This is the anthropic argument: the idea that the universe must have the properties required for the survival of the observers.
Looks like a two-dimensional universe?
But what about the more simple universes, for example, 2 + 1? Physicists have assumed that two spatial dimensions may not provide sufficient complexity to support life. They also believe that gravity will not work in two dimensions, so objects in the solar system can not be formed. But is it really?
James Scargill from the University of California at Davis, contrary to all expectations, showed that 2+1-dimensional universe could support both gravity and complex life. His work undermines the argument for the anthropic cosmologists and philosophers, who will have to find another reason why the universe takes the form that it takes.
First a little background. One of the great scientific mysteries is why the laws of physics seem to be sharpened (or finely tuned) for life. For example, the numerical value of the fine structure constant seems to be random (about 1/137), and still different physics pointed out that if it is even slightly different, atoms and more complex objects could be produced. In such a universe life would be impossible.
The anthropic approach is that if the fine structure constant took any other value, there would be observers who would be able to measure it. That's why it has the value that we measure!
In the 1990-ies Max Tegmark, now a physicist at mit, has developed a similar argument for the number of dimensions in the universe. He argued that if there is more than one temporal dimension, the laws of physics did not have the properties required observers to predict. It definitely would eliminate the existence of physicists, and perhaps of life itself.
We now turn to the properties of universes with four spatial dimensions. In this space, the laws of motion of Newton would be very sensitive to tiny perturbations. One consequence of this is that stable orbits could not form, so there would be no solar systems or other similar structures. "In the space with more than three dimensions may not be traditional atoms and perhaps stable structures," says Tegmark.
Thus, the living conditions seem unlikely in the universes with a higher number of dimensions than we do. But the argument is that universes with fewer dimensions less safe.
There is a perception that General relativity does not work in two dimensions, so gravity can not be.
But James Scargill thinks otherwise. In his article, he shows that a much simpler, purely scalar gravitational field may be possible in two dimensions and it is possible to get a stable orbit and a reasonable cosmology. It remains only to show how complexity can arise in dimension 2 + 1. The Scargill approach the problem from the point of view of neural networks. He points out that the complexity of biological neural networks may have different special properties, which should play any 2D system.
Among them, the property "small world" model of communication that allows you to bypass the complex network of several small steps. Another property of brain networks is that they operate in a regime that is delicately balanced between the transition from high activity to low activity mode of criticality. It is also possible only in networks with a modular hierarchy in which small subnets into a single, larger network.
The question asked by the Scargill is there any 2D network, which has all of these features — the small world properties, the modular hierarchy and critical behavior.
At first it seems unlikely, because in the 2D graphs, the nodes are connected via edges that intersect each other. But Scargill shows that the 2D network can indeed be build in a modular fashion and that these graphs have certain properties, small world.
It also shows that these networks can work at the point of transition between the two behaviors, thus demonstrating the criticality. And that's an amazing result, which suggests that a two-dimensional network can actually support a surprisingly complex behavior. Of course, this does not prove that the universe is 2+1 actually can support life. You will need to do more work to find out for sure.
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