Macrobius on the Geomantic Figures

The demarcation between earth and water is called Necessity by natural philosophers because it is believed to bind and solidify the clay of which bodies are made. Hence when Menelaus, in Homer's Iliad, was invoking evil upon the Greeks, he said, "May all of you be resolved into earth and water," referring to the muddy substance of which human bodies were first made. The demarcation between water and air is called Harmony, that is, a compatible and harmonious union: for this is the interval which unites the lower with the upper, reconciling incongruent factors. The demarcation between air and fire is called Obedience; for whereas the muddy and heavy bodies are joined to the things above by Necessity, the things above associate with what is muddy by Obedience, with Harmony in the middle promoting a union of both.

(Macrobius, Commentary on the Dream of Scipio VI)

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I find it fascinating how well these names and descriptions—Necessity, Harmony, Obedience—correspond to the natures of the geomantic figures, Fortuna Major, Conjunctio, and Fortuna Minor. Given that Macrobius was one of the main philosophical texts available in the middle ages, one wonders whether it exhibited some manner of direct or indirect influence on the development of geomancy.

The Computability of Plotinus' Metaphysics

Quite some time ago, I was speculating on the computability thesis and how it relates to Plotinus' metaphysics. I think Enneads VI 6 really solidified everything in my mind, but while I was discussing this all with a friend yesterday, it occurred to me that I never wrote up where my thoughts ended up. I figure I'll briefly remedy that.

There are many models of computation—that is, "how can one define an algorithm?"—but it turns out that we've proven all of them that we can actually make equivalent to a particularly famous one called a Turing machine. (You can think of it as a simple kind of computer that can do one thing at a time.) The fact that they're all equivalent led several famous mathematicians to propose that something is computable if and only if it can be computed by a Turing machine (or one of these other, equivalent, systems).

I note that doing one-thing-at-a-time is characteristic of souls, and Plotinus says that this is why time exists in the sensible world (e.g. because it is generated by one-thing-at-a-time souls). Consequently, let us assume that the computability thesis is true for the sensible world.

The next level above souls, Mind, differs from them in that it doesn't operate sequentially: rather, it operates comprehensively, in an everything-at-once manner. The obvious variation on such a Turing machine is that, instead of doing operations one-at-a-time, it does all-operations-at-once. (The reason we can't build such a machine is that the number of operations may become infinite, and one cannot get to the end of an infinite sequence of steps in a finite amount of time. However, we're saying here that the Mind can because time doesn't exist.) Such hypercomputers have been discussed by mathematicians, and unless I misunderstand the literature, this one is effectively equivalent to what's called an Oracle machine (which is just a machine you can instantly get the "right" answer to whatever problem you want). Therefore, I think the psychic world is hypercomputable in the sense of Oracle machines. (I therefore half-joke that heaven, for a computer programmer, is to finally get to solve all those pesky NP-complete problems that have been bugging us for generations.)

The next world up is the mental world, where the Mind itself exists. Plotinus already answered this one for us, since the Mind is the definition of truth. That is, this is simply the world in which computation itself is defined. That is, it is the world in which all questions, all answers to those questions, and all means of finding those answers, are all defined. Therefore it is above computation of all kinds.

Finally, of course, in the highest world, the One itself, computation isn't its own thing because what would you distinguish it from? Everything in the One is just the One.