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Can life exist in the lower dimensions? The idea of two-dimensional life is very tempting, but it is widely believed that there can be no life in two-dimensional space. Two important reasons are that two-dimensional gravity is difficult to maintain the stability of planetary orbits, and the complexity of two-dimensional neural networks cannot support life activity.
But UC Davis physicist James Scargill (J.H.c.scargill) published a paper on the preprint site. Here, space is two-dimensional, while time is one-dimensional. In the paper, Skargier argues about the above two points by proving that in two-dimensional space, life is entirely possible.
Stability of the two-dimensional solar system
First, Skargier discusses the stability of the two-dimensional solar system from the perspective of gravity.
A distinctive feature of gravity is that once space is not three-dimensional, the magnitude of gravitational force is no longer inversely proportional to the square of the distance. This has serious consequences – the Earth's orbit around the Sun becomes unstable. Any faint disturbance, such as a meteorite falling on Earth, will cause the Earth to leave its current orbit.
In non-three-dimensional space, there can be no stable Orbit of the Earth around the Sun without modifying the current theory of gravitational attraction (general relativity). The Earth is either drawn to the Sun, falls into the Sun and burns down, or drifts away from the Solar System.
In two-dimensional space, in addition to the problem of orbital stability, gravity itself is also a resistance to the existence of life. Since the gravitational pull of two-dimensional space has no degrees of freedom, here, there is not even a real gravitational force.
To solve this problem, Skargier introduced a scalar field in two-dimensional space, modifying the entire theory of gravity to produce an entirely new two-dimensional gravitational field. Under these conditions, Skargier demonstrated that there could be a stable circular orbit that depicts the Earth orbiting the Sun, and that two-dimensional organisms live on this two-dimensional Earth.
If only physics is considered, the most important interaction in the two dimensions is of course gravity, because gravity is the macroscopic and determines the structure of space-time. Of course, Skargier didn't mention in his research how the other three interactions— electromagnetic interactions, strong interactions, and weak interactions— would become in two-dimensional space.
The possibility of the existence of two-dimensional life forms
Subsequently, Skargill mathematically proved that in two-dimensional space, the complexity of neural networks has the conditions to support life. Relatively inferior organisms, such as nematodes, have been drawn up with complete neural networks. Judging from the current research conclusions, for the human brain neural network, a basic point of current brain science research is that the human brain neural network shows the characteristics of the small world. The characteristics of the small world can be understood as the fact that the world is actually very small, and you only need to know everyone in the world through 6 people, including the president of the United States or the village chief of a village in Africa.
For two-dimensional organisms, the situation is a little special: the nerve fibers in the brain of two-dimensional organisms cannot cross, so the neural network of their brains must be flat, which in a sense limits its complexity. As a result, some studies argue that two-dimensional worlds are too simple to allow complex life to emerge.
But can two-dimensional neural networks also exhibit small-world features? This is exactly what Skargill needs to solve.
Cui Xiaohua, an associate professor at the School of Systems Science at Beijing Normal University, said: "Skargill constructed some floor plans with rings in the paper. Rings are important in networks because looped networks can produce self-cyclical behavior. Some studies believe that an important mechanism for the brain to process time information is to use local neural circuits to record information. ”
In his paper, Scargill demonstrated that two-dimensional neural networks with rings can exhibit small-world properties. In addition to the small-world characteristics, Skargill also mentioned two other characteristics of the topology of brain neural networks in the paper, hierarchical and modular, and proved that two-dimensional neural networks can also exhibit these characteristics. Therefore, from the perspective of neural networks, there may also be life forms in two-dimensional space.
Although Skargier argues for the possibility of the existence of two-dimensional life, this is still a long way from proving two-dimensional life. There are other reasons to think that life like ours cannot exist in two-dimensional space. For example, Hawking mentioned in A Brief History of Time that in two-dimensional space, the connection between the mouth and the anus of a living organism (the digestive tract) would divide the organism into two parts, so that the two-dimensional life cannot exist—of course, this is discussed from the perspective of the digestive system. Perhaps, we have a hard time finding answers as to whether there is life in other dimensions.
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