After watching the movie <Interstellar> a couple times, it made me think about the concept of higher dimensions. Merely bringing up this concept might be more than enough to intimidate some people. But it just seems to me that every time we mention 4 or 5 dimensions, we compel ourselves to do the impossible. We try to ‘visualize’ the 4 or 5 perpendicular axes in three dimensional space, giving ourselves a small stroke. But the point is not ‘visualizing’ the high dimensional space, but conceptualizing and utilizing it.

Those ‘fifth dimensional beings’ in <Interstellar> would look at us pretty similar to how we look at ants.In other words, ants would have small strokes thinking about the three-dimensional space. Then, how would ant-Christopher Nolan in ant-world, render the ‘cube’ scene with ant-Cooper ‘floating’ in 2D space? If the third dimension here is a ‘z-axis’ for 3d space, ant-Nolan would render intersecting one-dimensional lines each showing a certain time in 2D space, projected onto the line. Well, that’s not so comprehensive, so let’s give the third dimension to ‘time’. Certainly time also flows the same in 2D as in 3D. This time, the intersecting lines would be projections of a single 2D space in different points of time and ant-Cooper is floating around his two-dimensional world pushing one-dimensional book shelves sending messages to ant-Murphy.

How about a practical example in our everyday lives. If theoretical physicists like Einstein or Stephen Hawking tried to conceptualize higher dimensions in theory, composers like J.S. Bach or L.V. Beethoven has already mastered the concept in their guts and was frankly leaping through countless dimensions. All different voices in polyphonic music are accountable as independent components. For example, Bach’s fugue in C# minor in his first book of the Well Tempered Claviers is a triple fugue(this means it has 3 separate subjects) with four voices. This is conceptually equivalent to three people hopping around 4 dimensions. Pretty much like Cooper floating around the four-dimensional cube?

I could go on and on with different examples all around everything. But what really fascinates me is that within a selected scope, two things so radically different (Cooper’s four-dimensional cube and Bach’s Fugue) can be deduced to a single mutual concept.