Phase changes

I’ve been using this phrase a lot, so I have simultaneously been wondering what I mean by it. This brief post lays out the first draft of my ideas.

A phase change is a qualitative shift in the dynamic nature of a quantitative system, due to passing some inflection point predicted by the laws of dynamic interaction. It is easier to begin conceiving this in terms of thermodynamics, if you already speak that language. Water changes phases to ice and steam, and back, due to its temperature. The temperature is due, in turn, to the amount of energy in the system. By injecting energy into the system as heat, the particles in the system may begin to interact in a fundamentally different way than before.

The same thing can occur in a person’s brain, according to similarly basic quantities that are still speculative at this stage. I happen to think average activation potential of the neurons is one of them, and may be compared to the kinetic energy of a particle in a thermodynamic system.

Anytime you see a statistical-mechanical system with several differential operators in its equations of dynamics, you know that the dynamics will have some of these inflection points in it. By differential operators, I mean delta symbols or the small, cursive d differential that indicates a partial differential equation is in the works.

As a naive working example, let’s pretend that IQ depends on two fundamentally different substances, gray and white matter, which follow different sorts of logic to produce IQ. The effect of white matter is linearly proportional to the volume of white matter, and the effect of gray matter is exponentially proportional, such that gray matter is like money: the more you have, the more effectively you can use each individual dollar. But wait, let’s also say that the IQ contribution of white matter somehow depends on gray matter, and vice versa, to create a dynamic system between them. Thus, more gray matter increases the effectiveness of the white matter, and more white matter increases the effectiveness of the gray matter.

In this system, an increase in gray matter increases the effectiveness of each individual gray matter neuron (remember, we’re pretending they are completely different substances following different logical rules), and increases the IQ contribution of all the white matter in aggregate, which turns around and increases the gray matter’s IQ contribution. Such a dynamic system would undergo qualitative shifts in personality after passing the inflection points that the partial differential equations predict.

But I’m reasoning backwards (because I’m unfortunately not smart enough to do it the right way). Because we can observe this sort of qualitative phase change occur in ourselves and/or the people around us, we ought to infer that this sort of dynamic system is responsible, underneath. A person who has seen ice melt into water can infer the same thing when they see steam condense into water: there is an analogous, dynamic system underneath which predicts these inflection points.

About Aeoli Pera

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8 Responses to Phase changes

  1. Heaviside says:

    phase changes/topological evolution/dialectical materialism

    Prigogine had kind words for Hegel because of this.

  2. Aeoli Pera says:

    >I have thought for years that phase changes have something to do with intuition. Once one occurs another can happen quicker if you integrate the new one faster.

    Yup yup. If I know differential equations already, and I learn plumbing, then I’m going to start thinking about the pipes in terms of fluid dynamics. If I don’t know differential equations, I’m not going to look at the pipes the same way.

    Some ideas map well onto other domains (diff eqs -> fluid dynamics), and some don’t (diff eqs -> phonetics).

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