Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

4D Toys: a box of four-dimensional toys

marctenbosch.com

Post reply on HN
Print view View original

141–148 of 148 posts

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

#141

Post by ShrubberyKnight »

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…

Purely theoretical, but the presence of a 3D object can be detected by a 2D creature, by it's shadow, depending on relative positioning of object, 2D surface, and light source. What would a 3D shadow look like, with no need for a wall or flat surface onto which the shadow would be cast? For that matter, what would 4D light look like, if it even differs. Maybe the light we see is only a shadow of something from the 4th Dimension, or maybe a portal or doorway we have not yet learned to use to it's potential.

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

#142

Post by JoeDaDude »

There are several 4D games, but the one I found gave me the best grasp of the 4D world is this one [1], a puzzle in which you manipulate a hypercube. You first play in 2D and 3D before going to 4D. You end up with an intuitive understanding of 4D.

[1] http://harmen.vanderwal.eu/hypercube/

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

#143

Post by Crespyl »

pbhjpbhj wrote: post #140
Crespyl wrote: post #80

Earlier quoted context omitted.

It might help if you consider spheres as a surface . 3D spheres are a 2D surface wrapped into a 3D space, likewise, hyperspheres would be a 3D surface wrapped into a 4D space. There's no "infinite spheres on its surface", I think the "rotation" is a better analogy. Take a line rotated around an orthogonal axis and you have a circle, a circle rotated around an axis orthogonal to the other two is a sphere, a sphere rot…

Are all spheres hyperspheres? When you rotate in the 4th, or higher ordinal, dimensions don't you get the same shape?

I guess it would depend on whether you consider all circles to be spheres (or all spheres circles)?

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

#144

Post by collinmanderson »

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…

I would like to see _four_ simultaneous 3d projections of the 4d space, each ignoring (or flattening) one of the 3 dimensions.

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

#145

Post by JadeNB »

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…

> Moreover any vector z can be uniquely expresseed as p+q where p is in W and v is in symp(W)

Of course, crucially, this is only true if `W` is non-degenerate; as you'll know, one of the important things about symplectic spaces is the existence of half-dimensional, totally isotropic subspaces. (In fact, there's nothing particularly symplectic per se about this issue; it is not the (conjugate-)symmetry of the usual inner product so much as its positive definiteness that means that no such extra non-degeneracy condition must be imposed. Indeed, the study of non-positive definite but symmetric inner products, as in the geometry of relativistic spacetime, carries its own challenges to intuition.)

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

#146

Post by mabbo »

fao_ wrote: post #99
mabbo wrote: post #71

Earlier quoted context omitted.

A favorite novel of mine actually! Hard to believe that it was written in the 1800s, yet still Abbott understood the 4th dimension better than most people today.

> Hard to believe that it was written in the 1800s Aside from all the misogyny and the style of writing, you mean?

It was the 1800s. I'm sure that 150 years from now, everything you and I are writing now will be offensive in ways we don't understand today.

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

#147

Post by hcs »

KeyboardFire wrote: post #6

It's a shame it's only for iOS and Vive. I wonder how difficult it would be to make an open source desktop/browser version? Even if it's a lot simpler, it would be neat to feel what it'd be like to play around in 4 dimensions.

4D Toys is now available for non-VR PC, I just noticed this tweet from the author: https://twitter.com/marctenbosch/status/871073480573202432

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

#148

Post by thanatropism »

JadeNB wrote: post #145
thanatropism wrote: post #45

Earlier quoted context omitted.

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…

> Moreover any vector z can be uniquely expresseed as p+q where p is in W and v is in symp(W) Of course, crucially, this is only true if `W` is non-degenerate ; as you'll know, one of the important things about symplectic spaces is the existence of half-dimensional, totally isotropic subspaces. (In fact, there's nothing particularly symplectic per se about this issue; it is not the (conjugate-)symmetry of the usual i…

My name is thanatropism and I approve JadeNB's message.
Post reply on HN