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?
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First off a dimension just represents an axis you can move along without having to also move along another different dimension’s axis.
Simplest example is the 2D xy grid. You likely understand easily that you can move along the X axis without having to move along the Y, thus we can say there is an X dimension and a Y dimension to the grid.
In a mathematical sense you can easily extend this infinitely in concept if not in visualization. You just conceive of another dimension you’re moving along in. If a 2D xy grid has a coordinate written X, Y and a 3D xyz space has a coordinate written X, Y, Z we can easily extrapolate that a 5D xyzab superspace has coordinates written X, Y, Z, A, B or w/e.
So purely mathematically when it comes to higher dimensions, that should be easy to grasp.
What you’re likely though having trouble with is that we also use the concept of multiple dimensions to describe our experience of the phenomenon of spacetime, but we can grasp physical dimensions too by going back to the first sentence I wrote. A dimension just represents an axis you can move along without necessarily moving along another. In reference to actual physical space this is easy to understand as 3D as you understand you can move forward/back without having to move up/down or left/right. We can thus say spacetime has ‘width’, ‘length’, and ‘height’ dimensions to it.
But what if you want to move in some direction which isn’t those six? In physical space, that isn’t possible that dimension just isn’t there. That being said we can see our experience with the phenomenon of time and its intimate relationship with space as an additional dimension. We know we can “move” through time without having to move within the six physical directions. But we don’t HAVE to call time the 4th dimension or something, that’s just a way to think of it.
We could just as conceivably make an axis of emotions ranging from hate to love or something and describe experiencing different emotions as moving along this axis in which case we could say ’emotion’ is the 4th dimension that we can move along without moving in 3D space, etc. We could then come up with all kinds of other dimensions and claim humans actually exist in N-dimensional space but how useful those dimensions / this idea would actually be in explaining reality would be questionable.
TL;DR A dimension is just a concept. Some real life phenomenon can be described using dimensions, but a ‘higher dimension’ is just an idea like a ‘bigger number’ it doesn’t reflect anything about reality.
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