1. Mathematics is a language.
Because of the circles I’ve grown up in, I’ve developed a violent kneejerk reaction against mathematical models. I am cautiously becoming more comfortable with math-y models, the more I study both economics and mathematics. Though it’s true that mathematical models can obfuscate the phenomenology of “choice”, when you understand the meaning of the models, the translations are much simpler. When you understand how to speak in mathematics, it’s much easier to read these models. A mathematical model is not the source of our insights, but they can be a useful way to communicate our insights. Mathematics should be judged the same way that we judge an AI translation program. If I can translate a sentence from English to Greek and back to English without loss of meaning, then I am satisfied with the accuracy of the program. Still, don’t let mathematical models scare you into believing them by their elegance, but to judge them you need to speak the language. You wouldn’t want someone critiquing your verbal model if they didn’t speak English, would you?
2. Questions can be more powerful than answers.
Once you give yourself a set of axioms, it’s not too difficult to find the fullness of their implications. Given a philosophical revolution, give or take a few centuries before that paradigm is dead, no matter how much “progress” it lead to. Once you find yourself in one of these paradigms it takes a special kind of attention, to find the foundations and subvert them. The set of axioms or assumptions that you choose is an art, and for those who want a “final, objective, authoritative” science, that’s hard to admit. If you can ask a meaningful and interesting question within an existing scientific framework, you can keep the wisdom of older thinkers while opening up a new frontier for discovery. In an academic career (especially early on), such questions should be your quarry.
3. Game theory has near limitless potential, especially for new institutional economics.
Before you comment, remember this is after my *first* year, not my second year. I will have a different, more humble opinion by then. I have become totally smitten with the style of institutional analysis that Greif promotes in his 2005 book, and in a number of his papers. From my brief skimming, he characterizes all institutions as a confluence of elements that people recognize and remember. Historically, this has been called a “spirit of the age” or zeitgeist. The narrowest that Greif defines institutions is as a regularity of behavior that everyone recognizes, and sees as external to them. The institution is an irreducible pattern that’s actualized by many different rituals of recognition and remembrance. Which is basically what a spirit is. There are multiple Nash equilibria that can be actualized, it’s not deterministic which ones are present. Economics is a set of tools for testing “plot holes” in the real world. Every story that you can tell about the world has to “make sense” in economic terms. But the “economic variables” constraints etc don’t dictate which story takes place. Many models include expectations, beliefs, interpretive frames without a good investigation of those terms and with a casual inclusion of their relevance. I want to get into that. It sounds fascinating.