More Flat Science

[ffutures]

Still trying to work out how movement works, and realised something that may be important - if they're only one atom thick, Flatlanders must be incredibly light. For example the narrator, A Square, is 6" (150mm) square. Assuming a generous thickness of 1 nanometer (10^-6mm) his volume is 2250 / 10^-6 mm³ or 0.00225 mm³. So if he's made of something like flesh, density a little less than 1, his mass is about 0.002 mg. Most other common materials still give very low masses - lots of rounding follows (and hopefully not too many errors):

Glass / silicates - 0.005mg
Sapphire - 0.008mg
Steel - 0.016mg
Lead - 0.025mg
Gold - 0.05mg

This means that relatively weak forces, e.g. electrostatics, could be enough to move him.

Of course this light mass gives its own problems. Ignoring the possibility that he's something really exotic like neutronium, he still has tiny mass and a relatively big perimeter, about 600mm, with a surface area around the edges of 0.0006mm³ (yes, I know there's all sorts of reasons why this is nonsense, but bear with me, this is all hand-waving anyway).

So... with that big a perimeter he must experience a significant number of molecular collisions every second. My question - and this is where I need help - are we talking so many that they even out, or few enough that Brownian motion could occur? And if so, how do we go about converting random impacts into controlled movement? Would it be possible to change the number of impacts in a particular part of the perimeter by e.g. vibrating an edge slightly?

Comments

[vodex.livejournal.com]

Hello, just encountered your wonderful LJ.

This has probably been raised before, but I thought the Flatlanders were explictly two-dimensional? In which case they would not have a very low 3D mass and be easy affected by static, wind etc. anymore than we would have a very low 4D mass. We may be easily affected by 4D Brownian motion or electrostatics (now there's an idea - The Man Who Was Bumped Outwards By Hyperspace Smoke Particles) but we are nice and massive enough to live in the 3D world. Perhaps it's the same for the Flatlanders, depiction of their environment notwithstanding? A 3D force comes along (e.g. the Sphere brushes them and they flutter) but left by themselves they're much more... erm... solid?

[ffutures.livejournal.com]

This is unfortunately true - thanks for pointing it out.