Surprise, entropy and living systems resisting the second law

Older writers used surprise in its everyday sense. Darwin (1859), in On the Origin of Species, argued that people accept rarity in a species without surprise but marvel at its extinction. He compared this to accepting sickness while wondering at the death that follows.¹ James (1890), in The Principles of Psychology, held that surprise arises only when a sensation differs from the one expected.² Jennings (1906) used the word for the reception of an experiment. He argued that swimming spores gave no cause for surprise, because the slight differences in light were not perceived by the organisms.³ None of these authors links surprise to entropy.

Friston, Daunizeau and Kiebel (2009) defined the quantity agents minimise as self-information, called surprise in information theory and negative log-evidence in statistics. They reported that colleagues object that an agent should then retreat to a dark room. Their reply was that the world offers no stable fixed point. Sooner or later the agent meets surprising states such as dehydration.⁴ Friston and Ao (2012) set this against reinforcement learning, which maximises expected reward. They held that surprise need not be learned, because being a particular agent already defines which states are surprising, as a fish out of water is.⁵

Friston (2013), in Life as we know it, stated that under ergodic assumptions the long-term average of surprise is entropy. Minimising free energy by sampling sensory input therefore bounds the dispersion of sensory states. He drew the conclusion that biological systems resist the second law, or more exactly the fluctuation theorem for open systems.⁶ Calvo, Baluška and Sims (2016) applied the idea to plants and other organisms. They gave a snowflake that melts and a fish that dries out as examples of surprising states.⁷ Calvo and Friston (2017) added that surprise is Bayesian model evidence with the sign reversed, so a plant that minimises it behaves like a statistician.⁸

Friston and colleagues (2009) conceded that avoiding surprise is not a simple matter. Environmental dynamics preclude a fixed solution, and the best an agent can do is minimise surprise under perturbation.⁴ Bruineberg, Kiverstein and Rietveld (2018) questioned the explanatory role given to the system inside a Markov blanket. In their two-clock example, internal and external dynamics are symmetric. They granted that average surprisal of the coupling is lowest when coupled systems synchronise, but they read this as attunement of the whole system, not as special to the agent.⁹