# Thread: How would physics, chemistry, biology be different in a 2-D universe? e.g. "Flatland"

1. ## How would physics, chemistry, biology be different in a 2-D universe? e.g. "Flatland"

Hi all,

I have been re-reading a great little book "The Planiverse" published in the 80's - similar in theme to Edwin Abbots's "Flatland".

https://en.wikipedia.org/wiki/The_Planiverse

I was wondering if complex life could evolve due to limitations in arrangements of 2-d atoms.
Could there be some 2-d gene/DNA mechanism?
Assuming gravity would work in an analagous way... would a flat-landers laws of motion be different?

2. If an “object” were literally two-dimensional, it would have no volume and hence no mass, and therefore no concern of physics or chemistry. However, such might provoke interesting thought experiments!

If we accept a third dimension just wide enough to permit planar molecules, then chemistry should be possible.

I think I have a copy of Planiverse. Author was A. K. Dewdney, and I believe that he wrote some Scientific American articles on the subject. I’ll have to review it.

3. Aren't our 3D subatomic particles 'point particles' with no volume? I thought mass was due to interaction with the Higg's field. I can't see why a theoretical 2-D atom in a 2-D universe would have no mass as long as there was a 2-D Higg's-like field?

4. Ah! There I go thinking in conventional math terms!

5. I've been exploring anatomical biophysics of 2D critters.

This is my solution to the transfer of fluids:

pic_2dvalve.gif

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Originally Posted by plant
Hi all,
Assuming gravity would work in an analagous way... would a flat-landers laws of motion be different?
One way gravity would be different is instead of decreasing in strength according to an inverse square law 1/r^2 it would decrease according to just an inverse law, 1/r. This also leads to the side effect of there being no such thing as an escape velocity, which means that no matter how far away you get from an object you are guaranteed to fall back to it (or go into orbit).

Electricity and magnetism would be effected in the same way, but I don't know how that would effect things like atomic orbitals and the chemistry that is dependent upon them. I would think that it would make it drastically different, and who knows what effect that would have on life (nothing good, I would assume).

As far as the laws of motion, those I don't see why they would be any different.

DaveC426913
I've been exploring anatomical biophysics of 2D critters.

This is my solution to the transfer of fluids:

Attachment 24650
That is fascinating! That is a really ingenious solution.

7. I was wondering if you consider an electromagnetic 'wave' as electric/magnetic at 90 degrees to each other.. that would be impossible in 2-D?
Or do you just have 2-D photons vs 3-D photons?

img_emishield_01.jpg

8. Yes I'd read something about the problem of escape velocity.. but i don't really understand why?
If gravity falls off in proportion to distance between 2 objects rather than square of distance, it will be stronger ... but doesn't that mean escape velocity will just have to be higher?

9. Originally Posted by plant
Aren't our 3D subatomic particles 'point particles' with no volume? I thought mass was due to interaction with the Higg's field. I can't see why a theoretical 2-D atom in a 2-D universe would have no mass as long as there was a 2-D Higg's-like field?
I would think the people of the four dimensional universe are saying the same thing about how a universe couldn't work with only three dimensions. Such is the nature of multidimensional chauvinism.

10. Originally Posted by plant
Yes I'd read something about the problem of escape velocity.. but i don't really understand why?
If gravity falls off in proportion to distance between 2 objects rather than square of distance, it will be stronger ... but doesn't that mean escape velocity will just have to be higher?
I haven't run through the calculus but I imagine that it would suggest that because gravity doesn't fall off nearly as fast, it will succeed eventually at reducing your speed to zero. With inverse square fall off, that is not the case.

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I think chemistry would be extremely simplified. The molecular bonds we know in 3D work because of the shapes of electron orbitals, and it seems to me that flattened orbitals wouldn't have nearly as many ways of bonding. Think about all the different 3D shapes you can make with different carbon compounds -- nowhere hear as much variety if you flatten it.

OP mentioned biology, but don't think any kind of complex life could exist in 2D. As 3D organisms, we have a bloodstream that moves numerous substances around our bodies. How would that work in 2D? Bones have to be attached to each other to provide support, and a muscle should be attached from one bone to another to work well. For even the simplest nervous system (like in insects, for example) you still need nerves to connect not only to sensory organs and muscles but also to each other. How would all these systems coexist, if none of them can cross over each other? (See: The 3-utility problem. It's impossible on a flat plane)

Even for single-celled organisms, I can imagine using something like a vacuole to absorb nutrients and expel waste, but how would their DNA-analog work? One of the requirements of a life form is self-replication, and for that you have to store your "blueprint" somehow, with the ability to copy it and translate the instructions into proteins -- is this even possible in 2D?

I would be interested in hearing how 2D sound waves would work. If wave propagation is limited to the plane, then would that make sound carry farther? It seems like it should, if it doesn't have 3 dimensions to disperse into.

12. i think there is a component of dimensional chauvinism.... perhaps one needs to think 'outside the box'. and 'into the plane'.

Re: Biology- a double gut opening (mouth and anus) would mean the organism woould fall apart (though Dewdney in 'The Planiverse' suggests 'zipper-like' structures)... but a single mouth/anus like a starfish would work.. or multiple microscopic 'mouths' with external digestion allowing diffusion into a central 'blood cavity' would work. Hydrostatic 'muscles' would work i think- no bones/muscles required. Neuron networks would be simpler.. and brains probably larger if you're after intelligence...

Re: DNA.. not sure why a 2-D DNA is difficult. The 3-D helical structure of our DNA is not critical for function- just saves space. I can't see any reason why polymers such as DNA, proteins, carbohydrates could not exist in a 2-D world.(Although I doubt that they would evolve again in the same way even on another 3-D world in our universe...). Some form of digital information storage with complementary molecules would be possible??

13. From this website: https://speculativeevolution.fandom....ki/Exotic_life

Physics in a 2-dimensional Universe would obviously be radically different from the one we're accustomed to in many ways. For example, in a 3-d space the force of gravity decreases proportionally to the square of the distance: this leads satellites to move in an elliptical orbit, as ellipses are described by a quadratic equation (one with a squared variable). Yet, stable orbits are still possible in a 2-d plane: they would trace a vaguely star-shaped hypotrochoid (see here, figure 2), of which the ellipse is a special case.

Light and other electromagnetic radiations would also be very different, as in our Universe they have two components oscillating in planes perpendicular to each other; they might be replaced by something similar to particle beams. Also, fluids, if they exist at all, would probably appear denser and more viscous, as they have less directions in which to be displaced by objects, and thus would exert more resistence.
2-dimensional fish

A 2-dimensional fish-like creature.
There are yet more direct obstacles to life itself: for example, a tube or channel going through a body from end to end would cut it in half. However, the transportation of matter through the body could be accomplished by a flow of vesicles, which could carry food inside and waste outside, and even merge together to form organs. In this thread on the forum, the user Kain proposes organisms composed by two jagged ribbons that fit into each other like a zipper, pushing "water" backwards. Also, intelligence could be severely limited by the fact that 2-d neurons would have less neighbours to connect with, but in his The Planiverse (1984), A. K. Dewdney proposes crossovers that allow signal-carring wires to cross each other, thereby increasing the possible connections.

The square-cube law would presumably still apply, even though it would become a "line-square law": for example, the body mass would be determined by its area, and the strength of bones and muscles by their width. 2-dimensional "animals" would probably have an external skeleton, and an open circulatory system with no blood vessels, but only heart(s) that keep fluids in movement: this is because internal bones and closed tubes couldn't pass around each other.

14. Also a great essay on the subject from the late-great Martin Gardner.

15. Originally Posted by plant
internal bones and closed tubes couldn't pass around each other.

Originally Posted by dgh64
OP mentioned biology, but don't think any kind of complex life could exist in 2D. As 3D organisms, we have a bloodstream that moves numerous substances around our bodies. How would that work in 2D?... How would all these systems coexist, if none of them can cross over each other?
As demonstrated in post 5.

16. Originally Posted by plant
Also a great essay on the subject from the late-great Martin Gardner.

I've always been fascinated with this world. Looks like my reading has fallen behind. I read Flatland years ago and concluded that he had it sideways. It should be vertical, like Dewdney has done.

I had a mental project on the shelf to build it up from atoms, just like Dewdney has done. (I called mine "Sliceland").

You know what guys? This needs to be created. Like Second Life, or Minecraft.

Imagine crowd-sourcing a whole civilization. We'd need houses, doors, doorknobs, vehicles, etc. - all designed from scratch. The faucet in the article is a perfect example.

"... planiversal clock, telephone, book, typewriter, car, elevator or computer? Will some machines need a substitute for the wheel and axle? Will some need electric power?"

Users would be craftsmen, and smiths, designing and releasing innovative products, which would wax and wane in popularity,based on cost and efficacy.
Last edited by DaveC426913; 2019-Nov-07 at 03:43 PM.

17. Originally Posted by DaveC426913
I've always been fascinated with this world. Looks like my reading has fallen behind. I read Flatland years ago and concluded that he had it sideways. It should be vertical, like Dewdney has done.

I had a mental project on the shelf to build it up from atoms, just like Dewdney has done. (I called mine "Sliceland").

You know what guys? This needs to be created. Like Second Life, or Minecraft.

Imagine crowd-sourcing a whole civilization. We'd need houses, doors, doorknobs, vehicles, etc. - all designed from scratch. The faucet in the article is a perfect example.

"... planiversal clock, telephone, book, typewriter, car, elevator or computer? Will some machines need a substitute for the wheel and axle? Will some need electric power?"

Users would be craftsmen, and smiths, designing and releasing innovative products, which would wax and wane in popularity,based on cost and efficacy.
Yes that would be amazing. You could zoom down to the quantum level and up to the planetary level... reminds me of a great physics engine siimulation i played with years ago when my kids were little.. it's probably evolved since then. Perhaps you can make it in this world?

http://www.algodoo.com/

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Originally Posted by Dave241
Electricity and magnetism would be effected in the same way, but I don't know how that would effect things like atomic orbitals and the chemistry that is dependent upon them. It would have a huge effect, they wouldn't work at all. First of all, we could look at star formation, needed to even get advanced elements. I would think that it would make it drastically different, and who knows what effect that would have on life (nothing good, I would assume).
Yeah, any change that dramatic would change a lot, and likely require different physical constants, if it would be possible at all. There may be anthropic arguments that if there are lower-dimensional multiverses, life only appears in three or more dimensions, and those might be more rare.

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John Conway's Game of Life operates in two dimensions and can be set up to simulate a digital computer, so I'd guess that complicated 2D physics is at least possible although 2D life might be too improbable to get started. But 3D life might be improbable too.

20. "Why, sometimes I’ve believed as many as six impossible things before breakfast"
The Red Queen
Lewis Carol

Maybe the 4-D intelligences are thinking the same about us.... "Look, without the full 4-D, how are their neurons going to connect in enough ways to form a brain capable of thinking? It'd have to be the size of a hyper-cantaloupe!!... "

If # dimensions equals more complexity.... would a 4-D, 5-D, 1000-D universe have more possibilities for developing complex life due to a greater variety of complex atoms/ molecules? If so, why don't we live in a 4-D universe or greater? Can you have it both ways..? 2-D is too restrictive for complex life, but 4-D is too..???complex????

Can someone tell me if these anthropic arguments hold any meaning logically?
Last edited by plant; 2019-Nov-11 at 08:29 AM.

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The logical value of the anthropic argument applied to dimensionality only appears if you have some way to decide how likely it is for a universe to have a given number of dimensions. That's always the issue, we find more living creatures in temperature zones than in the arctic because the conditions are better, but this comes with the additional assumption that there is not a million times more area in the arctic zones. (If there were, you might actually find more life in the arctic than in the temperate zones, just because of the greater sample space). But if you did have some hypothesized distribution of universes as a function of dimensionality, then you could eliminate all the dimensions where life is impossible, and expect to find it in the most numerous of the remaining options. Perhaps there is a steep falloff in number of universes as the dimensionality rises, and then you'd expect most life to be found in the smallest dimensionality where life is possible.

That's perfectly good logic, but the problem for making it useful is to be able to figure out the distribution of universes over dimensions-- not to mention the distribution over everything else that matters also (physical constants, etc.). Generally speaking, anthropic arguments provide very convoluted ways to get around fine-tuning problems, but are only of value if you think a fine-tuning problem is worse than a convoluted argument problem. What you are in effect doing is introducing a whole bunch of new parameters in your model in order to make the old set of parameters seem generic rather than fine-tuned, but you have so much freedom in how you introduce the new parameters (since there are so unconstrained by observation) that you swap out the fine-tuning problem in favor of a huge ambiguity problem.

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Originally Posted by Chuck
John Conway's Game of Life operates in two dimensions and can be set up to simulate a digital computer, so I'd guess that complicated 2D physics is at least possible although 2D life might be too improbable to get started. But 3D life might be improbable too.
I wonder if some of the work-arounds might be of use in the care and tending of lightsails in flight

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