and uniform particles is more stable

 than the former and heavy

 being stiffened by its uniformity

 but when fire enters into it and breaks it up

 it loses its uniformity 

and gains more power of motion

 and as soon as it has become mobile

 it is thrust by the surrounding air

 and spread out upon the earth

 and it has received names 

descriptive of either process

 melting of the dissolution of the mass

 flowing of the extension on the ground.

 But when the fire goes forth from it again

 seeing that it does not issue into empty space

 the neighbouring air receives a thrust

 and while the liquid mass is still mobile

 it forces it to fill up the vacant places

 of the fire and unites it with itself

 And being thus compressed and recovering its uniformity

 seeing that fire the creator of inequality 

is quitting it, it settles into its normal state

 And the departure of fire we call cooling

 and the contraction that ensues on its withdrawal

 we class as solidification

 Of all the substances which 

we have ranked as fusible kinds of water

 that which is densest

and formed of the finest and most uniform particles,

 a unique kind, combining brightness with a yellow hue,

 is gold a most precious treasure

 which has filtered through rocks and there congealed:

 and the 'offspring of gold'

 which is extremely hard 

owing to its density 

and has turned black

 is called adamant

 Another has particles resembling those of gold

 but more than one kind

 in density it even surpasses gold

 and has a small admixture of fine earth

 so that it is harder, but lighter,

 because it has large interstices within

 this formation is one of the shining

 and solid kinds of water and is called bronze

 The earth which is mingled with it

 when the two through age begin to separate again

 becomes visible by itself and is named rust

 And it were no intricate task to explain

 all the other substances of this kind

 following the outline of our probable account

 For if we pursue this as a recreation

 and while laying down the principles of eternal being

 find in plausible theories of becoming

 a pleasure that brings no remorse in its train

 we may draw from it a sober and sensible amusement

 during our life

 Now therefore setting out in this way

 let us go on to discuss the probabilities

 that lie next on the same subject.