"Triangle." The latter figure, along with the square and circle, are more eloquent and scientific descriptions of the order of the evolution of the Universe, spiritual and psychic, as well as physical, than volumes of descriptive Cosmogonies and revealed "Geneses." The ten Points inscribed within that "Pythagorean Triangle" are worth all the theogonies and angelologies ever emanated from the theological brain. For he who interprets these seventeen points (the seven Mathematical Points hidden)—on their very face, and in the order given—will find in them the uninterrupted series of the genealogies from the first Heavenly to Terrestrial Man. And, as they give the order of Beings, so they reveal the order in which were evolved the Kosmos, our Earth, and the primordial Elements by which the latter was generated. Begotten in the invisible "Depths," and in the Womb of the same "Mother" as its fellow-globes-he who masters the mysteries of our own Earth will have mastered those of all others. Whatever ignorance, pride or fanaticism may suggest to the contrary, Esoteric Cosmology can be shown to be inseparably connected with both Philosophy and Modern Science. The Gods and Monads of the Ancients-from Pythagoras down to Leibnitz-and the Atoms of the present materialistic schools (as borrowed by them from the theories of the old Greek Atomists) are only a compound unit, or a graduated unity like the human frame, which begins with body and ends with Spirit. In the Occult Sciences they can be studied separately, but they can never be mastered unless they are viewed in their mutual correlations during their life-cycle, and as a Universal Unity during Pralayas. La Pluche shows sincerity, but gives a poor idea of his philosophical capacities, when declaring his personal views on the Monad or the Mathematical Point. He says: A point is enough to put all the schools in the world in a combustion. But what need has man to know that point, since the creation of such a small being is beyond his power? À fortiori, philosophy acts against probability when, from that point which absorbs and disconcerts all her meditations, she presumes to pass on to the generation of the world. Philosophy, however, could never have formed its conception of a logical, universal, and absolute Deity, if it had had no Mathematical Point within the Circle upon which to base its speculations. It is only the manifested Point, lost to our senses after its pregenetic appearance in the infinitude and incognizability of the Circle, that makes a recon THE MATHEMATICAL POINT. 673 ciliation between Philosophy and Theology possible-on condition that the latter should abandon its crude materialistic dogmas. And it is because Christian theology has so unwisely rejected the Pythagorean Monad and geometrical figures, that it has evolved its self-created human and personal God, the monstrous Head whence flow in two streams the dogmas of Salvation and Damnation. This is so true, that even those clergymen who are Masons, and who would be Philosophers, have, in their arbitrary interpretations, fathered upon the Ancient Sages the queer idea that: The Monad represented [with them] the throne of the Omnipotent Deity, placed in the centre of the empyrean to indicate T.G.A.O.T.U. [read the "Great Architect of the Universe"].* A curious explanation this, more Masonic than strictly Pythagorean. Nor did the "Hierogram within a Circle, or equilateral Triangle," ever mean "the exemplification of the unity of the divine Essence"; for this was exemplified by the plane of the boundless Circle. What it really meant was the triune coëqual Nature of the first differentiated Substance, or the con-substantiality of the (manifested) Spirit, Matter and the Universe-their "Son"-which proceeds from the Point, the real, Esoteric Logos, or Pythagorean Monad. For the Greek Monas signifies "Unity" in its primary sense. Those unable to seize the difference between the Monad-the Universal Unit-and the Monads or the manifested Unity, as aiso between the ever-hidden and the revealed Logos, or the Word, ought never to meddle with Philosophy, let alone with the Esoteric Sciences. It is needless to remind the educated reader of Kant's Thesis to demonstrate his second Antinomy.f Those who have read and understood it will see clearly the line we draw between the absolutely ideal Universe and the invisible though manifested Kosmos. Our Gods and Monads are not the Elements of extension itself, but only those of the invisible Reality which is the basis of the manifested Kosmos. Neither Esoteric Philosophy, nor Kant, to say nothing of Leibnitz, would ever admit that extension can be composed of simple or unextended parts. But theologian-philosophers will not grasp this. The Circle and the Point-the latter retiring into and merging with the former, after having emanated the first three Points and connected them with lines, thus forming the first noumenal basis of the Second Triangle in the Manifested World-have Pythagorean Triangle, by the Rev. G. Oliver, p. 36. + See Kant's Critique de la Raison Pure, Barni's transl., II. 54. ever been an insuperable obstacle to theological flights into dogmatic empyreans. On the authority of this Archaic Symbol, a male, personal God, the Creator and Father of all, becomes a third-rate emanation, the Sephira standing fourth in descent, and on the left hand of Ain Suph, in the Kabalistic Tree of Life. Hence, the Monad is degraded into a Vehicle-a "Throne"! The Monad-the emanation and reflection only of the Point, or Logos, in the phenomenal World—becomes, as the apex of the manifested equilateral Triangle, the "Father." The left side or line is the Duad, the “Mother," regarded as the evil, counteracting principle;* the right side represents the "Son," "his Mother's Husband” in every Cosmogony, as being one with the apex; the base line is the universal plane of productive Nature, unifying on the phenomenal plane FatherMother-Son, as these were unified in the apex, in the supersensuous World. By mystic transmutation they became the Quaternary-the Triangle became the Tetraktys. This transcendental application of geometry to cosmic and divine theogony-the Alpha and the Omega of mystical conception—was dwarfed after Pythagoras by Aristotle. By omitting the Point and the Circle, and taking no account of the apex, he reduced the metaphysical value of the idea, and thus limited the doctrine of magnitude to a simple Triad-the line, the surface, and the body. His modern heirs, who play at Idealism, have interpreted these three geometrical figures as Space, Force, and Matter-"the potencies of an interacting Unity." Materialistic Science, perceiving but the base line of the manifested Triangle-the plane of Matter-translates it practically as (Father)-Matter, (Mother)-Matter, and (Son)-Matter, and theoretically as Matter, Force, and Correlation. But to the average Physicist, as remarked by a Kabalist: Space, and Force, and Matter, are what signs in Algebra are to the Mathematician, merely conventional symbols, or Force as Force, and Matter as Matter, are as absolutely unknowable as is the assumed empty space in which they are held to interact.‡ * Plutarch, De Placitis Philosophorum. + In the Greek and Latin Churches-which regard marriage as one of the sacraments-the officiat ing priest during the marriage ceremony represents the apex of the triangle; the bride, its left feminine side, and the bridegroom the right side, while the base line is symbolized by the row of witnesses, the bridesmaids and best men. But behind the priest there is the Holy of Holies, with its mysterious containments and symbolic meaning, inside of which no one but the consecrated priests should enter. In the early days of Christianity the marriage ceremony was a mystery and a true symbol. Now, however, even the Churches have lost the true meaning of this symbolism. New Aspects of Life and Religion, by Henry Pratt, M.D., p. 7. Ed. 1886. SPACE, FORCE, AND MATTER. Symbols represent abstractions, and on these The physicist bases reasoned hypotheses of the origin of things 675 he sees three needs in what he terms creation: A place wherein to create. A medium by which to create. A material from which to create. And in giving a logical expression to this hypothesis through the terms space, force, matter, he believes he has proved the existence of that which each of these represents as he conceives it to be.* The Physicist who regards Space merely as a representation of our mind, or extension unrelated to things in it, which Locke defined as capable of neither resistance nor motion; the paradoxical Materialist, who would have a void there, where he can see no Matter, would reject with the utmost contempt the proposition that Space is A substantial though [apparently an absolutely] unknowable living Entity.† Such is, nevertheless, the Kabalistic teaching, and it is that of Archaic Philosophy. Space is the real World, while our world is an artificial one. It is the One Unity throughout its infinitude: in its bottomless depths as on its illusive surface; a surface studded with countless phenomenal Universes, Systems and mirage-like Worlds. Nevertheless, to the Eastern Occultist, who is an objective Idealist at bottom, in the real World, which is a Unity of Forces, there is "a connection of all Matter in the Plenum," as Leibnitz would say. This is symbolized in the Pythagorean Triangle. It consists of Ten Points inscribed pyramid-like (from one to four) within its three sides, and it symbolizes the Universe in the famous Pythagorean Decad. The upper single point is a Monad, and represents a Unit-Point, which is the Unity whence all proceeds. All is of the same essence with it. While the ten points within the equilateral Triangle represent the phenomenal world, the three sides enclosing the pyramid of points are the barriers of noumenal Matter, or Substance, that separate it from the world of Thought. Pythagoras considered a point to correspond in proportion to unity; a line to 2; a superfice to 3; a solid to 4; and he defined a point as a monad having position, and the beginning of all things; a line was thought to correspond with duality, because it was produced by the first motion from indivisible nature, and formed the junction of two points. A superfice was compared to the number three because it is the first of all causes that are found in figures; for a circle, which is the principal of all round figures, comprises a triad, in centre-space-circumference. But a triangle, which is the first of all rectilineal figures, is included in a ternary, and receives its form according to that number; and was considered by + Ibid., p. 9. Ibid., pp. 7, 8. the Pythagoreans to be the author of all sublunary things. The four points at the base of the Pythagorean triangle correspond with a solid or cube, which combines the principles of length, breadth, and thickness, for no solid can have less than four extreme boundary points.* It is argued that "the human mind cannot conceive an indivisible unit short of the annihilation of the idea with its subject." This is an error, as the Pythagoreans have proved, and a number of Seers before them, although there is a special training needed for the conception, and although the profane mind can hardly grasp it. But there are such things as "Meta-mathematics" and "Meta-geometry." Even Mathematics pure and simple proceed from the universal to the particular, from the mathematical indivisible point to solid figures. The teaching originated in India, and was taught in Europe by Pythagoras, who, throwing a veil over the Circle and the Point-which no living man can define except as incomprehensible abstractions-laid the origin of the differentiated cosmic Matter in the base of the Triangle. Thus the latter became the earliest of geometrical figures. The author of New Aspects of Life, dealing with the Kabalistic Mysteries, objects to the objectivization, so to speak, of the Pythagorean conception and the use of the equilateral triangle, and calls it a "misnomer." His argument that a solid equilateral body— One whose base, as well as each of its sides, form equal triangles-must have four co-equal sides or surfaces, while a triangular plane will as necessarily possess five, t -demonstrates on the contrary the grandeur of the conception in all its Esoteric application to the idea of the pregenesis, and the genesis of Kosmos. Granted, that an ideal Triangle, depicted by mathematical, imaginary lines, Can have no sides at all, being simply a phantom of the mind to which, if sides be imputed, these must be the sides of the object it constructively represents. But in such case most of the scientific hypotheses are no better than "phantoms of the mind"; they are unverifiable, except on inference. and have been adopted merely to answer scientific necessities. Furthermore, the ideal Triangle-"as the abstract idea of a triangular body, and, therefore, as the type of an abstract idea"-accomplished and carried out to perfection the double symbolism intended. As an emblem applicable to the objective idea, the simple triangle became a solid. When repeated in stone, facing the four cardinal points, it • Pythagorean Triangle, by the Rev. G. Oliver, pp. 18, 19. + P. 387. + P. 387. |