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.
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.
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.
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.
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.
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.
OP was referring to an orbit in the dynamical systems sense: 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.
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?
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).
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.
In 2d electromagnetism splits light waves into TE and TM modes that don't couple to each others (until you add a dielectric). That is unusual to our 3d picture, but doesn't break electromagnetics.
And the generalization of the cross product, the wedge product works just fine in 2d. If you take the wedge of two 1-forms (vectors) in 2d you get a 2-form. In 3d that is equivalent to a (3-2)-form or in other words a (pseudo-)vector. In 2d you get a (2-2)-form or in other words a pseudo-scalar 0-form. That is of course nothing but the z component of the resulting pseudo-vector if you had done it in 3d. So EM in 2d might get flat landers started on weird group theory a bit early, but it is not fundamentally incompatible with life.
Magnetism doesn't use a cross product; it uses a wedge product[0]. It generalizes perfectly well to 2d, you just have <<xy>> instead of <<xy,xz,yz>>, just like you have <x,y> instead of <x,y,z>.
Edit: the reason 2d doesn't have a cross product is because you can no longer misinterpret a bivector <<xy,xz,yz>> as a (1-)vector <yz,xz,xy> by confusing each basis bivector with the basis vector[1] orthogonal to it.
1: Actually one of the two (positive or negative) possible basis vectors; this is why cross products have a right-hand-rule versus left-hand-rule ambiguity.
Maxwell did not use a cross product in his original publications. In fact, the development of the cross product was a response to the longer (quaternion based) formulation of electromagnetism equations at the time.
I'm confused by GP's reasoning. Is it valid to assume that since we have an equation that requires three dimensions to show how a force reacts, that if you remove a dimension that force doesn't exist?
Isn't it just as possible that there's a different equation for how that force would work in two dimensions (or to assume our current equation is a specialized version of a general equation that works in all dimensions)?
It just seems rather odd to assume that since our understanding doesn't extend to a circumstance that means something is impossible there. Or is there some aspect of this I'm missing?
Edit: Perhaps I was misinterpreting the GP contextually. Maybe they were just asking if we have an equation for it, rather than questioning how it could exist.
It's a bit complex for a comment, but electromagnetism defined in terms of differential forms generalizes nicely to all dimensions. There certainly is a 2+1D electromagnetism.
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.
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.
Yeah, that's what made it such a fun read to me, like you said it just continually gets more and more out there. It explores some really interesting ideas that I haven't seen touched on in much of the sci-fi I've read. Another personal favorite is Iain M. Banks Culture series, which is much different than Liu's work but does the same thing - exploring these really interesting ideas of a far future society and how humans fit into that world.
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!)
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.
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.
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.
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:
People don't have any real control with what happens in their life.
Sure they do. Saying that people don't have control over anything is like saying "the light switches in my house don't control the lights because the switches can't do anything without a person flipping them". Just because there's no spontaneous self-generated action that a switch can perform by itself doesn't mean that the switch isn't controlling something.
Looking at this from a different angle, do you believe that a digital simulation of your brain would produce the same kind of subjective experience of consciousness within the computer that you yourself perceive? Is subjective experience simply a side effect of certain types of computation? That may be true, but if you believe that, you start to get into some profoundly bizarre implications about the nature of reality. Check out the novel "Permutation City" by Greg Egan for a great exploration of this topic.
> Sure they do. Saying that people don't have control over anything is like saying "the light switches in my house don't control the lights because the switches can't do anything without a person flipping them". Just because there's no spontaneous self-generated action that a switch can perform by itself doesn't mean that the switch isn't controlling something.
I disagree with your interpretation of control. The word is human expression and shared between one another. So you can have a different understanding of the word than mine and neither of us can truly hold power over the word. As for me control doesn't exist in reality because the light bulb doesn't actually control the outcome of the light turning on or off. The beginning of all events is really what controlled the forces to make the force of the light switch going on or off.
> Looking at this from a different angle, do you believe that a digital simulation of your brain would produce the same kind of subjective experience of consciousness within the computer that you yourself perceive?
Yes, I'll take a look at the novel you recommended.
That's a fairly limited view of physics. We don't actually fully understand how our bodies interact with the quantum (or Newtonian, really) physics realms that we exist within. There's a lot more to the brain than just (just! hah!) neurotransmitters and neural layout.
Determinism isn't a limited view of physics. There are people who understand determinism and then there are people who prefer faith than understanding determinism.
The closer we look into quantum phenomena the less deterministic it looks, so there seems to be plenty of room in between faith and determinism for will, and many other possibilities to boot.
That’s a common misconception of not understanding quantum physics and determinism. Do you want me to explain how quantum physics doesn’t change anything about you not having free will.
Absolutely not. We don't even understand larger scale phenomenon such as turbulent flow in fluids, so there's no way we could understand the interaction between turbulent flow and quantum phenomenon in our brain. Given that gap, the insistence that physics provides the determinism that means all our outcomes are predetermined is just your desire to believe you know something.
I assume you should read about determinism but you likely won't because you don't understand the underlining problem "how you're unable to have a will that's truly our own" and your writing appears to me that you're stubborn; and or unwilling to ever discover you don't have control that's truly your own by actually understanding determinism.
Even if a thought (an external force) occurred that truly wasn't deterministic. You still would be shaped by it and from all the preceding forces exerted upon you playing a part as well.
Furthermore, (non related) Quantum physics may just be local hidden variables and or another deterministic universe intertwined with our deterministic universe and making the results we're unable to measure appear random. Many people fear determinism and so they put so much faith into quantum physics without understanding how it doesn't change your outcome to be truly your own.
We very well may be in a universe that's different than another and that has you & I never conversing because a deterministic system (outside our universe) is making "random occurrences" (that aren't really random) just not measurable in our lifetimes; thus making one universe verge off from another in the deterministic outcomes. That doesn't give us a will that's our own.
Similar if we prayed to God for an event in our life to occur or not to happen. All the forces exerted upon us, up until us praying is what made the event occur and not even a God could have a will that's his/her own because any being is shaped by the events experienced. Simply, you cannot make a decision that wasn't effected by all the events (forces exerted upon you) that occurred against you in life. You're the product of what encompasses you and all the forces chain-back to the very beginning of life.
Sure, I don't believe in complete control either. But what benefit would it bring to believe that I have absolutely no control over my life? That would in fact be self-defeating, especially if it turns out that we do have some marginal amount of control. What a waste that would be! And if I believe that I have control (which itself isn't something I can control in your model) when in fact I don't, then why would that change anything about my life? What positive effect would this revelation of lack of control have? The only outcome of your belief system is to deny control when it does exist. I'll keep my belief system, thanks. If your philosophy works for you, keep on being an automaton dude. L8tr.
>But what benefit would it bring to believe that I have absolutely no control over my life?
You're ignorant of understanding reality and similar to the majority of people because of religion. The society we live in has been shaped around assuming we have control by the roots of religion being ingrained for centuries. The great travesty I observe is ignorance born from assuming free will and it needs to be erased for humanity to not be evil. Currently many humans are in prison for being born into the life with a horrible outcome and without any control of not being influenced to be penalized unjustly by fate. The injustice is equivalent to the holocaust. Society is imperfect with how people develop by genetics & the environment being different. The scapegoat has been blaming victims and assuming they have free will.
>And if I believe that I have control (which itself isn't something I can control in your model) when in fact I don't, then why would that change anything about my life?
No matter at the end of the day, fate will decide how you end up being is true. Fate for me has made me converse how reality is with as many people and because I think it's the right thing to do; while understanding the preceding. I would be immoral if I didn't discuss it once in awhile and while knowing how against people are when it comes to understanding free will is an illusion because they've been conditioned their whole life to think the contrary.
>What positive effect would this revelation of lack of control have?
Understanding the collective unconscious is really the key. The evolution of humans (behaviour & interaction) is built by the foundation of what people share in their mind. I'm a firm believer that faith (the belief in something with no evidence) is evil because of what I've experienced in life by people that were very controlling; against lgbtq people. Thus, I find free will evil and the reason for what has occurred upon society because of it. Understanding why knowing free will is an illusion takes awhile to truly understand the benefit. Furthermore, I likely would have murdered the people who abused me if I didn't come to realize they had no control to how they became to be as persons. I'm grateful that fate was at least kind enough to me to not become a murderer. I'm disfigured forever as a visible transgender woman because of these people that had no control in reality. Luckily fate is going to allow me an exit soon.
You haven't thought about how you couldn't have free will is what I assume when reading what you responded. I don't think there is anything you can write to show that you have free will and everything proves otherwise when concerning scientific research. I still like to see what people think and when they believe to have free will. Whatever the response you make is by fate is understood. As well as your opinion being by fate and if you want to stay delusional or accept reality. Me writing I think you cannot accept reality was fated and it doesn't mean your mind won't ever get the variables to understand reality. Heck, you may even understand everything after reading about it as well and that would be by fate if so.
Btw, I really care that people don't live in delusions and so if you ever want to know why you shouldn't be deluded.. Let me know.
Your comments no decision and ‘stay delusional’ also assume free will... if we don’t have free will, that means the existence of dollar general is wrapped up in the laws of physics, and that we should find an unlimited number of these stores once we can check the universe :)
Words are for human expression and to attempt of sharing one expression to another. You don't hold power over "stay delusional" and similar to I. What's written by me is declaring your stance as delusional because you're not witnessing the truth of reality. Yes it's possible you'll stay delusional if its fate's will and or eventually accept reality which would be by fate as well. Only one of those will happen for you and it's predetermined by the chain of events you lived with whatever's to follow.
Your definition of free will may be causing dissonance in this conversation because your will might be to forever assume you have choice. I'm not negating that people have a will or as we name volition. I'm writing we don't have a choice over our will in how it came to be and or what follows till our death; by determinism.
The universe is expanding and with infinite variables that can align again and or have an external force differ from another equal chain of forces. Yes we can have infinite worlds or phrased as events and that reoccur to a point where an interference of a unique force breaks the chain compared to another chain that didn't have such a force upon it. That has nothing to do with free will and even if we could check another universe. The variable of checking the universe would still be a force upon us and with the preceding forces fitting in the equation for what would follow.
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.
Let's say you want to represent 1cm*1cm 2d space in 1d. There is infinite number of points in both dimensions of this space. While you can completely represent one of its "slices" with a 1cm segment of 1d space, for a complete model you will need infinite number of 1cm segments stacked, thus requiring infinite 1d space.
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).
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.
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.
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.
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.
Yep. This is officialy the sickest joke I ever made on an internet forum. Sorry if it offends anyone, feel free to ban, but I couldn't resist at the moment.
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.
"The Cheela develop sentience and intelligence, despite their relative small size[...] and an intense gravity field that restricts their movement in the third dimension."
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.
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.
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.
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.
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.
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
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.
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?
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.
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.
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.
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.
> 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"...
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.
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).
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.
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.
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.
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.
Assuming that you accept that the fundamental particles have a negligible third-dimensionality: chemically, the limitation to planar molecules seems very limiting.
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.
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.
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).
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.
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.
Couldn't help but think of the book Flatland and the parts about two-dimensions.
https://en.wikipedia.org/wiki/Flatland
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.
I had this book, it had fun illustrations and thoughts about a hypothetical world.
https://en.wikipedia.org/wiki/The_Planiverse
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.
Same here - especially the part about how a 2d creature poops...
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...
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.
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.
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.
OP was referring to an orbit in the dynamical systems sense: 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.
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?
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).
That assumes your universe is essentially Euclidean, at least at a scale where these effects matter.
Not all spaces are Euclidean - or even approximately Euclidean via a mapping and/or at specific scales.
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.
Stable orbits, I get it. Why is cross product such a fundamental requirement for life?
This one doesn't use cross products, but instead creates different particles that react differently to each other:
https://youtu.be/12lyvmLdecc
How would electromagnetism work in a world without a cross product?
In 2d electromagnetism splits light waves into TE and TM modes that don't couple to each others (until you add a dielectric). That is unusual to our 3d picture, but doesn't break electromagnetics.
And the generalization of the cross product, the wedge product works just fine in 2d. If you take the wedge of two 1-forms (vectors) in 2d you get a 2-form. In 3d that is equivalent to a (3-2)-form or in other words a (pseudo-)vector. In 2d you get a (2-2)-form or in other words a pseudo-scalar 0-form. That is of course nothing but the z component of the resulting pseudo-vector if you had done it in 3d. So EM in 2d might get flat landers started on weird group theory a bit early, but it is not fundamentally incompatible with life.
Magnetism doesn't use a cross product; it uses a wedge product[0]. It generalizes perfectly well to 2d, you just have <<xy>> instead of <<xy,xz,yz>>, just like you have <x,y> instead of <x,y,z>.
Edit: the reason 2d doesn't have a cross product is because you can no longer misinterpret a bivector <<xy,xz,yz>> as a (1-)vector <yz,xz,xy> by confusing each basis bivector with the basis vector[1] orthogonal to it.
0: https://en.wikipedia.org/wiki/Wedge_product
1: Actually one of the two (positive or negative) possible basis vectors; this is why cross products have a right-hand-rule versus left-hand-rule ambiguity.
You could use the exterior product.
Maxwell did not use a cross product in his original publications. In fact, the development of the cross product was a response to the longer (quaternion based) formulation of electromagnetism equations at the time.
I'm confused by GP's reasoning. Is it valid to assume that since we have an equation that requires three dimensions to show how a force reacts, that if you remove a dimension that force doesn't exist?
Isn't it just as possible that there's a different equation for how that force would work in two dimensions (or to assume our current equation is a specialized version of a general equation that works in all dimensions)?
It just seems rather odd to assume that since our understanding doesn't extend to a circumstance that means something is impossible there. Or is there some aspect of this I'm missing?
Edit: Perhaps I was misinterpreting the GP contextually. Maybe they were just asking if we have an equation for it, rather than questioning how it could exist.
It's a bit complex for a comment, but electromagnetism defined in terms of differential forms generalizes nicely to all dimensions. There certainly is a 2+1D electromagnetism.
It would exist but not in a nice way, with electricity and magnetism inducing each other.
If we’re imagining a 2d world why not imagine all new forces and particles to go with it?
Very interesting take on this in the novel Death's End by cixin lu
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.
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.
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.
Yeah, that's what made it such a fun read to me, like you said it just continually gets more and more out there. It explores some really interesting ideas that I haven't seen touched on in much of the sci-fi I've read. Another personal favorite is Iain M. Banks Culture series, which is much different than Liu's work but does the same thing - exploring these really interesting ideas of a far future society and how humans fit into that world.
He's first name is Liu.
Isn't it customary to put a Chinese person's family name first?
I think this is pointing out a typo rather than prescribing an ordering.
He's just correcting a misspelling
Isn't Liu his family name?
typo sorry
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.
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!)
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.
> 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.
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
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.
That is life like but I would not call it life.
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.
Since the universe may be encoded on lower-dimensional boundary, that means that you are not alive, per your definition:
https://en.wikipedia.org/wiki/Holographic_principle
One can simulate life using Turing machine.
What is a 1D computer? A computer made with a single line of atoms?
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:
Is a simulation of life the same as life?
Yes. People don't have any real control with what happens in their life. Similar to a computer simulation with 3d objects.
People don't have any real control with what happens in their life.
Sure they do. Saying that people don't have control over anything is like saying "the light switches in my house don't control the lights because the switches can't do anything without a person flipping them". Just because there's no spontaneous self-generated action that a switch can perform by itself doesn't mean that the switch isn't controlling something.
Looking at this from a different angle, do you believe that a digital simulation of your brain would produce the same kind of subjective experience of consciousness within the computer that you yourself perceive? Is subjective experience simply a side effect of certain types of computation? That may be true, but if you believe that, you start to get into some profoundly bizarre implications about the nature of reality. Check out the novel "Permutation City" by Greg Egan for a great exploration of this topic.
> Sure they do. Saying that people don't have control over anything is like saying "the light switches in my house don't control the lights because the switches can't do anything without a person flipping them". Just because there's no spontaneous self-generated action that a switch can perform by itself doesn't mean that the switch isn't controlling something.
I disagree with your interpretation of control. The word is human expression and shared between one another. So you can have a different understanding of the word than mine and neither of us can truly hold power over the word. As for me control doesn't exist in reality because the light bulb doesn't actually control the outcome of the light turning on or off. The beginning of all events is really what controlled the forces to make the force of the light switch going on or off.
> Looking at this from a different angle, do you believe that a digital simulation of your brain would produce the same kind of subjective experience of consciousness within the computer that you yourself perceive?
Yes, I'll take a look at the novel you recommended.
That's a fairly limited view of physics. We don't actually fully understand how our bodies interact with the quantum (or Newtonian, really) physics realms that we exist within. There's a lot more to the brain than just (just! hah!) neurotransmitters and neural layout.
Determinism isn't a limited view of physics. There are people who understand determinism and then there are people who prefer faith than understanding determinism.
The closer we look into quantum phenomena the less deterministic it looks, so there seems to be plenty of room in between faith and determinism for will, and many other possibilities to boot.
That’s a common misconception of not understanding quantum physics and determinism. Do you want me to explain how quantum physics doesn’t change anything about you not having free will.
Absolutely not. We don't even understand larger scale phenomenon such as turbulent flow in fluids, so there's no way we could understand the interaction between turbulent flow and quantum phenomenon in our brain. Given that gap, the insistence that physics provides the determinism that means all our outcomes are predetermined is just your desire to believe you know something.
I assume you should read about determinism but you likely won't because you don't understand the underlining problem "how you're unable to have a will that's truly our own" and your writing appears to me that you're stubborn; and or unwilling to ever discover you don't have control that's truly your own by actually understanding determinism.
Even if a thought (an external force) occurred that truly wasn't deterministic. You still would be shaped by it and from all the preceding forces exerted upon you playing a part as well.
Furthermore, (non related) Quantum physics may just be local hidden variables and or another deterministic universe intertwined with our deterministic universe and making the results we're unable to measure appear random. Many people fear determinism and so they put so much faith into quantum physics without understanding how it doesn't change your outcome to be truly your own.
We very well may be in a universe that's different than another and that has you & I never conversing because a deterministic system (outside our universe) is making "random occurrences" (that aren't really random) just not measurable in our lifetimes; thus making one universe verge off from another in the deterministic outcomes. That doesn't give us a will that's our own.
Similar if we prayed to God for an event in our life to occur or not to happen. All the forces exerted upon us, up until us praying is what made the event occur and not even a God could have a will that's his/her own because any being is shaped by the events experienced. Simply, you cannot make a decision that wasn't effected by all the events (forces exerted upon you) that occurred against you in life. You're the product of what encompasses you and all the forces chain-back to the very beginning of life.
Sure, I don't believe in complete control either. But what benefit would it bring to believe that I have absolutely no control over my life? That would in fact be self-defeating, especially if it turns out that we do have some marginal amount of control. What a waste that would be! And if I believe that I have control (which itself isn't something I can control in your model) when in fact I don't, then why would that change anything about my life? What positive effect would this revelation of lack of control have? The only outcome of your belief system is to deny control when it does exist. I'll keep my belief system, thanks. If your philosophy works for you, keep on being an automaton dude. L8tr.
>But what benefit would it bring to believe that I have absolutely no control over my life?
You're ignorant of understanding reality and similar to the majority of people because of religion. The society we live in has been shaped around assuming we have control by the roots of religion being ingrained for centuries. The great travesty I observe is ignorance born from assuming free will and it needs to be erased for humanity to not be evil. Currently many humans are in prison for being born into the life with a horrible outcome and without any control of not being influenced to be penalized unjustly by fate. The injustice is equivalent to the holocaust. Society is imperfect with how people develop by genetics & the environment being different. The scapegoat has been blaming victims and assuming they have free will.
>And if I believe that I have control (which itself isn't something I can control in your model) when in fact I don't, then why would that change anything about my life?
No matter at the end of the day, fate will decide how you end up being is true. Fate for me has made me converse how reality is with as many people and because I think it's the right thing to do; while understanding the preceding. I would be immoral if I didn't discuss it once in awhile and while knowing how against people are when it comes to understanding free will is an illusion because they've been conditioned their whole life to think the contrary.
>What positive effect would this revelation of lack of control have?
Understanding the collective unconscious is really the key. The evolution of humans (behaviour & interaction) is built by the foundation of what people share in their mind. I'm a firm believer that faith (the belief in something with no evidence) is evil because of what I've experienced in life by people that were very controlling; against lgbtq people. Thus, I find free will evil and the reason for what has occurred upon society because of it. Understanding why knowing free will is an illusion takes awhile to truly understand the benefit. Furthermore, I likely would have murdered the people who abused me if I didn't come to realize they had no control to how they became to be as persons. I'm grateful that fate was at least kind enough to me to not become a murderer. I'm disfigured forever as a visible transgender woman because of these people that had no control in reality. Luckily fate is going to allow me an exit soon.
I’m sorry that happened to you. It is not just, it is not right.
Thank you
That is true of your life maybe, but not mine!
Oh how so? I'm guessing you just don't want to accept reality.
Your comment assumes I have free will ;)
You haven't thought about how you couldn't have free will is what I assume when reading what you responded. I don't think there is anything you can write to show that you have free will and everything proves otherwise when concerning scientific research. I still like to see what people think and when they believe to have free will. Whatever the response you make is by fate is understood. As well as your opinion being by fate and if you want to stay delusional or accept reality. Me writing I think you cannot accept reality was fated and it doesn't mean your mind won't ever get the variables to understand reality. Heck, you may even understand everything after reading about it as well and that would be by fate if so. Btw, I really care that people don't live in delusions and so if you ever want to know why you shouldn't be deluded.. Let me know.
Your comments no decision and ‘stay delusional’ also assume free will... if we don’t have free will, that means the existence of dollar general is wrapped up in the laws of physics, and that we should find an unlimited number of these stores once we can check the universe :)
Words are for human expression and to attempt of sharing one expression to another. You don't hold power over "stay delusional" and similar to I. What's written by me is declaring your stance as delusional because you're not witnessing the truth of reality. Yes it's possible you'll stay delusional if its fate's will and or eventually accept reality which would be by fate as well. Only one of those will happen for you and it's predetermined by the chain of events you lived with whatever's to follow.
Your definition of free will may be causing dissonance in this conversation because your will might be to forever assume you have choice. I'm not negating that people have a will or as we name volition. I'm writing we don't have a choice over our will in how it came to be and or what follows till our death; by determinism.
The universe is expanding and with infinite variables that can align again and or have an external force differ from another equal chain of forces. Yes we can have infinite worlds or phrased as events and that reoccur to a point where an interference of a unique force breaks the chain compared to another chain that didn't have such a force upon it. That has nothing to do with free will and even if we could check another universe. The variable of checking the universe would still be a force upon us and with the preceding forces fitting in the equation for what would follow.
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)
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.
Let's say you want to represent 1cm*1cm 2d space in 1d. There is infinite number of points in both dimensions of this space. While you can completely represent one of its "slices" with a 1cm segment of 1d space, for a complete model you will need infinite number of 1cm segments stacked, thus requiring infinite 1d space.
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).
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.
> keeping him together
But note that we too are "split" into a myriad of pieces with nothing but empty space between them.
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.
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.
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.
I would call this a 2D amoeba. In 3D, they eat and excrete pretty much as you describe.
You want Pacman to puke digested white ball shit? I finally understand why they fade out between levels!
I probably laughed more than I should have at that
Yep. This is officialy the sickest joke I ever made on an internet forum. Sorry if it offends anyone, feel free to ban, but I couldn't resist at the moment.
The intestinal track could be zipper shaped so two halves but not physically separable.
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.
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?"
Original title of paper as published and posted: "Can Life Exist in 2 + 1 Dimensions?"
You wrote "and" where it is a plus. That isn't in the title of the publication.
Title is incorrect. It's 2+1 dimensions, 2 space and 1 time, not "2 and 1 dimensions."
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 ...
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.
https://66.media.tumblr.com/2e04d006ac322f0b8556e376df8e81d5...
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.
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.
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.
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.
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
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.
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?
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.
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.
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.
What about a permeable membrane? I.e. an organism absorbing nutrients through a wall that still maintains structure?
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.
> 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"...
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.
Thanks for the clarification that makes sense.
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).
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.
Yes! Like this: https://youtu.be/gaFKqOBTj9w
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.
Gliders in the Game of Life, clever people exploring GoL have made forms that can pull or push patterns along.
The only life form we know has DNA and the DNA is a 3D molecule. With our current knowledge, it doesn't seem possible.
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.
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.
I've been experimenting with 2d life, simular to cellular automaton, but with floating point directions, called PPS:
https://youtu.be/gaFKqOBTj9w
Were you inspired by Hiroki Sayama's swarm chemistry?
http://bingweb.binghamton.edu/~sayama/SwarmChemistry/
https://www.youtube.com/watch?v=9psDJIWBnp8
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.
Assuming that you accept that the fundamental particles have a negligible third-dimensionality: chemically, the limitation to planar molecules seems very limiting.
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.
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.
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).
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.
2d life simulator:
https://youtu.be/I6bHpJ2GV0Y
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...
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
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.
not necessarily. instead of a tube, it would be a series of "locks" like a canal.
Regurgitation solves that specific showstopper.
https://users.renyi.hu/~daniel/tmp/noitdoesnt.jpg
That's a pretty slick solution there.
Your two separate pieces could still interlock, so that you wouldn't "fall apart".
you assume a 2d being needs to need or requires a digestive tract. What if that being doesn't necessarily it?
Food may also serve as the glue.
I believe this was answered on a 1997 Halloween episode of The Simpsons.
Commentary: https://www.technologyreview.com/s/613788/life-could-exists-...
There are no such things as dimensions outside your head.
Life exist in water - a liquid with particular properties which makes protein folding possible. Dimensionality is irrelevant.
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