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 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.
Highlights
The question of why we experience the number of dimensions we do is one with a long history, which I do not attempt to cover here, instead referring the reader to [1,2,3,4,5] and references therein
Tegmark [5] convincingly argues for the existence of precisely one temporal dimension by requiring hyperbolic equations of motion, and predictability, which leaves us with the question of why there are three spatial dimensions
The anthropic argument against there being more than three large spatial dimensions is well known: in Newtonian gravity in more than three dimensions, orbits are unstable against small perturbations and anything like a solar system is impossible
Summary
The question of why we experience the number of dimensions we do is one with a long history, which I do not attempt to cover here, instead referring the reader to [1,2,3,4,5] and references therein. Tegmark [5] convincingly argues for the existence of precisely one temporal dimension by requiring hyperbolic equations of motion, and predictability (which certainly does seem a requirement if scientists are to emerge), which leaves us with the question of why there are three (large) spatial dimensions Various arguments for this have been proposed, including that it might be entropically or thermodynamically favored [6,7], or that it might have a dynamical reason, such as string gas cosmology [8,9], or evaporation of D-branes [10], or even that it might be due to properties of the Weyl equation [11]. It behoves me to mention the pioneering work of Dewdney who has thought extensively about the possibility
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