How Do Flatlanders Move?

None of this actually explains how Flatlanders move. We know various things about their locomotion; that travelling somewhere involves some form of effort, that it is harder to travel North than in other directions, especially for women, and that femails "undulate" as they travel, although this is more of a safety measure than a necessity.

A mundane explanation, but one that causes a few problems, is the use of very short cilia-like mobile hairs for propulsion. This assumes that Flatland air is extremely dense, of course. If the hairs were short enough and spent most of their time flattened against the body they wouldn’t affect the process of angular recognition, and their motion might only be perceptible as a slight rippling in the brightness of a movin flatlander. Streamlining would be an advantage, so Isosceles and women would move faster than anyone else. A snag is that anything carried (such as the pouches shown in illustrations of some of the characters) would obstruct the hairs and slow Flatlanders down. This idea also doesn’t explain why women should find it difficult to go North.

Magnetism is another possibility; if there is a strong magnetic field across Flatland, and the Flatlanders can generate electric currents along their sides, they could harness them for movement. The normal diagram for this form of movement requires three dimensions, with field at right angles to current and both at right angles to movement, but there would presumably be some twodimensional equivalent. Or they could be harnessing magnetic fields from the 3D universe, which would probably be at an angle to Flatland. Females, being a single line in essence (their bodies are shown as two narrow parallel lines separated by softer organic matter for game purposes, but this is not canon) would have problems generating a strong electrical current across the width of their bodies, which might explain why they find it difficult to travel North. Unfortunately it would make any other direction just as difficult. Isosceles would be a little better off, but their narrow bases would make them slow and clumsy, although they might get a little more thrust by running current down their longer sides. By comparison squares and higher figures would find it easy to control their movements, especially if they could run current along several sides, and would be much more agile. This contrast in abilities doesn’t seem to apply in Flatland, so there’s probably another answer.

Perhaps they use light pressure. Flatland appears to get its light from 3D space, which ought to mean that it packs a vast amount of energy compared to most other forces in Flatland. If Flatlanders have evolved an ability to harness it, their movement could be the effect of organs roughly equivalent to solar sails inside their bodies. This won’t work very well if the light is exactly perpendicular to the plane of Flatland, but more or less works if light radiates from a source slightly to the North and above or below the plane of Flatland. As already noted, most light would normally pass through Flatlanders without being absorbed or reflected, but if Flatlanders have an internal organ or organs with varying reflectivity, like the elements of an LCD panel, they could be “switched on” to reflect light, or “switched off” to allow light to pass through the body. When light is reflected it exerts a microscopic amount of pressure; if that pressure is exerted at an angle it should produce a little thrust. Flatlanders might not know how they moved, but they would move. For fine control it would be useful to have multiple reflective organs, switched on or off to control rotation and possibly even allow tacking towards the light source, to the North. In the illustration a sixteen-sided aristocrat is using these organs (shown black) to move forward and slightly to the left; a second smaller reflective patch to the right of the centre line adds a little off-centre pressure, so that he is slowly rotating anticlockwise as he advances. The yellow arrows show the primary and secondary thrust.

This could explain why women have trouble going North; since they have very thin bodies they would have comparatively poor directional control and might find it …when the Medical Board has reported that recovery is improbable, I would suggest that the Irregular offspring be difficult to tack. This may also be the reason why they are described as the “weaker sex”, since A Square makes it clear that they are more dangerous than other Flatlanders and probably just as strong. Some form of energy would be needed to power the process, hence feelings of tiredness after a long “walk”.

All of this requires an immense amount of handwaving, especially in explaining how Flatlanders absorb enough energy to move without frying themselves, and referees may prefer to tackle the problem by refusing to explain it. After all, it’s what A Square and his literary agent Edwin A Abbott did.