# The Theoretical Minimum

I’ve always enjoyed explaining physics. For me it’s much more than teaching: It’s a way of thinking. Even when I’m at my desk doing research, there’s a dialog going on in my head. Figuring out the best way to explain something is almost always the best way to understand it yourself.

That’s when I first found out about Stanford’s Continuing Studies program. This program offers courses for people in the local nonacademic community.

it was very satisfying in a way that teaching undergraduate and graduate students was sometimes not. These students were there for only one reason: Not to get credit, not to get a degree, and not to be tested, but just to learn and indulge their curiosity.

world whose evolution is discrete could be called stroboscopic.

The variables describing a system are called its degrees of freedom.

The rule that dynamical laws must be deterministic and reversible is so central to classical physics that we sometimes forget to mention it when teaching the subject. In fact, it doesn’t even have a name. We could call it the first law, but unfortunately there are already two first laws—Newton’s and the first law of thermodynamics. There is evan a zeroth law of thermodynamics. So we have to go back to a minus-first law to gain priority for what is undoubtedly the most fundamental of all physical laws—the conservation of information. The conservation of information is simply the rule that every state has one arrow in and one arrow out. It ensures that you never lose track of where you started.

We could do it the other way, but we won’t.

The greek letter theta, θ, is defined to be the angle opposite the altitude, and the greek letter phi, φ, is defined to be the angle opposite the base.

One suspects that Aristotle never went ice skating,

Why are all systems described by action principles and Lagrangians? It’s not easy to say, but the reason is very closely related to the quantum origins of classical physics. It is also closely related to the conservation of energy. For now, we are going to it take as given that all known systems of classical physics can be described in terms of the action principle.

Lenny had trouble reading maps. It always seemed like whichever way he was facing must be north. He wondered why he had more trouble with NSEW than he did with up and down. He could almost always get up and down right.