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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

#111

Post by SomeStupidPoint »

thaumasiotes wrote: post #56
SomeStupidPoint wrote: post #28

Earlier quoted context omitted.

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 rota…

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.

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

#112

Post by wruza »

marctenbosch wrote: post #88
octalmage wrote: post #39

Earlier quoted context omitted.

Same issue here. Has anyone reached out to the developer?

I am aware of the issue and fixing right now!

This app is very cool. Do you have a plan to add projection mode in addition to crosssection?

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

#113

Post by indescions_2017 »

chmod775 wrote: post #16

I'm curious how this would look if the 4D space was projected onto the 3D space instead of taking a cross-section, much like we already project 3D space onto 2D space (your display), to create "3d" graphics.

One application of these projections would be a point light source in the 4-th Dimension that would be obscured by solid 4-D toys and subsequently cast 4-D shadow "voxel maps" into the 3-D cube space. Having shadows and radiosity illumination would absolutely help with the "disappearing" cubes problem during game play. But it represents a substantial calculation for real-time physics and rendering engines.

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

#114

Post by wruza »

amelius wrote: post #90

I wonder if, after playing many hours with this game, the brain will suddenly "grasp" the concept of 4d.

I think it will. I'm aware of two somewhat related experiments: upside-down vision and magnetic field vision. In first experiment, participant wore vertical flipping glasses for a week. He was walking, eating, cycling and so on, never taking glasses off. At the end of experiment he was pretty good at it and it seemed natural. When glasses were finally off, he felt very discomfortable for some time. https://en.wikipedia.org/wiki/Neural_adaptation#History -- one of these experiments.

In the second experiment participant wore belt (iirc) that signaled north pole location to his skin. After wearing it for a long time, that feeling turned completely into new sense of magnetic field. You simply know where "north" is, anytime. After taking it off, he responded that it was pretty stressful, like you lose one of your senses or limbs. Experiment group was concerned to that they stopped these experiments. (no link found, but seen on HN)

All this shows that our brain is probably not specific to available senses/setting and can "grasp" any concept, if exposed to it for a long time, but both in and out may take a hard time.

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

#115

Post by eriknstr »

jacobolus wrote: post #72
eriknstr wrote: post #32

Earlier quoted context omitted.

Another quote from the video I linked in parent comment. 6:19 > As complex numbers are to real numbers, quaternions are to complex numbers. It's like a way to build up even further. [...] Real numbers are one-dimensional. Complex numbers are two-dimensional. [...] For three dimensions there is no natural number system, but for four dimensions there is and it looks like this.

That’s really misleading. The complex numbers are not a two-dimensional Euclidean space directly, but are a space of transformations (scaling & rotation) on two-dimensional Euclidean vectors, where 1 represents the identity transformation, and i represents a quarter turn anticlockwise. In a similar way, the quaternions are the space of transformations (scaling & rotation) of three-dimensional vectors. (It’s a little…

>The complex numbers are not a two-dimensional Euclidean space directly, but are a space of transformations (scaling & rotation) on two-dimensional Euclidean vectors, where 1 represents the identity transformation, and i represents a quarter turn anticlockwise.

You might be right, I don't know. Could you explain a bit more how you mean?

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

#117

Post by tgb »

HiroshiSan wrote: post #97
p1mrx wrote: post #81

Earlier quoted context omitted.

We see in 2D, with a tiny bit of depth metadata. True 3D vision would allow you to look at someone, and see the entire volume of all their internal organs simultaneously.

Wouldn't that be xray vision?

The comparison here is, as usual, to go down a dimension. Imagine living in a world where everything is constant vertically, like those old 3D maze screen savers or Wolfenstein 3D. You're really seeing a 1D amount of information about a 2D world (in fact, this is how the calculation is for Wolf3D and other games of its era). You can infer depths to objects if you have two eyes.

Now contrast that to if you were plucked up vertically 'above' the game's level to look down upon it. Now you can see the entire 2D extent of the maze at once. Before, your vision was blocked by the walls, now you see the walls and what's on the other side of the walls simultaneously in a way that's entirely distinct from simply seeing through a transparent object.

Now, like seeing a 1D amount of information about a 2D maze while live inside it, we see a 2D amount of information about a 3D world around us (a picture demonstrate's this 2D amount of information - it's planar). Now imagine being lifted out the 3D plane of existence so that you could behold the entirety of the 3D world at once. That's the rough analogy.

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

#118

Post by wruza »

fao_ wrote: post #98
squeaky-clean wrote: post #85

Earlier quoted context omitted.

I remember playing a flash or java game years ago that did exactly this. It was a 4d maze, rendered in stereoscopic 3d. It displayed the images side by side and you crossed your eyes to get the 3d effect. It was really disorienting (the 4d, but also the eye-crossing), and like the post author says, just bundles of lines rather than solid shapes. Still very cool. Ooh, I found it! http://www.urticator.net/maze/

Thank you so much! I've wanted something like this for ages. Now to figure out how to cross my eyes consistently with astigmatisms...

Idk where I found these. Not 3d though, just stereoscopic 2d. Tetris may be nice for stereo-training, as it doesn't involve any complex movements. But it was harder to me than seeing stills.

http://www.hidden-3d.com/games_stereogram_tetris.php

http://www.hidden-3d.com/stereogram_games.php

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

#119

Post by hcs »

eriknstr wrote: post #115
jacobolus wrote: post #72

Earlier quoted context omitted.

That’s really misleading. The complex numbers are not a two-dimensional Euclidean space directly, but are a space of transformations (scaling & rotation) on two-dimensional Euclidean vectors, where 1 represents the identity transformation, and i represents a quarter turn anticlockwise. In a similar way, the quaternions are the space of transformations (scaling & rotation) of three-dimensional vectors. (It’s a little…

>The complex numbers are not a two-dimensional Euclidean space directly, but are a space of transformations (scaling & rotation) on two-dimensional Euclidean vectors, where 1 represents the identity transformation, and i represents a quarter turn anticlockwise. You might be right, I don't know. Could you explain a bit more how you mean?

I suspect the important point is that rotations cycle around (keep rotating and you come back to where you started)

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

#120

Post by i_cant_speel »

sp332 wrote: post #7
pmilla1606 wrote: post #5

This looks like fun, going to try this out over the weekend. This is the same person who made this game (that also looks like good fun): http://miegakure.com/ that I remember reading about some years ago but never got a chance to play with

The game isn't out yet.

Yes it is.
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