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4D Toys: a box of four-dimensional toys

marctenbosch.com

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Re: 4D Toys: a box of four-dimensional toys

#51

Post by thanatropism »

thanatropism wrote: post #45
yathern wrote: post #15

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…

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 , 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" dif…

That didn't come up too intuitive.

Ok, think of two vectors in "three dimensions" (but not really). Draw X,Y,Z axes. So these pseudovectors will have a determinant which you can project on XY space and YZ space. Now, because our vectors have 4 dimensions and not 3, these projections will not be the same! Then your four-dimensional symplectic form (in some applications an "exterior product") is the sum of those two projections.

So you're pseudovisualizing a 4D object in 3D space as you might pseudovisualize a 3D object in 2D space but with a different concept of projection/perspective/etc. because we're not in the inner product geometry, we're in the symplectic geometry.

Re: 4D Toys: a box of four-dimensional toys

#52

Post by d0mine »

yathern wrote: post #36
malnourish wrote: post #26

Earlier quoted context omitted.

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.

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 play…

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

Re: 4D Toys: a box of four-dimensional toys

#53

Post by martin-adams »

Qantourisc wrote: post #46

What annoys me most: "thing disappear" I don't recall 3D -> 2D mapping making things disappear, just surfaces hiding other surfaces. But this might not work in 4D? With the 2D->3D they are taking cross-section, I really don't like these. Just throw it all on there ! This would also mean you project your 4D world on a 3D camera, you project on a 2D surface to display. https://www.youtube.com/watch?v=BVo2igbFSPE <= thi…

Now I'm happy to be completely wrong here, but I have a feeling that the disappearing of a 4D object in a 3D world cannot avoid using time to reveal the 4D nature of it.

Just like a in a 2D plane, to represent a 3D object and see all of it, you have to iterate though time to see it all, so parts will disappear from our perception at a given time interval.

Re: 4D Toys: a box of four-dimensional toys

#54

Post by tyingq »

comboy wrote: post #29
tyingq wrote: post #4

Reminded of this Carl Sagan video that I watched as a kid. https://www.youtube.com/watch?v=xTL02N9EHzU

These videos are such a treasure. All these years and nobody came even close (new Cosmos is ok, but not that profound). This is how you make a nation great. You can do whatever you want with the economy, but without proper education you still have a nation of.. people.. who choose their president.. based on their beliefs and understanding of the world.

Shows the relative importance of a great presenter too. The props he uses are laughably cheap, yet he does a better job getting the point across than vastly more expensive productions.

Re: 4D Toys: a box of four-dimensional toys

#55

Post by mabbo »

indspenceable wrote: post #40
yathern wrote: post #15

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…

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 dimensio…

Watch the part about the slicing of 2d world looking at the 3d objects. That slice is infinitely large in both dimensions, yet it can't see the 3D objects when they aren't in the same plane.

Now apply the same analogy to our world: our 3D world is just an infinitely large 3D plane in a 4D world. When the objects aren't in our 'plane', we can't see them.

Re: 4D Toys: a box of four-dimensional toys

#56

Post by thaumasiotes »

SomeStupidPoint wrote: post #28
yathern wrote: post #15

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…

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.

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.

Re: 4D Toys: a box of four-dimensional toys

#57

Post by thaumasiotes »

zitterbewegung wrote: post #12

As a person who studied knot theory and sitting through other peoples presentations about higher dimensional knots this looks like a neat treat! After hearing about the concept I bought the game and tried it out. I like how you replace actual physical actions to objects in 4 dimentions. Usually this is projected on the time axis but with this interface it makes it much more fun to play with it instead of having basic…

Higher dimensional knots? I thought one of the first things you learned in knot theory was that knots are only possible in three dimensions?

Re: 4D Toys: a box of four-dimensional toys

#58

Post by coldpie »

wyager wrote: post #43

Does anyone have any resources on orthographically projecting 4D objects to 3D or 2D spaces? I'm curious if it looks better than taking a cross-section. It seems like it should work similarly; deform a 4-frustum into a 4-cube and drop one or two of the axes. I guess the number of axes you can drop depends on the symmetry of the frustum...

I tried googling "orthographically projecting 4D objects to 3D" to see if I'd strike gold and, boom: http://eusebeia.dyndns.org/4d/vis/vis

Edit: In particular, this page shows a good summary of how the "slices" shown in the game relate to the hypercube projection you're familiar with. http://eusebeia.dyndns.org/4d/vis/09-interp-1#Interpreting_4...

Re: 4D Toys: a box of four-dimensional toys

#59

Post by ucarion »

js8 wrote: post #44
indspenceable wrote: post #40

Earlier quoted context omitted.

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 dimensio…

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.

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.

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