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

[cdybedahl.livejournal.com]

The number of collisions would depend a lot on the air pressure, wouldn't it? If it's anything close to our atmosphere, even that area should be hit by more than enough molecules for it to average out. And it suddenly occurs to me that I have no idea what a gas behaves like in a space that narrow, really.

Also, what are the top and bottom edges of the space like? I guess treating them as frictionless infinitely rigid surfaces make the most sense...

[ffutures.livejournal.com]

I don't think they can be completely frictionless; objects stay put, and there's nothing to suggest that Flatlanders have trouble stopping once moving.

[gbsteve.livejournal.com]

There's this constant light everywhere. How about Flatlanders can vary the albedo of their surfaces to change the light pressure on them? This allows them to move around.

Perhaps they can only change the albedo of one side at a time. This would mean that those with more sides would be capable of finer control of their movement and that those with fewers sides might tend to rush about less controllably.

[ffutures.livejournal.com]

Neat - like a radiometer. That'd work for me, I think. Many thanks for the suggestion.

[raygungothic.livejournal.com]

Potential problem: the common soldiery would accelerate fastest sideways (rather reducing their martial potential, if I remember correctly) unless there are (genetic?) reasons why isosceles triangles can't change the albedo of their longer sides.

I think of the Flatland fog as being very cold, which might reduce the effects of Brownian motion. There are a lot of parameters that can be varied.

[ffutures.livejournal.com]

Yes, that's true. Bugger...

Unless there is a lot of friction with the environment, of course, in which case the narrow isosceles and females, being the most streamlines, would have the advantage going forward. Remember that they have to push everything in their path out of the way to the sides - even in air of normal-ish density there'd be a LOT of air resistance for the higher figures.

This still doesn't explain how females move, unfortunately - no width to speak of, so very little force propelling them forwards - so maybe we need another answer.

[parakkum.livejournal.com]

Though I don't know the setting, having not read the book, one possible mechanism at that scale is some kind of Brownian ratchet -- that is, some way of hooking onto the environment in a unidirectional manner. Many transport proteins work this way. Basically, the flatlander would think "going forward now" and stick out its Brownian ratchets, which would then bend or otherwise freely allow movement in one direction, but lock (like a standard ratchet) against movement from other directions. In this case, molecular bumps that move you the way you want to go are able to push you that way, but you're braced against bumps that would move you in other directions.

Movement will be a bit saltatory, but it does work.

Having said all that, I think at 2uG, Brownian motion probably isn't a factor. :) Electrostatics could definitely work -- heck, geckos stick to walls via Van der Waals forces, and they're big.

[ffutures.livejournal.com]

Electrostatics does seem to be the one that has the least problems - presumably they move charge to push against the air etc., and use more focused charge transfers to handle objects etc.

I think I'm going to have to reread the book to see if there are any "clues" I'm overlooking. I know that Abbott wasn't thinking in these terms at all, but it could be that something I'm overlooking will suggest an answer.

[raygungothic.livejournal.com]

High friction/drag/whatever would, tidily, provide yet another reason why the lowest orders are the best soldiers. Not only are they spiky, they're fast.

(I noticed Sgt. S'harper had a gun - I didn't think they fought that way?)

[ffutures.livejournal.com]

The general social feel of the setting is Napoleonic / Victorian, so I decided that it was time for them to invent guns, and that the higher figures might occasionally use swords etc. for self defence. Guns are HORRIBLY dangerous, especially to the person firing them... but if you're a Square officer and the gunner is an Isosceles private that isn't likely to worry you much.

[raygungothic.livejournal.com]

Ah, that makes sense. The higher orders would want to have something like a sword, because they're not sharp enough for unarmed combat.

I presume they'd still only be able to make two dimensional swords, not one, so a woman would be more lethal than any sword. That feels right :-)

[ffutures.livejournal.com]

And when I reread it I realised they already had artillery, I'd just forgotten that this was in the book.

[robertprior.livejournal.com]

Given that A Square is much denser than the 1-atom-thick atmosphere, and a relatively large object (compared to atoms) I don't think you have to worry about Brownian motion.

Wind, possibly, but there are apparently ways for the Flatland critters to anchor things to the non-existent ground.

[dsample.livejournal.com]

I agree, Brownian motion would be about as noticeable for macroscopic Flatlanders as it is in the real world.

I think that rather than gravity and such, it would be best to think of Flatlanders' swimming through some sort of liquid medium. Perhaps they propel themselves with millions of microscopic cilia around their perimeters. There may be different types of media. A river would be a current of a denser liquid through the thinner "air."

[ffutures.livejournal.com]

Cillia work pretty well as a propulsion and manipulation system, given a sufficiently thick atmosphere, but they don't really fit in with the Flatlans obsession with perfect regularity - I suppose they could be smaller than their instruments can measure or something.

[ffutures.livejournal.com]

One consequence - assuming the one atom thick flatlander, the movement of the cillia would be perceived as a constant change in the reflection along the edge of a Flatlander. Maybe this is why they think that living things look brighter than everything else.

[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.