I get 1, 2, and 3 dimensions and their visual representations. For instance, 3-dimensional space has width, length, and depth but how about a 6-dimensional space, how can we grasp it in n intuitive manner free of mathematical analysis?
In: 8
Think of dimension as a mathematical term for “ingredient”.
The colours on our screen can be considered 3D colours. They have THREE ingredients red, green and blue.
Physics is often interested in 3 dimensions, because the space that we live in has 3 dimensions. There are three ingredients that go into WHERE you are. It takes three numbers to describe how much of each direction equates to your position.
But some problems care about more than position. A common additional ingredient is time. To describe WHEN you are requires another number (for a total of 4 dimensions). Sometimes physicists are interested in where you are and where you are moving toward (velocity), so you’d need a total of 6 dimensions (3 for your current position and 3 for the position you would be at in 1 second, if you continued at your current speed).
The more complicated the problem, the more dimensions you are likely to be interested in. Temperature, momentum, magnetic field, number of cookies, happiness, probability of snow. Every aspect is going to add a new “dimension” to the problem.
Mathematicians often imagine shapes that are 4-Dimensional. Shapes that require 4 numbers to describe where you are on the shape. You may argue that you never such a thing in real life, but mathematicians don’t care about what shapes can appear in real life and which can’t, they only care about the mathematical properties of these shapes.
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