Multi-dimensional complexity

It’s been said — of course I can’t remember by whom — that if humans could only see in multiple dimensions, much of the complexity of data analysis and machine learning would be solved.

I was thinking about some of this on my way back from work, and about how we deal with representing multiple dimensions. One of my favorite representations is from Iain M. Banks, talking about a ship moving through hyperspace. He describes an inner space between three dimensional reality and a sea of pure energy, with huge waterspouts — black holes, draining back matter into wherever it came from.

We haven’t even begun to talk about how we would access another dimension, so it sounds a little premature to discuss how we would handle it. Physiological effects aside, would we even be able to comprehend the new reality?

The City and the City by China Mieville manages to convey a sense of this. If I remember correctly, the “Immer” is the in-between space which needs to be traversed to get across most of the known universe in a reasonable time. But the traversal requires a certain kind of brain to comprehend it  — a kind of “sideways thinking”. One has to be selected, then trained.

But if we’re unable to run multi-dimensional computations through our brains, how is it that our brains can learn, comprehend and remember incredibly generic patterns?

Because the way that neural models work is about as generic as it gets. They’re a black box of finely-tuned weights. It doesn’t mean that they’re entirely analogous to the human brain, but they are multi-purpose. And our brains are technically just multi-purpose learning machines.

So how do our brains learn?

I’m not sure where or how I read about this, but I vaguely remember a suggestion about our brains performing computations in another dimension. It all sounds very X-Files-ish (do not, I beg you, spoil anything for me) but we manage to do a substantial amount of things with our brains. Quora and Scientific American give you some idea, and anything in the petaflops is absurdly fast, but how are we doing it?


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