ruby sparks
Contributor
Cool, up to speed on that, Abbot, Rucker and so on.
But that assumes, quite incorrectly, that I only have a posteriori resources to play with. That's never true. I always have a priori tools as well and I can imagine and work with as many dimensions as I like in that universe as in this, by, for example defining a logical space with position described indexically, or any other geometrical tool of pure maths I fancy bringing to bear.
This is what the possible existence of higher dimensions means.
I'm not sure it is.
From our 3-D perspective we know a 2-D being wouldn't have an answer, even though there is one: we can look around and see the 3-D matter all those 2-D slices are made from. So we reason by analogy, and recognize that there might be a 4-D world full of 4-D matter that 3-D slices could be made from. The fact that we can't see any or even visualize it with our evolved-for-3-D brains isn't a good reason to conclude it doesn't exist.
But now you are being inconsistent - on the one hand you are assuming we'd lack the a priori tools to think about x dimensions and on the other hand you are assuming we have them to reason about by analogy - sure, but we have far sharper tools than that. As it happens, I suggest you read Rucker's blatantly named The Fourth Dimension and How to Get There. It's a bit of a kerfuffle, but I can assure you that we can visualise four dimensions.
With that preamble, consider the following scenario. You have a mass of lava that flowed into a volcano that didn't quite erupt. As the lava cools, it starts to freeze. Freezing is localized -- the whole mass doesn't suddenly change from liquid to solid all at once. Crystals form and then they grow. If you've looked closely at a crystal you've probably seen flaws in the crystal structure, little lines where the molecules don't all line up. Flaws are visible because they're much bigger than rock molecules, because the molecules don't freeze onto a growing crystal at random. Rather, where they fasten depends on what's already there on the crystal's surface that they can fasten onto. So an initial random irregularity at one point on the surface can propagate to layer after layer. Flaws grow along with the crystal, in directions that depend on their initial conditions. Two adjacent flaws can grow in different directions, and may bump into one another as more layers of molecules are added. If you could somehow get into the liquid rock and watch the crystal growing, you'd see a solid surface with little defects on it. And as the crystal grows, the defects would move, not just toward you as the crystal grows, but relative to one another. Study them long enough and you could work out a whole physics of within-surface defect movement.
Sure, look at the simulated annealing in spinglasses model used as the learning algorithm in Boltzmann machines. It already exists, but...
And if the rules were complicated enough, maybe organisms made of moving crystal surface defects could evolve.
Ok, but you are setting up an immensely complex and baroque experiment to get across a simple idea - 2d is a slice of 3d and things that appear unconnected can be connected.
Presto: from their point of view, 2-D beings in a 2-D world, asking themselves how there could possibly be a third dimension, a dimension of time.
Cool. I get it.
Now here's the problem. If we lived in a world like that, then we'd be constantly struck by the consequences of that connection. For example, action at a distance woudl be commonplace - imagine a 3d tree growing through a 2d slice - pull one branch along a 2d plane and other branches would move mysteriously. I could carry on, but once I point out this issue, I assume as many problem cases as you wish will become clear. You know, variable inertia depending on how much stuff we can't see the thing is connected to and so on. If this model was right then physics as we understand it simply wouldn't work. Induction would fail and the world would be much older than it is.
Then of course there's the fact that time isn't a dimension in the same way as a tesseract inhabits the fourth dimension - the traditional model is something like 'at ninety degrees' time isn't like that at all.
Spatial metaphors for time are just a bad idea.
Yes, I was thinking about this. Sort of. If we imagine beings who live in a 2-D world, they couldn't imagine a 3-D one. Got it. But, if they only experienced 2-D but were in a 3-D world, that would be different, because weird stuff would happen in their 'little world' constantly, to the point that it would be unpredicatble and irregular (to them). A bird might poop on their little flat heads for starters. It'd be 'fuck where did that come from?'