Higher dimensions behave in strange ways

[Retro]

This fascinating video by Zach Star explores the strange effects that higher physical dimensions have on shapes and volumes. It's quite counterintuitive in some places. For example, there are only 5 platonic solids in three dimensions. Do you think that number goes up or down in higher dimensions? Does it level off? It's weirder than you think.

Finally, I can't imagine what the fourth dimension looks like and apparently nor can anyone else because we exist in three dimensional space. Can you try to imagine it - a direction perpendicular to all of our three directions?

Nerd level: on a higher plain.

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[Crims]

Search 4d shapes on google, the straight lines of dimensional transposition become easier. Like... 3d to 2d mapping, 4d to 2d projections etc.

 

[Retro]

The video goes through that. The point is, that we inherently can't comprehend it.

 

[Crims]

alright. Though in the past I was a 3d 4d game designer. If we had a robot we should send it out to space to map 4d structures.
The idea is neat mostly

 

[Retro]

There aren't any 4d structures in our 3D universe, so that's not possible.

What we can do however, is to mathematically model 4d structures in a computer, but can't actually display them. The best we can do is a 3D shadow projection which is what's shown in the above video.

There's a fascinating game on Steam called 4D Toys that allows 4d shapes to be manipulated. It's quite cheap, I've got it and it's well worth the money. The website gives you a taste of what it's like.

4D Toys. An interactive toy for 4D children.

4dtoys.com

 

[Crims]

Slightly semantic... We moved from 3d physics in 1950 assuming we have a hypersphere universe. The google result for is the entire universe 4d returns a yes.

 

[Retro]

No, it's not semantics. We can't access anything in higher dimensions in the physical world. We don't even know if higher dimensions actually exist, in fact.

 

[Retro]

Wanna add, if you've not seen the video yet, do give it a watch as it's fascinating.

 

[Retro]

There aren't any 4d structures in our 3D universe, so that's not possible.

What we can do however, is to mathematically model 4d structures in a computer, but can't actually display them. The best we can do is a 3D shadow projection which is what's shown in the above video.

There's a fascinating game on Steam called 4D Toys that allows 4d shapes to be manipulated. It's quite cheap, I've got it and it's well worth the money. The website gives you a taste of what it's like.

4D Toys. An interactive toy for 4D children.

4dtoys.com

Everyone, in addition to the above, 4D Toys creator Marc ten Bosch has a video demonstrating the principles behind 4D Toys and then goes into hardcore technical details of working in n-dimensional space with generalised equations. Warning: contains lots of impenetrable squiggly maths. This is beyond nerdy and requires an IQ of about 300 to understand fully!

SIGGRAPH 2020 Technical Paper: N-Dimensional Rigid Body Dynamics « mtbdesignworks Blog [Miegakure, 4D Toys, Marc ten Bosch]