Prime Eval, Part 7

There was an illustrated book that I encountered in a bookstore in Saint Anthony Main in Minnesota in the mid-1980’s that told the story of a two-dimensional character that lived in, and explored a “flatland”. I can’t remember the title, and I’m having trouble tracking it down. It’s not Edwin Abbott’s Flatland (1880), but was probably inspired by it. The book I’m remembering had stick figures, while Abbott used multi-sided polygons, and there was some discussion of how the internal organs of the characters were designed with interlocking valves that would keep people from splitting into pieces while still allowing them to eat and digest food. Occasionally, there’d be rain storms, which would drown anyone silly enough to live underground, because water had no place to go except sideways or down; and when two people encountered each other when traveling opposite directions, one of them would have to climb over the other in order for them to get past each other.

I haven’t read Abbott’s Flatland, but according to the wiki, the first half discusses the mechanics of the 2D world, while the second half is a parody of Victorian society. However, looking at the website for the CG animated movie based on the book, it does raise some interesting questions. First and foremost would be, “do you need gravity?” In the movie, the characters move around like blood cells on a slide under a microscope. There’s no blatantly obvious form of locomotion. Instead, everyone just spins, or advances in a kind of ineffectual-looking rocking motion. We see the polygons face-on, and there is no real “up” or “down”. In the book I’d read, (I’ll call it “Stickland” for now) all the characters are stick figures, and there is a definite “up” and “down”, with “gravity” holding everyone to the ground line.

Both approaches exhibit a bias inherent to 3D creatures. With Stickland, we have gravity without a system representing mass, while in Flatland we have movement without friction (that is, the characters aren’t pushing off against a surface in order to propel themselves forward). In effect, the Flatland characters should be stuck in place, spinning helplessly in circles like an astronaut without a jetpack. Granted, both works are fiction and not intended to be questioned too closely. But still, the questions are there.

“Do you need gravity?” How would you move around in a 2D space? Stick figures on a cross sectional landscape have the obvious advantage of being able to move by pushing their feet against the ground line, assuming that their legs don’t cross. But this means that being bipedal is an evolutionary dead end. It’d be better if they were more amoeba-like, or had more of a rolling motion. On the other hand, being polygonal lets you move left-right and back-forth, giving you the ability to sidestep obstacles. If only there were something to push off of for propulsion (i.e. – the “ground” “under” you), or if there was some way to differentiate between movable and non-movable objects. Again, a more amoeba-like shape gives rise to something like a squid or octopus, which could move using a kind of air-jet.

All of this speculation is silly, because there’s no option for food, or other energy intake, and being 2-dimensional none of the creatures would be able to “see” (sense) each other, since they’d just appear as infinitely thin line segments edge-on. But there is one other aspect that is related to the previous post regarding cross sections, and that is, with an upright, stick figure-style world, the landscape could be in the shape of a big circle and the inhabitants would never be able to tell. If there’s a “sun” in the middle of the circle, the light would obscure the opposite side if you looked “forward and up”. Otherwise, the “ground” would be between you and the sun and the universe would appear black. If the “ground” is mostly flat with some hills and valleys, this would raise a different philosophical question. Which is, How could you tell if the world is a long, fluctuating line, and not a 3D plane that slides sideways as you “pretend” to walk forward and backward? That is, is movement illusionary and you’re actually traversing a 3D map whose cross section (the value of y) changes as x changes? The answer is, you wouldn’t be able to tell.

So, how would that translate for a 3-dimensional character within a 4D space?

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