And I’m not exactly strong in the ways of rationality yet, still reading and re-reading the Sequences (I keep getting lost somewhere halfway into the QM sequence,
Skip it. It’s the least important of all the sequences.
Oh I’ve already gone past and read Metaethics and the stuff past it. I just keep coming back to QM because I don’t understand it, and I’d very much like to. Partially because I’m interested in how the world works, partially because I just don’t like that I don’t understand it.
You can read it for fun (it is fun to read), but it’s the most controversial one and it teaches you little about rationality. The whole thing has maybe one equation, and if you think you can understand QM without the relevant math, your critical thinking is not up to par. Basically, Harry’s musings in MoR on partial transfiguration cover the essence of EY’s views on QM, if you discard the many worlds advocacy.
Loosely. I’m only entirely in my area with math up to trig and medium-level calculus. I can sometimes feel my earwax burning as I stumble through the more complex QM stuff. I have a few textbooks on it I bought awhile back, and I’m thumbing through them trying to get more comfortable with it, and looking to the QM sequence as a more ‘human’ understanding of what’s going on under it all.
Linear algebra is useful. Not necessarily on much advanced level, just notions of vector spaces, operators, eigenvalues and eigenvectors, commutativity of operators; this is the language of QM. Knowing this (and complex numbers, but that I assume you certainly know already) is enough to fully understand simplest QM systems described by observables attaining finite number of possible values. Unfortunately, this means spin, and spin can be very unintuitive for beginners because it has no exact classical counterpart (and the “partial” classical counterpart, angular momentum, is also not the easiest quantity to reason about). If you want to deal with observables with infinite (or even continuous) spectrum of values (which means position, momentum, energy), you have to know also a bit of calculus and basic differential equations, since you will have to upgrade the linear-algebra formalism to infinite-dimensional spaces, and vectors in such spaces are usually represented by functions.
An important note: to understand QM on gut level you don’t need to know the whole deduction tree of calculus or linear algebra. Linear algebra and especially calculus courses are usually taught as mathematics, the definition-theorem-lemma-proof style. This illustrates well the consistency and elegance of the mathematical discipline, but unless you want to investigate some more subtle problems of QM, much of that is useless for your goal. You certainly should have an intuitive idea about what integration is, but you don’t need to worry about difference between Riemann and Lebesgue integral or between weak and strong convergence of operator series; you should be able to diagonalise a matrix, but don’t worry about Jordan blocks or pseudo-inverses.
Skip it. It’s the least important of all the sequences.
Oh I’ve already gone past and read Metaethics and the stuff past it. I just keep coming back to QM because I don’t understand it, and I’d very much like to. Partially because I’m interested in how the world works, partially because I just don’t like that I don’t understand it.
You can read it for fun (it is fun to read), but it’s the most controversial one and it teaches you little about rationality. The whole thing has maybe one equation, and if you think you can understand QM without the relevant math, your critical thinking is not up to par. Basically, Harry’s musings in MoR on partial transfiguration cover the essence of EY’s views on QM, if you discard the many worlds advocacy.
Do you understand QM (the mathematical formalism, how to make predictions etc.)? If not, the QM sequence is not the right text to learn it.
Loosely. I’m only entirely in my area with math up to trig and medium-level calculus. I can sometimes feel my earwax burning as I stumble through the more complex QM stuff. I have a few textbooks on it I bought awhile back, and I’m thumbing through them trying to get more comfortable with it, and looking to the QM sequence as a more ‘human’ understanding of what’s going on under it all.
Linear algebra is useful. Not necessarily on much advanced level, just notions of vector spaces, operators, eigenvalues and eigenvectors, commutativity of operators; this is the language of QM. Knowing this (and complex numbers, but that I assume you certainly know already) is enough to fully understand simplest QM systems described by observables attaining finite number of possible values. Unfortunately, this means spin, and spin can be very unintuitive for beginners because it has no exact classical counterpart (and the “partial” classical counterpart, angular momentum, is also not the easiest quantity to reason about). If you want to deal with observables with infinite (or even continuous) spectrum of values (which means position, momentum, energy), you have to know also a bit of calculus and basic differential equations, since you will have to upgrade the linear-algebra formalism to infinite-dimensional spaces, and vectors in such spaces are usually represented by functions.
An important note: to understand QM on gut level you don’t need to know the whole deduction tree of calculus or linear algebra. Linear algebra and especially calculus courses are usually taught as mathematics, the definition-theorem-lemma-proof style. This illustrates well the consistency and elegance of the mathematical discipline, but unless you want to investigate some more subtle problems of QM, much of that is useless for your goal. You certainly should have an intuitive idea about what integration is, but you don’t need to worry about difference between Riemann and Lebesgue integral or between weak and strong convergence of operator series; you should be able to diagonalise a matrix, but don’t worry about Jordan blocks or pseudo-inverses.