Frames of Reference

I was rearranging my bookshelves today and came across one of my old college texts, a small novel called Flatland. The story takes place in a two-dimensional world, told from the point of view of A Square. At one point A Square is visited by an extra-dimensional visitor: a sphere. The sphere takes A Square on a tour of the dimensions, from 0 up through 3, and maybe even 4. I forget; I last read the book almost ten years ago.

One concept which I still find fascinating is one of the incidentals to extra-planar travel (as described in Flatland) — namely, that from the point of view of dimension n+1 , an observer can see into the middle of a solid which resides in dimension n . Consider: from the point of view of the 3-dimension world in which we exist while traveling through 4d space, we can see into the middle of a 1d (line) or a 2d (plane) object. A square, seen from within it’s own dimension, is a line. A line, seen from within its own dimension, is a point. And a point(0d) is the only thing which exists within its own frame of reference.

So an observer in 4d space would be able to see into the middle of a 3d object. This intuitively makes sense. Assuming time to be the fourth dimension, pick a point at a particular location in space and time, and watch: When a 3d solid intersects that point, the part of that solid which occupies that point will be visible.

And, as these thing go, I have been reading more on memetics, and the points of view of the inhabitants of Flatland, when encountering an occupant of Sphereland , correspond with a concept I studied briefly in college — memetic engulfment .

Memetic engulfment is that which happens when you get so caught up in your your self-reinforcing world-view that you forget that what you see and experience is not the entire world. I studied this in the context of The University, and the idea that the what was taught — the experiences and information imparted to students — was becoming more and more removed from what was actually necessary for existing in “the real world”. The University Meme slowly crowds out the rest of the world.

But all of that was a long time ago, and now I wonder if, given the appropriate metaphors and practices, a person could perceive, with 3d sensory apparatus, the 4d world from the point of view of a 5d frame of reference. In other words, perceive the flow of time, from outside the flow of time…

And if you managed it, how would you get back?

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