James speculates that a Hilbert Table might be just the thing for a banquet in heaven. I knew it must have something to do with David Hilbert the eminent turn-of-the-century mathematician, but had to look it up.
"...as many dimensions as guests, everybody sitting next to Jesus and kitty-corner with every other guest."
6 comments:
But can you have three-or-four way conversations also? Because multidimensions can be understandable without being picturable, I fall apart quickly.
In Neoplatonic metaphysics, the Noetic realm (which is often by Christian Neoplatonists said to be something like 'the mind of God') is unextended, so all things are together and interpenetrating; there is no need of movement* because everything and everyone is already gathered all together in a single place, i.e., God's mind.
* Indeed, properly there is said to be no possibility of movement because everything is fully actual. Movement requires potential, such as the potential to be here or there or the potential to become something else. Things that already are fully what they are, like God and his ideas, lack potential because they are fully realized.
3 or 4-way is just as easy, since everybody is kitty-corner from them too.
My guess is that James is alluding to the Hilbert Hotel, which Hilbert made up to illustrate the properties of infinite sets. The hotel has an infinite number of rooms. Even if all of them are already full, it can still accommodate any number of additional guests, say N, by having every current guest move to the room of their current number + N. It can even accommodate an infinite number of new guests by having everyone move to a room with double the current room number. Cf. the "great crowd that no man was able to number" in Revelation.
Room service would get confused a lot.
I was thinking of a Hilbert space, with arbitrary (even infinite) number of dimensions but with finite distances. Just being silly...
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