How to imagine the 4-space

Question

We represent 1-space by a straight line, 2-space by two perpendicular line and 3-space by 3 perpendicular line. Do we represent 4-space by 4 perpendicular line? If it is, how can I imagine it ?

Answer 1

Yes you can represent any n-dimensional space by its values along n to each other perpendicular lines.

But since we are beings living in a 3 dimensional space, we can not really imagine such a space where n is greater then 3. I find it the easiest to just think of it in an abstract sense, in that each position point just has n values which describe it completely and uniquely.

For 4 dimensions you could imagine being somehow outside of time itself and looking down on it. Then every event would have a unique position due to its physical position and the time it was happening. But as I said there is ultimately no way to really imagine a higher dimensional space.