Comment by peter_d_sherman

>"One might as well ask how it's possible that our complex 3 dimensional world can be contained in the flat surface of a mirror, film strip, or camera sensor."

Space filling curves with three dimensions could potentially provide us with some clues:

https://en.wikipedia.org/wiki/Z-order_curve

"In mathematical analysis and computer science, functions which are Z-order, Lebesgue curve, Morton space-filling curve,[1] Morton order or Morton code map multidimensional data to one dimension while preserving locality of the data points (two points close together in multidimensions with high probability lie also close together in Morton order)."

Also, to answer the question, potentially Octrees might be interesting to research:

https://mathworld.wolfram.com/Octree.html

"An octree is a rooted tree that represents a three-dimensional region by recursively subdividing it into eight congruent, axis-aligned cuboids, usually cubes (Meagher 1982, Samet 1990). Each internal node represents a spatial cell and has eight children, one for each octant of the cell. A tree leaf represents a cell that is not subdivided further."

But, since "a picture is worth one thousand words":

https://www.google.com/search?q=octree&udm=2

Another thing to consider is that according to the Knuth Transform (aka Left-Child Right-Sibling (LCRS) representation), apparently any k-ary tree (Octree = 8-ary tree) can apparently be converted into a Binary Tree without losing information:

https://en.wikipedia.org/wiki/Left-child_right-sibling_binar...

So, is there a 1D (or 2D) representation for 3D reality?

Well, I personally don't know!

What I do know is that a certain popular rock group sang the following lyric in one of their popular rock songs, back in 1999:

"Space may be the final frontier -- but it's made in a Hollywood basement..."

-The Red Hot Chili Peppers, "Californication"

So, you decide! :-)