Are Multi-Dimensional Mathematics Possible?

Question

I recently have been putting together a theory regarding what I am calling "Multi-Dimensional" Mathematics.

The normal number line is limited to positive and negative numbers, which you can think of as a piece of paper. A piece of paper can hold information, though its only flat, and basic information. If this piece of paper was a box, the information would be much more dynamic, as it is 6 times the original flat surface.

The multi-dimensional mathematics would be much greater than the "Two-Dimension", "left-to-right" number lines of today. Instead of it being on a single axis, the equations would extend six ways (left, right, up, down, forward, back).

This is only a simple explanation, as I am only 14 years old, with a basic knowledge of advanced mathematics (I am interested in theoretical physics).

Answer 1

Well, yes, it is certainly possible. In fact, higher dimensional spaces are frequently used in mathematics, although often these spaces are simply extensions of lower dimensional ones. For example, think of Cartesian product spaces. It makes sense to make big things from something small that we understand well.



Complex numbers and quaternions are both extensions of the real numbers. Mathematicians routinely use vector spaces with an infinite number of dimensions.



Do you have something innovative, something amazing in your grasp? Possibly. This is impossible to tell from your brief description. You would need to think about (and explain) why your idea is different from a simple Cartesian product space in 6 dimensions.



Really, mathematics allows you to conceive of anything. Define the rules for manipulating this system. Make those rules consistent, so that no logical flaws arise. (It often helps if you can show that you have constructed a vector space, for example, since then all of the accumulated knowledge we have about vector spaces will apply too.) Is this system you have constructed of value? Even if there are no obvious uses for it initially, nothing prevents you from probing your creation. After all, this is mathematics. There need be no clear value in your creation, but tomorrow you may find a use. and the simple exercise of creating helps you to learn how to build something better tomorrow.



In the end, even if this turns out that you have created nothing new, don't be disillusioned. Use what you have learned in the process, and start anew tomorrow.

Answer 2

There already is something exactly like that; it's three-dimensional mathematics, and we study these spaces particularly in-depth starting in Multivariable Calculus and into higher-level mathematics.



Of course, there can be as many dimension as we like in mathematics, but it implies more convolution in naming and defining more variables, and keeping track of them.



So, this isn't exactly theoretical in that we as humans tap into more dimensions than just two of basic math; more variables is in fact more realistic because reactions and methods in real-life are not dependent on 1 other variable, but more so reliant on several if not infinite variables.



There you go. Hope that helps.

Answer 3

Sorry, but this already exists.

1,2,3, and 4th dimensions have already been greatly defined.

5 to much larger have been defined too.



In precalulus you will learn about the six directions and their proper nomenclature.