By Vipul Naik
Cross-posted from Less Wrong. Tangentially related content on the information wiki: physics learning benefits and mathematics learning benefits.
Many of the high school students who sought advice from Cognito Mentoring were interested in mathematics, computer science, and physics. This both makes sense and is valuable. Mathematics has many benefits: it underpins a lot of quantitative analysis, and helps us understand the world. Computer science is also quite important for obvious reasons: programming in particular is directly and indirectly useful, and a deeper understanding of algorithms and the theory of computation can help with algorithms.
Physics, however, is a little different. There are some benefits of learning physics. In particular, classical mechanics is often people’s first exposure to using mathematical structure in a nontrivial way to understand and model situations pertaining to the real world. Nonetheless, unlike mathematics or computer science, the benefits of physics for people who are not in science or engineering careers are fairly low. I find myself using high school-level mathematical intuition on a regular basis (for instance, understanding the growth trajectories of various things, or interpreting graphs), and I find myself using basic programming-like intuition quite often. But I rarely find myself using my physics intuition in the real world. Moreover, I think physics quickly hits diminishing returns in terms of teaching people about mathematical modeling: I’d say that the returns from physics beyond classical mechanics, DC circuits, and basic thermodynamics are near-zero. For instance, I’d say it’s more beneficial to learn microeconomics rather than electromagnetism, even though the latter is often considered more prestigious by smart people. Similarly, I think that behavioral economics is more valuable than quantum mechanics.
It’s also not clear that learning physics beyond the basics suggested above (classical mechanics, thermodynamics, DC circuits) passes a cost-benefit analysis for people in the vast majority of science-based and engineering-based careers. Even the extent to which they crucially rely on these basics is questionable, given that most people don’t learn the basics well and still manage to go on to do decent jobs. I’d like to hear any opinions on this. On a related note, I recently asked on Quora the question In what ways is knowledge of Newtonian classical mechanics helpful to people pursuing biomedical research? and there were a few interesting answers.
So my question: what attracts smart and curious young people to physics? Are the smartest people too attracted by physics, relative to its real-world applicability? Does the intellectual stimulation provided by physics justify the attraction? Is there some sort of mood affiliation going on here, where the smartest people are pulled to physics to distinguish themselves from the crowd, insofar as physics is more difficult and repels the crowd? To the extent that people overvalue physics, does it make sense to push them at the margin away from physics and in the direction of computer science or economics or some other subject? Or should their interest in physics be encouraged?
Thoughts on your personal experience, as well as thoughts on the general points about the usefulness and attractiveness of learning physics, would be appreciated.
PS: In a video, Eric Mazur describes research related to the Force Concept Inventory: people often learn how to solve complicated mechanics problems by pattern-matching but fail to demonstrate clear understanding of Newton’s Third Law. Similarly, people can predict potential differences and current flows in complicated circuits using Kirchhoff’s laws, yet fail to predict that if you short a circuit, all the current will flow through the short. (The latter failure of prediction occurred in an end-of-course examination co-taught by Mazur to Harvard University first-year students, many of whom were planning to go on to medical school.
PS2: My collaborator Jonah Sinick’s Quora post (no login needed to view) titled Is math privileged for gifted children is somewhat related.