Why do we live in a universe with threespatial and one time dimension - 3 +1, as cosmologists would say? Why exactly this combination, and not 4 + 2 or 2 + 1? Over the past decade, physicists have investigated this question many times, conceiving other universes with different properties, in order to understand whether there could be a difficult life in them or not. And inevitably they came to the conclusion that it could not exist in the universe with four spatial dimensions or with two temporal dimensions. So people will inevitably end up (and end up) in the universe with dimensions of 3 +1.

This is the anthropic argument: the idea that the universe must have the properties necessary for the survival of observers.

What does a two-dimensional universe look like?

But what about the simpler universes,for example, 2 + 1? Physicists have suggested that two spatial dimensions cannot provide enough complexity to sustain life. They also believe that gravity will not work in two dimensions, so objects like the solar system will not be able to form. But is it really?

James Scargill of the University of CaliforniaDavis, contrary to all expectations, showed that a 2 + 1-dimensional universe could support both gravity and complex life. His work undermines the anthropic argument for cosmologists and philosophers, who will have to look for another reason why the Universe takes the form it takes.

First, a little background. One of the great scientific mysteries is why the laws of physics seem sharpened (or fine-tuned) to life. For example, the numerical value of the fine structure constant seems arbitrary (about 1/137), and yet different physicists have indicated that if it were even slightly different, atoms and more complex objects could not be formed. In such a universe, life would be impossible.

The anthropic approach is that ifthe fine structure constant took on some other value; there would be no observers who could measure it. That is why it has a value that we measure!

In the 1990s, Max Tegmark, now a physicistThe Massachusetts Institute of Technology, developed a similar argument for the number of dimensions of the universe. He argued that if there were more than one time dimension, the laws of physics would not have the properties necessary for observers to predict. This would definitely exclude the existence of physicists and, possibly, of life itself.

We now turn to the properties of universes with fourspatial dimensions. In such a cosmos, Newton's laws of motion would be very sensitive to tiny disturbances. One consequence of this is that stable orbits could not have formed, so there would be no solar systems or other similar structures. “In a space with more than three dimensions, there can be no traditional atoms and possibly stable structures,” says Tegmark.

Thus, the conditions for life seemunlikely in universes with more dimensions than ours. But the argument is that universes with fewer dimensions are less secure.

There is an opinion that the general theory of relativity does not work in two dimensions, therefore gravity cannot be.

But James Scargill thinks differently. In his article, he shows that a much simpler, purely scalar gravitational field can be possible in two dimensions and this would allow obtaining stable orbits and a reasonable cosmology. It remains only to show how complexity can arise in measurements of 2 + 1. Scargill approaches this problem from the point of view of neural networks. He points out that the complexity of biological neural networks can be characterized by various special properties that any 2D system should reproduce.

Among them, the property of "small world", modelconnection, which allows you to bypass a complex network in several small steps. Another property of brain networks is that they operate in a mode that is finely balanced between the transition from high activity to low activity — the critical mode. This also seems possible only in networks with a modular hierarchy, in which small subnets merge into larger networks.

The question that Scargill asks is whether there are any 2D networks that have all these functions — the properties of the small world, the modular hierarchy, and the critical behavior.

At first it seems unlikely because2D-graphs nodes are connected through edges intersecting each other. But Scargill shows that 2D networks can indeed be built on a modular principle and that these graphs have certain properties of a small world.

It also shows that these networks can workat the point of transition between the two types of behavior, thus demonstrating criticality. And this is a terrific result, which suggests that 2D networks can indeed support surprisingly complex behavior. Of course, this does not prove that the 2 + 1 universe can actually support life. It will take more work to figure this out for sure.

But now cosmologists and philosophers have new food for thought. Do you agree? Tell us in our chat in Telegram.