Chapter 1. Once you run into a problem, there's a sense of a solution, and there's a way of doing the solution that you can just move on and work on something else. And so a person may spend 30 minutes of their day thinking about a problem, and they write a 10 page email, and they're working on the problem until lunch or dinner, and then they maybe write two more pages, or maybe they don't get it, and so they start working on something else, but that's just part of the process. And so as I said, productivity in software engineering is very high when people are in the zone. And there's a feeling that this is hard, but once you get it, it's a very valuable skill that you can have. The issue is, how do you get into the zone? And how do you get out of the zone? So this is where we talk about time, and specifically managing time. You know, time is probably the most valuable resource you have. And again, it's a really common thing that it takes a few seconds to recognize when your mind is in the zone, and the rest of the time, you're probably bothering, so it's the amount of time it takes you to start doing something, and the amount of time it takes you to start coding. And there's a lot of things to talk about that, but I want to give you one example of a way that we can measure this. And this is a talk that a good friend of mine gave named Dan O'Hara at PyCon. If you've never seen it, he wrote this talk, and he got an A+, but he got a huge round of applause at the end for this. And what it's about is this problem called the Lobster problem, and it was given by an economist by the name of James Hamilton. It's just, in a nutshell, take a lobster, throw it in boiling water, let it boil for five minutes, and then take out the meat. But the trick is, do you want to kill the lobster by putting it in boiling water? Or do you just want to kill it by boiling it for 5 minutes? But the whole question is, if you just boiled it for 5 minutes, you know what would happen? The lobster would stay alive just the same. But it wouldn't be cooked at all. And do you want to kill the lobster or not? And so the question that's embedded in the name of this thing is if you want to make it cooked, is it okay to boil it for 5 minutes, or should you put it in hot water and boil it for 5 minutes? And the question is actually a little bit subtle, but understanding that, as an engineer, how we look at this is this, there are these two variables, the amount of time it takes to cook it, the time it takes to cook it. And then there's some constraint, in this case, there's a constraint that says, this variable has to be greater than this variable. The question is, what does the answer to the question really depend on? What's the effect on that time, so the time it takes to cook it, and the amount of time it takes to cook it, what's the effect of that? And what you can do is take the time that you boil it for 5 minutes, and then take the amount of time it takes to cook it. And so the question is, what happens if you were to boil it for, for a given value of N, so say for N equals 5, boil it for 5 minutes, if you didn't change anything. And so what you're seeing is this interesting curve of some sort of function. And you can see that, the relationship here is time to cook, and this is the amount of time you boil it for, N. But the question is, if I find the value that maximizes this, I'm going to get a value that has, has, the number is growing, the difference between the two time. The time that it takes to boil it, and the time that it takes to cook it. And this is basically equivalent to that. So what's the question? In order to find the right number, you're really looking at this as the question, in order to cook it the best, how much time do I need to boil it? Now, I don't mean to say, after you boil it, how much time you have to cook it. The question is, how much time you need to boil it? And in order to boil it, you need to let it heat up first. And so this is actually a really important point. And what you find in order find this is a lot of times, this, this value is going to be a piecewise function, like this. Because it's different ways to cook something, what matters here, is the amount of time that it takes to boil it. It's not about cooking it. It's not like it needs to be something cooking it, it just needs to be boiling it. And you start to say, in order to boil it, I need this amount of time, and this amount of time. And so the amount of time you need to boil it is a lot more important than how much time it takes you to cook it. And if this is true, if this function is a piecewise function, it's not a linear function, which means it doesn't have a piecewise function of some sort, and you just see some smooth function. And it's not hard to see where this is the case. Because the number of things that you can boil in, let's say, boiling water is relatively high. You can boil pots of water, you can boil pans of water, you can boil pans of water. And so that this would be a more efficient way to boil water. But let's say you're cooking something, and let's say you have this as your time. So that's a total of N plus the time it takes to boil it, and so that's the limit of how fast you can boil it. And so you see, if this was constant, you couldn't boil anything. But if this was a number that got bigger, then it would get faster to boil things. And so, in the limit, it doesn't, in the limit you don't have to cook it. And so the question is, it's not a linear function, it's a piecewise function. And so the only way that really the constraint is linear is if the amount of time it takes you to boil it is completely independent of how long you cook it. And if the amount of time it takes you to boil it was completely independent of how long you cook it, then it would be a linear function. And so that's not the case, so the constraint function is a piecewise function, and so that's the thing that you can see, that if you have a piece wise function, you're not going to get the function completely for free. And so in order to get the best bang for the buck, we have to take the lowest amount of time to boil, to pick the biggest value, and so that's, if you do, this