## Are Cloth and Paper Impossible in 4D ?

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

### Are Cloth and Paper Impossible in 4D ?

Suppose you have two crossed threads in a 4D universe. One thread can easily pass by the other.

This means that cloth as we know it could not exist. Paper is similar. Indeed, thread is fibers twisted together. If the fibers could pass by one another, then thread, string, or rope couldn't exist.

Perhaps there could be 2D warp and 1D woof. But that is a bit much for my meager mind. I don't konw how that could be done. Perhaps this is obvious to someone else.
PatrickPowers
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### Re: Are Cloth and Paper Impossible in 4D ?

Weaving and knotting are different things.

Cloth etc is possible in 4D, and higher, as long as the fibers are made of N-2 dimensions. This is also the maximal dimensions that would let wind pass around it.

The main difference between knotting and weaving is that you don't want the threads to end up at the bottom of the weave. This can only happen if the thread is a line in 3d, extended into further dimensions.
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wendy
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### Re: Are Cloth and Paper Impossible in 4D ?

Wendy is correct for the threads. Another aspect of this is that you will be making an N-1 dimensional (3d) cloth. That's the thing that I think Humans cannot completely understand. Humans cannot conceive of an object that is flat yet 3D.
Dionian

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### Re: Are Cloth and Paper Impossible in 4D ?

Actually, I've come to work with things that are 3D yet flat quite well. It took a long time to get used to it, but these days it's not that hard to fathom. It's all a matter of training your mind to think differently from what you're used to.

As for cloth, yes, for the "fibres" not to come apart quickly, you need something with 2D extent. So, in 3D-centric thinking, it would be knotting 2D sheets together to make a 3D cloth. 4D has this interesting (and sometimes rather strange and annoying) property that it's possible for two wireframe meshes to pass right through each other without ever touching, even if the meshes each span a large volume. The "holes" between the edges of the mesh are a higher order of hole than we have in 3D, and contain enough space for another mesh to glide right through. You need something that covers a solid span of 2D area in order for something to knot in 4D.
quickfur
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### Re: Are Cloth and Paper Impossible in 4D ?

2D threads as sheets being woven to make cloth seems impractical to me. Tape is more like it. That is, the two large dimensions need not be of equal size. One dimension must be very long, but the second need be only slightly wider than the threads have freedom to move. Not much.
PatrickPowers
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### Re: Are Cloth and Paper Impossible in 4D ?

PatrickPowers wrote:2D threads as sheets being woven to make cloth seems impractical to me. Tape is more like it. That is, the two large dimensions need not be of equal size. One dimension must be very long, but the second need be only slightly wider than the threads have freedom to move. Not much.

The problem with tape of limited width is that it effectively behaves like the analogue of a short piece of string in 3D. You probably could knot it, but it'd be fiddly and fall apart easily. The extra spatial dimension can be very annoying in this respect.

OTOH, you could wrap the 2D sheets around into cylindrical sheets, then thread spherindrical strings through the gap in the middle, and it would hold. So it'd be more like a string-and-loop way of knotting than tying two strings together, but because of the way holes in 4D work, this might be a more practical option than knotting large sheets together.
quickfur
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### Re: Are Cloth and Paper Impossible in 4D ?

I believe I have finally figured it out how cloth works. No matter how many dimensions the woof is 1D, the warp is N-2D.

In 3D a bolt of cloth is four to six feet wide and however long. In ND there would be one long dimension, one minimal dimension, and N-2 dimensions that are 4 to 6 feet wide. Well, they would be less, but all the same amount.

The warp always gets threaded between poles that are approx. 1D. Here is a video of weaving, https://www.youtube.com/watch?v=VbNl_nYI5qc, a remarkably complex and time-consuming process.
PatrickPowers
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### Re: Are Cloth and Paper Impossible in 4D ?

Cloth in 4D is a 3D surface made of 2D fibers. In my opinion, one possible shape of the fiber is a long and thin tube like pasta. a tube is a 2d surface, but when it gets longer and thinner, it can be used like a normal 1D thread to weave 4d cloth, but the difference from the real 1d thread is: When two threads cross over each other in 3d, one must pass through another thread's tubular hole to avoid being unknotted in 4d.
This idea is from a youtube video called knots in 4D(https://www.youtube.com/watch?v=nYz3pRk1cCA) who introduced a family of 2d tubular knots called Ribbon surfaces, and the video demonstrated many of these knots are not trivial(cannot be unknotted).
Maybe the disadvantage of tubular fiber is its weaving complexity: It's hard to weave a 3d cloth using just 1d thread. The threads must be very very long.
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