Newtonian Mechanics
I’ve started reading the book Lagrangian Mechanics for Non-Physicists. I’m very excited to get to the variational calculus chapters, but the book starts off with a long chapter on Newtonian mechanics. Since Lagrangian mechanics explicitly seeks to replace and go beyond Newtonian mechanics, it makes sense for the book to at least start with that. I was expecting to be a bit bored, so I was pleasantly surprised to get a lot of insight into standard mechanics.
While everyone learns about Newton’s three laws of motion in school, I think people often don’t learn how to really interpret and use the laws. The second law, for example, is the justification for the F=ma method of solving dynamics problems (problems how how objects move when acted on by various forces). In high school I learned this, but I didn’t learn much about the reason or use of the first or third law.
The first law, it turns out, sets the stage for the second. The first law (an object in motion tends to stay in motion), implicitly defines the idea of an inertial reference frame. It’s these reference frames that the second law can be used in. Non-inertial reference frames exist, and using Newtonian mechanics in them is quite difficult.
The third law is defining what a force is in Newton’s framework: something pushes on another thing, and both objects experience a force.
The importance of Newton’s three laws is that they set up the entire paradigm of solving dynamics problems using forces. Most of the rest of first-quarter physics class was just mathematical tricks for solving the equations that Newton’s laws help to formalize.
Newton’s laws have their limits (as Newton himself knew). The aforementioned non-inertial reference frames are very tricky to deal with. Some forces, such as gravity, are posited to apply instantly everywhere (faster than the speed of light), and conservation laws are assumed.
All of these are easier to deal with in Lagrangian mechanics. That said, Lagrangian mechanics is difficult to use for Forces that aren’t modeled by potentials. Gravity and the electromagnetic field are easily modeled as potentials. Friction and physical interactions are not.
I’m looking forward to reading the rest of the book learn more.
Fixing things for yourself
Our electric hair clippers broke last week. It’s probably over ten years old, and it had seen a lot of use. I thought about just ordering another one from Amazon. They range from $12 to $60, so it wouldn’t have been a hardship.
Instead, I disassembled the clippers and figured out what was wrong with it. Turns out the wire had broken inside its insulation, just at the point that the wire entered the body of the clippers. It only took about ten minutes to cut the broken section of wire out and then splice the (slightly shorter) remainder into the clippers. I lost the nice strain-relieved wire insertion point, but that was where the wire broke originally so maybe it’s not a big loss. I ended up supporting the new wire with hot glue. It won’t last another ten years, but it may last a few.
This wasn’t a very difficult project. All told it probably took me about an hour. If I had ordered a new one from Amazon, I would have paid less than I make in an hour of work. Nevertheless, I’m very satisfied with the choice to fix these clippers.
I think people sometimes focus too much on the financial value of their products. There are several types of value: financial, but also social, psychological, and functional. Repairing the clippers and buying new clippers both would have given me the same functional value (working hair clippers). In other domains, they differ in value.
A utilitarian might argue that all of these values can be denominated in dollars. I agree with that in theory, and in practice doing so would make it very clear that spending the cost to buy a new set of clippers was actually much more expensive in utility.
Buying new clippers would have been better financial value, but worse social and psychological value. By repairing them myself, I was able to show my kids what’s inside a machine that they’ve used in their own lives. I was able to demonstrate that when things break, they’re often fixable. This idea that the world is malleable and that people’s actions can impact it in a direct way is very important, and I would pay an enormous amount of money to make sure my kids understood that. Realistically, there’s no way to get that by paying money. Instead, I have to make choices and spend other resources to do it.
ToDo lists
I carry a small notebook around in my pocket all the time. I tell myself its to record ideas and keep track of my ToDo list. In practice, I don’t use it very often. I think I once went six months with this thing in my pocket every day, and never once wrote in it for that period of time.
I’m trying to use it more now. A big part of that is just letting myself write dumb shit in there. If I try to only use it for important things, then I end up never using it and it doesn’t help me.
Lately I’ve been using it for my ToDo list again. I’m getting more done, and I’m happier and excited about it too. The trick to this, for me, is that I have to use it for “dumb” “easy” things, like shaving. I also sometimes write something down just to cross it off.
This has a practical use: getting me to look at the notebook and remember that it’s something I can use for less “dumb” stuff.
It also has an emotional use: actually making sure I shave regularly is good, and it’s ok to write it on my ToDo list if that helps me get it done.