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So I was sitting and reading the various takes on visualising the 4th dimension in this popular question. And I was thinking of how people are simply struggling. They are often trying to use drawings and the use of eyes to visualise it and I thought that might not be the best way to look at it.

So I thought, hey, why not try visualising it with touch and your ears. Several thought experiments later, and I thought of some real world examples, especially in quantum physics.

So I have to ask before I take things too far with these thought experiments: can a point have an attitude?

Wikipedia article on Attitude

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To answer your question. Yes. in a sense this concept is known as a tensor field. This is where each point in $\mathbb R^2$ or $\mathbb R^3$ is assigned a value or a vector. Does that answer your question? Sometimes the assigned values can even be complex (i.e. $\mathbb C^n$).

Sentinel135
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