(9) the Pure intelligence so called because it purifies the Numerations, it proves and corrects the designing of their representation, and disposes their unity with which they are combined without diminution or division.

(4) We have said that all must be brought back to a unity: this must be an authentic unity, not belonging to the order in which multiplicity is unified by participation in what is truly a One; we need a unity independent of participation, not a combination in which multiplicity holds an equal place: we have exhibited, also, the Intellectual Realm and the Intellectual-Principle as more closely a unity than the rest of things, so that there is nothing closer to The One. Yet even this is not The purely One.

This purely One, essentially a unity untouched by the multiple, this we now desire to penetrate if in any way we may.

Only by a leap can we reach to this One which is to be pure of all else, halting sharp in fear of slipping ever so little aside and impinging on the dual: for if we fail of the centre, we are in a duality which does not even include The authentic One but belongs on both sides, to the later order. The One does not bear to be numbered in with anything else, with a one or a two or any such quantity; it refuses to take number because it is measure and not the measured; it is no peer of other entities to be found among them; for thus, it and they alike would be included in some container and this would be its prior, the prior it cannot have. Not even essential number can belong to The One and certainly not the still later number applying to quantities; for essential number first appears as providing duration to the divine Intellection, while quantitative number is that which furnishes the Quantity found in conjunction with other things or which provides for Quantity independent of things, if this is to be thought of as number at all. The Principle which in objects having quantitative number looks to the unity from which they spring is a copy of the Principle which in the earlier order of number looks to the veritable One; and it attains its existence without in the least degree dissipating or shattering that prior unity: the dyad has come into being, but the precedent monad still stands; and this monad is quite distinct within the dyad from either of the two constituent unities, since there is nothing to make it one rather than the other: being neither, but simply that thing apart, it is present without being inherent.

But how are the two unities distinct and how is the dyad a unity, and is this unity the same as the unity by which each of the constituents is one thing?

Our answer must be that the unity is that of a participation in the primal unity with the participants remaining distinct from that in which they partake; the dyad, in so far as it is one thing, has this participation, but in a certain degree only; the unity of an army is not that of a single building; the dyad, as a thing of extension, is not strictly a unit either quantitatively or in manner of being.

Are we then to take it that the monads in the pentad and decad differ while the unity in the pentad is the same as that in the decad?

Yes, in the sense in which, big and little, ship is one with ship, army with army, city with city; otherwise, no. But certain difficulties in this matter will be dealt with later.

(21) How then does the universal Intellect produce the particulars while, in virtue of its Reason-Principle, remaining a unity? In other words, how do the various grades of Being, as we call them, arise from the four primaries? Here is this great, this infinite Intellect, not given to idle utterance but to sheer intellection, all-embracing, integral, no part, no individual: how, we ask, can it possibly be the source of all this plurality?

Number at all events it possesses in the objects of its contemplation: it is thus one and many, and the many are powers, wonderful powers, not weak but, being pure, supremely great and, so to speak, full to overflowing powers in very truth, knowing no limit, so that they are infinite, infinity, Magnitude-Absolute.

As we survey this Magnitude with the beauty of Being within it and the glory and light around it, all contained in Intellect, we see, simultaneously, Quality already in bloom, and along with the continuity of its Act we catch a glimpse of Magnitude at Rest. Then, with one, two and three in Intellect, Magnitude appears as of three dimensions, with Quantity entire. Quantity thus given and Quality, both merging into one and, we may almost say, becoming one, there is at once shape. Difference slips in to divide both Quantity and Quality, and so we have variations in shape and differences of Quality. Identity, coming in with Difference, creates equality, Difference meanwhile introducing into Quantity inequality, whether in number or in magnitude: thus are produced circles and squares, and irregular figures, with number like and unlike, odd and even.

The life of Intellect is intelligent, and its activity has no failing-point: hence it excludes none of the constituents we have discovered within it, each one of which we now see as an intellectual function, and all of them possessed by virtue of its distinctive power and in the mode appropriate to Intellect.

But though Intellect possesses them all by way of thought, this is not discursive thought: nothing it lacks that is capable of serving as Reason-Principle, while it may itself be regarded as one great and perfect Reason-Principle, holding all the Principles as one and proceeding from its own Primaries, or rather having eternally proceeded, so that "proceeding" is never true of it. It is a universal rule that whatever reasoning discovers to exist in Nature is to be found in Intellect apart from all ratiocination: we conclude that Being has so created Intellect that its reasoning is after a mode similar to that of the Principles which produce living beings; for the Reason-Principles, prior to reasoning though they are, act invariably in the manner which the most careful reasoning would adopt in order to attain the best results.

What conditions, then, are we to think of as existing in that realm which is prior to Nature and transcends the Principles of Nature? In a sphere in which Substance is not distinct from Intellect, and neither Being nor Intellect is of alien origin, it is obvious that Being is best served by the domination of Intellect, so that Being is what Intellect wills and is: thus alone can it be authentic and primary Being; for if Being is to be in any sense derived, its derivation must be from Intellect.

Being, thus, exhibits every shape and every quality; it is not seen as a thing determined by some one particular quality; there could not be one only, since the principle of Difference is there; and since Identity is equally there, it must be simultaneously one and many. And so Being is; such it always was: unity-with-plurality appears in all its species, as witness all the variations of magnitude, shape and quality. Clearly nothing may legitimately be excluded , for the whole must be complete in the higher sphere which, otherwise, would not be the whole.

Life, too, burst upon Being, or rather was inseparably bound up with it; and thus it was that all living things of necessity came to be. Body too was there, since Matter and Quality were present.

Everything exists forever, unfailing, involved by very existence in eternity. Individuals have their separate entities, but are at one in the unity. The complex, so to speak, of them all, thus combined, is Intellect; and Intellect, holding all existence within itself, is a complete living being, and the essential Idea of Living Being. In so far as Intellect submits to contemplation by its derivative, becoming an Intelligible, it gives that derivative the right also to be called "living being."

(2) It may be suggested that, while in the unities of the partial order the essence and the unity are distinct, yet in collective existence, in Real Being, they are identical, so that when we have grasped Being we hold unity; Real Being would coincide with Unity. Thus, taking the Intellectual-Principle as Essential Being, that principle and the Unity Absolute would be at once Primal Being and Pure Unity, purveying, accordingly, to the rest of things something of Being and something, in proportion, of the unity which is itself.

There is nothing with which the unity would be more plausibly identified than with Being; either it is Being as a given man is man or it will correspond to the Number which rules in the realm of the particular; it will be a number applying to a certain unique thing as the number two applies to others.

Now if Number is a thing among things, then clearly so this unity must be; we would have to discover what thing of things it is. If Number is not a thing but an operation of the mind moving out to reckon, then the unity will not be a thing.

We found that anything losing unity loses its being; we are therefore obliged to enquire whether the unity in particulars is identical with the being, and unity absolute identical with collective being.

Now the being of the particular is a manifold; unity cannot be a manifold; there must therefore be a distinction between Being and Unity. Thus a man is at once a reasoning living being and a total of parts; his variety is held together by his unity; man therefore and unity are different- man a thing of parts against unity partless. Much more must Collective Being, as container of all existence, be a manifold and therefore distinct from the unity in which it is but participant.

Again, Collective Being contains life and intelligence- it is no dead thing- and so, once more, is a manifold.

If Being is identical with Intellectual-Principle, even at that it is a manifold; all the more so when count is taken of the Ideal Forms in it; for the Idea, particular or collective, is, after all, a numerable agglomeration whose unity is that of a kosmos.

Above all, unity is The First: but Intellectual-Principle, Ideas and Being, cannot be so; for any member of the realm of Forms is an aggregation, a compound, and therefore- since components must precede their compound- is a later.

Other considerations also go to show that the Intellectual-Principle cannot be the First. Intellect must be above the Intellectual Act: at least in its higher phase, that not concerned with the outer universe, it must be intent upon its Prior; its introversion is a conversion upon the Principle.

Considered as at once Thinker and Object of its Thought, it is dual, not simplex, not The Unity: considered as looking beyond itself, it must look to a better, to a prior: looking simultaneously upon itself and upon its Transcendent, it is, once more, not a First.

There is no other way of stating Intellectual-Principle than as that which, holding itself in the presence of The Good and First and looking towards That, is self-present also, self-knowing and Knowing itself as All-Being: thus manifold, it is far from being The Unity.

In sum: The Unity cannot be the total of beings, for so its oneness is annulled; it cannot be the Intellectual-Principle, for so it would be that total which the Intellectual-Principle is; nor is it Being, for Being is the manifold of things.

(16) But here we may be questioned about these numbers which we describe as the primal and authentic:

"Where do you place these numbers, in what genus among Beings? To everyone they seem to come under Quantity and you have certainly brought Quantity in, where you say that discrete Quantity equally with the continuous holds place among Beings; but you go on to say that there are the numbers belonging to the Firsts and then talk of other numbers quite distinct, those of reckoning; tell us how you arrange all this, for there is difficulty here. And then, the unity in sense-things- is that a quantity or is quantity here just so many units brought together, the unity being the starting-point of quantity but not quantity itself? And, if the starting-point, is it a kindred thing or of another genus? All this you owe it to us to make clear."

Be it so; we begin by pointing out a distinction:

You take one thing with another- for we must first deal with objects of sense- a dog and a man, or two men; or you take a group and affirm ten, a decad of men: in this case the number affirmed is not a Reality, even as Reality goes in the sphere of sense, but is purely Quantity: similarly when you resolve into units, breaking up the decad, those units are your principle of Quantity since the single individual is not a unity absolute.

But the case is different when you consider one man in himself and affirm a certain number, duality, for example, in that he is at once living and reasoning.

By this analysis and totalling, you get quantity; but there are two objects under consideration and each of these is one; each of the unities contributes to the complete being and the oneness is inherent in each; this is another kind of number; number essential; even the duality so formed is no posterior; it does not signify a quantity apart from the thing but the quantity in the essence which holds the thing together. The number here is no mere result of your detailing; the things exist of themselves and are not brought together by your reckoning, but what has it to do with essential reality that you count one man in with another? There is here no resultant unity such as that of a choir- the decad is real only to you who count the ten; in the ten of your reckoning there cannot be a decad without a unitary basis; it is you that make the ten by your counting, by fixing that tenness down to quantity; in choir and army there is something more than that, something not of your placing.

But how do you come to have a number to place?

The Number inherent apart from any enumeration has its own manner of being, but the other, that resulting upon the appearance of an external to be appraised by the Number within yourself, is either an Act of these inherent numbers or an Act in accordance with them; in counting we produce number and so bring quantity into being just as in walking we bring a certain movement into being.

But what of that "Number within us having its own manner of being"?

It is the Number of our essence. "Our essence" we read "partakes of Number and harmony and, also, is Number and harmony." "Neither body nor magnitude," someone says: soul, then, is Number since it is essence. The number belonging to body is an essence of the order of body; the number belonging to soul constitutes the essences of souls.

In the Intellectuals, all, if the Absolute Living-Form, there is a multiple- a triad, let us say- that Triad of the Living-Form is of the nature of essence: and the Triad prior to any living thing, Triad in the realm of Being, is a principle of essence.

When you enumerate two things- say, animal and beauty- each of these remains one thing; the number is your production; it lay within yourself; it is you that elaborate quantity, here the dyad. But when you declare virtue to be a Tetrad, you are affirming a Tetrad which does actually exist; the parts, so to speak, make one thing; you are taking as the object of your act a Unity- Tetrad to which you accommodate the Tetrad within yourself.

(1) If, however, it be necessary, dismissing these particulars, to speak what appears to me to be the truth, you do not rightly infer “ that a knowledge of this mathematical science cannot be obtained, because there is much dissonance concerning it, or because Chæremon, or some other, has written against it .” For if this reason were admitted, all things will be incomprehensible. For all sciences have ten thousand controvertists, and the doubts with which they are attended are innumerable. As, therefore, we are accustomed to say in opposition to the contentious, that contraries in things that are true are naturally discordant, and that it is not falsities alone that are hostile to each other; thus, also, we say respecting this mathematical science, that it is indeed true; but that those who wander from the scope of it, being ignorant of the truth, contradict it. This, however happens not in this science alone, but likewise in all the sciences, which are imparted by the Gods to men.

(6) Granted, then, that there exist, apart from things, a unity absolute and a decad absolute in other words, that the Intellectual beings, together with their characteristic essence have also their order, Henads, Dyads, Triads, what is the nature of these numerical entities and how does it come into being? We cannot but think that some reason accounts for their origin.

As a beginning, what is the origin of the Ideas in general? It is not that the thinking principle thought of each Idea and by that act of thought procured their several existences; not because Justice and Movement were thus thought did they come to be; that would imply that while the thought is later than the thing- the concept of Justice must be later than Justice itself- yet the thought precedes what, as founded on the thinking, owes its existence to it. Besides, if justice is only a certain definite thought we have the absurdity that Justice is nothing more than a definition of Justice. Thinking of Justice or Movement is but grasping their nature; this would mean grasping the non-existent, an impossibility.

We may be reminded that in immaterial objects the knowledge is identical with the thing; but we must not misapply that statement; it does not say that the knowledge is the thing known, or that the reason surveying the thing is the thing, but that the immaterial thing, being an Intellectual object is also a thought; this does not imply a definition or conception of the object; the thing itself, as belonging to the Intellectual, can be nothing else than Intellect or knowledge. This is not a case of knowledge self-directed; it is that the thing in the Intellectual transmutes the knowledge, which is not fixed like the knowledge of material things; in other words it makes it true knowledge, that is to say no image of the thing but the thing directly.

Thus it is not the conception of movement that brings movement to be; movement absolute produces that conception; it produces itself as at once movement and the concept of movement, for movement as it exists There, bound up with Being, is a concept. It is movement absolute because it is the first movement- there can be none till this exist- and it is the authentic Movement since it is not accidental to something else but is the activity of actual Being in motion. Thus it is a real existent, though the notion of Being is different.

Justice therefore is not the thought of Justice but, as we may put it, a state of the Intellectual-Principle, or rather an activity of it- an appearance so lovely that neither evening nor dawn is so fair, nor anything else in all the realm of sense, an Intellectual manifestation self-rising, self-seen, or, rather, self-being.

(8) As then there is a Life-Form primal- which therefore is the Life-Form Absolute- and there is Intellectual-Principle or Being, Authentic Being, these, we affirm, contain all living things and all Number, and Absolute Justice and Beauty and all of that order; for we ascribe an existence of their own to Absolute Man, Absolute Number, Absolute Justice. It remains to discover, in so far as such knowledge is possible, how these distinct entities come to be and what is the manner of their being.

At the outset we must lay aside all sense-perception; by Intellectual-Principle we know Intellectual-Principle. We reflect within ourselves there is life, there is intellect, not in extension but as power without magnitude, issue of Authentic Being which is power self-existing, no vacuity but a thing most living and intellective- nothing more living, more intelligent, more real- and producing its effect by contact and in the ratio of the contact, closely to the close, more remotely to the remote. If Being is to be sought, then most be sought is Being at its intensest; so too the intensest of Intellect if the Intellectual act has worth; and so, too, of Life.

First, then, we take Being as first in order; then Intellectual-Principle; then the Living-Form considered as containing all things: Intellectual-Principle, as the Act of Real Being, is a second.

Thus it is clear that Number cannot be dependent upon the Living-Form since unity and duality existed before that; nor does it rise in the Intellectual-Principle since before that there existed Real Being which is both one and numerous.

(1) The integral omnipresence of a unity numerically identical is in fact universally received; for all men instinctively affirm the god in each of us to be one, the same in all. It would be taken as certain if no one asked How or sought to bring the conviction to the test of reasoning; with this effective in their thought, men would be at rest, finding their stay in that oneness and identity, so that nothing would wrench them from this unity. This principle, indeed, is the most solidly established of all, proclaimed by our very souls; we do not piece it up item by item, but find it within beforehand; it precedes even the principle by which we affirm unquestionably that all things seek their good; for this universal quest of good depends on the fact that all aim at unity and possess unity and that universally effort is towards unity.

Now this unity in going forth, so far as it may, towards the Other Order must become manifest as multiplicity and in some sense become multiple; but the primal nature and the appetition of the good, which is appetition of unity, lead back to what is authentically one; to this every form of Being is urged in a movement towards its own reality. For the good to every nature possessing unity is to be self-belonging, to be itself, and that means to be a unity.

In virtue of that unity the Good may be regarded as truly inherent. Hence the Good is not to be sought outside; it could not have fallen outside of what is; it cannot possibly be found in non-Being; within Being the Good must lie, since it is never a non-Being.

If that Good has Being and is within the realm of Being, then it is present, self-contained, in everything: we, therefore, need not look outside of Being; we are in it; yet that Good is not exclusively ours: therefore all beings are one.

(5) As a manifold, then, this God, the Intellectual-Principle, exists within the Soul here, the Soul which once for all stands linked a member of the divine, unless by a deliberate apostasy.

Bringing itself close to the divine Intellect, becoming, as it were, one with this, it seeks still further: What Being, now, has engendered this God, what is the Simplex preceding this multiple; what the cause at once of its existence and of its existing as a manifold; what the source of this Number, this Quantity?

Number, Quantity, is not primal: obviously before even duality, there must stand the unity.

The Dyad is a secondary; deriving from unity, it finds in unity the determinant needed by its native indetermination: once there is any determination, there is Number, in the sense, of course, of the real Number. And the soul is such a number or quantity. For the Primals are not masses or magnitudes; all of that gross order is later, real only to the sense-thought; even in seed the effective reality is not the moist substance but the unseen- that is to say Number and the Reason-Principle .

Thus by what we call the Number and the Dyad of that higher realm, we mean Reason Principles and the Intellectual-Principle: but while the Dyad is, as regards that sphere, undetermined- representing, as it were, the underly of The One- the later Number - that which rises from the Dyad and The One- is not Matter to the later existents but is their forming-Idea, for all of them take shape, so to speak, from the ideas rising within this. The determination of the Dyad is brought about partly from its object- The One- and partly from itself, as is the case with all vision in the act of sight: intellection is vision occupied upon The One.

(7) 5. “Whoever, therefore, is able to analyze all the genera which are contained under one and the same principle, and again to compose and con-numerate them, he appears to me to be the wisest of men, and to possess the most perfect veracity. Farther still, he will also have discovered a beautiful place of survey, from which it will be possible to behold divinity, and all things that are in co-ordination with, and successive to him, subsisting separately, or distinct from each other. Having likewise entered this most ample road, being impelled in a right direction by intellect, and having arrived at the end of his course, he will have conjoined beginnings with ends, and will know that God is the principle, middle, and end, of all things which are accomplished according to justice and right reason.”

(5) All that comes to be, work of nature or of craft, some wisdom has made: everywhere a wisdom presides at a making.

No doubt the wisdom of the artist may be the guide of the work; it is sufficient explanation of the wisdom exhibited in the arts; but the artist himself goes back, after all, to that wisdom in Nature which is embodied in himself; and this is not a wisdom built up of theorems but one totality, not a wisdom consisting of manifold detail co-ordinated into a unity but rather a unity working out into detail.

Now, if we could think of this as the primal wisdom, we need look no further, since, at that, we have discovered a principle which is neither a derivative nor a "stranger in something strange to it." But if we are told that, while this Reason-Principle is in Nature, yet Nature itself is its source, we ask how Nature came to possess it; and, if Nature derived it from some other source, we ask what that other source may be; if, on the contrary, the principle is self-sprung, we need look no further: but if we are referred to the Intellectual-Principle we must make clear whether the Intellectual-Principle engendered the wisdom: if we learn that it did, we ask whence: if from itself, then inevitably, it is itself Wisdom.

The true Wisdom, then is Real Being; and Real Being is Wisdom; it is wisdom that gives value to Real Being; and Being is Real in virtue of its origin in wisdom. It follows that all forms of existence not possessing wisdom are, indeed, Beings in right of the wisdom which went to their forming but, as not in themselves possessing it, are not Real Beings.

We cannot therefore think that the divine Beings of that sphere, or the other supremely blessed There, need look to our apparatus of science: all of that realm, all is noble image, such images as we may conceive to lie within the soul of the wise- but There not as inscription but as authentic existence. The ancients had this in mind when they declared the Ideas to be Beings, Essentials.

(37) Those ascribing Intellection to the First have not supposed him to know the lesser, the emanant- though, indeed, some have thought it impossible that he should not know everything. But those denying his knowing of the lesser have still attributed self-knowing to him, because they find nothing nobler; we are to suppose that so he is the more august, as if Intellection were something nobler than his own manner of being not something whose value derives from him.

But we ask in what must his grandeur lie, in his Intellection or in himself. If in the Intellection, he has no worth or the less worth; if in himself, he is perfect before the Intellection, not perfected by it. We may be told that he must have Intellection because he is an Act, not a potentiality. Now if this means that he is an essence eternally intellective, he is represented as a duality- essence and Intellective Act- he ceases to be a simplex; an external has been added: it is just as the eyes are not the same as their sight, though the two are inseparable. If on the other hand by this actualization it is meant that he is Act and Intellection, then as being Intellection he does not exercise it, just as movement is not itself in motion.

But do not we ourselves assert that the Beings There are essence and Act?

The Beings, yes, but they are to us manifold and differentiated: the First we make a simplex; to us Intellection begins with the emanant in its seeking of its essence, of itself, of its author; bent inward for this vision and having a present thing to know, there is every reason why it should be a principle of Intellection; but that which, never coming into being, has no prior but is ever what it is, how could that have motive to Intellection? As Plato rightly says, it is above Intellect.

An Intelligence not exercising Intellection would be unintelligent; where the nature demands knowing, not to know is to fail of intelligence; but where there is no function, why import one and declare a defect because it is not performed? We might as well complain because the Supreme does not act as a physician. He has no task, we hold, because nothing can present itself to him to be done; he is sufficient; he need seek nothing beyond himself, he who is over all; to himself and to all he suffices by simply being what he is.

(41) Intellection seems to have been given as an aid to the diviner but weaker beings, an eye to the blind. But the eye itself need not see Being since it is itself the light; what must take the light through the eye needs the light because of its darkness. If, then, intellection is the light and light does not need the light, surely that brilliance (The First) which does not need light can have no need of intellection, will not add this to its nature.

What could it do with intellection? What could even intellection need and add to itself for the purpose of its act? It has no self-awareness; there is no need. It is no duality but, rather, a manifold, consisting of itself, its intellective act, distinct from itself, and the inevitable third, the object of intellection. No doubt since knower, knowing, and known, are identical, all merges into a unity: but the distinction has existed and, once more, such a unity cannot be the First; we must put away all otherness from the Supreme which can need no such support; anything we add is so much lessening of what lacks nothing.

To us intellection is a boon since the soul needs it; to the Intellectual-Principle it is appropriate as being one thing with the very essence of the principle constituted by the intellectual Act so that principle and act coincide in a continuous self-consciousness carrying the assurance of identity, of the unity of the two. But pure unity must be independent, in need of no such assurance.

"Know yourself" is a precept for those who, being manifold, have the task of appraising themselves so as to become aware of the number and nature of their constituents, some or all of which they ignore as they ignore their very principle and their manner of being. The First on the contrary if it have content must exist in a way too great to have any knowledge, intellection, perception of it. To itself it is nothing; accepting nothing, self-sufficing, it is not even a good to itself: to others it is good for they have need of it; but it could not lack itself: it would be absurd to suppose The Good standing in need of goodness.

It does not see itself: seeing aims at acquisition: all this it abandons to the subsequent: in fact nothing found elsewhere can be There; even Being cannot be There. Nor therefore has it intellection which is a thing of the lower sphere where the first intellection, the only true, is identical with Being. Reason, perception, intelligence, none of these can have place in that Principle in which no presence can be affirmed.

(99) "Perfect numbers, therefore, are beautiful images of the virtues which are certain media between excess and defect, and are not summits, as by some of the ancients they were supposed to be. And evil indeed is opposed to evil, but both are opposed to one good. Good, however, is never opposed to good, but to two evils at one and the same time. Thus timidity is opposed to audacity, to both [of] which the want of true courage is common; but both timidity and audacity are opposed to fortitude. Craft also is opposed to fatuity, to both [of] which the want of intellect is common; and both these are opposed to prudence. Thus, too, profusion is opposed to avarice, to both [of] which illiberality is common; and both these are opposed to liberality. And in a similar manner in the other virtues; by all [of] which it is evident that perfect numbers have a great similitude to the virtues. But they also resemble the virtues on another account; for they are rarely found, as being few, and they are generated in a very constant order. On the contrary, an infinite multitude of superabundant and diminished numbers may be found, nor are they disposed in any orderly series, nor generated from any certain end; and hence they have a great similitude to the vices, which are numerous, inordinate, and indefinite."

(3) Now the intelligence of Nature can be won by quality of Cosmic Sense,—from all the things in Cosmos which sense can perceive. Concerning [ this ] Eternity, which is the second [one],—the Sense of this we get from out the senses’ Cosmos, and we discern its quality [by the same means]. But the intelligence of Quality [itself], the “Whatness” of the Sense of God Supreme, is Truth alone,—of which [pure] Truth not even the most tenuous sketch, or [faintest] shade, in Cosmos is discerned. For where is aught [of it] discerned by measurement of times,—wherein are seen untruths, and births [-and-deaths], and errors?

(18) It appears then that Number in that realm is definite; it is we that can conceive the "More than is present"; the infinity lies in our counting: in the Real is no conceiving more than has been conceived; all stands entire; no number has been or could be omitted to make addition possible. It might be described as infinite in the sense that it has not been measured- who is there to measure it?- but it is solely its own, a concentrated unit, entire, not ringed round by any boundary; its manner of being is settled for it by itself alone. None of the Real-Beings is under limit; what is limited, measured, is what needs measure to prevent it running away into the unbounded. There every being is Measure; and therefore it is that all is beautiful. Because that is a living thing it is beautiful, holding the highest life, the complete, a life not tainted towards death, nothing mortal there, nothing dying. Nor is the life of that Absolute Living-Form some feeble flickering; it is primal, the brightest, holding all that life has of radiance; it is that first light which the souls There draw upon for their life and bring with them when they come here. It knows for what purpose it lives, towards What it lives, from Whence it lives; for the Whence of its life is the Whither... and close above it stands the wisdom of all, the collective Intellectual-Principle, knit into it, one with it, colouring it to a higher goodness, by kneading wisdom into it, making its beauty still more august. Even here the august and veritably beautiful life is the life in wisdom, here dimly seen, There purely. For There wisdom gives sight to the seer and power for the fuller living and in that tenser life both to see and to become what is seen.

Here attention is set for the most part upon the unliving and, in the living, upon what is lifeless in them; the inner life is taken only with alloy: There, all are Living Beings, living wholly, unalloyed; however you may choose to study one of them apart from its life, in a moment that life is flashed out upon you: once you have known the Essence that pervades them, conferring that unchangeable life upon them, once you perceive the judgement and wisdom and knowledge that are theirs, you can but smile at all the lower nature with its pretention to Reality.

In virtue of this Essence it is that life endures, that the Intellectual-Principle endures, that the Beings stand in their eternity; nothing alters it, turns it, moves it; nothing, indeed, is in being besides it to touch it; anything that is must be its product; anything opposed to it could not affect it. Being itself could not make such an opposite into Being; that would require a prior to both and that prior would then be Being; so that Parmenides was right when he taught the identity of Being and Unity. Being is thus beyond contact not because it stands alone but because it is Being. For Being alone has Being in its own right.

How then can we deny to it either Being or anything at all that may exist effectively, anything that may derive from it?

As long as it exists it produces: but it exists for ever; so, therefore, do its products. And so great is it in power and beauty that it remains the allurer, all things of the universe depending from it and rejoicing to hold their trace of it and through that to seek their good. To us, existence is before the good; all this world desires life and wisdom in order to Being; every soul and every intellect seeks to be its Being, but Being is sufficient to itself.

(166) It is not proper to understand that Intelligible One with vehemence, but with the extended flame of far reaching Mind, measuring all things except that Intelligible. But it is requisite to understand this; for if thou inclinest thy Mind thou wilt understand it, not earnestly; but it is becoming to bring with thee a pure and enquiring sense, to extend the void mind of thy Soul to the Intelligible, that thou mayest learn the Intelligible, because it subsisteth beyond Mind.

(5) Another marked case is that of Zerah Colburn, the mathematical prodigy, whose feats attracted the attention of the scientific world during the last century. In this case, the child under eight years of age, without any previous knowledge of even the common rules of arithmetic, or even of the use and powers of the Arabic numerals, solved a great variety of arithmetical problems by a simple operation of the mind, and without the use of any visible symbols or contrivances. He could answer readily a question involving the statement of the exact number of minutes or seconds in any given period of time. He could also state with equal facility the exact product of the multiplication of any number containing two, three, or four figures by another number consisting of a like number of figures. He could state almost instantly all the factors composing a number of six or seven places of figures. He could likewise determine instantly questions concerning the extraction of the square and cube roots of any number proposed, and likewise whether it was a prime number incapable of division by any other number, for which there is no known general rule among mathematicians. Asked such questions in the midst of his ordinary childish play, he would answer them almost instantly and then proceed with his play.

(1) The prudent [i. e. the wise] man will especially become so as follows: In the first place, being naturally sagacious, possessing a good memory, and being a lover of labor, he should exercise his dianoetic power immediately from his youth in reasonings and disciplines, and in accurate theories, and adhere to genuine philosophy. But after this he should acquire knowledge and experience in what pertains to the Gods, the laws, and human lives. For there are two things from which the disposition of prudence is produced; one of which consists in obtaining a mathematical and gnostic habit; but the other, in a man perceiving by himself many theorems and things, and understanding other things through a certain different mode. For neither is he sufficient to the possession of prudence, who immediately from his youth has exercised his dianoetic power in reasonings and disciplines; nor he who being destitute of these, has heard and has been conversant with a multitude of things.

But the latter will have his dianoetic power blind, through judging of particulars; and the former through always surveying universals. For as in computations the amount of the whole is obtained by the addition of the parts, thus also in things, reason is able to delineate the theory of universals; but experience has the power of forming a judgment of particulars.