## 4D toys

Discussions about how to visualize 4D and higher, whether through crosseyedness, dreaming, or connecting one's nerves directly to a computer sci-fi style.

### 4D toys

There's a new app that let's you play with 4D shapes by the Miegakure developers
http://4dtoys.com/

Also can anyone explain why I saw a tiger (in orange) there? I thought only this forum knew its existence?
Secret
Trionian

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### Re: 4D toys

Marc ten Bosch is the only person developing Miegakure. He came to this forum to learn more about some of the 4D shapes. And, yes, that is a tiger you see! And the spheritorus, too. They're going mainstream now.
in search of combinatorial objects of finite extent
ICN5D
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### Re: 4D toys

I suspect that 3 axes of a 4D object would be at least visible to a 2D extended plane (3D) viewpoint and that none of these toys should fully disappear to it. Is this incorrect?

Hugh
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### Re: 4D toys

If you slide (translate) a 4D object far enough along a 4th axis (the one you can't see), the shape would be completely pulled out of the 3D plane, and disappear. He may be restricting the distance that you can slide, just enough to keep a small part (of the shape) stuck in the 3-plane.
in search of combinatorial objects of finite extent
ICN5D
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### Re: 4D toys

ICN5D wrote:If you slide (translate) a 4D object far enough along a 4th axis (the one you can't see), the shape would be completely pulled out of the 3D plane, and disappear. He may be restricting the distance that you can slide, just enough to keep a small part (of the shape) stuck in the 3-plane.

On his 4D toys page, there are some animations of some 4D toys moving around on what appears to be a table in front of you. As they move around, or fall down, some of them completely disappear. Would this actually happen? As you look along an z-axis, into the 3rd dimension, forwards along a 2D xy plane at the table in front of you, shouldn't that catch 3 axes of line of sight of any 4D object that would happen to be in front of you? The one to the right and left of you, up and down, and forward towards the table? A 4D toy would have those axes of space within it wouldn't it?

Hugh
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### Re: 4D toys

I've been thinking about this. The sandbox game uses 3 axes to explore a 4D toy. You can move the objects along any single or more axes at once.

Move along any of the 3 axes in our slicing plane, and we see an unchanging toy sliding around in 3D.

Move along the 4th axis that we don't see, and the toy stays in place while changing form (as we slice it top to bottom along the 4th axis).

Move along both an axis in our 3D plane and the 4th axis (diagonally), and we see a toy sliding towards the table, while changing form. Just moving in our 3D slicing space won't change the x-section of the 4D shape. We have to move along that 4th axis, too, to cut at different height levels in 4D.

So, when the toy moves towards the table and changes form/disappears, it's moving diagonally along a plane, in our slicing space and 4D.
in search of combinatorial objects of finite extent
ICN5D
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### Re: 4D toys

I did not expect a tiger either, nor did I expect gyrochora.
Anyways, this game seems like a good way to let beginners into the concept of a fourth dimension.

ubersketch
Trionian

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### Re: 4D toys

It's a very great tool. I am disappointed that there are no sphones, coninders, or cylindrones. There is not even a spherinder or cubinder, or cylindrone. But there is a geodesic prism that is kind of like a spherinder. At least there is the duocylinder and the tiger. There is an easter egg, if you click the pencil you can open it as a toy, it is actually a pencil prism. The one thing that I am shocked with is that there is no way to rotate the object you are holding by XW/YW/ZW. This is very fundamental but it was never added.
개구리
Mononian

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### Re: 4D toys

ICN5D wrote:So, when the toy moves towards the table and changes form/disappears, it's moving diagonally along a plane, in our slicing space and 4D.

I’m wondering how the toy can totally disappear though, if it is on a table, in front of us.

It occupies space across both the X axis (left and right) and Y axis (up and down) in our plane of vision as we look at it.

It has those dimensions of space within itself, no matter which way it is facing us, how can the space that those dimensions occupy disappear from the X and Y vision plane that is facing it?

Hugh
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### Re: 4D toys

You are only ever seeing a slice of the table at a time. In 3D, the top surface of tables are sections of planes, usually of the plane XZ if you consider Y to be the vertical direction of gravity. In 4D, the top surface of tables are sections of realms, usually of the realm XZW. In the game, there is a four dimensional space XYZW, but you are taking XYZ slices of the world along W, so you will always see the table "block" surface as just an XZ plane section. However, the rest of the "block" surface still exists, and since W is as perpendicular to gravity as X and Z, there is nothing stopping the polychoron from rolling to W, out of your XYZ viewing slice, which you see as it "disappearing". Really, it is just somewhere else on the "block" surface.

If you switched your view so that you were taking XZW slices along Y, then you would see something much different. At Y's minimum, you would see the surface of the 4-table, which would be a solid block filling the whole XZW slice. If you could see inside the solid block, you would see something like a point, line, disk, or some polygon "floating" inside of it. This is the point of contact of the polychoron that is sitting on this 3D surface. As you increased the Y of your slices, the "block" surface would suddenly disappear all at once, and you would see a small 3D slice of the polychoron in empty space, and as Y increased further, the polychoron would disappear (you reached past its height) and you would be left with only empty space as you approached the maximum of Y.
When you deal with slicing visualizations, you must always remember to "stack" everything that you see, even things that are not the polychoron that you are analyzing.

So when you have a glome in your XYZ view of XYZW, sitting on the 3D surface of a "hypertable", you simply see a sphere, that can roll around like an ordinary sphere in X and Z, but can also roll "away" in W, which you see as shrinking and disappearing. If you switched your view to XZW so that you see the whole "block" surface of the table at the same time, the glome would appear as a single point inside the block, and it could move around freely within the whole block, like a "fly" flying around a room. The glome hasn't disappeared to anywhere.
As a bonus, if you have a spherinder, then its point of contact in the block surface would be a line, and this line could move around freely except in any direction along its length (this is the spherinder rolling). The spherinder can even be "stood up" on the table, and its point of contact would be a sphere, which wouldn't move at all. If you had a cubinder on its side, then you would see its point of contact as a square, and when the cubinder rolls, the square point of contact would slide back and forth normal to its face. When the cubinder is stood up, its point of contact in the block would be a cylinder, which also doesn't move. So a glome can roll freely in three ways, a spherinder can roll freely in two ways, and a cubinder can only roll in one way.
One last thing to be noted is that the point of contact of a spheritorus would be a "fly", just like the glome, but this fly can only crawl around in one way, otherwise the spheritorus falls over and the fly becomes a circular point of contact (just the edge of the circle, not a disc).
개구리
Mononian

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### Re: 4D toys

I have fun playing with this app and definitely made me better understand 4D at least somewhat in a more tactile way. My issue is you cannot rotate on W and its rather frustrating to learn patterns when you can't rotate on all axis. I did find the in zero gravity rotating a shape on the "tip" in the 4th axis of a shape causes it to rotate along W axis but its still kinda hard to control. Ugh I wish I could play with in in stereoscopic VR, all I have ipad and iphone atm.
solarjackal
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