AUTHOR’S NOTE: I’ve covered this topic in bits-and-pieces over a number of previous essays, but I want to take a more integrated look at it. I was inspired by Benebell Wen’s observation in Holistic Tarot that the 2 of Swords “conceptualizes” the latent promise of the Ace of Swords by clothing it in the language of form. (As a scholarly study, the following analysis becomes rather academic after venturing into analogy, so bear with me if you have an interest in the numerical architecture of the tarot.)

Here I’m emulating a product-development cycle, in which a Design Engineer gets a bright idea (usually nudged by Marketing); the Production Engineering team determines whether it can be effectively (and profitably) turned into a marketable product (i.e. “conceptualizes” the visionary impulse of the Design Engineer); the Manufacturing organization kicks into gear by aligning various type of logistics (materials, manpower, infrastructure, etc) and mobilizes to begin manufacturing, after which the Production line begins cranking out the item.

My perception of the first four numbers has always adhered to Pythagorean principles. The One represents a hypothetical “point-in-space” that exhibits no mass or motion, it is pure potential or “Idea” that is awaiting activation. As I understand this formative condition, it does not signify the first step taken in an initiative, but rather the as-yet-unrealized intention to launch an effort that originates with the Ace of the tarot. Contrary to popular opinion it does not describe an action underway, but at that juncture only a mission that is being contemplated. The incentive to act is present but the “trigger has not been pulled” on its execution.

The Two symbolizes the Line, which moves away from the Point in a specific direction but faces an indeterminate distance to the target. Here the urge to act gets its feet on the ground with a destination in mind but no itinerary to get it there. We can set this goal purposely by “conceptualizing” the terminus, after which the reaction of the Two as it comes up against (and is constrained by) the newly-established end-point can resemble a pendulum swinging between two poles as the energy bleeds off, suggesting reciprocal or compensatory action that finds its expression in the duality of intent and the polarity of choices that are often presented by the tarot “Twos,” which can signify being “of two minds” in the matter at hand.

But this pattern represents a “closed loop” that is defined and limited by its initial trajectory and velocity; it can only progress at a fixed rate of speed in a linear fashion along its prescribed course, forever bound to repeat itself. I liken it to a “perpetual motion” desktop toy that will eventually come to a stop when the momentum of the colliding balls can no longer overcome their inertia. Another analogy is a mechanical clock that slowly winds down, producing what I’ve called the “Tick-Tock Effect” in the gradual decline of the interactive engagement symbolized by the Two after the thrill of discovery wears off. (A perfect example of this is a deteriorating romantic relationship after boredom sets in.)

In order to advance the potential of the Ace in a new direction, we must envision a third point that is offset from the linear pathway and connect it by a pair of lines to the opposite terminals to create the three-sided Plane, which expands the field of operation for the binary energy of the Two by providing a surface for it to occupy. This development gave rise to the tarot principle that all of the Threes represent growth, expansion and opportunity.

Finally, a fourth point is added outside the perimeter of the triangular Plane and joined by lines to two of the three previous points, generating a four-sided polygon that becomes the Square when the lengths of the four sides are equalized. When this stable figure is achieved, the initial thrust of the Two is exhausted. The Square is the geometric precursor of the solid Cube that is obtained by projecting the area of the regular polygon into three-dimensional space. In tarot terms, the Fours are considered to exhibit a state of admirable stability as well as the seeds of eventual stagnation. They represent arrested development or arrival at a “plateau” that can only be escaped via the seismic disruption of the Fives.

This numerical progression was the philosophical foundation for early assumptions about concrete reality until modern science changed the game. After the Four, the theories of esoteric number theory become more abstract and spiritual, and at that point I segue into the Qabalistic principles of numeration expressed by the Tree of Life and the premise of the “Descent of Spirit into Matter.” But that is an entire subject unto itself.