The strange case of sub-dimensional worlds

2019-10-20 @Creative

Imagine occupying a one-dimensional world. Think of all the constraints that places on your abilities. Movement along one axis is about all you can aspire to. No width, depth, or shape of any kind is to be evinced. No circumnavigating your obstacles. No taking advantage of express transport. No deploying communication channels.

Everything constitutes a line of varying length. You are trapped on this one-dimensional plane in hope that all citizens navigate at a mutually acceptable pace, like a conveyor belt pipeline. With such limited range of motion one wonders how everything doesn’t come to a blazing halt.

Such limits placed on mobility might even warrant obesity concerns. And yet, cursed by the inability to acquire thickness, worry you need not.

Color is certainly an option, as well as the ability to vary it, one would hope. Imagine this one-dimensional plane as a continuously pulsating chromatic fiasco. Does that sort of party not sound alluring?

Notwithstanding, life begins at one coordinate (point), and terminates at another. Perhaps with such limited motion, innovation leans towards something entirely meta-physical. How about teleportation or telepathy as the sole means to transcend the communication and transport barriers? Or maybe we cannot even fathom what a 1-dimensional brain might conceive when subjected to such tight constraints? Whatever it is, the 1D inhabitants need not fall victim to prime-time programming.

Two-dimensional world occupants may scorn at the one-dimensional constraints. However, the 2D landscape is also no walk in the park. Circumnavigation drastically improves without the need to resort to psychedelics. Road transport becomes possible, although in an awfully strange way, restricted by lack of certain perspective.

The 2D world architect must arrive at a crucial design decision:

  1. back/forth - left/right
  2. back/forth - up/down
  3. left/right - up/down

(Bear in mind, the above are 3D world projections, hence only a 3D world architect could adequately conceive of such choices. We differentiate between each plane with reference to the position of our three-dimensional head and the perception of forward or lateral movement in reference to our three-dimensional limbs. By similar reasoning, the architect of any N-dimensional world must originate from (N+1) dimensions, or at least have naturalized from such a place, in order to exercise proper strategy, insofar as envisioning the benefits/pitfalls of each respective plane.)

Empirical evidence collected in various simulations seems to favor option #2. Recall the classic side-scroller video games - Super Mario, Castlevania, Lemmings, etc. If we eliminate the cute backdrops of forestry and cloud formations (attempts to cheat and elicit 3D perspective), those are fairly legitimate simulations of what we can expect. Sideways circumnavigation is out of the question. However, we can climb, leap over obstacles, leverage varying fantastic forms of transport among magic carpets, cannonballs and saddled creatures (innovation heavily inclined towards vertical transport).

One might feel tempted by option #1. Among the three, it is the most suggestive of the first-person perspective we experience in the 3D landscape. Most of the time, we move back and forth, left and right, with plenty of options to side-step obstacles and mitigate traffic. Forget air transport, satellite communication or anything above.

One might think such limitations reasonable, considering the vast populace that hardly leaves the village. And yet the problem is more severe. You couldn’t even board a train, for there’s no vertical room to climb or opportunity to construct train tracks. At best we could leverage expedited transport in the shape of Euclidean 2D structures that we would just “consume”, in a manner of speaking, but definitely not climb or saddle. And forget perspective, shade, or the flexibility to glance over things - everything we take for granted in 3D land.

Option #3 is an interesting case, although in certain ways it bears notable resemblance to option 2. We gain all the benefits of vertical space, but instead of exercising back-and-forth acrobatic maneuvers most natural to us, we imagine a series of side-steps and cartwheels, a routine awfully reminiscent of beginner Capoeira lessons. This approach sort of worked for the original Atari rendition of Donkey Kong. I never played the arcades, but have witnessed the creature successfully ambulate laterally and vertically. On the other hand, I suspect further 3-dimensional leakage.

And what laws of physics would govern these whimsical landscapes? Is there conservation of energy? Is there Black Friday? How about Craniosacral therapy? Ponder among those questions. Meanwhile, be at liberty to return to and appreciate whatever N dimensions you normally occupy.

Questions, comments? Connect.