7 ms·

This looks fantastic. If I had a VR device I would get this immediately. I've always had a fascination with trying to grok higher dimensions. I think it's just

This looks fantastic. If I had a VR device I would get this immediately. I've always had a fascination with trying to grok higher dimensions. I think it's just about impossible to have an intuitive understanding of it - 3D spacial reasoning is in our wiring through both nature and experience. You know the theory of how language shapes your thinking? For example, in societies where there is no separate word for orange and red, they have extreme trouble telling the difference between them. In some native tribe where they use cardinal directions (North, South) - not relative (Left, Right) - they have an almost supernatural ability to know which direction they are without needing any other cues (sunlight, stars). Point being - would being able to completely think in four dimensions have an impact on how you understand the world?

malnourish 9y ago
I thought the majority of sapir-whorf thought had been disproven and at best only a mild amount had support? At least, that's what I remember learning in my linguistics courses in college. I'm willing to be wrong.
- throwaway91111 9y ago
  You have to look at how it was initially positioned. Linguistic determinism as a general purpose tool has not proved to be useful, but it doesn't mean that there isn't clear linguistic determinism in certain areas. Colors may be the easiest way to see some limited sapir-whorf in action.
- yathern 9y ago
  You're probably right - I actually suspected that may be the case - though I was only using that as a parallelism for what I'm saying. Language, in my understanding, operates at a lower level of abstraction in the brain than say, Math. I would suspect that Spacial Reasoning is similarly low-level. It would be interesting to see if there is any impact to the higher-level reasoning when the foundational blocks are played with. The difference probably wouldn't be very large, I'm now realizing. People who are blind since birth, as far as I know, don't have any observable differences in common patterns of thought. And that seems like a larger difference in low-level thought than being able to understand four dimensions versus three. (Not suggesting blind people lack spacial reasoning in three dimensions)
  - d0mine 9y ago
    The way people think about the same things ("translation schemes") can be different (blind or not). As an experiment, try to measure a minute by counting and doing something else http://youtu.be/lr8sVailoLw http://youtu.be/lr8sVailoLw
- js8 9y ago
  SW might have been disproven, but in this case, I think it would make a difference. I think if you had to have 4D vision rather than 3D, it would require much more processing power and memory to account for the extra dimension. So I think at minimum, a being that is capable of thinking in 4D would have to have higher brain capacity than a being that thinks just in 3D. And there is some strong evidence that our ability to navigate 3D world influences our general cognitive capabilities. For example, consider https://en.wikipedia.org/wiki/Method_of_loci https://en.wikipedia.org/wiki/Method_of_loci
  - andai 9y ago
    Could you please explain how the ability to navigate 3D world influences our general cognitive capabilities?
- SolarNet 9y ago
  I think the problem is that the mild amount of support was the only claim it was ever making. It was everyone else who blew it out of proportion. It's like the whole thing with CERN making micro black holes, and everyone freaking out about a black hole eating the solar system.
SomeStupidPoint 9y ago
You deal with 4 dimensions all the time -- up-down, left-right, forward-back, future-past. In reality, you deal with high dimensional objets all the time: the position you're in is composed of dozens to hundreds of muscles rotating a few dozen joints. We're fascinated by vision, but proprioception is where it's at if you want to think in high dimensions.
- thaumasiotes 9y ago
  An easy way to imagine a 4-dimensional structure is to associate every point in 3-space with a color or a temperature. Your mental visualization processes should have no trouble with that. But the system quickly breaks down; the imitation fourth dimension is not in the same class as the other three. You can easily visualize a three-dimensional object rotating around a line in 3-space, or a two-dimensional object rotating around a point in 2-space, or a two-dimensional object rotating around a line in 3-space. Try applying that process to a "three spatial dimensions plus one color dimension" model and you'll notice you have no idea what color a point should be in the rotated object. (You might think it should be the same color as it was before the rotation, but that's just as wrong as saying that if you rotate a point in 2-space 30 degrees around the origin, it should end up with the same x-coordinate that it started with.) Proprioception is deeply tied to a three-dimensional conception of space -- that is how you perceive its output. And the evidence is not strong that it is a function of muscle activation, since it will work just as well if you relax while someone else moves your hand around.
  - SomeStupidPoint 9y ago
    That's why I used time not color: you have an inherent notion of what it means to move things along that axis. Your point about color also doesn't quite hold -- it's easy enough to map the rainbow colors to rotation. It obviously takes practice, but it's not hard. (Helps to start with two spatial and a color.) And of course it's tied to 3 dimensional space -- the whole point is to couple the correspondence between a high dimensional phase space and a blob in 3 dimensions. But you do have an awareness of the phase space, not just the 3D location -- and you can use it to think about higher dimensional objects.
indspenceable 9y ago
Often when I see something about 4d it uses this same analogy: a 2d being seeing a crosssection of a 3d world, in 2d. However, the video is in 2d, and it's able to show 3d in a much better/more clear way, clearly, cause when it's showing that example it's got a cutout of the "3d" view (which is still 2d!). Why can't we do the same thing with 4d? Why does the object just disappear when it bounces into the 4th dimension, can't we maybe see a projection of it onto the 3rd dimension?
- js8 9y ago
  Maybe they could do something like a fog? That is, if the object was farther away in the 4th dimension, it would appear less distinct or more fuzzy/blurry, like being in the fog.
  - ucarion 9y ago
    That's a neat idea! But I think it might be a bit overwhelming and confusing. It would help with getting the bigger picture. Every 4d object would end up being a clear 3d cross-section where it intersects with our 3d world, plus a cloud of superimposed and increasingly hazier 3d cross-sections above and below us along the 4d ("w") axis, projected down onto w=0 3d-space.
  - hcs 9y ago
    Miegakure did something similar where it showed a shadow of the 3D space immediately adjacent to the currently visible slice. I think he since removed that, so I expect he must have experimented with something similar in 4D Toys and decided against it.
- deleted 9y ago
  [deleted]
- jerf 9y ago
  "Why does the object just disappear when it bounces into the 4th dimension, can't we maybe see a projection of it onto the 3rd dimension?" Yes, you can. This program just doesn't.
thanatropism 9y ago
My dissertation is about simulating conservative physical systems on a computer; but it is based in symplectic geometry, which exists only in even dimensions. Put it this way: Riemannian (and as a special case, "ordinary") geometry is based around the inner product <a,b>, which gives you both angles and projection (and 2D shadows from 3D objects, for example) and lengths. You learn a lot about this (not in the "curve" differential-geometric sense, but most of the intuition carries over) in college linear algebra: you learn to think about entire vector subspaces having orthogonal complements as defined by the inner product. On the other hand: length (even if curved) in that direction is the same as length in this direction, i.e. the inner product is a symmetric bilinear map. Symplectic geometry is built on a skew-symmetric bilinear map (the symplectic form) so that w(u,v)=-w(v,u). In 2D, the symplectic form is equivalent to the determinant: note that this is an oriented or signed area rather than an absolute-value one. And then in 3D, there is no symplectic form (it's rather fun to prove this) such that there is no vector (apart from the origin) that collapses all the other. Anyway, the challenging thing about this, writing my dissertation, is that unlike with linear algebra where you can gradually extend intuition from the real line to the plane to 3D space and then think "ok, I think I can grok this in 500 dimensions" (and go do multivariate statistics, for example), in symplectic geometry there is either the trivial case (and again, this is the determinant and not particularly "new" to you) or the 4D case next. And then you can't draw pictures. YOU CAN'T DRAW PICTURES. This is such an intuition-fucker. Books that need the symplectic form right away and can't waste time on the geometry merely note that the symplectic form at higher dimension is the sum of projections of 2D determinants. Ok, wait why? But here's the fun thing (that maybe I've spoiled by talking about inner products first): while you're proving that there can't be a symplectic form in odd-dimensional spaces, you stumble upon a parallelism between symplectic complements, i.e. the sets symp(W) = { u | w(u,v)=0 for all v in W} and orthogonal complements, i.e. the sets orth(W) = { u | <u,v>=0 for all v in W} Namely that they're kernel sets of the bilinear maps <.,.> and w(.,.) (and because w(u,v)=0 implies w(v,u)=0, they're both left- and right-kernels). Moreover any vector z can be uniquely expresseed as u+v where u is in W and v is in orth(W) or alternately p+q where p is in W and v is in symp(W) So Riemannian geometry and symplectic geometry are like ways to split a vector space in complementary parts. Now, because there's Riemannian/euclidean geometry on a line and on the plane, you can build a geometry where there are planes orthogonal to lines, i.e. a 3D geometry. And maybe you have a timeline across which 3D spaces are strung together, ie. 4D space. But this 4D space of yours isn't symplectic. So it's realy hard to see. So if you look for "symplectic geometry" on YouTube you're bound to find Dusa McDuff's lecture where she starts by writing in big bold letters in the blackboard: 4 = 3 + 1 4 = 2 + 2 ... and that's a way to "see" four dimensions: to see entirely different geometries built on it.
chrisshroba 9y ago
That's a really cool point about language and how it influences our perception! Do you have a source for the orange vs. red thing? I'd love to read more about that.

malnourish 9y ago

I thought the majority of sapir-whorf thought had been disproven and at best only a mild amount had support? At least, that's what I remember learning in my linguistics courses in college. I'm willing to be wrong.

throwaway91111 9y ago
You have to look at how it was initially positioned. Linguistic determinism as a general purpose tool has not proved to be useful, but it doesn't mean that there isn't clear linguistic determinism in certain areas. Colors may be the easiest way to see some limited sapir-whorf in action.
yathern 9y ago
You're probably right - I actually suspected that may be the case - though I was only using that as a parallelism for what I'm saying. Language, in my understanding, operates at a lower level of abstraction in the brain than say, Math. I would suspect that Spacial Reasoning is similarly low-level. It would be interesting to see if there is any impact to the higher-level reasoning when the foundational blocks are played with. The difference probably wouldn't be very large, I'm now realizing. People who are blind since birth, as far as I know, don't have any observable differences in common patterns of thought. And that seems like a larger difference in low-level thought than being able to understand four dimensions versus three. (Not suggesting blind people lack spacial reasoning in three dimensions)
- d0mine 9y ago
  The way people think about the same things ("translation schemes") can be different (blind or not). As an experiment, try to measure a minute by counting and doing something else http://youtu.be/lr8sVailoLw http://youtu.be/lr8sVailoLw
js8 9y ago
SW might have been disproven, but in this case, I think it would make a difference. I think if you had to have 4D vision rather than 3D, it would require much more processing power and memory to account for the extra dimension. So I think at minimum, a being that is capable of thinking in 4D would have to have higher brain capacity than a being that thinks just in 3D. And there is some strong evidence that our ability to navigate 3D world influences our general cognitive capabilities. For example, consider https://en.wikipedia.org/wiki/Method_of_loci https://en.wikipedia.org/wiki/Method_of_loci
- andai 9y ago
  Could you please explain how the ability to navigate 3D world influences our general cognitive capabilities?
SolarNet 9y ago
I think the problem is that the mild amount of support was the only claim it was ever making. It was everyone else who blew it out of proportion. It's like the whole thing with CERN making micro black holes, and everyone freaking out about a black hole eating the solar system.

SomeStupidPoint 9y ago

You deal with 4 dimensions all the time -- up-down, left-right, forward-back, future-past. In reality, you deal with high dimensional objets all the time: the position you're in is composed of dozens to hundreds of muscles rotating a few dozen joints. We're fascinated by vision, but proprioception is where it's at if you want to think in high dimensions.

thaumasiotes 9y ago
An easy way to imagine a 4-dimensional structure is to associate every point in 3-space with a color or a temperature. Your mental visualization processes should have no trouble with that. But the system quickly breaks down; the imitation fourth dimension is not in the same class as the other three. You can easily visualize a three-dimensional object rotating around a line in 3-space, or a two-dimensional object rotating around a point in 2-space, or a two-dimensional object rotating around a line in 3-space. Try applying that process to a "three spatial dimensions plus one color dimension" model and you'll notice you have no idea what color a point should be in the rotated object. (You might think it should be the same color as it was before the rotation, but that's just as wrong as saying that if you rotate a point in 2-space 30 degrees around the origin, it should end up with the same x-coordinate that it started with.) Proprioception is deeply tied to a three-dimensional conception of space -- that is how you perceive its output. And the evidence is not strong that it is a function of muscle activation, since it will work just as well if you relax while someone else moves your hand around.
- SomeStupidPoint 9y ago
  That's why I used time not color: you have an inherent notion of what it means to move things along that axis. Your point about color also doesn't quite hold -- it's easy enough to map the rainbow colors to rotation. It obviously takes practice, but it's not hard. (Helps to start with two spatial and a color.) And of course it's tied to 3 dimensional space -- the whole point is to couple the correspondence between a high dimensional phase space and a blob in 3 dimensions. But you do have an awareness of the phase space, not just the 3D location -- and you can use it to think about higher dimensional objects.

indspenceable 9y ago

Often when I see something about 4d it uses this same analogy: a 2d being seeing a crosssection of a 3d world, in 2d. However, the video is in 2d, and it's able to show 3d in a much better/more clear way, clearly, cause when it's showing that example it's got a cutout of the "3d" view (which is still 2d!). Why can't we do the same thing with 4d? Why does the object just disappear when it bounces into the 4th dimension, can't we maybe see a projection of it onto the 3rd dimension?

js8 9y ago
Maybe they could do something like a fog? That is, if the object was farther away in the 4th dimension, it would appear less distinct or more fuzzy/blurry, like being in the fog.
- ucarion 9y ago
  That's a neat idea! But I think it might be a bit overwhelming and confusing. It would help with getting the bigger picture. Every 4d object would end up being a clear 3d cross-section where it intersects with our 3d world, plus a cloud of superimposed and increasingly hazier 3d cross-sections above and below us along the 4d ("w") axis, projected down onto w=0 3d-space.
- hcs 9y ago
  Miegakure did something similar where it showed a shadow of the 3D space immediately adjacent to the currently visible slice. I think he since removed that, so I expect he must have experimented with something similar in 4D Toys and decided against it.
deleted 9y ago
[deleted]
jerf 9y ago
"Why does the object just disappear when it bounces into the 4th dimension, can't we maybe see a projection of it onto the 3rd dimension?" Yes, you can. This program just doesn't.

thanatropism 9y ago

My dissertation is about simulating conservative physical systems on a computer; but it is based in symplectic geometry, which exists only in even dimensions. Put it this way: Riemannian (and as a special case, "ordinary") geometry is based around the inner product <a,b>, which gives you both angles and projection (and 2D shadows from 3D objects, for example) and lengths. You learn a lot about this (not in the "curve" differential-geometric sense, but most of the intuition carries over) in college linear algebra: you learn to think about entire vector subspaces having orthogonal complements as defined by the inner product. On the other hand: length (even if curved) in that direction is the same as length in this direction, i.e. the inner product is a symmetric bilinear map. Symplectic geometry is built on a skew-symmetric bilinear map (the symplectic form) so that w(u,v)=-w(v,u). In 2D, the symplectic form is equivalent to the determinant: note that this is an oriented or signed area rather than an absolute-value one. And then in 3D, there is no symplectic form (it's rather fun to prove this) such that there is no vector (apart from the origin) that collapses all the other. Anyway, the challenging thing about this, writing my dissertation, is that unlike with linear algebra where you can gradually extend intuition from the real line to the plane to 3D space and then think "ok, I think I can grok this in 500 dimensions" (and go do multivariate statistics, for example), in symplectic geometry there is either the trivial case (and again, this is the determinant and not particularly "new" to you) or the 4D case next. And then you can't draw pictures. YOU CAN'T DRAW PICTURES. This is such an intuition-fucker. Books that need the symplectic form right away and can't waste time on the geometry merely note that the symplectic form at higher dimension is the sum of projections of 2D determinants. Ok, wait why? But here's the fun thing (that maybe I've spoiled by talking about inner products first): while you're proving that there can't be a symplectic form in odd-dimensional spaces, you stumble upon a parallelism between symplectic complements, i.e. the sets symp(W) = { u | w(u,v)=0 for all v in W} and orthogonal complements, i.e. the sets orth(W) = { u | <u,v>=0 for all v in W} Namely that they're kernel sets of the bilinear maps <.,.> and w(.,.) (and because w(u,v)=0 implies w(v,u)=0, they're both left- and right-kernels). Moreover any vector z can be uniquely expresseed as u+v where u is in W and v is in orth(W) or alternately p+q where p is in W and v is in symp(W) So Riemannian geometry and symplectic geometry are like ways to split a vector space in complementary parts. Now, because there's Riemannian/euclidean geometry on a line and on the plane, you can build a geometry where there are planes orthogonal to lines, i.e. a 3D geometry. And maybe you have a timeline across which 3D spaces are strung together, ie. 4D space. But this 4D space of yours isn't symplectic. So it's realy hard to see. So if you look for "symplectic geometry" on YouTube you're bound to find Dusa McDuff's lecture where she starts by writing in big bold letters in the blackboard: 4 = 3 + 1 4 = 2 + 2 ... and that's a way to "see" four dimensions: to see entirely different geometries built on it.

chrisshroba 9y ago

That's a really cool point about language and how it influences our perception! Do you have a source for the orange vs. red thing? I'd love to read more about that.