u/Lancelot3777

So I just watched this Terence Tao clip about high dimensional geometry and it made me think of the Culture Minds again.

https://youtu.be/GHwflk-l008?si=15rEqdzd2i2-YO8S

Basically Tao was saying that once you get into really high dimensions, shapes stop working the way our brains expect. Like a circle inside a square takes up a lot of the square, and a sphere inside a cube still takes up a decent amount. But if you do the same thing in like 100 or 1000 dimensions, the “ball” takes up basically none of the “cube”.

Which is insane and very unintuitive.

And the reason this matters now is that LLMs kind of live in higher dimensional spaces. Words and concepts get represented as vectors with hundreds or thousands of dimensions. So “meaning” is not stored like a normal file or sentence, it’s more like relationships in this giant weird mathematical space.

Anyway, that made me think about Banks describing Culture Minds as working largely in hyperspace. Not just “big fast computers”, but intelligences whose actual processing/storage is happening in spaces humans can’t really visualize.

Obviously Banks didn’t literally predict ChatGPT or transformers or whatever. AI existed as an idea way before that.

But I do think he got something really important right, which is that a true machine superintelligence probably wouldn’t just be a human brain but faster. It would think and store information in ways that don’t map cleanly onto normal human 3D intuition.

Modern AI is maybe like the baby version of that higher dimensional vector spaces for language and meaning.

Culture Minds are the insane sci-fi version godlike AIs using hyperspace and alien geometry as part of how they exist. Idk, maybe this is obvious to everyone else, but it made the Minds feel even cooler more plausible to me.

NOTE: I probably blurred two meanings of “dimension” here physical hyperspace in Banks vs mathematical vector dimensions in machine learning. Those are not the same thing. But the connection that still interests me is that both push against the same naive intuition intelligence doesn’t have to be organized in ways that feel spatially or cognitively natural to humans.