physics? (intercepting moving bodies in space)

I find the cross between Physics and Finance/Economics pretty interesting. There are some statistical methods that are used across both fields and some other stuff as well that I probably am not aware of, but what I find really intriguing is the cross migration of those in the respective fields. The beginnings of quantitative finance happened with a bunch of physics people going into finance. I have had profs who started out in physics and ended up in econ, and myself (and even also a Fed friend as well), the first academic field that I found interesting was physics (specifically the type of stuff you see in books like “The Universe in a Nutshell” by Stephen Hawking). I think it is pretty rare, however, for someone to start in econ/finance and end up in physics (probably in large part due to the money prospects in econ/finance and the extreme difficulty in making a mark in physics). Regardless, from time to time I get really interested in physics questions and now find myself with the math tools to be able to ask and answer very basic questions (and also for some reason, probably just because of my math training at CMU, find it so much easier to visualize and put into math the interactions that I am curious about). The attached document is regarding a question that I have thought about a lot and is something that I think a lot of people take for granted but is actually a lot more nuanced than one would think.

Before you get to the pdf though, I did want to talk about something in research and general projects across all academic fields. That is the work and bypassing of obstacles that don’t show up in the final product but are often times the most satisfying problem-solving and time expense during a project. I experienced this while writing my undergrad senior thesis as well, but there are often times so many roadblocks that require so much clever thinking, whether it is finding the best way to write your utility function or discover some neat math trick that lets you solve for equilibrium conditions. People will see the end product but not everything that came in between and the iterative steps of clever thinking. On one hand, it’s kind of sad for the writer, but for the reader, it makes sure that they aren’t inundated with stuff they need to interpret. I feel like it would be good for academia to find some sort of standard where paper writers/researchers can put their whole thought process down in an organized manner; that would both satisfy my desire to share all those rough moments but also, I think, increase transparency, which seems like something that is needed amidst a few scandals in faking data that happened a few years back in the econ community.

Finally, I also wanted to talk about one specific detail that seems to be the case with a lot of the problems/models of real-world interactions I build: the level of abstraction from reality that I should keep it at. In my head, I know there’s some sort of a tradeoff between adding yet another “lever” into a model, but so far, I’ve only tackled that issue with continuing to add levers until I get tired and then try to be satisfied with that end product, and I’m not sure if there’s a more systematic way of figuring that out. At what point do we stop trying to chase reality, and do we continue to chase it even if it is actually feasible in the first place.