by Jerry Bowyer
In a recent column, 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 (see his textbook on Logic) 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. But 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.
Poythress’ and Gilder’s views dovetail nicely with one another, even though neither shows up in the other’s writing. Gilder’s latest thought (represented by his new book, The Scandal of Money) deserves a column of its own. For more on Poythress, a partial transcript can be found below (edited for clarity) and for a much deeper dive listen to the full interview here.
POYTHRESS: The stock market is all about things you can’t predict as well as things that are regular, so I can understand why it would be relevant. In fact, I had a former Westminster student, a Westminster graduate who works for an investment organization, and he wrote to me after he found the book, and he was really enthusiastic about it. He said this is the kind of thing that my colleagues and I are doing all the time with this high-powered mathematics; we’re always relying on probabilities. So it was an interesting reaction. And I hadn’t thought of that dimension because my background is in science more than in finance.
BOWYER: I think there are more people running regressions on valuations and performance, probably, than there are people running regressions on, say, empirical data from the natural sciences.
POYTHRESS: Yeah, and of course there’s money in it. So that—you know, that makes it worthwhile for people to invest energy in it…Sociology is dominated by what you might call the vision of scientific sociology, where we’re going to do statistics and questionnaires and we’re going to analyze causal relationships and social tendencies by seeing correlations between statistics. So it’s heavily influenced by mathematics. But what’s happening is your vision of human nature is being reduced to what is quantifiable. And if you are Christian, you see God governs that. We’re not denying its significance or its importance or your ability to do really neat analyses on that level, but it’s not the whole.
And if I may talk about—I’m going out into my area of ignorance, but the things about the stock market, people who are modeling it, some of them are economists; they talk about the ideal rational agent.
POYTHRESS: Well, there’s no such thing.
POYTHRESS: Right? It is a simplification. Now, it’s a convenient simplification, but you’ve got to keep telling yourself this is a simplification, and it’s going to—in some cases — leave out things that are really, really significant. So I guess now, you know, people are on to the fact that when the market goes down—I just saw some — something fairly recently where they said that the stock market, as a whole, tends to inch up, inch up, and it’s gradually growing and gradually growing.
BOWYER: And then crashes.