
Can Life Exist in 2 and 1 Dimensions? - bookofjoe
https://arxiv.org/abs/1906.05336
======
mytec
Couldn't help but think of the book Flatland and the parts about two-
dimensions.

[https://en.wikipedia.org/wiki/Flatland](https://en.wikipedia.org/wiki/Flatland)

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

[https://en.wikipedia.org/wiki/The_Planiverse](https://en.wikipedia.org/wiki/The_Planiverse)

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mci
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](https://en.wikipedia.org/wiki/Bertrand%27s_theorem)

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

~~~
tempsolution
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
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.

~~~
openasocket
OP was referring to an orbit in the dynamical systems sense:
[https://en.wikipedia.org/wiki/Orbit_(dynamics)](https://en.wikipedia.org/wiki/Orbit_\(dynamics\))
which is far more general. It simply refers to a dynamical system where the
trajectory of a particle repeats. If you have a system of particles in 2D
space, governed by central forces between the particles, you won't have any
particles that behave periodically in general, regardless of what those forces
actually are. (There's actually some caveats to that statement. I believe the
theorem OP's quoting assumes that the system has rotational symmetry, but
giving up that symmetry may or may not actually give you stable orbits).
Having some underlying periodicity is pretty important for more complex
structures to emerge, otherwise it's just random chaotic motion.

~~~
jeremysalwen
I mean, there are obviously a huge number of caveats associated with that, to
the point that it's meaningless when we ate discussing "possible universes".
There is no rule that a n^-2 force cannot exist in a 2d universe... which
would obviously result in stable orbits.

I mean come on, we have forces in our universe which are not n^-2. All this
proves is that gravity couldn't work in the same way in a 2d universe.....
so?? Heck, what about discrete universes? What about nonlocal universes?

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

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edwinyzh
He's first name is Liu.

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

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saagarjha
I think this is pointing out a typo rather than prescribing an ordering.

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weregiraffe
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
> 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
[https://en.wikipedia.org/wiki/Rule_110](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.

~~~
empath75
That is life like but I would not call it life.

~~~
jolmg
That's the issue with this question. What is life? Common definitions would
never think to consider anything other than things in our 3D physical world.

Can Life Exist in 2 and 1 Dimensions? Sure, if we're willing to define "life"
generically enough. If not, then no.

------
yig
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).

~~~
eznoonze
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.

~~~
mdorazio
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.

~~~
ksaj
I would call this a 2D amoeba. In 3D, they eat and excrete pretty much as you
describe.

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ksaj
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.

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

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

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

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rrauenza
Vaguely related, but enjoyable read,

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

------
mruts
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
[https://66.media.tumblr.com/2e04d006ac322f0b8556e376df8e81d5...](https://66.media.tumblr.com/2e04d006ac322f0b8556e376df8e81d5/tumblr_o4f4xgLAK61rhdt2to5_1280.jpg)

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wtdata
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.

~~~
undersuit
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.

------
HarryHirsch
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
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.

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ssijak
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

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dr_dshiv
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.

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kouh
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?

~~~
yiyus
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.

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

~~~
PeterisP
The whole concept of a permeable membrane, i.e. essentially stuff that has
holes but still is "one piece" (something like a sieve or strainer or colander
or net or anyhing of the kind), is something that IMHO requires 3+ dimensions.
In two dimensions if a membrane has two or more holes then it's not a single
membrane anymore.

~~~
CogitoCogito
> The whole concept of a permeable membrane, i.e. essentially stuff that has
> holes but still is "one piece" (something like a sieve or strainer or
> colander or net or anyhing of the kind), is something that IMHO requires 3+
> dimensions. In two dimensions if a membrane has two or more holes then it's
> not a single membrane anymore.

By what reasoning would it not be a single membrane in two dimensions, but it
would be in three dimensions? As far as I can tell your only support/reasoning
is found when you write "IMHO"...

~~~
PeterisP
In 3 dimensions, the sieve/strainer/colander is an object that's connected
with itself despite having holes. There's material that goes around the holes.

In 2 dimensions, the membrane is essentially a line (or a linear sequence of
objects) - if that line is interrupted in one space to let stuff through, then
it's not connected anymore, it's two separate lines with nothing linking them,
it's broken with no possibility to connect "around the hole" because any
connection around the hole requires the third dimension, and any connection
through the hole closes that hole.

~~~
CogitoCogito
Thanks for the clarification that makes sense.

~~~
marksc
It actually doesn't make sense. A circle with a 1D point missing from its edge
is the same as a sphere with a 2D hole in it. Both have material connected
"around" it in another dimension. For a sphere the connection wraps around the
hole and for a circle the connection wraps around the point (comprising the
entirety of the circle's edge).

~~~
PeterisP
This fails with more than one hole (as I said in the inital comment, two or
more). A circle with two 1D points missing breaks apart, a sphere can have an
arbitrary number of 2d holes and still be fully connected.

------
mrbungie
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.

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

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

~~~
marksc
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.

------
jerf
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.

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

[https://youtu.be/gaFKqOBTj9w](https://youtu.be/gaFKqOBTj9w)

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voidoids
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.

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8bitsrule
Assuming that you accept that the fundamental particles have a negligible
third-dimensionality: chemically, the limitation to planar molecules seems
very limiting.

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solotronics
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
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
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).

------
cellular
2d life simulator:

[https://youtu.be/I6bHpJ2GV0Y](https://youtu.be/I6bHpJ2GV0Y)

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Mugwort
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...](https://preview.redd.it/8fvwyefjav601.jpg?width=640&crop=smart&auto=webp&s=4d5bb23d2e39d53d6b3cda77d5496c4302ee34df)

~~~
skinner_
[https://users.renyi.hu/~daniel/tmp/noitdoesnt.jpg](https://users.renyi.hu/~daniel/tmp/noitdoesnt.jpg)

~~~
undersuit
That's a pretty slick solution there.

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

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bookofjoe
Commentary: [https://www.technologyreview.com/s/613788/life-could-
exists-...](https://www.technologyreview.com/s/613788/life-could-exists-
in-a-2d-universe-according-to-physics-anyway/)

------
codeulike
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