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 (16x6=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.