My wife likes to make fun of my spatial reasoning skills. She’s an intern architect and a master closet packer, able to maximize the use of space in any situation. In contrast, whenever I try to imagine any but the simplest, most static of three-dimensional spaces, my brain starts moving very, very slowly. I mostly navigate the world by thinking about space in either the plan or elevation view.
As a kid, I always failed those tests where you had to imagine rotating a solid object and then pick it out from a list of similar solids. I never solved my Rubik’s cube, despite wasting man-months of my life in the attempt.
My condition couldn’t have been helped by the amount of time I spent racing around in the two-dimensional Nintendo dungeons of my formative years.
I’ve grown comfortable with the 3D interfaces that have become standard console game fare in the last decade or so. But it was not an easy transition. I remember one nauseous dream that consisted of being trapped in a sped-up Super Mario 64 level. I gave up after less than an hour of playing The Legend of Zelda: Ocarina of Time, declaring that no 3D Zelda could ever be as good as 2D A Link to the Past (now that I think about it, I’m not sure that this prediction was actually wrong).
But why stop with straightforward three-dimensional gameplay? One of the great things about virtual worlds is the possibility of bending even our most basic physical rules. Super Paper Mario for the Wii, and more recently the indy game Fez, have experimented with gameplay where the same virtual space can be 3D one minute, 2D the next, as if your in-game persona were the sphere from Abbott’s Flatland. One of last year’s biggest sleeper hits, Portal, throws you into a world where you can create wormholes that flatten distances and bend gravity around corners. 4D Tetris, anyone?
I’m in no position to review these games, since I haven’t played any of them. If I did, I think I would have smoke coming out of my ears. But I’m interested to see if games like this catch on, and what advances in science and mathematics might come from a generation that grew up playing them.
There’s been quite a bit of evidence that video games can teach the brain new tricks. Will the kids of tomorrow be as comfortable working in Hilbert space as the rest of us are on a Cartesian graph? Quantum mechanics, cosmology, systems analysis, topology, and game theory, among countless others, are fields that could benefit from minds that are natively hyperdimensional.
Then again, all those hours with the Rubik’s cube didn’t teach me anything.
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8 comments:
i might have let you know that when i was little, i liked to remove the stickers on the rubic's cube and rearrange them.
also, ocarina of time is EXCELLENT.
i hear that twilight princess is also really really good.
what really messes with your head is super mario galaxy, where you have to go upside down in the game with your wiimote and still continue jumping.
I agree with Kristi - Ocarina of Time rocked.
However, I don't think anyone will be able to work more comfortably in multidimensional-space graphing from playing these video games (although they may be more inviting of the concepts). These video games by necessity must be visually oriented, and 5th and higher dimensional spaces fall outside of the realm of visualization.
Hilbert space isn't especially hard to work with as it is. It's just another set of vectors to add to the equation. However, it is terribly daunting for the visually-oriented because you can't get a normal-senses image of what the equations describe unless you can diagonalize everything (which is rare). Daunting, but not impossible - just requiring that you relax about being able to visualize the world around you.
@kristi -
Yeah, I knew you were doing that. But I had given up on the cube a long time before you ever got your hands on it.
Given the glowing reviews of Ocarina, I guess I‘m going to have to give it another try.
@david -
Philosophers often make the distinction between the imagination and the intellect. Descartes illustrates the difference by asking the reader to first imagine a triangle, then to imagine a chiliagon, which is a 1000-sided figure.
Although we can understand (intellectualize) what a chiliagon is just as surely as we can understand what a triangle is, we can only create (imagine) an accurate mental picture of the triangle.
While it is possible to intellectualize Hilbert space, it appears to be impossible to imagine it. That hampers the physicist from making intuitive insights by means of his spatial reasoning ability.
While I think it's fair to call this ability “visualization” by analogy, I think it would be a mistake to conclude that an inability to literally visualize more than three dimensions would necessarily prevent one from developing the mental machinery to be able to mentally “picture” more.
I admit, though, that this is all quite speculative on my part.
True - but how does that tie to the video game's ability to aid the growing mental machinery in intellectualizing multidimensional reality (besides opening the path for the concepts to be planted)? Watching the demo for Portal and Fez, it seems that they would more likely enhance spatial reasoning, making it more difficult to visualize higher dimensions.
Also, four dimensions are what we normally visualize. Think about a car traveling away from you, at an angle to your line of sight. You're seeing the normal three and time (which holds an equivalent vector rank to any of the space dimensions, according to Einstein).
I'm not sure that Hilbert space needs to be imagined. In the end, physics is still a science, and thus its theories still have to be 'proven' (as much as anything can be proven). That means there is some detection limit in the physical, relegated to our four-dimensional perceptions. Like infinity, Hilbert space can be intellectualized but not imagined, and in the end the actual values at infinity or the higher dimensional workings are really unimportant except for their effect on the close-to-origin space or on the normal four dimensions that we know and love.
@david:
I still think you've got some ambiguity between literal visualization, i.e. imagination based exclusively on the visual sense, and "visualization," which is used, by analogy with literal visualization, for all kinds of imagination. I'll use scare quotes to indicate the latter, and no quotes to indicate the former, for the rest of this thread.
For instance, while it has been true since Einstein that we "visualize" space-time as four-dimensional, it nonetheless remains true that we are capable of visualizing only three dimensions. There's a good chance that this is a hard-wired limit of our visual cortex.
Is it possible that the games I mention strengthen our ability to visualize at the expense of our ability to "visualize"? It's entirely possible, and I must admit it hadn't occurred to me. My idea was that, since games simulate actually moving through a space, not merely watching something move through a space, that it would tap into our motor sense, which is surely a component of our "visualization" of space. Again, just speculation.
I'm sure that Hilbert space doesn't need imagination for normal scientific work. But the ability to imagine such a space could bring about some outside-the-box observations.
there's a 4 row rubic's cube in the coffee shop. it baffles me.
Somebody posted some studies on this question to Reddit: http://www.reddit.com/r/science/comments/bijjs/scientific_studies_sugests_that_we_can_think/
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