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I was watching an 18 month old walk around yesterday. Since I’ve been obsessed with pathfinding lately, I couldn’t help but be amazed at how, with no apparent effort, a toddler could navigate through a room full of furniture, getting where he wanted to go, generally along the shortest path.

And so I started thinking – how DO we actually perform a complex task such as finding the shortest path? At first glance, there is no answer really, “we just see it, it’s obvious.” But of course, something very complex IS happening, in the unconscious nether regions of the brain.

I think the first step in approaching the problem is to remove the visual sense, as it’s a distraction. The eyes bring information from any given scene in, but the visual sense doesn’t actually have anything to do with the actual pathfinding computation. Once the “scene” is in the brain, it exists as some sort of model, described by the brain’s fundamental language, and completely hidden from our conscious mind.

Another way to think about it is that the visual representation is simply a manifestation of the model that is in the brain. You can close your eyes and visualize the scene, and find the shortest path in your “mind’s eye,” but the work isn’t being done in the “mind’s eye,” it’s simply one view of the data residing elsewhere in the brain.

For me, getting rid of the visual sense makes things much easier to work with, because understanding what the sensation of vision actually is, and how it relates to our self-awareness, is kind of an intractable task. But now it’s out of the way!

So we’re left with trying to understand the technical details of how our biological computers solve the shortest path problem, which is far more approachable.

The next problem is – how is the model represented, fundamentally, in the brain? The brain obviously has it’s own, innate language. It has nothing to do with spoken language – a person who was raised in complete isolation (therefore had no concept of language) will still find the shortest path!

Of course, once you figure out the language of the brain, you now have to find out the rules by which it manipulates the data. If the language was binary, then the manipulation would be the logic gates, based on transistors (neurons).

But, as far as I know, we have no idea what the innate language of the brain is, or the rule-set by which it processes data. I imagine it is similar to trying to visualize the 4th dimension. I don’t remember which greek philospher/scientist it was, but he thought he’d proved the fourth dimension can’t exist, because all dimensions much be mutually perpendicular to each other. So he thought, if you take a stick, and lay it across another stick so that they form a cross, you have two dimensions. If you take a third stick and hold it perpendicular to the first two sticks, you have a representation of three dimensions. His proof that no more dimensions could exist was simply that you can’t add another stick that is mutually perpendicular to the first three.

What the fellow didn’t understand, however, was that our brains, never having encountered a fourth dimension, simply can’t comprehend it. It is like someone blind from birth trying to imagine what “red” looks like. That person can’t even begin to imagine it, because his brain has no concept of color, having never experienced it. Our physical world that we live in is 3-dimensioned, and so that is all our brain can comprehend. The fact is, in reality, there can be an arbitrary number of sticks, all perpendicular to each other. Don’t go trying that, of course. : )  For whatever reason, the physical state of the universe restricts our experience to 3 dimensions.

My point in going into that tangent was – I suspect that the language and processing of the brain might be genuinely beyond comprehension.

But that doesn’t mean it’s not solvable! Mathematically, working with 4 dimensions is only slightly harder than working with 3 (mainly because the equations get much longer). Just because we can’t comprehend the fourth dimension doesn’t mean we can’t work with it. Similarily, just because we might not ever comprehend how the brain works, we can still understand it, and work with it.

And figure out how it solves problems like finding the shortest path.

But who knows, maybe I’m wrong. Heck, maybe the brain works in binary. I kind of doubt it though - I imagine the brain does not even have a discrete alphabet forming it’s language, but rather a fuzzy, statistical alphabet. Maybe the answer will be found in quantum mechanics.

The last  observation has to do with artificial intelligence. So far, we haven’t been able to work with the 4th dimension (although it has been indirectly observed, as massive objects like the sun affect it by gravity). Indeed, it seems to be beyond the realm of our physical capacity (not capability, capacity) to work with it. In the same way, maybe it’s beyond our physical capacity to reproduce what the brain is doing.

That’s a hard chunk to swallow, but – we’ve observed the effects of gravity upon light via the 4th dimension, just as we’ve observed the effects of the brain’s operations.

So it maybe creating AI IS an intractable problem. That is – it’s not that the solution is difficult; it’s simply not possible.

Of course, again, maybe it all is just the biological equivalent to binary and transistors, in which case AI is inevitable (if humans are around long enough to figure it out).

In that case, maybe, when I find my way through an obstacle course along the shortest path, my brain actually applies a grid to the scene, and runs A* on it. : D