## Free Will and Entropy

In Sam Harris’ talk on free will (here: http://www.youtube.com/watch?feature=player_embedded&v=pCofmZlC72g) we have the following comment:

“if we caught a serial killer, we’d assume his responsibility because of his ability to have chosen otherwise. if we then discovered that he had a brain tumor which we could determine resulted in homicidal behavior, we’d determine that he was not responsible – that he was a victim of biology. this, however, is just a special case of any biological brain state – if we could know for certain how brain states generated behavior, we would just as certainly determine that he was not responsible for his actions and is just a victim of biology”

We have two parts of knowledge needed here: know for certain the current state and how (in detail) that state progresses to the macroscopic outcomes. From this we have a sort of determinism that is inconsistent with a simple notion of “free will”.

Now, I happened to be teaching the concept of entropy in my physics class at the same time I watched this, and I was struck by the parallel. I had thought of this before, last year, but never wrote about it. The concept of entropy arises when we don’t know the details of every single molecule in a system, knowing only some gross average features like the average energy or pressure. If we knew the current state of the system perfectly, and knew the laws of physics to forecast from that state, then we’d be able to reverse any process. However, given our lack of knowledge, the system moves in the single direction of increasing entropy, where the the energy is spread out the most, and the system has access to the most number of micro states consistent with the macro states we actually measure. The system is described in a non-deterministic way, even if all of the laws of physics underlying the motion of the molecules is entirely deterministic.

Perhaps our feeling of “free will” is real, in the same sense that entropy is real – it’s a non-deterministic description despite the underlying deterministic processes, arising from our practical lack of knowledge of the perfect details of those underlying processes. This idea needs more fleshing out, but it seems to be an interesting perspective to me.

I am a professor of Science and Technology at Bryant University in Smithfield, RI, and a research professor in the Institute for Brain and Neural Systems, Brown University. My research is in computational neuroscience and statistics. I teach physics, meteorology, astonomy, theoretical neuroscience, systems dynamics, artificial intelligence and robotics. My book, "Theory of Cortical Plasticity" (World Scientific, 2004), details a theory of learning and memory in the cortex, and presents the consequences and predictions of the theory. I am an avid python enthusiast, and a Bayesian (a la E. T. Jaynes), and love music.
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### 2 Responses to Free Will and Entropy

1. Rob says:

Interesting thought. I’m (just) a software engineer, but I’ve been interested in free will and entropy in the context of machine learning. One interesting article I saw recently was a physicist who tied the idea of “free will” to predictability, but as you point out, predictability is more or less a synonym for entropy. So I googled and found this post. Thank you!

It seems to me the idea of “free will” is pretty speculative and, practically, kind of useless ;), but the idea of entropy less so. So it may actually prove useful to leverage entropy, which we can calculate, to measure the “free will” in a system. That would make it less of an item of spirtual crisis and something that might actually be a useful measure of a system’s sophistication.

For example, I’ve been toying with the idea of calculating the entropy of a game of tic-tac-toe (which I think I can calculate) versus a game of chess.

If you have (or had) more thoughts on this topic, I’d be interested to see!

2. Jim Jozwiak says:

If you line up dominoes and push the first one over, the rest fall over in turn as a
demonstration of a mostly deterministic increase in entropy. In whatever way I might be like one
of the dominoes, I can eat food and use it to decrease my own entropy; although of course, the
process of my food-eating increases the entropy of the entire system of which I am a part. My decrease in entropy allows me to choose how to respond to events so that I have at least a little more free will than a domino.