Can Life Exist in 2 and 1 Dimensions?

https://arxiv.org/abs/1906.05336

by bookofjoe • 7 years ago

103 133 7 years ago

bookofjoe2• 7 years ago

Commentary: https://www.technologyreview.com/s/613788/life-could-exists-...

We know that life is possible in two dimensions. A.K. Dewdney writes about his encounter with Yendred from the planet Arda in his novel The Planiverse.

jhbadger• 7 years ago

You are getting downvoted probably because people aren't familiar with The Planiverse. While technically a novel, it isn't just fiction -- the author goes into great detail how physics, chemistry, and life could work in two dimensions. In fact, that's actually the point of the book -- the story is just there to string the explanations together.

ksaj3• 7 years ago

Is that AND? "&" and "+" aren't the same thing. (even in that sentence, 'plus' and 'and' aren't synonymous. Replacing 'and' with 'plus' completely changes the meaning...)

Everything about the way the article is written suggests it is about the potential for 2D life occurring in 3D space, and nothing about single dimensional realms.

Consider graphene, a 2 dimensional fabric in 3D space. I'm sure this is closer to the point.

PLUS, versus AND.

bookofjoe2• 7 years ago

Original title of paper as published and posted: "Can Life Exist in 2 + 1 Dimensions?"

ksaj3• 7 years ago

You wrote "and" where it is a plus. That isn't in the title of the publication.

messe• 7 years ago

The N+M dimensions notation from physics refers to N spatial and M time dimensions, in this case N = 2 and M = 1.

The title should be changed to "Can Life Exist in 2+1 Dimensions?"

kyriakos3• 7 years ago

Very interesting take on this in the novel Death's End by cixin lu

edwinyzh• 7 years ago

He's first name is Liu.

ionised• 7 years ago

Isn't it customary to put a Chinese person's family name first?

kyriakos3• 7 years ago

typo sorry

linuskendall• 7 years ago

Isn't Liu his family name?

agentwiggles2• 7 years ago

I found these parts of the book completely fascinating, but also the most "scientifically hand-waved" stuff in the whole series. I've never been a big stickler for "hardness" in my sci-fi, but I'd have liked to see the ideas expanded on more. Death's End is a hell of a book, really goes places.

kyriakos3• 7 years ago

At some point the technology and physics described are so far from our levels that I don't think the author could go into much detail. Really though just when you thought the story's scale has reached its maximum the next one comes up.

jerf2• 7 years ago

If you want universes that run on alternate topologies taken seriously, I mean, like, the maximum level of serious possible, you want Greg Egan.

For instance, Greg Egan seriously considering the nature of 2+2 universe, that is, two space, two time dimensions: https://www.gregegan.net/DICHRONAUTS/DICHRONAUTS.html (Don't miss the interactive simulation: https://www.gregegan.net/DICHRONAUTS/02/Interactive.html )

He's got a few others, too.

solotronics2• 7 years ago

What about 4+1 and higher? I think it already does and we just perceive in 3 spatial dimensions to be able to process information in an easily digestible format.

libeclipse• 7 years ago

There are problems that arise in 4 + 1, such as how gravitational orbits aren't really stable and the force between the electrons and the nucleus is too strong to allow chemistry to exist as it does.

krastanov• 7 years ago

You are absolutely right, but do check out Greg Egan's "Diaspora" for a hard scifi that tries to get around that constraint.

More seriously, and slightly less scifi, you can have more than 3 spacial dimensions and still have stable gravity/electromagnetism if the topology of these dimensions is a bit weirder (very small periodic dimensions for instance).

solotronics2• 7 years ago

Why couldn't the 4th physical dimension interact with our 3 spatial dimensions as something we have trouble explaining such as quanta or gravity? There is a lot our physical bodies are not even aware due of to our senses such as most of the electromagnetic spectrum and gravity.

mytec• 7 years ago

Couldn't help but think of the book Flatland and the parts about two-dimensions.

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

will_brown• 7 years ago

And of course Schlegel diagrams which are commonly used for visualizing four-dimensional polytopes.

It’s been over 100 years (very close in time to the publication of flatland) and I don’t think anyone has proposed an alternative diagram of a 4 cube/hypercube/Tesseract.

chazu• 7 years ago

The Planiverse by A. K. Dewdney is also a great read on this subject - its less of an allegory than Flatland and focuses more on what the physiology and society of 2D life might look like. Worth a look.

Isamu• 7 years ago

I had this book, it had fun illustrations and thoughts about a hypothetical world.

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

Upvoter33• 7 years ago

Same here - especially the part about how a 2d creature poops...

wtdata• 7 years ago

For a - very - humourous social critic related to the theme, I highly recommend: Flatland, by Edwin Abbott. A book from the 18. cen. with very actual insights to it.

undersuit4• 7 years ago

I am borrowing Flatland/Sphereland from the Library, just finished Flatland last night, read the intro by Isaac Asimov for Sphereland. Sat the book down and had some deep contemplation.

jerf2• 7 years ago

One thing to bear in mind is that while the papers tend to just elide over it with some references, and the popsci representations of these discussions tend to skip over this either because they don't think anyone else will understand it, or the authors don't understand it themselves, is that there are assumptions built into these declarations, and it can help to dig into them. It's not a bad thing that there are assumptions; they're entirely necessary to make the questions something amenable to serious analysis, since the infinite space of all possible physics isn't really something we can speak about intelligently except in some really limited ways. But you do want to keep that in mind as you read these things.

Generally some physics are carried over from the real universe, and you want to look at how much. For instance, in this case, we carry over a very general-relativity-inspired gravity, which is then modified anyhow since GR-gravity wouldn't work. I've also seen another paper which was based on the premise "Assuming the basics of string physics are correct and we only vary the number of spatial and temporal dimensions, is life possible?" It's an interesting question, but "assuming the basics of string physics" is a big beginning. It doesn't invalidate the results, you just have to consider the results in the context of that.

The objection to 4-space is that you can't have any stable orbits with an inverse-cube law of gravitation. As for the natural question "why can't we just assume inverse square gravity then, if we're trying to build a universe where life could exist?", and the answer is, you can! But you make it very hard on yourself to write a sensible, published paper in the process, because you've taken a huge step away from all known gravity theories and you're now on your own.

I've often mentally noodled around with the idea of a two-dimensional universe based on a cellular automata theory, but in which one of the things the cells can do is be split in half (or quarters) somehow, with some defined mechanism for interacting with the original outer cells, and then the ability to further recursively split inside, and where the clock ticks, say, twice as fast in the split cells, so you end up with a universe that is (presumably) Turing complete, and participants may end up with the ability to perform infinite computations in finite time due to the split mechanisms. Presumably, if something like this could be defined, some sort of life could run in it; it seems to me than any Turing-complete (suitably modified with our often-also-elided assumptions about being finite-but-large-enough to act more like a Turing machine and less like a state machine, even if it is finite) environment can support life, on some level or other, even if by simulating some other more congenial environment. And the space of "physics" that permits Turing machines strikes me as very, very large compared to the space of "physics" that is "like ours, but just slightly tweaked". But you can't really get a math-heavy physics paper out of that idea.

cellular4• 7 years ago

I've been experimenting with 2d life, simular to cellular automaton, but with floating point directions, called PPS:

https://youtu.be/gaFKqOBTj9w

kouh• 7 years ago

The fundamental premise of the title seems misleading to me. Life existence doesn't depend on dimensions, it's perception that does. As the author later says, the paper is predicated upon an anthropic consideration of reality: if it can't be observed or compatible with the human mental model, then it doesn't exist. Has that been proven to be the case?

yiyus2• 7 years ago

Life depends on dimensions up to some point too. The most typical example is that, in a 2D world, there cannot be organisms that consume food, because the digestive tube would split the organism in two.

CogitoCogito3• 7 years ago

What about a permeable membrane? I.e. an organism absorbing nutrients through a wall that still maintains structure?

Angostura• 7 years ago

I suppose I should point out that the sea anemone functions quite nicely with a gut that only has a single opening - take food in, digest, expel remains from the same opening.

We also have amoeba which ingest food through vacuoles. But yes, a through-gut would be impractical.

homonculus1• 7 years ago

You have it backwards. Existence is the property shared by things which are or could be observed. If [an alternate universe]/[god]/[exotic laws of physics] "exists" but can't interact with anything else around us in a measurable way, then what does it mean to exist anyway? It might as well not.

mci2• 7 years ago

Good luck living in a world without stable orbits and without a cross product. Stable orbits only exist in 3 dimensions [1]. Cross product only exists in 3 and 7 dimensions [2] thanks to quaternions and octonions.

[1] https://en.wikipedia.org/wiki/Bertrand%27s_theorem

[2] https://en.wikipedia.org/wiki/Seven-dimensional_cross_produc...

mrleinad• 7 years ago

Stable orbits, I get it. Why is cross product such a fundamental requirement for life?

Gladdyu• 7 years ago

How would electromagnetism work in a world without a cross product?

cellular4• 7 years ago

This one doesn't use cross products, but instead creates different particles that react differently to each other:

https://youtu.be/12lyvmLdecc

eesmith• 7 years ago

That's addressed in section 2, "Relativistic Gravity in Three Dimensions":

As is well known, general relativity in 2 + 1 dimensions does not have any local degrees of freedom; as a result of this, the spacetime outside of, e.g., a star is locally flat, and the presence of the object is only discernible globally, though the presence of a deficit angle. Clearly solar systems could not exist in such a world, and so this is commonly used as an argument against the possibility of life in two spatial dimensions. ...
... it seems not unreasonable to also modify the theory of gravity so as to include local degrees of freedom. The simplest way to do this is to include a gravitational scalar field, and for completeness and concreteness I will give an example of such a theory.
... In the previous subsections I have presented a purely scalar theory of gravity which may allow lifein 2 + 1 dimensions; this is not intended as a complete theory, but more as a proof-of-principle,and now I will briefly discuss a few other alternatives.

tempsolution• 7 years ago

Good luck assuming that life needs a planet and an orbit. All you need is a way for particles to make explicit decisions and experience some sort of consciousness (but even that is debatable, since few life forms on earth seem to have that).

And I would even question that you need particles. Particles might just be what we can experience in 3 dimensions.

I always find it funny how humans are so eager to draw generalized conclusions based on their own meager 100 years of scientific existence. We should be more humble and realize that we know jack shit about anything.

ijpoijpoihpiuoh• 7 years ago

I had a similar reaction to you. People seem to have very limited imaginations when thinking about the types of things that could exist. Or maybe the title is incomplete. Maybe the paper is saying something more like, "Could life exist in a plane that otherwise has the same or very similar physics and chemistry as the universe?" In which case I could understand the skepticism about life's existence.

mci2• 7 years ago

Stable orbits are not only about planets and stars. They are about the stability of a universe with any central forces. Take a wrong number of dimensions and your life form will collapse or explode (along with its environment).

openasocket2• 7 years ago

I had a couple thoughts on how you might get around Bertrand's Theorem, but I don't know if they would actually work.

1. Give up on central forces. Maybe instead of the particle being attracted to the position of another particle, it's to where that particle will be in 10 seconds if it maintains its current velocity, or to a point halfway between the two particles. No idea if something like that could result in a stable orbit, or what conditions would be required for that to happen.

2. Give up on rotational symmetry (which I believe Betrand's theorem implicitly requires, not positive). Have some defined "north" direction, and forces behave differently depending on how a particle is moving relative to it.

3. Maybe asymptotically stable orbits are enough for life, if they are very asymptotically stable.

codeulike• 7 years ago

_____ __ ____ __ __ __ _ _ __ __ __________ _ __ __ __ ___ __ _ _ ______________ __ __ _ _ ______

weregiraffe• 7 years ago

1. Life can exist in 3D.

2. A 2D or 1D computer can simulate life in 3D.

3. Therefore, life can exist in 2D or 1D.

a_wild_dandan• 7 years ago

A 2D or 1D computer can simulate life in 3D.

Can it? I'm not familiar with the limitations of lower dimensional computation, but it sounds like a fascinating subject.

Will_Parker• 7 years ago

https://en.wikipedia.org/wiki/Rule_110 A Turing Complete 1-dimensional cellular automaton.

Also Conway's Game of Life is a rabbit hole you could literally spend your whole life studying.

jolmg3• 7 years ago

I believe weregiraffe is referring to this[1][2]. Conway's Game of Life is a 2D "world" with 4 rules that define the "physics" in that world, and someone made a Turing Machine in it.

[1] https://www.ics.uci.edu/~welling/teaching/271fall09/Turing-M...

[2] http://www.rendell-attic.org/gol/tm.htm

Koshkin3• 7 years ago

One can simulate life using Turing machine.

IanSanders2• 7 years ago

I'd say approximate, not simulate. Or simulate an approximation of 3D.

(You need infinite 2D space for a complete model of a finite 3D space)

ralusek• 7 years ago

Why do you need infinite space? The number line of real numbers is basically a 1d space, and we can simulate finite N dimensional spaces with finite real numbers.

jackweirdy• 7 years ago

Is a simulation of life the same as life?

sysbin10• 7 years ago

Yes. People don't have any real control with what happens in their life. Similar to a computer simulation with 3d objects.

dTal• 7 years ago

QED.

To put it another way, "life" is basically a quine. As per the fixed-point theorem, all Turing-complete formal systems support (infinitely many) quines. Therefore, any universe whose laws of physics are powerful enough to support Turing-completeness, can support life.

(Of course you have to be careful with what you mean by "life" and "universe" and so forth. A 0-dimensional infinitesimal singularity capable of arbitrary computation can of course run Conway's Game Of Life all you want - but perhaps you'd prefer 'universe' to mean some kind of spatial construction with locality-preserving rules - in which case it's not even clear that our own universe counts!)

randyrand• 7 years ago

What is a 1D computer? A computer made with a single line of atoms?

jolmg3• 7 years ago

Like another post mentioned, this would be an example:

https://en.wikipedia.org/wiki/Rule_110

Atoms work on 3 dimensions, I believe, and 1D doesn't need to imply our physical 3D existence minus 2 dimensions. It can be a virtual 1D realm that runs on our own defined "physics".

The rules that define the "physics" in Rule 110 are:

  |-----------------+---------------------------|
  | current pattern | new state for center cell |
  |-----------------+---------------------------|
  |             111 |                         0 |
  |             110 |                         1 |
  |             101 |                         1 |
  |             100 |                         0 |
  |             011 |                         1 |
  |             010 |                         1 |
  |             001 |                         1 |
  |             000 |                         0 |
  |-----------------+---------------------------|

AgentME• 7 years ago

Sure, if your 2D or 1D world is started from a pattern designed by an intelligent being, then they could make a starting pattern that simulated a 3D world. But the more interesting question is whether life could arise in a 2D or 1D world that has simple physics and a simple starting pattern.

PhasmaFelis• 7 years ago

Title is incorrect. It's 2+1 dimensions, 2 space and 1 time, not "2 and 1 dimensions."

HvyMetalMG• 7 years ago

I believe this was answered on a 1997 Halloween episode of The Simpsons.

mruts• 7 years ago

Life in 2D couldn't have an esophagus or an intestinal track. Then the organism would be split in two. Maybe you could have an organism that surrounds something and spits it out after sucking up the nutrients.

As to 1D life, I find it hard to imagine an organism that could be 1D and exist.

I didn't read the paper, though.

disconcision• 7 years ago

https://66.media.tumblr.com/2e04d006ac322f0b8556e376df8e81d5...

cellular4• 7 years ago

2d life simulator:

https://youtu.be/I6bHpJ2GV0Y

rrauenza• 7 years ago

Vaguely related, but enjoyable read,

https://en.wikipedia.org/wiki/Dragon%27s_Egg

"The Cheela develop sentience and intelligence, despite their relative small size[...] and an intense gravity field that restricts their movement in the third dimension."

I read it based on another HN post ...

Mugwort• 7 years ago

A two dimensional being can't eat. Its digestive tract necessarily divides it into two distinct pieces and the being falls apart.

https://preview.redd.it/8fvwyefjav601.jpg?width=640&crop=sma...

aaronblohowiak• 7 years ago

not necessarily. instead of a tube, it would be a series of "locks" like a canal.

jng• 7 years ago

Regurgitation solves that specific showstopper.

Koshkin3• 7 years ago

Food may also serve as the glue.

undersuit4• 7 years ago

I don't know if I'm missing the joke, but why do we assume the 2D stork people have a digestive tract and not a series of manipulatable pores that facilitate the movement of particles in and out of the body or maybe similar to how an amoeba uses phagocytosis.

jetrink• 7 years ago

Two phyla of animals use a gastrovascular cavity[1] in which food enters and waste exits through the same orifice.

1. https://en.wikipedia.org/wiki/Gastrovascular_cavity

smartplaya2001• 7 years ago

you assume a 2d being needs to need or requires a digestive tract. What if that being doesn't necessarily it?

saalweachter• 7 years ago

Your two separate pieces could still interlock, so that you wouldn't "fall apart".

skinner_• 7 years ago

https://users.renyi.hu/~daniel/tmp/noitdoesnt.jpg

undersuit4• 7 years ago

That's a pretty slick solution there.

yig• 7 years ago

This reminds me of the problem of designing digestive tracts for m-dimensional creatures in an n-dimensional ambient space. For example, if Pac-Man had had an anus, he would have split in two (without additional biology keeping him together).

Koshkin3• 7 years ago

keeping him together

But note that we too are "split" into a myriad of pieces with nothing but empty space between them.

thfuran• 7 years ago

But none of those spaces are nearly as big as your anus. And I take issue with any definition of "empty" that includes interatomic spacing in a liquid. It's not maximally occupied but neither is it empty in any sense that is particularly useful in most contexts. You have to fight the electromagnetic interaction between electrons to put anything more in that space.

lloeki• 7 years ago

He could be held together by forces that are not mechanical. Fundamentally that’s what mechanical forces are at a low enough scale: electromagnetic ones.

This could apply to 1D too.

See Feynman’s video about why he’s not falling down through his armchair.

eznoonze• 7 years ago

That is like solving a 2D problem using a 3D technique. Think outside the box. An organism doesn't really need a digestive tract. You can digest/absorb externally.

hyperman12• 7 years ago

You want Pacman to puke digested white ball shit? I finally understand why they fade out between levels!

mdorazio• 7 years ago

Alternatively, your hypothetical digestive tract can split and rejoin around the food being processed as it moves through the tract so that at no point in time do you have an open path from one end to the other.

dokem• 7 years ago

The intestinal track could be zipper shaped so two halves but not physically separable.

vgrocha• 7 years ago

The only life form we know has DNA and the DNA is a 3D molecule. With our current knowledge, it doesn't seem possible.

marksc2• 7 years ago

DNA is not a 3D molecule. DNA is a molecule which can be represented as 3D. It can just as easily be represented with one or even two fewer dimensions without losing any information.

By the holographic principle, there may be no such thing as "3D" except as a concept for conscious minds to make sense of reality.

mrbungie• 7 years ago

Another relevant question, Can any kind of engine exist in 2 and 1 dimensions?.

If there is no work (as in disposanle energy), there is no life.

undersuit4• 7 years ago

Gliders in the Game of Life, clever people exploring GoL have made forms that can pull or push patterns along.

ssijak• 7 years ago

By holographic principle we may be a 2d hologram, so the answer is yes. Also, why could there not be a real 2d universe with intelligence in it? Not that this one is less strange anyway

dr_dshiv• 7 years ago

I've never understood why we think we live in 3 dimensional world.

Let's put aside time, brane dimensions, etc

But just from a human experience perspective, there are so many more dimensions than X,y,z. Color for instance. Or sound, or touch, or smell.

From a data science perspective, we treat each additional column in a table as an additional dimension. This isn't metaphorical, it is reality as we best define it.

8bitsrule• 7 years ago

Assuming that you accept that the fundamental particles have a negligible third-dimensionality: chemically, the limitation to planar molecules seems very limiting.

voidoids• 7 years ago

Definitely 2, since the life of a cell is encapsulated by the the motion of atoms. A spheroid cell converts to a circular plane with ease. All life is comprised of cells, so a 2D plane of life without depth will likely work.

One dimension would have to resolve all interactions to waveforms with the ability to pass through solid objects. So it would probably mean violating physical laws as we understand them. Things would need to seemingly teleport to different points within the dimension, I think.

Either that, or the single dimension is reduced to binary digits, interchangeable, without identity. Then, it's not really teleportation. It's more like kinetic transfer in a newton's cradle, like croquet balls or billiard balls. Spherical cows, perhaps.

Can Life Exist in 2 and 1 Dimensions?

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