ogc163
Superstar
One more unhinged rant before I turn the blog over to the Not Quite Noahpinion super-team.
When I was 15, I had an epiphany that changed my life. I had always been pretty good at math, but I found it boring. Who cared about all these abstract numbers? There was no pleasure in it for me. Even when you calculated the area of a back yard that could be enclosed by a certain length of fence, or whatever, it just seemed like an analogy, designed to make a boring pointless subject more interesting by relating it to something "real". Still boring. Despite teachers' entreaties, I never joined the math team in high school.
Then I took my first physics class. Flipping through the book, I groaned. There was so much boring math! But when I sighed and finally sat down to read the first chapter, the author told me an amazing thing. Math, he wrote, was the "language of nature". It could be used to represent reality. Those abstract numbers on the page weren't just something we made up; they were real things. At first I didn't even quite get what he was saying! Then I worked an example, using projectile motion to calculate the range of a cannonball. I suddenly imagined that I was a Turkish gunner, lobbing iron balls at the walls of Constantinople (yes, even then I was a history geek). Not realizing that gunners actually found their range by trial and error, or that the conquest of Constantinople came well before Galileo and Newton, I suddenly thought: "If I could do this simple math, I could hit the wall really accurately! But if I did the math wrong, I'd miss!" All at once, it hit me: Math could predict the future. Math conveyed power.
Math was real.
(Of course, later we confirmed the model's usefulness by predicting - very accurately! - a real metal ball in a real lab. But I was already sold on the concept.)
From then on I steadily began to enjoy math more. Eventually I discovered the abstract "beauty" that mathematicians talk about, especially when it came to proofs. But when I did physics math, there was always a special thrill that other math never held for me. It was the idea that I was mastering the real Universe with my abstract mind.
Fast-forward a few years later, and I had left physics behind (despite enjoying it and being good at it). When I entered econ grad school, I expected - naively, it turned out - that the math that people did would be like the math I had done in physics. I expected that economists' models would largely be reliable, well-tested tools for predicting the future, just like I had predicted the cannonball with high school algebra.
And actually, some of the econ math seemed to qualify. Game theory only annoyed me slightly. Though its assumptions weren't often satisfied in the real world, seemed like it would work if we could get the incentives right (and in fact, it very often does, in experiments). Consumer theory was a little more dubious - how could you measure a demand curve in practice? - but choice theory seemed like something that would work if people had stable preferences and you could nail them down empirically. I was a little disturbed by the misuse of the word "axiom" to refer to things that were actually testable (like revealed preference), but I let that one slide.
But macro was a different story.
In macro, most of the equations that went into the model seemed to just be assumed. In physics, each equation could be - and presumably had been - tested and verified as holding more-or-less true in the real world. In macro, no one knew if real-world budget constraints really were the things we wrote down. Or the production function. No one knew if this "utility" we assumed people maximized corresponded to what people really maximize in real life. We just assumed a bunch of equations and wrote them down. Then we threw them all together, got some kind of answer or result, and compared the result to some subset of real-world stuff that we had decided we were going to "explain". Often, that comparison was desultory or token, as in the case of "moment matching".
In other words, the math was no longer real. It was all made up. You could no longer trust the textbook. When the textbook told you that "Households maximize the expected value of their discounted lifetime utility of consumption", that was not a Newton's Law that had been proven approximately true with centuries of physics experiments. It was not even a game theory solution concept that had been proven approximately sometimes true with decades of economics experiments. Instead, it was just some random thing that someone made up and wrote down because A) it was tractable to work with, and B) it sounded plausible enough so that most other economists who looked at it tended not to make too much of a fuss.
When I was 15, I had an epiphany that changed my life. I had always been pretty good at math, but I found it boring. Who cared about all these abstract numbers? There was no pleasure in it for me. Even when you calculated the area of a back yard that could be enclosed by a certain length of fence, or whatever, it just seemed like an analogy, designed to make a boring pointless subject more interesting by relating it to something "real". Still boring. Despite teachers' entreaties, I never joined the math team in high school.
Then I took my first physics class. Flipping through the book, I groaned. There was so much boring math! But when I sighed and finally sat down to read the first chapter, the author told me an amazing thing. Math, he wrote, was the "language of nature". It could be used to represent reality. Those abstract numbers on the page weren't just something we made up; they were real things. At first I didn't even quite get what he was saying! Then I worked an example, using projectile motion to calculate the range of a cannonball. I suddenly imagined that I was a Turkish gunner, lobbing iron balls at the walls of Constantinople (yes, even then I was a history geek). Not realizing that gunners actually found their range by trial and error, or that the conquest of Constantinople came well before Galileo and Newton, I suddenly thought: "If I could do this simple math, I could hit the wall really accurately! But if I did the math wrong, I'd miss!" All at once, it hit me: Math could predict the future. Math conveyed power.
Math was real.
(Of course, later we confirmed the model's usefulness by predicting - very accurately! - a real metal ball in a real lab. But I was already sold on the concept.)
From then on I steadily began to enjoy math more. Eventually I discovered the abstract "beauty" that mathematicians talk about, especially when it came to proofs. But when I did physics math, there was always a special thrill that other math never held for me. It was the idea that I was mastering the real Universe with my abstract mind.
Fast-forward a few years later, and I had left physics behind (despite enjoying it and being good at it). When I entered econ grad school, I expected - naively, it turned out - that the math that people did would be like the math I had done in physics. I expected that economists' models would largely be reliable, well-tested tools for predicting the future, just like I had predicted the cannonball with high school algebra.
And actually, some of the econ math seemed to qualify. Game theory only annoyed me slightly. Though its assumptions weren't often satisfied in the real world, seemed like it would work if we could get the incentives right (and in fact, it very often does, in experiments). Consumer theory was a little more dubious - how could you measure a demand curve in practice? - but choice theory seemed like something that would work if people had stable preferences and you could nail them down empirically. I was a little disturbed by the misuse of the word "axiom" to refer to things that were actually testable (like revealed preference), but I let that one slide.
But macro was a different story.
In macro, most of the equations that went into the model seemed to just be assumed. In physics, each equation could be - and presumably had been - tested and verified as holding more-or-less true in the real world. In macro, no one knew if real-world budget constraints really were the things we wrote down. Or the production function. No one knew if this "utility" we assumed people maximized corresponded to what people really maximize in real life. We just assumed a bunch of equations and wrote them down. Then we threw them all together, got some kind of answer or result, and compared the result to some subset of real-world stuff that we had decided we were going to "explain". Often, that comparison was desultory or token, as in the case of "moment matching".
In other words, the math was no longer real. It was all made up. You could no longer trust the textbook. When the textbook told you that "Households maximize the expected value of their discounted lifetime utility of consumption", that was not a Newton's Law that had been proven approximately true with centuries of physics experiments. It was not even a game theory solution concept that had been proven approximately sometimes true with decades of economics experiments. Instead, it was just some random thing that someone made up and wrote down because A) it was tractable to work with, and B) it sounded plausible enough so that most other economists who looked at it tended not to make too much of a fuss.
