Would you like to know how these stupid MOTHERFUCKERS OPERATE?

1. Topological Preliminaries

Let us begin with a simple thought experiment from mathematician George Spencer-Brown, and the cryptic remarks that open his masterpiece Laws of Form:

Draw a distinction.

Call it the first distinction.

Call the space in which it is drawn the space severed or cloven by the distinction.

Call the parts of the space shaped by the severance or cleft the sides of the distinction or, alternatively, the spaces, states, or contents distinguished by the distinction.

Let any mark, token, or sign be taken in any way with or with regard to the distinction as a signal.

Call the use of any signal its intent.

Now let us imagine that we envision an indescribable “No-thing,” as we envisioned in the first chapter, utterly devoid of any distinguishing features whatsoever, infinitely “extended” in every “direction.” We might envision it as the empty space in this box, except of course, our box has no neat lines denoting its “edges”:

We have, in other words, an infinitely extended “No-thing” which, as we noted in the first chapter, has a perfect mathematical symbol, the empty hyper-set, symbolized by Ø, to describe it, or as Spencer-Brown calls it, a mark or “signal” of intention.

Now, within this space, we draw the simplest distinction: we cleave this space:

Remembering that our “box” really has no “edges,” what we really have is this:

In other words, we have two “spaces,” all that inside the circle, and all outside of it, or, in other words, we have what Spencer-Brown calls a “cloven space.” Note that the circle is a circumscription, a “writing around” or “peri-graphing,” which would be functionally symbolized by the paragraph symbol, ¶, as a symbol of the function of “drawing a distinction” or “cleaving the space.”

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Note two important things here: (1) we are dealing both with a “space” in the intellectual or conceptual sense, and (2) with a space in the real physics sense, at one and the same time. Additionally, because our original “box” is infinite, the circle or cloven space within it itself has no limits, save that there is a boundary or “side” as Spencer-Brown calls it, a surface as the topologists would say, between it and the space outside it. So we may assign symbols or marks to each of the three things now distinguished:

1)the space outside the circle we will designate as the “interior” of space 1, with the interior denoted by the topological “o” superscript above the signal or symbol Ø:

2)and similarly the space inside the circle as space 2, another “interior”:

3)and the common surface of the two, denoted by the partial derivative symbol ∂:

Notice that what we now have, as a result of performing one act of distinction, are three “distinguished nothings.” We have created a metaphor of a “one-three,” a kind of primordial trinity. Notably, because our original Ø was dimensionless or infinite, we cannot assign any real dimensionality to any of the entities thus distinguished either.62 Notice the all-important point that the signature of Ø will always remain in the formal description of the regions or surfaces no matter how many times the process is repeated. It remains in all contexts, and is thus a basis for analogical connections between all entities subsequently generated by repetitions of this process. One might view this as a kind of “formally explicit calculus of inter-contextual analysis,” or, in short, analogical calculus.

Now let us use this very abstract “topological metaphor” to examine its expression in various ancient cultures.

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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.72

Notice once again that we have the presence of a primordial Trinity, only this time it is not that of Vishnu, Brahma, and Shiva, nor even the Christian Father, Son, and Holy Spirit, or the Neoplatonic One, Intellect, and World Soul, but God, Space, and Kosmos. Note also that, with the exception of the term God, the other two enumerated entities are things, not persons.

But like the Vedic version of the metaphor, each of these three entities are distinguished by a dialectic of opposition based on three elemental functions, each of which in turn implies its own functional opposite:

As I have pointed out in previous books, each of these three entities—God, Space, and Kosmos—may thus be described as a set of functions or their opposites:

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In this version of the metaphor, it is space that becomes the common surface of the other two entities, since it comprises functional elements—as noted in the table above—of the other two entities. So, once again, we have our familiar three topological entities:

1)The “bracketed” region of nothing, or Ø1,, Hermes’ “Kosmos”;

2)The rest of the nothing, or Ø2, Hermes’ “God”; and,

3)The “surface” that the two regions share, or ∂Ø1.2, Hermes’ “Space.”

But this is not all there is to the Hermetic version of the metaphor.

In the Libellus II, there occurs a short, but very significant, exchange between Hermes and his disciple Asclepius:

Hermes: Now what was it that we said of that Space in which the universe is moved? We said, Asclepius, that it is incorporeal.

Asclepius: What then is that incorporeal thing?

Hermes: It is mind, entire and wholly self-encompassing, free from the erratic movement of things corporeal …74

In other words, in the Hermetic version of the metaphor, there is a direct interface between mind and space, or mind and the physical medium.