# Difficulty in visualizing more than three spatial dimension [closed]

Is there is any other way than abstract mathematics to visualize higher dimensions. Physicists working in high energy physics live in higher dimensions (pun intended), with their sophisticated mathematical tools they easily work there way out in higher dimensions. Take for a simple example of a $n$-sphere $S^N$ http://en.wikipedia.org/wiki/N-sphere.

• 0-sphere $S^0$ is a pair of points ${c − r, c + r}$, and is the boundary of a line segment (the 1-ball $B^1$).
• 1-sphere $S^1$ is a circle of radius $r$ centered at $c$, and is the boundary of a disk (the 2-ball $B^2$).
• 2-sphere $S^2$ is an ordinary 2-dimensional sphere in 3-dimensional Euclidean space, and is the boundary of an ordinary ball (the 3-ball $B^3$).
• 3-sphere $S^3$ is a sphere in 4-dimensional Euclidean space.

The problem is how hard I think it is impossible for me to visualize a 3-sphere.

• Is this a question? What are you asking? Feb 3, 2012 at 8:18
• You do not need to visualize higher dimensional spaces to understand them. Let me give you an analogy (the analogy I am giving is not isomorphic). How can one understand intuitively the meaning of a vector that lives in 5 dimensional space for example?
– Revo
Feb 3, 2012 at 8:36
• A student that takes 5 courses this semester say, his overall performance this semester depends on how he does in the 5 courses. Hence, you can think of his performance as a vector that lives in 5 dimensional space, one axis for every course. The axes can be graduated so you can assign a mark per course. Of course in this case the axes scales run from 0 to the max possible mark.
– Revo
Feb 3, 2012 at 8:36
• Please understand that my example is only an analogy to give you an intuitive feeling of higher dimensions. The student performance is not a vector in the mathematical sense.
– Revo
Feb 3, 2012 at 8:36
• I still don't understand the question... Feb 3, 2012 at 17:46