It’s time for a physics lesson! Don’t worry, we’ll keep it simple. We’re going to talk about work. If you’re unfamiliar with the concept, think about it kind of like the energy you use or you receive by moving something over a certain distance. In that respect, it’s exactly what you’d think it is. If you carry a heavy box up the stairs, you do work, if you carry a lighter box up the stairs, you do less work. There. Nice and simple.
More specifically:
The work done by any constant force F can be written simply as the dot product between that force and the displacement vector that describes the path traveled (in your freshman year, this is generally just a straight line). When you get a little more advanced, you can define the total work as an integral, dotting the force with a line element (dr). The complete line segment describes the path you took to get from point A to point B.
Now there is a special case of this phenomena. When the force is conservative (meaning there is no friction, for the sake of this discussion) then the total work done between points A and B is path-independent. What this means is that no matter what path you take to get from point A to point B, the total amount of work that you do is the same!
This is not the case for non-conservative forces.
There. Physics lesson over. Now onto the real juice of this post! We (and by “we” I mean “my classmates and I”) were sitting in Advanced Mathematical Physics today, and we were going to be talking about differential and integral operations. No big deal. Basically it’s a class about vector calculus. That shouldn’t be too bad, I’ve got five years of this stuff under my belt, and the last few classes I’ve taken have been absolutely loaded with high level application of these concepts.
Somehow, JP Hsu managed to confuse me. Here’s how the class was broken down (topic by topic, pulling right from my notes:
- Introduction to differential and integral operations
- Aside: Definition of a field
- Scalar fields
- Vector fields
- History lesson regarding how Faraday invented fields
- Discussion about Maxwell’s Equations
- Imagining six-vectors (Ex,Ey,Ez,Bx,By,Bz) at every point in space (ala Dyson)
- Definition of field lines
- Mathemagic (in which Hsu got halfway through a proof, got confused, and gave us the answer)
- Real numbers versus complex numbers
- Hamilton’s generalization (quaterions)
- 2×2 Matrices (Pauli-Spin matrices and abstraction in mathematics)
- Hypercomplex numbers
- Integral Operations [Wait... what? That's right. 13 topics (and 8 pages of notes) later we're just getting back to one of the topics we started the class with? Anyway...]
- Line integrals, surface integrals, volume integrals
- 4-volumes
- Generalizing volume in 4-d spacetime
- Complications of unification between quantum theory and relativity
- Probability interpretation of wave functions, and the process of normalization
- Boundary conditions of space and time
- Div, grad, and curl [This section actually started right as class ended, he had us stay 5 extra minutes so he could say something about them]
Now that’s a long list… and I was already familiar with just about everything on it. You can see that the flow of thought (with a couple of exceptions where he switched directions) makes sense (more or less). The only problem is, that the path we took to get from the beginning to the end was so damned confusing that we all had a hard time understanding what he was trying to teach us.
So after class, I have a chat with Kaptain Khanna and Space, and we decided that teaching is not path independent. Though you are travelling from point A (the beginning of class) to point B (the end of class), the amount of understanding one gets is inversely related to the length of the path taken to get there (where path is meant to imply the path taken by the lecture, not the actual passage of time).
Not only that, when you follow certain odd paths, you actually end up in a region of spacial-understanding that is not where you expected to be. Specifically, there is some strange non-zero curl of the knowledge-field surrounding point B, such that you may spiral around understanding, but never truly settle into it (i.e. div(B)=0). This can be true even when points A and B are well-understood by the students.
The moral of this story? I don’t know, it took too long to get here. All I know is that Advanced Mathmematical Physics is going to be the end of me in one way or another.
Physics, pseudoscience, teaching
class, confusion, jp hsu, kaptain khanna, Physics, pseudoscience
