This post started out as a riff on the postulate “horror vacui” attributed to Aristotle and later restated by Francois Rabelais as “Nature abhors a vacuum,” and was going to be a cautionary tale about filling blog space with miscellaneous “stuff” when nothing new presents itself to the blogger’s scrutiny (in this case, me and my resolve to write something original every day, no matter how brief). But in reading an excerpt from Aristotle’s Physics, Book IV, Section 8, in which he argues against the hypothetical existence of a vacuum in nature, I came across the statement “a line does not exceed a point unless it is composed of points!” This got me thinking about the nature of the Point and the Line in esoteric number theory, and then about the similarities between the Fool and the Aces, something I’ve long held to be self-evident but never captured in writing.
Both represent a point of origin without imparting any sense of purposeful motion or direction (the Fool is inherently aimless and the Aces suggest an unstructured infusion of elemental energy), in essence the abstract Point, which has neither mass nor movement and suggests the idea underlying any action rather than the actual first step in taking it. They have typically been interpreted as “the beginning” of something, but I think that definition is a little too inclusive. I would describe them more as the immanent “source” or “inspiration” and not the physical “execution” of an initiative, the urge to act but not the consummation, the itch that needs to be scratched. When I see them in a reading, I’m convinced that the querent realizes, perhaps only vaguely, that something must be done but has yet to “pull the trigger” on it. The reading then focuses on flushing that impression out into the open and examining it.
The Fool has been characterized as capable of appearing as a catalyst anywhere in the series of trump cards, not just at the beginning or end, and the Aces supply the impulse that motivates each of the following numbers, from Two to Ten, although its influence wanes as inertia increases. Aleister Crowley made a valiant but rather abstruse stab at illuminating this concept of the gradual elaboration of the original “root power” in his “Naples Arrangement” from The Book of Thoth (although he discussed its attenuation elsewhere in the book).
“Thus appears The Point, which has ‘neither parts nor magnitude, but only position’.
But position does not mean anything at all unless there is something else, some other position with which it can be compared. One has to describe it. The only way to do this is to have another Point, and that means that one must invent the number Two, making possible The Line.
But this Line does not really mean very much, because there is yet no measure of length. The limit of knowledge at this stage is that there are two things, in order to be able to talk about them at all. But one cannot say that they are near each other, or that they are far apart; one can only say that they are distant. In order to discriminate between them at all, there must be a third thing. We must have another point. One must invent The Surface; one must invent The Triangle. In doing this, incidentally, appears the whole of Plane Geometry. One can now say, ‘A is nearer to B than A is to C’.
But, so far, there is no substance in any of these ideas. In fact there are no ideas at all) except the idea of Distance and perhaps the idea of Between-ness, and of Angular Measurement; so that plane Geometry, which now exists in theory, is after all completely inchoate and incoherent.. There has been no approach at all to the conception of a really existing thing. No more has been done than to make definitions, all in a purely ideal and imaginary world.
Now then comes The Abyss. One cannot go any further into the ideal. The next step must be the Actual—at least, an approach to the Actual. There are three points, but there is no idea of where any one of them is. A fourth point is essential, and this formulates the idea of matter.
The Point, the Line, the Plane. The fourth point, unless it should happen to lie in the plane, gives The Solid. If one wants to know the position of any point, one must define it by the use of three co-ordinate axes. It is so many feet from the North wall, and so many feet from the East wall, and so many feet from the floor.
Thus there has been developed from Nothingness a Something which can be said to exist. One has arrived at the idea of Matter. But this existence is exceedingly tenuous, for the only property of any given point is its position in relation to certain other points; no change is possible; nothing can happen. One is therefore compelled, in the analysis of known Reality, to postulate a fifth positive idea, which is that of Motion.
This implies the idea of Time, for only through Motion, and in Time, can any event happen. Without this change and sequence, nothing can be the object of sense. (It is to be noticed that this No.5 is the number of the letter He’ in the Hebrew alphabet. This is the letter traditionally consecrated to the Great Mother. It is the womb in which the Great Father, who is represented by the letter Yod which is pictorially the representation of an ultimate Point, moves and begets active existence).
There is now possible a concrete idea of the Point; and, at last it is a point which can be self-conscious, because it can have a Past, Present and Future. It is able to define itself in terms of the previous ideas. Here is the number Six, the centre of the system: self-conscious, capable of experience.
At this stage it is convenient to turn away for a moment from the strictly Qabalistic symbolism. The doctrine of the next three numbers (to some minds at least) is not very clearly expressed. One must look to the Vedanta system for a more lucid interpretation of the numbers 7, 8 and 9 although they correspond very closely with the Qabalistic ideas. In the Hindu analysis of existence the Rishis (sages) postulate three qualities: Sat, the Essence of Being itself; Chit, Thought, or Intellection; and Ananda (usually translated Bliss), the pleasure experienced by Being in the course of events. This ecstasy is evidently the exciting cause of the mobility of existence. It explains the assumption of imperfection on the part of Perfection. The Absolute would be Nothing, would remain in the condition of Nothingness; therefore, in order to be conscious of its possibilities and to enjoy them, it must explore these possibilities.“
Regarding his efforts to formulate a “sound ontology,” Crowley did say in Magick Without Tears that “the ‘Naples Arrangement’ in The Book of Thoth dodges it with really diabolical ingenuity.” So in my transparently devious Crowleyan attempt at deflecting responsibility, I will leave you here with a couple of quotes from that book: “It is very important as a mental exercise to work out for oneself these correspondences” and “It is for the student to build these living stones into his living Temple.” In other words, you’re on your own.