Grid of the Gods (16 page)

We are dealing, rather, with the “topological metaphor” of the physical medium itself, as I noted in the appendix to chapter nine of
The Giza Death Star Destroyed
,
²⁰
and again in
The Philosophers’ Stone
,
²¹
and it is worth recalling what I stated there concerning the emergence of this “trinity” from the information-creating processes of the physical medium as viewed in yet
other
ancient traditions, in this case, the Neoplatonic and Hermetic.

In order to understand what the ancients meant by all the variegated religious and metaphysical imagery they employed to describe this topological metaphor — in order to
decode
it — let us perform a simple “thought experiment.” Imagine an absolutely undifferentiated “something.” The Neoplatonists referred to this “something” as “simplicity” (απλωτης). Note that, from the
physics
point of view
and from that of Hinduism itself
, we are dealing with a “nothing,” since it has no differentiated or distinguishing features whatsoever.

Now imagine one “brackets” this nothing, separating off a “region” of nothing from the rest of the nothing (Vishnu’s ejaculation
metaphor). At the instant one does so, one ends up with
three
things, each a kind of “differentiated nothing.” One ends with:

1) the “bracketed” region of nothing;

2) the
rest
of the nothing; and,

3) the “surface” that the two regions share.

Note something else. From a purely physics point of view, this occurs without
time
, since time is measured only by the relative positions of differentiated things with respect to each other. The “regions of nothing” and their common surface are, so to speak, still eternal, and yet, at the same instant, a kind of “time” has emerged simultaneously with the operation of differentiating itself.

In short, from a non-quantifiable “nothing,” information begins to emerge with the process of “bracketing” or “differentiating” itself, including the concept of
number.
On the ancient view, then, numbers do not exist in the abstract. They are, rather, functions of a topological metaphor of the physical medium.
²²

Now let us go further into this topological metaphor by notating our three differentiated nothings mathematically. There is a perfect symbol to represent this “nothing”, the empty hyper-set, whose symbol is
, and which contains no “things” or “members.” Now let our original “nothing” be symbolized by
. A surface of something is represented by the partial derivative symbol ∂, for after all, a “surface” of something, even a nothing, is a “partial derivative” of it.

So, we would represent our three resulting entities as follows:

1) the “bracketed” region of nothing, or
;

2) the
rest
of the nothing, or
; and,

3) the “surface” that the two regions share, or
.

Note now that the three “nothings” are still nothing, but now they have acquired information, distinguishing each nothing in a
formally explicit
manner from each other nothing. Note something else:
the relationship between them all is analogical in nature, since each bears the signature of having derived from the original undifferentiated nothing; each retains, in other words, in its formal description, the presence of
. And this will be true
no matter how many times one continues to “bracket” or “differentiate” it.
On this ancient cosmological view, in other words, everything is related to everything else by dint of its derivation via innumerable steps of “differentiation” from that original nothing. It is this fact which forms the basis within ancient civilizations for the practice of sympathetic magic, for given the analogical nature of the physical medium implied by these ancient cosmologies, in purely physics terms, everything is a coupled harmonic oscillator of everything else.
²³
Finally, observe how this formal explicitness dovetails quite nicely with the Hindu conception that the created world is, in fact, illusion, a “nothing,” but a differentiated nothing.

Now let us take the next step in the decoding of this topological metaphor in ancient texts and cosmologies. It is understood within the kind of mathematical metaphor that we are exploring here, that
functions
can be members of the empty hyper-set without destroying its “emptiness,” for the simple reason that
functions
are not “things” or objects, but pure processes. Thus far, we have dealt with regions, and surfaces, now we add
functions
.

Here is what I wrote in
The Giza Death Star Destroyed
about the three entities when examined from the standpoint of a passage of the
Hermetica:

The passage is the
Libellus II:1–6b
, a short dialogue between Hermes and his discipline Asclepius:

“Of what magnitude must be that space in which the Kosmos is moved? And of what nature? Must not that Space be far greater, that it may be able to contain the continuous motion of the Kosmos, and that the thing moved may not be cramped for want of room, and cease to move? —
Ascl.
Great indeed must be that Space, Trismegistus. —
Herm.
And of what nature must it be Aslcepius? Must it not be of opposite nature to Kosmos? And of opposite nature to the body is the incorporeal…. Space is an object of thought, but not in the same sense that God is, for God is an object of thought primarily to Himself, but Space is an object of thought to us, not to itself.”
²⁴

This passage thus evidences the type of “ternary” thinking already encountered in Plotinus, but here much more explicitly so, as it is a kind metaphysical and dialectical version of topological triangulation employed by Bounias and Krasnoholovets in their version in their model. However, there is a notable distinction between Plotinus’ ternary structure and that of the
Hermetica
: whereas in Plotinus’ the three principle objects in view are the One, the Intellect, and the World Soul, here the principal objects in view are the triad of Theos, Topos, and Kosmos (Θεος, Τοπος, Κοσµος), or God, Space, and Kosmos, respectively.

These three — God, Space, and Kosmos — are in turn distinguished by a dialectic of opposition based on three elemental functions, each of which in turn implies its own functional opposite:

So in Hermes’ version of the metaphor, the following “triangulation” occurs, with the terms “God, Space, Kosmos” becoming the names for each vertex or region: