entropy Article Fact, Fiction, and Fitness Chetan Prakash 1, Chris Fields 2 , Donald D. Hoffman 3, Robert Prentner 3 and Manish Singh 4,* 1 Department of Mathematics, California State University, San Bernardino, CA 92407, USA;
[email protected] 2 Independent Researcher, 23 rue des Lavandières, 11160 Caunes Minervois, France; fi
[email protected] 3 Department of Cognitive Sciences, University of California, Irvine, CA 92697, USA;
[email protected] (D.D.H.);
[email protected] (R.P.) 4 Department of Psychology and Center for Cognitive Science, Rutgers University, New Brunswick/Piscataway Campus, NJ 08854, USA * Correspondence:
[email protected] Received: 1 March 2020; Accepted: 22 April 2020; Published: 30 April 2020 Abstract: A theory of consciousness, whatever else it may do, must address the structure of experience. Our perceptual experiences are richly structured. Simply seeing a red apple, swaying between green leaves on a stout tree, involves symmetries, geometries, orders, topologies, and algebras of events. Are these structures also present in the world, fully independent of their observation? Perceptual theorists of many persuasions—from computational to radical embodied—say yes: perception veridically presents to observers structures that exist in an observer-independent world; and it does so because natural selection shapes perceptual systems to be increasingly veridical. Here we study four structures: total orders, permutation groups, cyclic groups, and measurable spaces. We ask whether the payoff functions that drive evolution by natural selection are homomorphisms of these structures. We prove, in each case, that generically the answer is no: as the number of world states and payoff values go to infinity, the probability that a payoff function is a homomorphism goes to zero.