Could you say more about the value proposition of chemistry?
The value prop of physics as I understand it, and I’m pretty behind on physics myself, is
classical mechanics is the bare bones proof of concept for working with “the scientific method”
included in 1. is a bare bones instance of predicting and modeling, which gives you firm ground for your feet when you’re predicting and modeling things that aren’t so straight forward.
if you’re a logic freak it trains you to be comfortable with the insufficiency of symbols, memes and jokes of mathematicians and physicists disagreeing about notation reveals an underlying controversy about the question “what are symbols actually for?”, and sophisticated thinking about this question is a major asset.
if you’re a logic freak it gets you out of your comfort zone
if you’re a logic freak it trains you to be comfortable with the insufficiency of symbols, memes and jokes of mathematicians and physicists disagreeing about notation reveals an underlying controversy about the question “what are symbols actually for?”
I don’t think this is an accurate description of the cultural difference between physicists and mathematicians. Tiny respective minorities of die-hard instrumentalists and formalists aside, both fields agree that the symbols are just tools for talking about the relevant objects of study more clearly and concisely than natural language permits. Plenty of published math research is formally incorrect in an extremely strong sense, but no one cares as long as all the errors can be corrected trivially. In fact, an important aspect of what’s often called “mathematical maturity” is the ability to make those corrections automatically and mostly unconsciously, instead of either falling into genuine sloppiness or getting hung up on every little “the the”.
The real core difference is the obvious one. To zeroth order: physicists study physics, and mathematicians study math. To first order: physicists characterize phenomena which definitely exist, mathematicians characterize structures which may or may not.
The universe definitely exists, it definitely has a structure, and any method which reliably makes correct predictions reflects a genuine aspect of that structure, whatever it might be. Put another way: physicists have an oracle for consistency. Mathematicians don’t have that option, because structures are the things they study. That’s what makes them mathematicians, and not physicists. They can retreat to higher and higher orders, and study classes of theories of logics for …, but the regress has to stop somewhere, and the place it stops has to stand on its own, because there’s no outside model to bear witness to its consistency.
If all known calculations of the electron mass rely on some nonsensical step like “let d = 4 - epsilon where d is the dimensionality of spacetime”, then this just means we haven’t found the right structure yet. The electron mass is what it is, and the calculation is accurate or it isn’t. But if all known “proofs” of a result rely on a nonsensical lemma, then it is a live possibility that the result is false. Physics would look very different if physicists had to worry about whether or not there was such a thing as mass. Math would look very different if mathematicians had a halting oracle.
I roughly agree with that value prop for physics. I’d add that physics is the archetype of the sciences, and gets things right that haven’t necessarily been made a legible part of “the scientific method” yet, so it’s important to study physics to get an intuitive idea of science-done-right beyond what we already know how to explain well. (Gears-level models are a good example here—physics is a good way to gain an intuition for “gears” and their importance, even if that’s not explicitly brought to attention or made legible. Your point about how we use symbols and logic in physics is another good example.)
The main value proposition of 101-level chemistry is to just to understand the basics of stoichiometry, reaction kinetics, and thermodynamics, especially in biological systems. Beyond that, chemistry is one of my dump stats, for good reason: more advanced chemistry (and materials science) tends to have relatively narrow focus on particular domains, like polymers or ceramics or whatever, and doesn’t offer much generalizable knowledge (as far as I can tell).
I roughly agree with that value prop for physics. I’d add that physics is the archetype of the sciences, and gets things right that haven’t necessarily been made a legible part of “the scientific method” yet, so
I would argue that physics can make very accurate quantitative predictions under the right circumstances...and that it nonetheless poses philosophical challenges much more than other quantitave sciences.
Could you say more about the value proposition of chemistry?
The value prop of physics as I understand it, and I’m pretty behind on physics myself, is
classical mechanics is the bare bones proof of concept for working with “the scientific method”
included in 1. is a bare bones instance of predicting and modeling, which gives you firm ground for your feet when you’re predicting and modeling things that aren’t so straight forward.
if you’re a logic freak it trains you to be comfortable with the insufficiency of symbols, memes and jokes of mathematicians and physicists disagreeing about notation reveals an underlying controversy about the question “what are symbols actually for?”, and sophisticated thinking about this question is a major asset.
if you’re a logic freak it gets you out of your comfort zone
practice with calculus/geometry.
I don’t think this is an accurate description of the cultural difference between physicists and mathematicians. Tiny respective minorities of die-hard instrumentalists and formalists aside, both fields agree that the symbols are just tools for talking about the relevant objects of study more clearly and concisely than natural language permits. Plenty of published math research is formally incorrect in an extremely strong sense, but no one cares as long as all the errors can be corrected trivially. In fact, an important aspect of what’s often called “mathematical maturity” is the ability to make those corrections automatically and mostly unconsciously, instead of either falling into genuine sloppiness or getting hung up on every little “the the”.
The real core difference is the obvious one. To zeroth order: physicists study physics, and mathematicians study math. To first order: physicists characterize phenomena which definitely exist, mathematicians characterize structures which may or may not.
The universe definitely exists, it definitely has a structure, and any method which reliably makes correct predictions reflects a genuine aspect of that structure, whatever it might be. Put another way: physicists have an oracle for consistency. Mathematicians don’t have that option, because structures are the things they study. That’s what makes them mathematicians, and not physicists. They can retreat to higher and higher orders, and study classes of theories of logics for …, but the regress has to stop somewhere, and the place it stops has to stand on its own, because there’s no outside model to bear witness to its consistency.
If all known calculations of the electron mass rely on some nonsensical step like “let d = 4 - epsilon where d is the dimensionality of spacetime”, then this just means we haven’t found the right structure yet. The electron mass is what it is, and the calculation is accurate or it isn’t. But if all known “proofs” of a result rely on a nonsensical lemma, then it is a live possibility that the result is false. Physics would look very different if physicists had to worry about whether or not there was such a thing as mass. Math would look very different if mathematicians had a halting oracle.
I roughly agree with that value prop for physics. I’d add that physics is the archetype of the sciences, and gets things right that haven’t necessarily been made a legible part of “the scientific method” yet, so it’s important to study physics to get an intuitive idea of science-done-right beyond what we already know how to explain well. (Gears-level models are a good example here—physics is a good way to gain an intuition for “gears” and their importance, even if that’s not explicitly brought to attention or made legible. Your point about how we use symbols and logic in physics is another good example.)
The main value proposition of 101-level chemistry is to just to understand the basics of stoichiometry, reaction kinetics, and thermodynamics, especially in biological systems. Beyond that, chemistry is one of my dump stats, for good reason: more advanced chemistry (and materials science) tends to have relatively narrow focus on particular domains, like polymers or ceramics or whatever, and doesn’t offer much generalizable knowledge (as far as I can tell).
I would argue that physics can make very accurate quantitative predictions under the right circumstances...and that it nonetheless poses philosophical challenges much more than other quantitave sciences.