Passages similar to: Secret Teachings of All Ages — Pythagorean Mathematics
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Western Esoteric
Secret Teachings of All Ages
Pythagorean Mathematics (136)
The decad--10--according to the Pythagoreans, is the greatest of numbers, not only because it is the tetractys (the 10 dots) but because it comprehends all arithmetic and harmonic proportions. Pythagoras said that 10 is the nature of number, because all nations reckon to it and when they arrive at it they return to the monad. The decad was called both heaven and the world, because the former includes the latter. Being a perfect number, the decad was applied by the Pythagoreans to those things relating to age, power, faith, necessity, and the power of memory. It was also called unwearied, because, like God, it was tireless. The Pythagoreans divided the heavenly bodies into ten orders. They also stated that the decad perfected all numbers and comprehended within itself the nature of odd and even, moved and unmoved, good and ill. They associated its power with the following deities: Atlas (for it carried the numbers on its shoulders), Urania, Mnemosyne, the Sun, Phanes, and the One God.
The ten numbers formed from nothing are the Decad: these are seen in the fingers of the hands, five on one, five on the other, and over them is the...
(3) The ten numbers formed from nothing are the Decad: these are seen in the fingers of the hands, five on one, five on the other, and over them is the Covenant by voice spiritual, and the rite of Circumcision, corporeal (as of Abraham).
These Ten Numbers, beyond the Infinite one, have the boundless realms, boundless origin and end, an abyss of good and one of evil, boundless height...
(5) These Ten Numbers, beyond the Infinite one, have the boundless realms, boundless origin and end, an abyss of good and one of evil, boundless height and depth, East and West, North and South, and the one only God and king, faithful forever seated on his throne, shall rule over all, forever and ever.
Chapter XVI: Gnostic Exposition of the Decalogue. (4)
This is the physical Decalogue of the heaven.
(4) And the Decalogue, viewed as an image of heaven, embraces sun and moon, stars, clouds, light, wind, water, air, darkness, fire. This is the physical Decalogue of the heaven.
Ten are the numbers of the ineffable Sephiroth, ten and not nine, ten and not eleven. Learn this wisdom, and be wise in the understanding of it,...
(4) Ten are the numbers of the ineffable Sephiroth, ten and not nine, ten and not eleven. Learn this wisdom, and be wise in the understanding of it, investigate these numbers, and draw knowledge from them, fix the design in its purity, and pass from it to its Creator seated on his throne.
Chapter XVI: Gnostic Exposition of the Decalogue. (3)
That ten is a sacred number, it is superfluous to say now. And if the tables that were written were the work of God, they will be found to exhibit...
(3) That ten is a sacred number, it is superfluous to say now. And if the tables that were written were the work of God, they will be found to exhibit physical creation. For by the "finger of God" is understood the power of God, by which the creation of heaven and earth is accomplished; of both of which the tables will be understood to be symbols. For the writing and handiwork of God put on the table is the creation of the world.
What then is the veritable nature of Number? Is it an accompaniment upon each substance, something seen in the things as in a man we see one man, in...
(5) What then is the veritable nature of Number?
Is it an accompaniment upon each substance, something seen in the things as in a man we see one man, in a being one being and in the total of presentations the total of number?
But how explain the dyad and triad? How comes the total to be unitary and any particular number to be brought under unity? The theory offers a multiplicity of units, and no number is reducible to unity but the simple "one." It might be suggested that a dyad is that thing- or rather what is observed upon that thing- which has two powers combined, a compound thing related to a unity: or numbers might be what the Pythagoreans seem to hold them in their symbolic system in which Justice, for example, is a Tetrad: but this is rather to add the number, a number of manifold unity like the decad, to the multiplicity of the thing which yet is one thing. Now it is not so that we treat the ten things; we bring them together and apply the figure ten to the several items. Or rather in that case we say ten, but when the several items form a unity we say decad. This would apply in the Intellectual as in the sensible.
But how then can number, observed upon things, rank among Real Beings?
One answer might be that whiteness is similarly observed upon things and yet is real, just as movement is observed upon things and there is still a real existence of movement. But movement is not on a par with number: it is because movement is an entity that unity can be observed upon it. Besides, the kind of real existence thus implied annuls the reality of number, making it no more than an attribute; but that cannot be since an attribute must exist before it can be attributed; it may be inseparable from the subject but still must in itself be something, some entity as whiteness is; to be a predicate it must be that which is to be predicated. Thus if unity is observed in every subject, and "one man" says more than "man's oneness being different from the manness and common to all things- then this oneness must be something prior to man and to all the rest: only so can the unity come to apply to each and to all: it must therefore be prior also to even movement, prior to Being, since without unity these could not be each one thing: of course what is here meant is not the unity postulated as transcending Being but the unity predicable of the Ideas which constitute each several thing. So too there is a decad prior to the subject in which we affirm it; this prior would be the decad absolute, for certainly the thing in which the decad is observed is not that absolute.
Is this unity, then, connate and coexistent to the Beings? Suppose it coexistent merely as an accidental, like health in man, it still must exist of itself; suppose it present as an element in a compound, there must first exist unity and the unity absolute that can thus enter into composition; moreover if it were compounded with an object brought into being by its agency it would make that object only spuriously a unity; its entry would produce a duality.
But what of the decad? Where lies the need of decad to a thing which, by totalling to that power, is decad already?
The need may be like that of Form to Matter; ten and decad may exist by its virtue; and, once more, the decad must previously exist of its own existence, decad unattached.
The number nine is divine, receives its completion from three triads, and attains the summits of theology, according to the Chaldaic philosophy as...
(186) The number nine is divine, receives its completion from three triads, and attains the summits of theology, according to the Chaldaic philosophy as Porphyry informeth us.
To everyone they seem to come under Quantity and you have certainly brought Quantity in, where you say that discrete Quantity equally with the continu...
(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.
Ten are the numbers, as are the Sephiroth, and twenty-two the letters, these are the Foundation of all things. Of these letters, three are mothers,...
(2) Ten are the numbers, as are the Sephiroth, and twenty-two the letters, these are the Foundation of all things. Of these letters, three are mothers, seven are double, and twelve are simple.
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...
(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.
Chapter XI: The Knowledge Which Comes Through Faith the Surest of All. (6)
There are body and soul, the five senses, speech, the power of reproduction - the intellectual or the spiritual faculty, or whatever you choose to cal...
(6) For out of the heart proceed thoughts." This, as I think, is the true and just measure according to God, by which things capable of measurement are measured, the decad which is comprehensive of man; which summarily the three above-mentioned measures pointed out. There are body and soul, the five senses, speech, the power of reproduction - the intellectual or the spiritual faculty, or whatever you choose to call it. And we must, in a word, ascending above all the others, stop at the mind; as also certainly in the universe overleaping the nine divisions, the first consisting of the four elements put in one place for equal interchange: and then the seven wandering stars and the one that wanders not, the ninth, to the perfect number, which is above the nine, and the tenth division, we must reach to the knowledge of God, to speak briefly, desiring the Maker after the creation. Wherefore the tithes both of the ephah and of the sacrifices were presented to God; and the paschal feast began with the tenth day, being the transition from all trouble, and from all objects of sense.
The dodecad symbolizes war, the triad of amity, the triad of enmity, three which are life-giving, three which are death-dealing, and God, the faithful...
(3) And out of the triad one stands apart; and in the heptad there are two triads, and one standing apart. The dodecad symbolizes war, the triad of amity, the triad of enmity, three which are life-giving, three which are death-dealing, and God, the faithful king, rules over all from the throne of his sanctity. One above three, three above seven, and seven above twelve, and all are linked together, and one with another.
It may be suggested that the decad is nothing more than so many henads; admitting the one henad why should we reject the ten? As the one is a real...
(11) It may be suggested that the decad is nothing more than so many henads; admitting the one henad why should we reject the ten? As the one is a real existence why not the rest? We are certainly not compelled to attach that one henad to some one thing and so deprive all the rest of the means to unity: since every existent must be one thing, the unity is obviously common to all. This means one principle applying to many, the principle whose existence within itself we affirmed to be presupposed by its manifestation outside.
But if a henad exists in some given object and further is observed in something else, then that first henad being real, there cannot be only one henad in existence; there must be a multiplicity of henads.
Supposing that first henad alone to exist, it must obviously be lodged either in the thing of completest Being or at all events in the thing most completely a unity. If in the thing of completest Being, then the other henads are but nominal and cannot be ranked with the first henad, or else Number becomes a collection of unlike monads and there are differences among monads . If that first henad is to be taken as lodged in the thing of completest unity, there is the question why that most perfect unity should require the first henad to give it unity.
Since all this is impossible, then, before any particular can be thought of as a unit, there must exist a unity bare, unrelated by very essence. If in that realm also there must be a unity apart from anything that can be called one thing, why should there not exist another unity as well?
Each particular, considered in itself, would be a manifold of monads, totalling to a collective unity. If however Nature produces continuously- or rather has produced once for all- not halting at the first production but bringing a sort of continuous unity into being, then it produces the minor numbers by the sheer fact of setting an early limit to its advance: outgoing to a greater extent- not in the sense of moving from point to point but in its inner changes- it would produce the larger numbers; to each number so emerging it would attach the due quantities and the appropriate thing, knowing that without this adaptation to Number the thing could not exist or would be a stray, something outside, at once, of both Number and Reason.
This also is worthy, in my opinion, of intellectual attention, that the tradition of the Oracles concerning the Angels affirms that they are thousand...
(1) This also is worthy, in my opinion, of intellectual attention, that the tradition of the Oracles concerning the Angels affirms that they are thousand thousands, and myriad myriads, accumulating and multiplying, to themselves, the supreme limits of our numbers, and, through these, shewing clearly, that the ranks of the Heavenly Beings cannot be numbered by us. For many are the blessed hosts of the supermundane minds, surpassing the weak and contracted measurement of our material number, and being definitely known by their own supermundane and heavenly intelligence and science alone, which is given to them in profusion by the supremely Divine and Omniscient Framer of Wisdom, and essentiating Cause and connecting Force, and encompassing Term of all created things together. Next: Caput XV. Sacred Texts | Christianity « Previous: The Works of Dionysius the Areopagite: On the Heavenly Hi... Index Next: The Works of Dionysius the Areopagite: On the Heavenly Hi... » Sacred Texts | Christianity
Yaldabaoth’s World Order (Yaldabaoth’s World Order)
Yaldabaoth is the first ruler, who took great power from his mother. Then he left her and moved away from the place where he was born. He took...
Yaldabaoth is the first ruler, who took great power from his mother. Then he left her and moved away from the place where he was born. He took control and created for himself other realms with luminous fire, which still exists. He mated with the mindlessness in him and produced authorities for himself: The name of the first is Athoth, whom generations call the reaper. The second is Harmas, who is the jealous eye. The third is Kalila-Oumbri. The fourth is Yabel. The fifth is Adonaios, who is called Sabaoth. The sixth is Cain, whom generations of people call the sun. The seventh is Abel. The eighth is Abrisene. The ninth is Yobel. The tenth is Armoupieel. The eleventh is Melcheir-Adonein. The twelfth is Belias, who is over the depth of the underworld. Yaldabaoth stationed seven kings, one for each sphere of heaven, to reign over the seven heavens, and five to reign over the depth of the abyss. He shared his fire with them, but he did not give away any of the power of the light that he had taken from his mother. For he is ignorant darkness. When light mixed with darkness, it made the darkness shine. When darkness mixed with light, it dimmed the light and became neither light nor darkness, but rather gloom. This gloomy ruler has three names: the first name is Yaldabaoth, the second is Sakla, the third is Samael. He is wicked in his mindlessness that is in him. He said, I am god and there is no other god but me, since he did not know where his own strength had come from. The rulers created seven powers for themselves, and the powers created six angels apiece, until there were 365 angels. These are the names and the corresponding appearances: The first is Athoth and has the face of sheep. The second is Eloaios and has the face of a donkey. The third is Astaphaios and has the face of a hyena. The fourth is Yao and has the face of a snake with seven heads. The fifth is Sabaoth and has the face of a snake. The sixth is Adonin and has the face of an ape. The seventh is Sabbataios and has a face of flaming fire. This is the sevenfold nature of the week. Yaldabaoth has many faces, more than all of these, so that he could show whatever face he wanted when he was among the seraphim. He shared his fire with them and lorded it over them because of the glorious power he had from his mother’s light. That is why he called himself god and defied the place from which he came. In his thought he united the seven powers with the authorities that were with him. When he spoke, it was done. He named each of the powers, beginning with the highest: First is goodness, with the first power, Athoth. Second is forethought, with the second power, Eloaios. Third is divinity, with the third power, Astaphaios. Fourth is lordship, with the fourth power, Yao. Fifth is kingdom, with the fifth power, Sabaoth. Sixth is jealousy, with the sixth power, Adonin. Seventh is understanding, with the seventh power, Sabbataios. Each has a sphere in its own realm. They were named after the glory above for the destruction of the powers. While the names given them by their maker were powerful, the names given them after the glory above would bring about their destruction and loss of power. That is why they have two names. Yaldabaoth organized everything after the pattern of the first realms that had come into being, so that he might create everything in an incorruptible form. Not that he had seen the incorruptible ones. Rather, the power that is in him, that he had taken from his mother, produced in him the pattern for the world order. When he saw creation surrounding him, and the throng of angels around him who had come forth from him, he said to them, I am a jealous god and there is no other god beside me. But by announcing this, he suggested to the angels with him that there is another god. For if there were no other god, of whom would he be jealous?
Chapter XVI: Gnostic Exposition of the Decalogue. (20)
And they say that the embryo is perfected exactly in the sixth month, that is, in one hundred and eighty days in addition to the two and a half, as Po...
(20) For the motion of the sun from solstice to solstice is completed in six months - in the course of which, at one time the leaves fall, and at another plants bud and seeds come to maturity. And they say that the embryo is perfected exactly in the sixth month, that is, in one hundred and eighty days in addition to the two and a half, as Polybus the physician relates in his book On the Eighth Month, and Aristotle the philosopher in his book On Nature. Hence the Pythagoreans, as I think, reckon six the perfect number, from the creation of the world, according to the prophet, and call it Meseuthys and Marriage, from its being the middle of the even numbers, that is, of ten and two. For it is manifestly at an equal distance from both.
All things being undefined and yet unwrought, the light things were assigned unto the height, the heavy ones had their foundations laid down...
(2) All things being undefined and yet unwrought, the light things were assigned unto the height, the heavy ones had their foundations laid down underneath the moist part of Dry Space, the universal things being bounded off by Fire and hanged in Breath to keep them up. And Heaven was seen in seven circles; its Gods were visible in forms of stars with all their signs; while Nature had her members made articulate together with the Gods in her. And [Heaven's] periphery revolved in cyclic course, borne on by Breath of God.
These ten Sephiroth which are, moreover, ineffable, have their end even as their beginning, conjoined, even as is a flame to a burning coal: for our...
(7) These ten Sephiroth which are, moreover, ineffable, have their end even as their beginning, conjoined, even as is a flame to a burning coal: for our God is superlative in his unity, and does not permit any second one. And who canst thou place before the only one?
VII. The Plane of the Consciousness of the Gods If, as we have seen, it is most difficult to speak in understandable terms concerning the phases of...
(31) VII. The Plane of the Consciousness of the Gods If, as we have seen, it is most difficult to speak in understandable terms concerning the phases of life and activity on the last mentioned Plane of Consciousness, what must be the difficulty of even hinting at the life and activities of the highest plane of all—the Plane of the Consciousness of the Gods On this highest of all Planes of Consciousness, however, dwell beings so high in the scale of knowledge, power, life, and bliss that even the imagination of the advanced student or teacher can scarcely grasp the idea. This is the Plane of the Gods, in verity—of being so far advanced that they are practically akin to the conception of the Gods created by man to account for the Universe, and to serve as objects of worship.