MATHEMATICS # 2
Page 10-15
Chapter II
IN THE NATURE OF THINGS
We are prepared now to step into the realm of "pure" mathematics, that is to say, mathematics for its own sake and not seeking any practical application. The modern way of thinking is to view mathematics as a tool of science or industry; in fact, numbers are not held to have any significance in themselves other than as a means to an end. Of course, the curious properties of numbers have long been recognized, but studies along this line are usually relegated to the realm of recreational mathematics.
As we pursue this study, the various geometrical figures will be presented as a means whereby we may clarify our understanding of the ancient wisdom teachings. At this point, one might very well ask: What has Theosophy to do with Geometry?
If the study of the geometrical figures to be presented here were confined to a strictly mathematical treatise, it would be a great study in itself. The astonishing relationships between certain geometrical solids known as the regular polyhedral would excite wonder in the mind of any student, and it is to be regretted that so little attention has as yet been paid to these figures. But, on the other hand, if such a purely mathematical treatment of the subject should fall into the hands of someone already versed in the teachings of Theosophy, he might well see for himself the relationships between these geometrical figures and the processes of world-building, the Nature of man, and his place in Nature. This is an approach that appeals to a certain type of mind, a mathematically mystical mind. Other methods of approach will serve the purpose better to other minds and hearts. The aim is to find an ally oneself with the Higher Self.
In a higher sense, the study of mathematical symbolism does have a practical application; nor does this conflict with the opening words, i.e., that we are now stepping into the realm of pure mathematics, with little utilitarian value. On the contrary, if this study can help bring the student an awareness of the all-pervading Divine Life in which we live and move and have our being, then it is an aid to his progress.
What then is a symbol? Is it something in which truth is hidden so that it is not easily detected by those not entitled to it? In some instances, truths have been veiled in myths, legends, and parables because there have always been beginners searching for truth which cannot grasp the whole meaning of the philosophy. It must be given to them in such a manner as can be accepted. The truth is always available to anyone who is seriously in search of it. But at any particular time, it is available to the degree that the student himself has the faculty of taking it. When we do receive even limited teaching, it is with the assurance that we shall receive I in ever fuller measure as our understanding grows. It can never be forced upon us, but we can go forth and receive it of our own will.
Now we shall come in time to regard the Dodecahedron as a symbol of manifested Nature, or Prakriti. This is because its relationships to the other regular polyhedra demonstrate the most concise manner in which the truths about the manifested Universe can be presented. Why is this so? We can only say, "It is like things." There is no other reply. This applies to all the symbols that will be presented. Why are we conscious? It is like things. Why is the Boundless the source of all that is? It is like things. Why are we embarked upon an age-long pilgrimage back to the source from which we sprang? Again, we must say it is like things. Why does a moving circle generate a series of marvelously related geometric forms?
Once more, it is like things. Why do these forms represent the journey of the Eternal Pilgrim back to the Home from which he issued forth? Again, it is like things. Having thus set the stage, I would like to quote from the opening passage of H.P. Blavatsky's Proem to her Secret Doctrine.
"An Archaic Manuscript—a collection of palm leaves made impermeable to water, fire, and air, by some specific unknown process—is before the writer's eye. On the first page is an immaculate white disk within a dull black ground. On the following page, the same Disk, but with a central point. The first, the student knows to represent Kosmos in Eternity, before the re-awakening of still slumbering Energy, the emanation of the Word in later systems. The Point in the hitherto immaculate Disk, Space and Eternity in Pralaya denotes the dawn of differentiation. The Point in the Mundane Egg, the germ within the latter which will become the Universe, the ALL, the boundless, periodical Kosmos, this germ being latent and active, periodically and by turns. The one circle is divine Unity, from which all proceeds, whither all returns. Its circumference—a forcibly limited symbol, because of the human mind's limitation—indicates the abstract, ever recognizable PRESENCE and its plane, the Universal Soul, although the two are one. Only the face of the Disk being white and the ground all around black shows clearly that its plane is the only knowledge, dim and hazy though it still is, attainable by man. It is on this plane that the Manvantaric manifestations begin, for it is in this SOUL that slumbers, during the Pralaya, the Divine Thought, wherein lies concealed the plan of every future Cosmogony and Theogony."
Again, quoting from page 4:
"The first illustration being a plain disk, the second one in the Archaic symbol shows a disk with a point in it—the first differentiation in the periodical manifestations of the ever-eternal nature, sexless and infinite "Aditi in THAT' (rig-Veda), the Point in the Disk, or potential Space within abstract Space. In its third stage, the Point is transformed into a diameter (Fig.2). It now symbolizes a divine immaculate Mother-Nature within the all-embracing absolute Infinitude. Finally, when a vertical one crosses the diameter line, it becomes the mundane Cross (Fig.3)."
Footnote See Fig. 1, Fig. 2, and Fig. 3. In the Secret Doctrine, these figures are interspersed within the text, but for the reader's convenience, these are set forth here as separate figures. In addition, I have added the downward pointing arrow to the Cross in Fig. 3.
Referring to the explanation of the Three Logoi in Chapter One, we may indicate that the plain Disk represents the Boundless. As it lies upon a dark background on the original parchment described by H. P. Blavatsky, duality is suggested and illustrated in our studies by Parabrahman (outside the Disk)—Mulaprakriti (within the Disk). The Point within the circle now represents the First Logos (the unmanifested. Mdb) Brahman-Pradhana, the Point indicating differentiation, although no manifestation is apparent.
When the diameter appears, we now represent the Second Logos, Brahma-Prakriti or Svabhavat, semi- or quasi-manifestation (Fig.2). The Third Logo, Mahat, is represented when the vertical line crosses the diameter. But note that this is not a static symbol. In Fig. 3, the vertical line ends in an arrow, indicating MOTION. The circle will be made to descend, representing the action of the Third Logos in manifestation. In the occult representation of the Cross, the horizontal diameter represents the feminine, and the vertical line the masculine aspects of Svabhavat.
On page 29 of The Secret Doctrine, note verse 10 of Stanza III of the Book of Dzyan:
"Father-Mother spins a web whose upper end is fastened to Spirit—the light of the one darkness – and the lower one to its shadowy end, matter; and this web is the universe spun out of the two substances made in one, which is Svabhavat."
Let us now observe that the horizontal line has been lettered AB, and since it is taken to represent the feminine Energy, let us see what it will accomplish. Turning to Fig. 4, we see that the circle has descended its diameter. The stage is now set for the springing into the life of the seeds of manifestation brought over from previous cycles. The new position of the circle represents this. It no longer intersects any portion of its old position, the latter now represented by the broken line circle. In other words, the circle occupies an entirely new position in Space.
See figures 1, 2, 3, and 4.
The stanzas of The Book of Dzyan are not easy to understand, but they reveal, to the person willing to study them, a sublime description of cosmic evolution: the reawakening of the universe after a period of quiescence, the differentiation of forms, the process of world formation, the appearance of humanity on earth, and the early evolution of our species.
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