Can someone out there make a website called "Via" who we can join forces with?
Is Fortuna Minor—the figure of assistance—unsatisfactory? It seems rather on-point to me!
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.
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.
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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.