Okay, this post is going to be a little bit out there… very low on the fine detail and pretty half-baked, but, so what, I guess this blog doesn’t need to be extra serious all the time.

The basic premise is this, I think one day we’ll come to see that the mind undergoes something akin to phase transitions in condensed matter systems. Here is the correspondence I’m trying to conjecture:

From the theory of phase transitions, we have that there are certain “critical points” in parameter space where the free energy of the system experiences a non-analyticity. In more generic terms, the free energy of a system is a function of macroscopic parameters of your system which has the property that its local minima will determine the state of your system with respect to those parameters.

For instance, lets say we eventually determine that neural networks in human brains can be described by some numbers. As a guess, lets say these numbers are related to graph invariants, or perhaps things like the average number of connections in various regions of the brain, or whatever else you can think of. Clearly there is a microscopic way to parameterize the brain, if you give the position and momentum of every molecule, teasing out the right macroscopic variables to describe some behavior in the general case is probably a bigger job than we can imagine. However, all we’re asking for here is *some* parameterization. This idea hinges on the fact that we can come up with a finite set of numbers, which we can given that the system is made up of a finite number of molecules. If we want to talk about “free energy” though, we need macroscopic parameters for the system, which are a smaller set of “bulk” numbers derived from all the microscopic parameters defining the microstate of the system. Let’s not dwell on the thermodynamics however…

If we suppose that a free energy can be constructed for the mind, then a critical point is a point where the macrostate of the system will undergo a sudden “gapped” change. I think such a description should exist for when someone changes their mind about something. The idea here is that the state of your brain is what determines your decision making. If your brain is in state A, then you think sending troops to Syria is a good idea, but if your brain is in state B, then you think that’s a bad idea. If someone changes their mind about sending troops to Syria, then their brain has underwent a phase transition.

This might be a pretty vacuous idea, however, because the previous example did not provide any sort of predictive power. The cynic asks “So what if we think about a changing your mind as a phase transition, who cares, what does that do for us?”

That’s a great question that you should ask yourself whenever you want to see if an idea is just a novelty. One prediction from the theory of phase transitions is the idea that near a critical point, there is a scale invarience in the theory. A natural question to ask is, how does this scale invarience manifest in the brain when one is changing their mind? I think this has to do with being able to see multiple points of view. When you have the ability to see multiple points of view, to appreciate both the benefits of sending troops to Syria and the issues with it, then your brain is near a critical point. When you change your mind about an issue, your brain undergoes a phase transition. Perhaps this model could inform how we get people to look at new topics. If we understood the variables at play here and the location of these critical points in that parameter space, there might be some cool results that follow!