By Jerry Bowyer
I spoke with Dr. Vern Poythress, mathematician, scientist, theologian. Poythress teaches at Westminster Seminary and has six academic degrees including graduate degrees from Harvard and Cambridge. Poythress’ recent book, Chance and the Sovereignty of God, puts probability theory back where it started, among the theologians. Doing so means that he puts a foundation beneath it, but it also means that he puts limits around it.
This question of limits should be of particular interest here because it offers a view about the application of mathematical modeling to markets. Economics and finance are social sciences. Modern social sciences suffer from “physics envy,” which has tempted them to be overconfident about the degree to which mathematical models can accurately represent and predict human action. But recognizing the limits of mathematics blends well with Austrian economic theory, which emphasizes the role of subjectivity and is highly skeptical about the extreme pervasiveness of mathematical modeling in economics curricula.
For Poythress one of the implications of Gödel’s Incompleteness Theorem is that human beings have the ability to transcend lower systems of thought by writing higher sets of logical rules which incorporate the lower ones.
No model can capture everything, because humans can take any model, and then create a ‘higher’ model which incorporates the lower one. Even if one could create a mathematical model which fully captures all market activity, it would become obsolete the moment that it came into existence. Think of it this way: the moment someone creates the perfect stock price prediction algorithm, people would start to use it and they would change the dynamics so that the model no longer worked. Then they would start to analyze when it works and when it doesn’t and why it does and why it doesn’t, and at that point they’re creating larger models which incorporate the formerly perfect model. As long as people can keep thinking, they can keep innovating, and that means they keep transcending the prior math. This means that market participants will not fit into the ‘rational actor’ category no matter how much analysts of markets want them to.
The problem is not just the behavioral finance insight that people can be unreasonable, it’s also the Gilderian insight that people transcend the old reasoning by creating new things, new ideas, new information, new technologies, new knowledge.
For Gilder, the mathematics of physics and engineering is only appropriate to markets at the point of equilibrium, but equilibrium is not the goal. When equilibrium becomes normal, the economy is dead. For Gilder, information theory is the mathematics which can describe this reality, but information theory is by its nature about surprise: it’s about new information. New information is by definition not predicted, it’s discovered when it’s revealed.
Jerry Bowyer is an American economist, author, and columnist.
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