As a society, I think we’ve all been conditioned to think of anything mathematical as “truth.” After all, if I have 2 apples, and I eat one, then I only have 1 apple left. Who could argue with that as truth? But what if I have 2 apples, and 2 oranges, and decide to eat an orange instead of an apple? Why did I choose the orange? What if I chose an apple? Were there social forces behind choosing the orange over the apple? What is the likelihood of my choosing an orange over an apple in the future? Now the “truth” is not so clear, and as even mathematicians point out, math is very much about philosophy.
The typical response I get, even from the Academy when it’s discovered that I hold an advanced degree in Economics, is along the lines of: “Oh, I can’t do math.” The fact is that 99% of Economists don’t actually “do math” (except as a prerequisite in Grad School). Economists largely, “do” 2 things: regression modeling and accounting. Neither of these fall in the realm of “math as truth,” and instead fall into math as a philosophy – that admittedly, gets peddled as “truth”, largely by Economists, knowing full well that what they are actually “doing” is philosophy (sometimes a euphemism for ideology).
Then there is the other side of the fence – the masses in society who have drank the Kool Aid in believing that just about anything involving math is “absolute truth.” There is a distinct difference between social activities that involve math, and social activities result in math. The orange and apple example involve math. People moving from the east to the west to find jobs is a social activity that results in math (labour data, demographics, GDP, etc). In neither case does this describe absolute truth.
So there are a few rules to what I call the “non-math”, or math as a philosophy versus math as absolute truth that apply. This is especially true in what Market Economists and Finance specialists do, which is largely regression modeling (including DSGE models. More on that in a minute).
- All regressions rely on statistics.
- All statistics happened in the past
- Math is 2+2=4.
- “Non-math” is: 2+2=the coefficient of the variables used, at the intercept point
- It is not humanly possible to account for all variables (DSGE modeling).
- All forecasting models use 1-5, and are only as good as their variables
The philosophy of math is about the social constructs that we build around variables. Why are apples and oranges my only variables? What if in reality, I had the entire produce department from my local supermarket at my disposal? Would I only have one substitution choice out of hundreds of fruits if apples were out of season, or the price too high? What if a hurricane came and destroyed my stock of apples and oranges? These are the types of things that DSGE models try to answer, by tossing in every variable in, including the kitchen sink.
There are 2 main problems with DSGE models: 1) they have been historically horrible at predicting natural disasters, even though there is a variable for that. 2) they have been horrible at predicting human social behavior based on social constructs. Two examples come to mind: the 2008 Financial Armageddon, and the Hurricane Katrina in New Orleans. DSGE models were front and center as a method, and the fate of people’s lives were at stake.
This does not mean that modeling is useless. The best example of regression modeling can be found in Climate Change science. Using past data to predict future results in climate change has actually been pretty accurate. Katrina was the exception, and since then, climate scientists have tossed out the variable, and shifted to the statement: “storms will be worse than in the past.” That’s a pretty accurate statement! This is also in the realm of “natural sciences” which tends to be more accurate anyway.
Within social science, the best regressions can tell us trends that happened in the past, only up to the present time. For example, we know from regression models that the longer it takes for unemployed people to find jobs, the more likely it will be that they will stop looking for one. This is useful for policy, social safety nets, and digging deeper into issues such as discrimination. Forecasting though, predicting the future, has been underwhelming in its accuracy.
And then there are things that models cover up, instead of reveal. The best example is the gender unemployment gap versus the racial unemployment gap. While it is a “social fact” that women make less than men, in the United States, they still have a better chance of employment at all versus African Americans and Hispanics. Sociologists love to point out that being a black women in America is infinitely worse than just being a women, but it’s still better than being a Black man in America:
We can model this chart! But both Sociologists and economists rarely do. So while models told us that gender was an issue in the labour market, and that gender coupled with race was also an issue, it covered up the fact that there is inequality in labour markets within groups as well.
The philosophy of math actually has little to do with actual math. The philosophy of math is more about methodology. Perhaps it is time that both academics and the general public to stop being afraid of the math that’s actually “non-math”, and stop accepting the “non-math” as absolute truth.