Ok, but no matter how we cut it, every healthy human can "identify" a "real" cube as essentially a 6-sided rigid object with 8 hard corners. The token "cube" immediately comes to mind as the "wave label" for the "distinct entity" called "cube." A cube in our "finite" world loses its definition the moment we take elements away from it where we can't recognize it anymore. This doesn't happen in the mind. The definition is static and innate. Once the token "cube" is assigned to it, we use "cube" to identify this 3D geometry.That may the most common but that may not be the only way to describe a cube.
Underlying is the fact that we must all agree on the way we represent something.
For example, if we denote dE as being the distance between dots, if we start from the point (0,0) and darw a line left to right to the point (1,0), then double back and draw the next line from the point (0,dE) to (1,dE), then double back again and draw a line from (0,2*dE) to (1,2*dE), then double back again and again until we reach the point (1,1) with the last line then we would have draw a shaded square. Draw an infinite number of those squares and we would have drawn a shaded cube.
Now interestingly, we could associate each point in that cube with a SINGLE number which is the enumeration of the 'dots' that it took to get there. Welcome to the world of the 1d universe,
Of course there is also nothing stopping us from defining the cube in terms of 3d angles also such as in spherical coordinates however that is still 3d not 1d.
There is also the intrinsic coordinates which define things from the inside out more or less.
So the question remains — if we can identify one, and it doesn't exist in our brain as-described — where exactly does it exist, as-described? This is the 900 pound gorilla in the room, in my estimation, and I believe all reasoning on the topic has to flow from this fundamental question.
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