Imagine that you're looking at a point, a dimensionless dot. Now move your head to one side, and aha, you see it was a line, just aimed straight at you.

So now look at that line, and move your head to one side in another direction: aha, it was an infinitely thin plane, just edge-on to you.

And now look at that plane, then move your head to one side: aha, it was a solid block, just flat-face toward you.

Now look at that block and shift your viewpoint in another dimension: aha, ...

(cf. SimplifyingThroughComplexity (1999-05-31), One Transcend Suffices (2009-10-14), ...) - ^z - 2012-08-23

Let's denote a point, a line, a plane and so forth by the symbols a₀ a₁ a₂ and so on.

If the object in question is of type a_i , For i > 1, is there any direction from which it will appear to be of type a_i-2 , let alone of type a_i-j for j > 2? –DougReingold