Does two dimensional life exist
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 4 dimensions or 2 dimensions? Is there something special about three dimensions that makes life possible? Scientists have presumed that life could only exist on 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 this this bias is not really rooted in science?
This is the question that Cosmologist Dr. James Scargill recently examined and released in a preprint on June 2019. I personally spoke to Dr. Scargill, and I think you are going to be surprised what science has to say about this. Can life exist in another dimension? And what does this say about our place in the universe…that’s coming up right now!
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There a great story written by an English school teacher, Edwin Abbot in 1884 about geometrically shaped creatures that lived in a two 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 show called The Orville on Hulu, which BTW I think is the real heir apparent to the Star Trek tv franchise, even though it’s not in the same universe, the crew of the Orville encounters a 2 dimensional universe. They didn’t get into details of the two dimensional creatures that lived in it, 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? Could two dimensional creatures actually exist or Is there something special about our 3 dimensions that makes it so that life could not exist if there were any other number of dimensions? And if life did exist, what would it be like?
You’re going to be shocked at the answers that are coming up right now…
Lets 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 3 large dimensions. At least not life as we know it. Why? Because orbits would be unstable against small perturbations from gravity coming from the extra dimensions beyond 3, and so planets could not orbit stars, and solar systems could not exist.
Because stable elliptical orbits and stars are not possible in more than 3 dimensions. The force of gravity gets weaker the more dimensions you add. For example in 4 dimensions, Gravity varies as the inverse cube of the radius rather than the square of the radius. As a result, even small disturbances such as the pull of other planets would send an orbiting earth either towards the sun or spiraling away from the sun. No orbits means no solar system, and presumably no life.
The other reason is the latest data from the detection of gravity waves using LIGO suggest that there are no higher large 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 very small scales – 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 an atom could fit on these scales. If an atom was the size of the earth, these smaller dimensions would be the size of a marble or smaller.
If an atom was the size of the earth, these dimensions would be much smaller than even the size of a lady bug.
So life probably does not exist in a fourth or higher dimension.
But what about 2 dimensions, why can’t life exist in 2 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 advisor 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 3 spatial and 1 time dimension. In other words, there would not be enough degrees of freedom for space-time to curve.
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 2 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 mass/energy. 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 is not enough freedom in how space-time can curve, and it is instead completely determined by the matter/energy content of the spacetime.
This seems to present the same problem of no obits that we had for 4 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. 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. Dr. Scargill showed that even though there are fewer degrees of freedom for space-time geometry in two dimensions, the equations still allow scalar gravity to exist in the spaces between masses.
What about the rest of physics? Would the other three fundamental forces from the standard model 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 2 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 2% of the mass of atoms comes from the Higgs Field, almost the entire mass of atoms and presumably then most of the universe come from energies present in the nucleus of atoms. I have video on that if you want more details. And scientists who have studied the idea of a universe without the weak nuclear force have concluded that such a universe would not be devoid of life.
What about the complexity of life because of the limitations on the number of neuronal connections that you could have?
Dr. Scargill shows in a series of planar 2D graphs, 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 1000 connections per neuron. Because of the limitations of two dimensional planar connections, our two dimensional neurons could have only 3 connections each. But our neurons are limited in active and inactive phases. In other words, they can only process so much information. It is estimated that only about 10% of the connections are working at any given time. So the effective number of connections is 100 per neuron.
A human brain has about 1000 connections per neuron. Because of the limitations of two dimensional planar connections, our two dimensional neurons would have on 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 is estimated that only about 10% of the connections are working at any given time. So the effective number of connections is 100 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 than human brains, it is possible that their processing capacity could approach that of the human brain. This may be a stretch, but perhaps 2D creatures could emulate less complex brains. it is known for example that nematodes have only 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 limitations for two dimensional life forms. The 2D universe would be a surface. planets would be small circles. and we would be two-dimensional beings composed of molecules (two dimensional strings of beads). Organic chemistry 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 1980’s, 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, 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 anthorpic 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(Pie)r^2, whereas the surface area in 2D would simply be 2(pie)r. 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 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 is 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 two dimensional life exists? We can’t even demonstrate that three dimensional life outside of earth even exists, 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 should pat ourselves on the back for having the privilege to be alive here and now. Each of us we would be well advised to get over ourselves. The universe does not revolve around us, and we may not be all that special.
