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Science, Math, & Technology

2-dimensional life

Posted Over 15 Years ago by Tmeister

[unparsed]Is life possible in such a universe?

On the atomic level, there's not much different from 3D. You could still have protons, neutrons, electrons, and quantum fields. Molecular structures would be different: you could not have a DNA-like double helix. This means either that genetic information must be stored in single-stranded molecules, or in flat untwisted double strands. In the first case, the strand is likely to get stuck to itself, so the second scenario is more likely

A long continuous DNA strand would have a tendency to get in the way of itself, so the strands would be short - one gene per strand. This way, the strands do not have to be broken in order to be read, and a gene can be blocked by sticking inhibitor proteins on its ends.

Membranes are a bit more of a problem. You could not have a porous membrane, since even the smallest pores would break the membrane into lots of tiny pieces. Transportation across membranes would have to take the form of bubbles that surround the material to be transported and then merge with the membrane. Even the smallest molecules (water, oxygen, etc.) would have to undergo this, which is inconvenient but I suppose not impossible.

Multicellular organisms are trickier. If the cells are all packed together, then most of the cells will be completely isolated from the outside environment. If, however, they are separated, then they will break apart and disperse. You could have a long filament-like organism that is only two cells thick, or you could suppose that materials are transported into and out of inner cells by way of other cells, which strains the limits of transportation via bubbles.

Elaborating on the filament snake, you could have a creature like this:
[img:d3f36d15c1]http://img217.imageshack.us/img217/6312/57106858mg5.gif[/img:d3f36d15c1]
These organisms could grow quite large, but the appendages must not touch each other, since that would isolate the inner cells. In the water, the appendages could be used to swim around; on land, the cells must develop strong cell walls so that it can hold up the appendages and keep them separate from one another. Otherwise, in the absence of buoyancy, they would flop down under gravity and cause cells on the interior to die. However, cell walls this strong probably cannot form bubbles for cross-membrane transportation, so life on land is ruled out.

Am I being too restrictive? Is there any way that more complex organisms could develop? Otherwise, I am led to the conclusion that complex life (let alone intelligent life) is impossible.

There are 9 Replies


[unparsed]
I am glad you asked.
This is an interesting and complicated question.
I have seen magazine articles -- in "Scientific American", for instance -- and books that discussed this question. Unfortunately at the moment I can't remember the titles nor authors nor dates.
Often one thing that's more difficult in 2D than in 3D is offset by another thing that's easier. In the end I'm left with the impression "I don't know".
I welcome speculation.

Over 15 Years ago
eldin raigmore
 

[unparsed]A 2d universe would have fundamentally different physics. Your post pretty much describes a universe that is 3d, but with the third dimension limited in size to one atom. You can't think in 3d terms like that with a 2d universe.

I believe life could exist in such a universe if the forces were sufficiently complex.

Please check out the game of life:
http://en.wikipedia.org/wiki/Conway's_Game_of_Life
I can't make a full link to that without the forum screwing it up (not even html works) so I'm afraid you'll have to copy and paste that or Google it.


That is more of a 2d universe. Fundamentally different rules. Life could almost certainly form in a simulation like that if the field were large enough and the simulation were allowed to run long enough.

Over 15 Years ago
Blake
 

[unparsed]Try to find a copy of

The Planiverse : computer contact with a two-dimensional world / A.K. Dewdney

The story not only is about a 2d conworld, but it goes in depth into a lot of the mathematic, chemistry, and physics of a 2d world. The parts not dealing with the conworld are pretty weak and can be skipped, but over-all it makes a great example (and reference, even though its fiction). :)

Over 15 Years ago
fmra
 

[unparsed]IMO a 2D world would work better without gravity than with, assuming the physics allows things to be fixed in place without having to touch things. You can walk round things rather than walking over them. Battles are survivable, rather than consisting of staring at the back of someone's head for hours, fighting for 30 seconds, then dying. You can own a house with multiple doors and windows.

There are some interesting points made at http://tetraspace.alkaline.org/ (involving a vertical 2D world). The 2D world I am most familiar with is Flatland, which is horizontal. (There is also a film out, which looks good to me, though I don't have it. Not to be confused with some of the other cinematographic version.)

Over 15 Years ago
simon.clarkstone
 

[unparsed]In a 2D world, atoms and planetary orbits would be unstable, because both electromagnetic force and gravitation would follow an inverse-linear rather than an inverse-square law. You need [i:ae0b593e7b]a lot[/i:ae0b593e7b] of handwaving to allow complex structures in a 2D universe.

Over 15 Years ago
WeepingElf
 

[unparsed]Are you sure? I thought that it was 4D in which orbits were unstable, but not 2D. I would have thought that the logic that makes orbits unstable in 4D would make them stable in 2D.

There have been some experiments with 2D atoms and they were stable, but I don't know what the attraction law was in that case. The 2D atoms were simulated by electrons constrained to the surface of a piece of silicon, and orbiting a positively-charged quantum dot. The periodic table in that case was a simple staircase down and staircase up. I forget what the orbitals looked like, but presumably they corresponded to the harmonics of a vibrating circle, in the same way the 3D orbitals correspond to the harmonics of a vibrating sphere (they do, check it out).

Over 15 Years ago
simon.clarkstone
 

[unparsed][quote:0c1fd296d5="simon.clarkstone"]Are you sure? I thought that it was 4D in which orbits were unstable, but not 2D. I would have thought that the logic that makes orbits unstable in 4D would make them stable in 2D.

There have been some experiments with 2D atoms and they were stable, but I don't know what the attraction law was in that case. The 2D atoms were simulated by electrons constrained to the surface of a piece of silicon, and orbiting a positively-charged quantum dot. The periodic table in that case was a simple staircase down and staircase up. I forget what the orbitals looked like, but presumably they corresponded to the harmonics of a vibrating circle, in the same way the 3D orbitals correspond to the harmonics of a vibrating sphere (they do, check it out).[/quote:0c1fd296d5]

What you describe is a planar system [i:0c1fd296d5]within 3D space[/i:0c1fd296d5], wherein the attraction law is still inverse-square, resulting in stable orbits. [i:0c1fd296d5]In 2D space[/i:0c1fd296d5], you'd have an inverse-linear attraction law, wherein only perfectly circular orbits were possible, but not elliptic ones - hence, orbits would be unstable because perfectly circular orbits are infinitely unlikely.

Over 15 Years ago
WeepingElf
 

[unparsed]
[quote="WeepingElf"]
What you describe is a planar system within 3D space, wherein the attraction law is still inverse-square, resulting in stable orbits. In 2D space, you'd have an inverse-linear attraction law, wherein only perfectly circular orbits were possible, but not elliptic ones - hence, orbits would be unstable because perfectly circular orbits are infinitely unlikely.

At least in 3D space, any central force following any inverse-power law other than an inverse-square law has no periodic solutions to the two-body problem other than circular orbits. [EDIT]: (Decades ago I read a number of books on Celestial Mechanics and on Central Forces, as well as on Ljapounov's Method and similar and related mathematics. I'm saying what I remember.) [/EDIT]

How certain are you that that applies also in 2D and 4D? *

And why wouldn't circular orbits be stable against sufficiently small perturbations even if the law was inverse-linear or inverse-cube? I don't know that they are and I don't know that they aren't. *

  • [EDIT]: I just read your post in the other thread where you said Scientific American said these orbits would be unstable against small perturbations if the inverse-power law was not an inverse-square law. Perhaps they also said these conclusions apply in 2D and 4D? Do you remember? [/EDIT]

    If no three-body problem has a stable solution (one towards which the system will tend to return if slightly perturbed), that would also mean no solar-systems. I don't know whether a gravitation law of inverse-power other than inverse-square, would rule out, for instance, the L4 and L5 libration points or some substitute for them; but if multi-body problems had no stable periodic or quasi-periodic solutions (two or more periods some of whose ratios are irrational constitute a system that is quasi-periodic rather than periodic), "solar systems" with more than one "planet" couldn't last very long.

    The argument that there couldn't be atoms if Coulomb's law made electric attraction/repulsion vary inversely as the distance or as its cube rather than as its square, because non-circular orbits wouldn't exist, has a flaw as I see it; the solar-system model of the atom is out-of-date in the quantum age. FAIK the conclusion could still be correct, but the argument seems to me unconvincing.

  • Over 15 Years ago
    eldin raigmore
     



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    chiarizio
     

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