While I was reviewing those year-old Parmenides commentary notes over lunch to post on KALLISTI, something in one of them about points reminded me of something that I have just read in the Timaeus commentary, so I’m sharing them in juxtaposition!
For the point is said to be in the line, obviously as being in something else; for the point is one thing, and the line is another, and yet just because it is in something else it is not for this reason contained on all sides by the line, nor does it touch the line at many of its parts. One may reply to this difficulty by saying that even if the line does not contain the point spatially, yet it contains it in some other way; for it contains its characteristics; for the point is merely a limit, whereas the line is both a limit and something else besides that, being a length without breadth. Again, the point has no extension, whereas the line is both without extension and in another direction is extended. And in general, since the point is not the same thing as the One, it is necessary that the point should be multiple, not as having spatially distinct parts, for in this respect it is partless, but as having a number of characteristics which go to make it up, and in this way having the equivalent of parts, and since the line comprehends these, it may be said to touch the point in many places. That the point and the One are not the same is plain; for the latter is the first principle of all things, whereas the former is first principle only of magnitudes; but the point is not on the one hand prior to the One; for the monad is one, and so is also the partless unit of time. The remaining possibility, then, is that the point is subsequent to the One, and partakes of the One, so that it is also not One, but if this is the case, then there is nothing preventing it from having a number of incorporeal characteristics which are present in the line, and for it to be contained by this. One can, then, answer the difficulty in this way, but that does not get us nearer to a view of how Plato took the sense of being in something, and what class of beings he is looking to when he denies this characteristic of the One.
Better then, following the lead of my own father (sc. Syrianus), to proceed along that most sensible and safest course, and say that he is denying of the One here just what is asserted of the One Being in the Second Hypothesis and he is denying it in the same way as it is asserted there, and indeed one should view the meaning of being “in another” as being the same as that which the philosopher clearly understands it to be in that place.
Proclus’ Parmenides commentary, 1141ff
At the time, I was trying to visualize what the Parmenides was discussing, and it was very intimidating — it took me a while to actually get enough that I felt like I wasn’t flailing in pitch lightlessness and bumping into intelligibles all along the way — so I remember (and wrote in the margins) some probing questions about whether it would be OK to model the One as a point given the lack of dimensionality (except points do tend to line up, don’t they?), and I ultimately rejected that as a, “Yikes, Kaye, just read the translation,” moment.
However, something that Proclus wrote in the Timaeus commentary about points and the One is really interesting when considering both at the same time because it is a different way to think about these dimensional things.
The extensionless point is prior to the line, and surely in the same way the intellect precedes the soul, having included it in a manner that is undivided and antecedently comprehended it indivisibly. For while what is partless is appropriate to intellect, the soul is that which is primarily divisible. But the point and the straight line are exactly things of this sort. So he (the Demiurge) properly distinguished them, and the account connects the straight line, and subsequent to this the circle — both of which we say are simple lines — to the soul, while the point connected to intellect. But the point, on the other hand, is dedicated to intellect. It is due to this fact that the account of the soul is revealed like something from within the forbidden, innermost sanctuary; displaying the partless [character] of intellect and announcing its secret and ineffable unification. But intellect itself is founded in itself in a stable manner (monimôs), cognising all things in a manner that is peaceful and quiet, it has the status of a point or centre in relation to the soul. If the soul is a circle, with intellect as its centre, then the soul is the power of the circle. But if the soul is like a straight line, then intellect will be the point; including what is extended in a mode that is unextended, what is divisible in a mode that is indivisible, and the circular form in the manner of the centre. Intellect in turn has the status of the circle in relation to the nature of the Good around which it converges as a whole at every point by dint of its yearning for the One and its contact with the One.
Proclus’ Timaeus commentary, 243.1-16
I really like the last sentence of this, but also, the reference to the forbidden, innermost sanctuary reminds me of Plotinus and the way he discusses ineffable union.
Anyway, I thought that was interesting!
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(As a tangent to my tangent, after reading things like this in Proclus, I find it slightly amusing that New Age ascendancy involves higher-dimensional consciousness because that is the exact opposite of what it seems like one would want? I’m thinking of the relationship between 10, 100, and 1000 as discussed in the Myth of Er commentary essay and the links between those numbers and Zeus, Poseidon, and Plouton, plus some other things. This is probably only funny because I was thinking earlier today about the differences between New Age Occult ascended masters and the bracketed set [heroes + daimones + pure souls + teachers] because I have a disdain for the ascended masters stuff — I associate it with 2012 conspiracy theories and wishy-washiness — yet love the bracket and consider it fairly grounded, and I occasionally do mental walkthrough checks with myself about things like this.)
KALLISTI 
Such passages are very nice for demonstrating how we can use analogies, like that between the principle of individuation and the point, to help us grasp difficult aspects of the former, as long as we don’t think that there aren’t important differences. Understanding that a geometrical point isn’t to be confused with the dot we might use to represent it, because the former is strictly defined by its intelligible function, which requires it to be dimensionless, helps us to understand the negativity required by the principle of individuation in order to perform its function, though we necessarily say all sorts of things about “it”. And the way in which we posit the point based on the complex figures we can actually encounter, through multiple stages of idealization, helps us to understand how we ascend to the first principle through similar intermediary steps.
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