If anyone wants to play with a 4D toy right now in their web browser, here is an interactive tesseract (4d cube) that I built.
http://transdimensional.xyz
It doesn't have physics but features a novel interface that I designed to help build an intuition about different rotations. (There are six axes of rotation in 4 dimensions)
4D toys
91–100 of 112 posts
Re: 4D toys
#92The video ends saying that trying to fit a 4D cube in a 4D hole is like a child playing with toy blocks. Hypothetically, if a child was raised with regular VR simulations that allowed the child to manipulate 4D objects, would their brain "learn" it and in a way unlock the 4th dimension?
I was wondering this too as I watched the video. As an adult I know how physics works and I know that what I'm seeing is not normal based on decades of experience. If you showed this to a 1 year old and let them play with 4D virtual toys for a few years, would they more intuitively understand 4D objects? Or would it still remain foreign due to the fact that they can't see things moving around the fourth dimension?
As I played around with 4D toys, I did start to gain a sense of things that were "Behind" or "In Front" of me in 4D space, that is I could start to feel their presence after they had been pushed out of sight, if I knew in what direction they were moving in the 4th dimension. If I didn't know that I could only feel that they were near.
It helps that there is a little visualization that is just a line-per-object showing where you are, and where all the objects are intersecting the 4th dimension, that you also use to move "back and forth."
One thing I found myself doing was grabbing objects at one of their edges in the 4th dimension, by moving myself to near their boundary, and then using them like brooms. It's really easy to understand with the case of a hypersphere, since at its edge it's just a smaller sphere than at the middle. So you grab that small sphere at the edge, and push in the direction towards its middle in the 4th dimension, and it will act like a bowling ball. You won't see the stuff you are pushing around because the sphere is "ahead" of you, unless they roll around the sphere, then you'll pass them. Once you reach the edge of the 4th dimension, all the stuff you kept pushing will be there.
Predicting how 3D intersections change as objects rotate about in the 4th dimension still seems like chaos to me though, except in the case of hyperspheres, which basically don't change as they rotate, but I only played around for about an hour or so. The only way I found to rotate objects in the 4th dimension was to have them collide with each other, or the walls and floor, which makes it kind of hard to carefully experiment with their rotations.
Re: 4D toys
#93Here's a thought I had watching the bit with 2D man: Actually, the 3D view that 2D man does not understand but which we do understand is... still 2D. My screen is flat. You can use a 2D viewport to render a 3D scene in a way that is natural and easy to understand for us humans: A human watching the 2D scene can very quickly surmise from a glance at the viewport: Which objects are in the scene, and where are they loca…
There are YouTube videos where people attempt to render 4D scenes, usually by slicing a mesh along the fourth component of its position, then drawing it as 3D. But since we lack the intuition for 4D space it just looks like a bunch of objects popping in and out of existence.
Re: 4D toys
#94Using the 4th Dimension, the two interlocking rings can be separated. However, what would be the equivalent puzzle for the 3rd dimension? What 2D system requires the 3rd dimension to be separable? Is there even an equivalent? Clearly a circle within a circle is one such system, but it corresponds to a ball wholly contained by another ball in 3D, not a pair of interlocking rings.
It would be a ring with a stick through it. In a 2D slice down the middle, it would look like a donut with a circle (the slice of the stick) in the hole. The circle appears to be stuck inside it, with no way out in 2D. In 3D, you just pull the stick out of the ring.
Re: 4D toys
#95Some might remember this excellent treatment of higher dimensions [1] in which you first manipulate shapes to solve a puzzle in 2D, then 3D, and finally 4D. YYou develop a keen sense of 4D objects:
Re: 4D toys
#96Here's a thought I had watching the bit with 2D man: Actually, the 3D view that 2D man does not understand but which we do understand is... still 2D. My screen is flat. You can use a 2D viewport to render a 3D scene in a way that is natural and easy to understand for us humans: A human watching the 2D scene can very quickly surmise from a glance at the viewport: Which objects are in the scene, and where are they loca…
Study from 45 years ago: Heinz von Foerster’s 1970-1971 experiment at the Biological Computing Laboratory for apprehending the fourth dimension is unique ... combining four dimensional geometry, stereoscopic vision, and joystick manipulation of objects on the screen. ... The fourth dimension was chosen as the knowledge to be acquired because there was no chance that any subjects would have attempted such knowledge be…
The next thing to come from the same person, Miegakure[1], is going to be even more epic and mind-blowing. But it will take a while for it to be done.
Re: 4D toys
#97Earlier quoted context omitted.
The problem is that while everything you see on your (2D) monitor is effectively 2D our brain is good at taking 3D cues (shadows, perspective, parallax etc...) to reconstitute 3D "data" from it. For instance look at 3D rotating cube on your monitor: https://www.youtube.com/watch?v=5E10zYKln3g Even though there's no shading, a bad resolution and zero context anchoring it in a familiar setting you immediately see it as…
Here is one version of 4D that our brain understands and can easily map from 4D back to 3D, and that's when the 4th dimension is time (or motion): http://www.dyscario.com/arts-and-culture/sculptures-in-motio...
I like that. It would be very interesting to have something that would use real life resolution human models and an option to control the time step.
Re: 4D toys
#98Earlier quoted context omitted.
FWIW this is really not true. (The bit about stereo vision being required to see 3D.) When I was in college I was fairly decent on the ping pong table, call it high amateur. I also have very very bad vision - -5 diopters in one eye and -6 in the other. At the time I wore contacts and I was also really really poor. At some point I lost one of my contacts and for six months I was effectively blind in one eye for the pu…
Did you play with only one eye open, or just one contact lens? I have worse vision than you (-8.0, -7.50), and I know that I can still function with just one lens in of needed. You definitely still have stereo vision even if one input is blurred. Your brain does quite a bit of compensation, and I can imagine if you operated this way for months that your brain would be even better at assimilating the noisy information…
I played with one contact, and if you have vision as bad as mine you know there is essentially no chance that I would be able to build a stereo image of the ball with one eye uncorrected. I know this because I had to relearn how to play, and I found myself using other cues for depth, like what the ball was occluding.
Re: 4D toys
#99Earlier quoted context omitted.
I asked the same question a few seconds before you :) found this: https://youtu.be/S-yRYmdsnGs?t=252 and even better, this: https://youtu.be/dy_MUfBuq2I
Yes, and I think this just shows how a 3d representation on 2d gives our brain the _illusion_ of 3d. This doesn't work for 4d, because our brain doesn't have an internal understanding of 4d objects.
>our brain doesn't have an internal understanding of 4d objects
I agree and I think it will never have. We can certainly speculate but ultimately it'd be like an animal with monochromatic vision trying to see colours.
Re: 4D toys
#100Agreeably playing with 4d objects is mindboggling enough, but still I would like to somehow visualize myself moving around in 4d space. I am not quite sure how a 4d room would look like and what kind of doors to other 4d rooms would be like, bit for sure navigating around a 4d house could be fun...