4:54

Earth: "Ight imma head out"

**Can life exist in 2D? The physics of a 2D Universe**

- By : Oliver Santos
- Category : Articles, Blog
- Tags: 2d life forms, 2d real life, 2d universe, 3d universe, 4d universe, 4th dimensional beings, a k dewdney, anime, can life exist at the planck scale, can life exist in 2d, dimensions, flatland, gravity in 2D, higher dimensions, James scargill, multidimensional lifeforms, physics of 2d, Quantum Mechanics, Quantum Physics, That, the, the physics of higher dimensions, two dimensional life forms, waifus, waifus are real, what would the physics of, yt:cc=on

Why is everything three-dimensional? We

have three spatial dimensions plus one time dimension.

You don’t need sophisticated scientific instruments to confirm this. This is

obvious to any observer. Why aren’t there four dimensions? Or two dimensions? Is

there something special about three dimensions that makes life possible?

Scientists have presumed that life could only exist in our three dimensions

because the laws of physics, as we understand them, wouldn’t quite work the

same way. But is this really true, or is this just our self-centered anthropic bias talking? Could it be that this bias is not really rooted in

science? This is the question that cosmologists dr. James Scargill recently

examined, and released in a preprint on June 2019.

I personally spoke to Dr. Scargill, and I think you’re going to be surprised what

science has to say about this. Can life exists in another dimension? And what

does this say about our place in the universe? That’s coming up right now… There was a great story written by an

English school teacher Edwin Abbott in 1884 about geometrically shaped creatures that lived in a 2-dimensional world called flatland. There was a strict

hierarchical social structure based on the shape that you were born with.

Besides being a social commentary, it examined what life would be like from

the perspective of sentient two dimensional beings. And more recently, on

a TV show called The Orville on Hulu, which by the way, I think is the

real heir apparent to Star Trek, the TV franchise, even though it’s not in the

same universe, the crew of the Orville encounters a

two-dimensional universe. They didn’t get into the details of the two-dimensional

creatures that lived in that universe, but it was an intriguing concept. This

idea of creatures living in two dimensions has been the purview of

science fiction. But is the science really all that far-fetched? Let’s look

at the case for higher dimensions first. One reason we don’t see four or five

large spatial dimensions is that, according to science, life cannot exist

in more than three large dimensions, at least not life as we know it. Why?…because

stable elliptical orbits around stars are not possible in more than three

dimensions. The force of gravity gets weaker the more dimensions you add. For

example, in four dimensions, gravity varies as the inverse cube of the

distance, rather than the square of the distance. As a result, even small

disturbances such as the pull of other planets, would send an orbiting earth

either toward the Sun or spiraling away from the Sun. No orbits means no solar

system, and presumably no life. And thus life presumably could not exist. Another

good reason is that the latest data from the detection of gravity waves, using

LIGO, suggested that there was no higher dimensions because if higher dimensions

existed, we would expect to see some of the gravity leaking into these other

dimensions, weakening it by the time it reached earth. But this weakening was not

seen. So if higher dimensions exist, they exist on a very small scale, on the scale

of Planck lengths, where the tiny strings of string theory can vibrate. You might

ask, “why can’t life exist on these small scales?” Well, these scales are so small

that not even atoms could fit on these scales. If an

atom was the size of the earth, these dimensions would be much smaller than

even the size of a ladybug! But what about two dimensions? Why can’t

life exist in two dimensions? Unlike higher dimensions, we know for sure that

two large dimensions actually exist. Most scientists had believed that

two-dimensional life was impossible. But Dr. Scargill found that the barriers to

existence of life in two dimensions are not insurmountable. I spoke with Dr.

Scargill and he generously agreed to be the technical adviser for this video. The

link to his website and paper are in the description below. There have been two

main arguments against the possibility of life in two dimensions. First, because

gravity according to general relativity requires three spatial dimensions and

one time dimension. In other words there would not be enough degrees of freedom

for space to curve in two dimensions. And second, scientists have believed that the

neural networks for complex brains which require hundreds of connections per

neuron could not form enough connections in two dimensions, because the number of

connections would be physically limited compared to three dimensions. Let’s first

look at what is needed for life to exist in two dimensions. And let’s start with

the problem of gravity. In two dimensions if only the equations of general

relativity were applied, it turns out gravity would exist only inside the

mass-energy components. And so outside a star, where there is no matter, space-time

must be flat, meaning no gravity. And hence there are no orbits. Why does this

happen? Simply put, there’s not enough freedom in

how space-time can curve. And it is instead, completely determined by the

matter energy content of the space-time. This seems to present the same problem

of no orbits that we had for four dimensions. But nothing forces gravity to

be only defined by general relativity. In particular, there could be other degrees

of freedom, such as a simple scalar field. It would allow stable orbits around

point sources. And it really would be equivalent to the kind of

two-dimensional bending, like a rubber mat, or trampoline that you

commonly see for 3-dimensional gravity, except that it would be a more accurate

representation of the two-dimensional gravity. You should note that this

graphic is not what scalar gravity actually physically looks like, because

there would be no third dimension for the two-dimensional universe to bend

into. The bending just represents the effect of gravity encoded in the

geometry of space-time, including 2d space-time.

Dr. Scargill showed that even though there are fewer degrees of freedom for

space-time geometry in two dimensions, the equation still allows scalar gravity

to exist in the spaces between the masses. What about the rest of physics?

Would the other three fundamental forces from the standard model still exist — the

strong nuclear force, the weak nuclear force, and electromagnetism?

According to Dr. Scargill, they would. Two dimensions would not be a limiting

factor since two dimensions provides enough degrees of freedom for the

respective equations to work. So for example, two-dimensional atoms could

exist, because the strong nuclear force binding protons and neutrons together in

the nucleus would be present. electrons could orbit around the nucleus,

since electromagnetism should also exist. In addition, the Higgs field would exist

with no problem, in principle. Dr. Scargill says that it is interesting to

note that the Higgs field and the weak nuclear force are probably NOT required

for life to exist. Only about two percent of the mass of an atom comes from the

Higgs field. Almost the entire mass of atoms, and presumably then most of the

universe’s mass, comes from energies present in the nucleus of atoms. I have a

video on that if you want more details. And scientists who have studied the idea

of the universe without a weak nuclear force have concluded the such a universe

would not be devoid of life! And what about the complexity of life, because of

the limitations of a number of neuronal connections that you could have? Dr.

Scargill shows in a series of planar 2d graphs, that connections could be made

with nodes such that they exhibit complex communications networks. They

would not have the complexity of three-dimensional brains,

but they could come close if the brains were much larger. A human brain has about

a thousand connections per neuron. Because of the limitations of 2

dimensional planar connections, the two-dimensional neurons would have an

average less than 6 connections each. But our neurons are limited in active and

inactive phases. In other words, they can only process so much information. It’s

estimated that only about 10% of the connections are working at any given

time. So the effective number of connections is about a hundred per

neuron. Two-dimensional creatures, on the other hand could be 100% efficient. So

now we have a ratio of 6 to 100. But if the two-dimensional brains were about 16

times larger (16×6=96) than the human brain, it’s possible that their processing capacity

could approach that of the human brain. Now this may be a stretch, but perhaps 2d

creatures could emulate less complex brains. It’s known, for example, that

nematodes, or roundworms, have about 300 neurons with 30 connections each. A

two-dimensional creature could probably more easily match that kind of

processing power. So what would be some of the real limitations for

two-dimensional life-forms? The 2d universe would be a surface. Planets

would be solid circles, and creatures would be 2 dimensional beings composed

of molecules which would be like two-dimensional strings of beads. The

organic chemistry, that we’re used to, depends on the 3d shapes of molecules, as

well as their composition. So this kind of chemistry would be a limitation in 2d.

However, this does not preclude some other form of equally effective organic

chemistry to rule the 2d universe. In fact, in the 1980s, scientists such as A K

Dewdney thought a lot about biochemistry of 2d molecules. And their studies

suggested that 2d chemistry, while simpler than 3d chemistry, could be quite

sophisticated. For any organism to exist and thrive, it has to be able to consume

and process energy. It could not have a digestive tract going one way completely

through its body like you and I have, because this would cut the organism in

half. But it could consume food in the same orifice that it releases its waste.

This may be disgusting to us, but again that is just an anthropic projection of

our values to other life-forms. Heat dissipation would be an issue, because

the relative surface area for 2d creatures would be much smaller than for

3d creatures. So for example, in 3d, the surface area of a sphere, is 4*PI*R^2, whereas the surface area in 2d would simply be 2*PI*R. So for any given

radius, the surface area would be much smaller in two dimensions. So the

creature, in order to increase its surface area for heat dissipation, would

likely not be smooth. It would have multiple folds, like a radiator in your

car, to dissipate more heat away from its body. It may also have a sophisticated

cooling system like your car. Everything inside the creature would likely be

connected to everything else, so the inside of the creature might look nearly

like a solid. There’s a famous line from Jeff Goldblum’s character Dr. Malcolm in

the movie Jurassic Park, “Life finds a way.” I want to emphasize that just because we

can show something can exist, does not mean that it does exist. Can we

demonstrate that 2-dimensional life exists? We can’t even demonstrate that

three-dimensional life, outside of Earth, even exist yet. So demonstrating

two-dimensional life seems out of the question right now. But what Dr. Scargill

shows is that to understand the true nature of our universe, we need to think

beyond our self-centered anthropic point of view. In other words while every

indication is that earth is rare and indeed, we’re lucky to be alive here and

now, each of us would be well advised to get over ourselves. This universe does

not revolve around us. Life in our 3d universe may not be all that unique. And

we may not be all that special.