Is a 3D Equation System the Future of Advanced Mathematics?

[Jonnyb42]

I realize that we describe many dimensional and abstract things with only shapes that fit on 2 dimensions. All the operators, objects, sets, Integrals, derivatives, higher math I don't know yet, is all described by equations that could be written down on a 2-dimensional surface, such as paper. I believe we could get help in describing more advanced things if we used 3 dimensions.

Equations have been written on paper and other surfaces for a long time, and with our advances, (and many more advances to come) in computers, I believe we should try to devise a system of representing equations in 3 dimensions. Such a system would only be accessible on a computer or some other device.

If it is not advantageous whatsoever, then I still think we should do it because it would be very interesting.

(PS. If there already is such a system in development, PLEASE show me.)

 

[Pengwuino]

How does being able to visualize an equation in 3 dimensions do us any good in the way you're talking? If I were to make an equation "cube"... how would I see anything that isn't simply on the surface?

 

[Jonnyb42]

You would be able to see more than what's on the surface because a computer program that implements such a system would allow you scan through the "cube" (by the way it doesn't necessarily have to be a cube, but let's say for example,) so you can see a three dimensional structure.

If you are talking about literally a cube, with 6 sides, that is not what I am talking about. I take you saying a cube to mean some structure in the general shape of a cube, there isn't technically the literal surface of a cube.

 

[Hurkyl]

Actually, arithmetic expressions are rather one-dimensional. An example of a truly two-dimensional arithmetic would be that of string diagrams.


I find it unlikely that any physical notational system with more than two dimensions would be useful, due to the sheer difficulty of actually using it.

 

[Jonnyb42]

It is probably not useful, but I wanted to throw the idea out there.

 

[LukeD]

It is certainly useful and it is used, but being able to write stuff simply on paper is so useful that people are more interested in being able to reduce the math to the 2d case than in figuring stuff out about the 3d case.

 

[Xezlec]

Sure, whenever you have any function or operator that has multiple arguments, you can represent all the arguments and the result as coming out of it in different directions in 3 dimensions. I don't think it would be all that useful though since it has to be presented in 2D to the user anyway. You might as well use a conventional representation and just move around the terms in a computer the usual way rather than making it 3D and moving them around that way.