One of the fields of human inquiry that make extensive use of mathematics and calculus is economics. Contemporary economic theory relies heavily on mathematical concepts and ideas to make sense or and theorize about economic phenomenon to devise economic models/policies. Anyone who doesn’t know the basics of calculus and mathematical analysis can’t hope to become an economist—because there’s no way to conduct economic analysis without math.
The concepts of differentiability play a significant role in devising functions that explain economic behavior, identifying efficiency conditions, and other essential factors. My Algebraic General Topology, considering that its primary concern is continuity and differentiability, can very well change how we theorize about economic behavior altogether.
The Role of Calculus in Economics
Econometrics is a field of statistical analysis that’s often used in economic experiments to create predictive models that might present accurate forecasts on economic behavior. Even at the most basic levels, students are taught the concepts of marginal utility, price elasticity, and optimization using ideas of the Lagrangian optimization function and vector calculus.
The Shortcomings of Econometrics
Underlying this use of mathematics is the idea that human behavior is easily modeled using principles of mathematics, but there’s a lot of grey area in this assumption. Regression analysis—the underlying mathematics in econometrics—assumes that human behavior is like any other variable that mathematics can explain. Critics of existing econometric techniques often say that the application of homogenous models across entire economic contexts—basically to whole societies—is faulty because they presume a causal pattern within any economic setting. A gaping loophole in this thought is the fact that existing mathematics is fully capable of expressing all the possible causal chains within the economic sphere of society.
The question here is one of possibility rather than of a critique—economic behavior is rational only in so far as it complies with the laws of calculus. But what if we do not fit mathematics into economic behavior—what if instead, we fit economic behavior into mathematical laws? How do the limits of mathematics determine what we understand about economic behavior?
If I were to consider the possibility that there is some economic behavior that isn’t expressible in existing mathematical models, would that behavior also be classified as irrational? That’s really a very flimsy standard to set for economic rationality.
The Possible Role of AGT in Analysis
Algebraic General Topology is a new field of mathematical analysis that presents a new expression for continuity and differentiability. When used correctly, it can even be used to describe limits for arbitrary discontinuous functions—some of which might also describe economic behavior.
The possibilities of AGT within the context of economics are boundless. With a new way of talking about mathematical concepts, we’ll have a new way of discussing economic behavior. If you’re interested in AGT, you should read my math research book titled Algebraic General Topology Volume 1. For any questions on my work, you should get in touch with me—I always welcome any questions that I can answer or entertain any criticism of my work.