Can life exist in 2 (spatial) dimensions (instead of 3)?
What a weird question, you may think. Of course, it can:
Well, yes. But taking into account that we do not even know what life is, we’d better restrict ourselves to life as we know it, i.e. with an evident anthropic bias.
There are anthropic reasons to suspect that life in more than three spatial dimensions is not possible. In Newtonian gravity in more than three dimensions, orbits are unstable against small perturbations, and hence anything like a solar system is impossible.
J. H. C. Scargill thinks that the arguments against there being fewer than three seem, however, not so robust. He identifies two main issues in previous literature: the lack of a local gravitational force and Newtonian limit in 3D general relativity, and the possibilities of a planar topology are `too simple’ for life to exist. Complex life would face topological obstructions in two dimensions. He examines both arguments looking for reasonable work arounds.
There are anthropic reasons to suspect that life in more than three spatial dimensions is not possible, and if the same could be said of fewer than three, then one would have an anthropic argument for why we experience precisely three large spatial dimensions. There are two main arguments levelled against the possibility of life in 2 + 1 dimensions: the lack of a local gravitational force and Newtonian limit in 3D general relativity, and the claim that the restriction to a planar topology means that the possibilities are `too simple’ for life to exist. I will examine these arguments and show how a purely scalar theory of gravity may evade the first one, before considering certain families of planar graphs which share properties which are observed in real-life biological neural networks and are argued to be important for their functioning.Scargill, J. H. C. ‘Can Life Exist in 2 + 1 Dimensions?’ ArXiv:1906.05336 [Gr-Qc, Physics:Hep-Th, Physics:Physics], June 2019. arXiv.org, http://arxiv.org/abs/1906.05336.
Just beware, because in that case, the phantom zone might become a real prison…