Existence of life in 2 + 1 dimensions

Abstract

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 leveled against the possibility of life in 2+1 dimensions: the lack of a local gravitational force and Newtonian limit in three-dimensional 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.