FQXi Essay 2015
“Confronted with a pythagorean jingle derived from simple ratios, a sequence of 23 moves from knot theory, and the interaction between a billiard-ball and a zero-gravity field, a young detective soon realizes that three crimes could have been avoided if math were not so unreasonably effective in describing our physical world. Why is this so? Asimov’s fictional character Prof. Priss confirms to the detective that there is some truth in Tegmark’s Mathematical Universe Hypothesis, and reveals him that all mathematical structures entailing self-aware substructures (SAS) are computable and isomorphic. The boss at the investigation agency is not convinced and proposes his own views on the question.”
This is the abstract of ‘Let’s consider two spherical chickens‘, my contribution to the FQXi 2015 Essay Contest ‘Trick or Truth? The Mysterious Connection Between Physics and Mathematics’, which obtained a Third Prize and the mention for ‘Most Creative Presentation’, out of 203 submissions.
I wish to dedicate this essay and these results to the memory of my father Giampaolo, who was very amused by the spherical chickens concept, referring to the habit of some theoretical physicists to make over-simplifications when developing models of real systems. As a chemist he must have considered himself immune from this attitude!
tommaso bolognesi 
I really liked your story! It had some quite interesting ideas about the fundamental nature of our universe and consciousness, two topics that I like to think about as well. There is something that is a bit confusing, however. Near the end, you mention the Priss-Godel-Priss Theorem, which basically states that all mathematical structures that entail conscious entities are defined by total computable functions and isomorphic. I know that your story is technically fiction (albeit fiction that involves real scientific, computational, and mathematical ideas. However, I am not sure how, even now, whether such a theorem is even possible, for several reasons. First, as Max Tegmark notes, there are many possible mathematical structures that correspond to many different possible laws for a universe. These structures do not have to possess features such as relativity, quantum mechanics, et cetra, but they are still mathematically consistent. How could it be proven that, among an infinity of possibilities, only our particular universe could have consciousness? Second, even if I accept for now that consciousness only naturally arises out of one set of natural laws, what prevents it from arising in a structure that doesn’t always follow some laws? (As some critics of the MUH have noted, if all mathematical structures exist, it may be hard to explain why our laws are so regular, because there should also be many mathematical structures in which irregularities arise, even ones that are noticeable yet don’t threaten our existence. An analogy would be to, say, the graph of “y=x+1 , except at x = 41, where y = 41.”) After all, it seems that once you have a conscious substructure, you can add it to another structure. For example, if a conscious being is simulated, its outside environment in the simulation can be pretty much anything the simulators desire. Surely a simulation should correspond to a mathematical structure/possible universe? I am interested in this topic because I like thinking about universes with very different natural laws; there could be interesting stories about them. That said, I still have not learned a lot about mathematics, so is there something, even something obvious, that I am missing? Anyway, thank you for this amazing piece of writing!