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Several eternities ago, when I was in Sunday School—I must have been nine or ten—the church elder instructing us mentioned that the doctrine of the Trinity was not to be found in the Bible. I raised my hand and, when called upon, asked him, "By what authority do you teach something that doesn't come from the Bible? Also, if the Trinity doesn't come from the Bible, where does it come from?"
Of course, he told me to shut up.
Since then, I've always wondered where the doctrine came from, since it always seemed bizarre to me. I still don't have the "where," but at least Plotinus is good enough to tell us "why" with his usual logical rigor.
1. There is an Intellect.
2. Intellection implies duality (of subject and object).
3. Unity precedes multiplicity.
4. Therefore, there is something unitary prior to Intellect, something primarily Intellective (e.g. the subjective Intellect), and something secondarily Intellective (e.g. the objective Intellect; e.g. the Soul).
5. Being prior to Intellect, the First is not intellective.
6. If we consider the First to be Good, the Second is only Good to the degree it is intellective of the First, and the Third is only Good to the degree it is intellective of the Second, and so on.
Point 6, above, is of course why Plotinus considers matter to be evil: something can only be good in participating with that which is above it. Don't look down!
Plotinus gives us a very elegant analogy in §4: the One is light, the Intellect is the sun (something giving off light), and Soul is the moon (something reflecting light).
Incidentally, most modern commentators describe Plotinus as advocating a trinitarian view; I don't believe this is so! While he only proves the top three here, both he and Porphyry frequently refer to the four highest beings: the One, the Intellect, Soul, and Nature. (Unless I am much mistaken, Plotinus likens these to the Hesiodic Ouranos, Kronos, Aphrodite Ourania, and Eros, respectively.) What's more, it's hard not to see the Pythagorean one-two-three-four and the Empedoclean fire-air-water-earth in these. (One might think this sequence can continue indefinitely, but Plotinus explicitly says it does not: beyond this, the creative power is spent and too weak to continue further; all that remains is to play with every possible combination of principles within these.)
While playing around with these notions, I found a neat geometric correspondence. If one wishes to produce a tetractys with circles alone, it takes six circles, to wit:
Note how we are given two points to begin the construction with. We might as well assign these to the dyadic Intellect, right?—since where else would we assign them? But this is kinda like how Plotinus proves the whole structure also beginning with the Intellect.
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Date: 2023-03-13 06:34 pm (UTC)Regardless of the ultimate truth of the origins of Geomancy, I find it quite amazing that-- as long as one looks at one hemisphere at a time, at least-- a Geomancy chart doesn't just resemble a tetractys. Mathematically speaking, each half IS a tetractys, with the Witnesses each being a top point. It's just that the three figures per tetractys which are not traditionally included in a geomancy chart are the ones mathematically superfluous to the end calculation of the tetractyses' point. *IF* that's the origin of Geomancy, it's quite reasonable that they would get cut out for the sake of simplification.
At the very least, it's a rock-solid answer to the Geomancy beginner's question of "Why don't you add Mothers 2 & 3 also?" But it might mean much more than that.
(I must admit I'm still sore at JMG's response. He'd gotten several Magic Monday questions over the years asking if there was any relationship between the tetractys and Geomancy. I actually demonstrated an actual mathematical equivalence... and he said all I did was insert a whole bunch of extra figures.)
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Date: 2023-03-13 07:03 pm (UTC)Precisely! :) If I wasn't used to synchronicity being so damned creepy by now, I'd be creeped out!
Eh, don't be! On the one hand, he's a very by-the-book, Saturnine personality—always talking about preserving and conserving and following the tradition exactly as written—and you're throwing a Lætitia-ish flight of fancy at him. On the other, the whole point of a meditation isn't that it's objectively true, but that it's subjectively valuable! If nothing else, you've learned something that programmers need years to grasp—how to simplify boolean formulae in Algebraic normal form—and who knows how that'll come in handy down the line?
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Date: 2023-03-14 05:53 am (UTC)So if you are "Amissio" and I am "Conjunctio", then I guess the nature of our relationship is... Fortuna Minor??? Can someone out there make a website called "Via" who we can join forces with? Or a "Caput"? Or even "Rubeus"?
With your geometric presentation of the Tetractys, I notice that even if one is inclined to add a seventh and eighth circle for symmetry's sake, one would only end up with a single point more at the very bottom. In line with Plotinus, this development is hardly generative, perhaps it could even be seen as degenerative. The Subnatural Realm?
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Date: 2023-03-14 04:27 pm (UTC)Is Fortuna Minor—the figure of assistance—unsatisfactory? It seems rather on-point to me!
This is, in fact, true of almost every construction (and, indeed, almost every mathematical or logical proof): the elegance of a construction, I think, is a measure of how much you get divided by how much it takes to get there and how much superfluous matter you are left with. For example, in the case of the construction you mention would be more elegant by first removing the large circle, since the it is wholly redundant (add no new intersection points to the construction). As another example, the construction I made above has a couple wasted points... but there's actually no way to construct just the ones we want without some waste, and so the tradeoff I made was to use as few circles as possible.
To compare to philosophy, consider Plotinus who manages a remarkably sophisticated and useful metaphysics out of very, very little—a few core concepts and a few simple proofs. The elegance of it is, in fact, why it's so difficult: every piece fits so perfectly into all the other pieces, you mostly have to "get it" all-at-once, rather than being able to start with a base and add to it piecemeal.
This is the exact opposite approach taken by, for example, Euclid: he almost never uses the simplest or most elegant way to prove something, and the reason for it is that he's not trying to build a system—he's trying to teach! So he introduces concepts one-at-a-time in order to make it easier to follow in the long run.
I might say that Plotinus' way is more Intellectual and Euclid's way is more Psychic (that is, "of the Soul"). Euclid is easier to learn (because it has a linear ordering) but is less beautiful (because it's complicated), while Plotinus' is harder to learn (because it's nonlinear and diffuse) but is more beautiful (because it's simple).
This is part of why I'm curious to tackle Proclus—at first glance, the Elements of Theology seems to be attempting to Euclid-ize Plotinus. That is either extremely misguided (e.g. Proclus is unaware of the tradeoff he's making) or an attempt to make Plotinus more accessible (e.g. Proclus recognizes the tradeoffs he's making and accepts those limitations). I'm very interested to try and get a sense of which it is.
But that's all to say that yes, it's something akin to the subnatural realm you reference. To Plotinus, the more complicated something is, the less it participates in the One (which is absolutely simple), and thus the less Good it is. The Neoplatonists wouldn't go so far as Steiner as to say it's evil: they're pretty firm on positive evil not existing.