## Interdisciplinitis: Do entropic forces cause adaptive behavior?

Reinventing the square wheel. Art by Mark Fiore of San Francisco Chronicle.

Physicists are notorious for infecting other disciplines. Sometimes this can be extremely rewarding, but most of the time it is silly. I’ve already featured an example where one of the founders of algorithmic information theory completely missed the point of Darwinism; researchers working in statistical mechanics and information theory seem particularly susceptible to interdisciplinitis. The disease is not new, it formed an abscess shortly after Shannon (1948) founded information theory. The clarity of Shannon’s work allowed a metaphorical connections between entropy and pretty much anything. Researchers were quick to swell around the idea, publishing countless papers on “Information theory of X” where X is your favorite field deemed in need of a more thorough mathematical grounding.

Ten years later, Elias (1958) drained the pus with surgically precise rhetoric:

The first paper has the generic title “Information Theory, Photosynthesis and Religion” (title courtesy of D. A. Huffman), and is written by an engineer or physicist. It discusses the surprisingly close relationship between the vocabulary and conceptual framework of information theory and that of psychology (or genetics, or linguistics, or psychiatry, or business organization). It is pointed out that the concepts of structure, pattern, entropy, noise, transmitter, receiver, and code are (when properly interpreted) central to both. Having placed the discipline of psychology for the first time on a sound scientific base, the author modestly leaves the filling in of the outline to the psychologists. He has, of course, read up on the field in preparation for writing the paper, and has a firm grasp of the essentials, but he has been anxious not to clutter his mind with such details as the state of knowledge in the field, what the central problems are, how they are being attacked, et cetera, et cetera, et cetera

I highly recommend reading the whole editorial, it is only one page long and a delight of scientific sarcasm. Unfortunately — as any medical professional will tell you — draining the abscess is treating the symptoms, and without a regime of antibiotics, it is difficult to resolve the underlying cause of interdisciplinitis. Occasionally the symptoms flare up, with the most recent being two days ago in the prestigious Physics Review Letters.

Wissner-Gross & Freer (2013) try to push the relationship between intelligence and entropy maximization by suggesting that the human cognitive niche is explained by causal entropic forces. Entropic force is an apparent macroscopic force that depends on how you define the correspondence between microscopic and macroscopic states. Suppose that you have an ergodic system, in other words: every microscopic state is equally likely (or you have a well-behaved distribution over them) and the system transitions between microscopic states at random such that its long term behavior mimics the state distribution (i.e. the ensemble average and time-average distributions are the same). If you define a macroscopic variable, such that some value of the variable corresponds to more microscopic states than other values then when you talk about the system at the macroscopic level, it will seem like a force is pushing the system towards the macroscopic states with larger microscopic support. This force is called entropic because it is proportional to the entropy gradient.

Instead of defining their microstates as configurations of their system, the authors focus on possible paths the system can follow for time $\tau$ into the future. The macroscopic states are then the initial configurations of those paths. They calculate the force corresponding to this micro-macro split and use it as a real force acting on the macrosystem. The result is a dynamics that tends towards configurations where the system has the most freedom for future paths; the physics way of saying that “intelligence is keeping your options open”.

In most cases to directly invoke the entropic force as a real force would be unreasonably, but the authors use a cognitive justification. Suppose that the agent uses a Monte Carlo simulation of paths out to a time horizon %latex \tau\$ and then moves in accordance to the expected results of its’ simulation then the agents motion would be guided by the entropic force. The authors study the behavior of such an agent in four models: particle in a box, inverted pendulum, a tool use puzzle, and a “social cooperation” puzzle. Unfortunately, these tasks are enough to both falsify the authors’ theory and show that they do not understand the sort of questions behavioral scientists are asking.

If you are locked in a small empty (maybe padded, after reading this blog too much) room for an extended amount of time, where would you chose to sit? I would suspect most people would sit in the corner or near one of the walls, where they can rest. That is where I would sit. However, if adaptive behavior is meant to follow Wissner-Gross & Freer (2013) then, as the particle in their first model, you would be expected to remain in the middle of the room. More generally, you could modify any of the authors’ tasks by having the experimenter remove two random objects from the agents’ environment whenever they complete the task of securing a goal object. If these objects are manipulable by the agents, then the authors would predict that the agents would not complete their task, regardless of what the objects are since there are more future paths with the option to manipulate two objects instead of one. Of course, in a real setting, it would depend on what these objects are (food versus neutral) on if the agents would prefer them. None of this is built into the theory, so it is hard to take this as the claimed general theory of adaptive behavior. Of course, it could be that the authors leave “the filling in of the outline to the psychologists”.

Do their experiments address any questions psychologists are actually interested in? This is most clearly interested with their social cooperation task, which is meant to be an idealization of the following task we can see bonobos accomplishing (first minute of the video):

Yay, bonobos! Is the salient feature of this task that the apes figure out how to get the reward? No, it is actually that bonobos will cooperate in getting the reward regardless of it is in the central bin (to be shared between them) or into side bins (for each to grab their own). However, chimpanzees would work together only if the food is in separate bins and not if it is available in the central bin to be split. In the Wissner-Gross & Freer (2013) approach, both conditions would result in the same behavior. The authors are throwing away the relevant details of the model, and keeping the ones that psychologists don’t care about.

The paper seems to be an obtuse way of saying that “agents prefer to maximize their future possibilities”. This is definitely true in some cases, but false in others. However, it is not news to psychologists. Further, the authors abstraction misses the features psychologists care about while stressed irrelevant ones. It is a prime example of interdisciplinitis, and raises the main question: how can we avoid making the same mistake?

Since I am a computer scientists (and to some extent, physicist) working on interdisciplinary questions, this is particularly important for me. How can I be a good connector of disciplines? The first step seems to publish in journal relevant to the domain of the questions being asked, instead of the domain from which the tools being used originate. Although mathematical tools tends to be more developed in physics than biology or psychology, the ones used in Wissner-Gross & Freer (2013) are not beyond what you would see in the Journal of Mathematical Psychology. Mathematical psychologists tend to be well versed in the basics of information theory, since it tends to be important for understanding Bayesian inference and machine learning. As such, entropic forces can be easily presented to them in much the same way as I presented in this post.