Not much has happened this week. I’ve spent most of my time at Kyoto University, studying. The material I have to read is… very very difficult. The main obstacle is that we’ve had no introduction to this topic in neither the Bachelor nor Master, so I have to catch up as much as I can in a very short period, and then produce something sensible as well ðŸ˜‰

I’ve had some questions about my internship, so I’ll tell you a bit about it.

Category theory, or general abstract nonsense as it was apparently once called, is a way of looking at math. A very abstract way of looking at mathematical objects, in fact. Instead of inspecting certain objects, you inspect the category that contains these objects. So instead of studying a specific system, you study systems of **that type**, to see what they have in common, so to speak. It cannot be explained unless you have some mathematical background, so I’m not going to explain it here. Those who are interested may study it themselves.

Instead, for those of you who do absolutely nothing with math, I’ll give an example that is easier to grasp, the classical example of a coffee machine. Mathematicians, Computer Scientists and nitpickers: You may want to skip this, this is mainly for family and non-mathematical friends ðŸ˜‰

A coffee machine may be in a certain state (toestand, in Dutch). Maybe it is serving someone, or it is available to take your order, or – don’t we hate it when that happens – it’s out of coffee. Depending on what **input** the machine gets, it does something and goes to a new state. For example, you put a quarter in it. The machine will then go to a new state, namely the state “quarter was put in machine”. Then you press the button for coffee. Then the machine will go to “give coffee” and it will give you coffee. Or maybe not, if there is no coffee. And if you take your cup out, the machine will be available for the next person. Now, instead of looking at that coffee machine, we decide to look at **machines** in general. That is, a system that takes some input, does something internal, and then gives you an output. Such machines can be studied without knowing exactly what the system itself does. You may later make a system that gives tea. Or maybe you’ll make a system that locks a door and won’t open until you have pressed the right code to open it. Right now, we don’t care, we just want to see what properties this type of system has. We can study that, without knowing exactly what kind of system you’re going to make.

We can study **two** systems, and see how alike they are. Mathematicians everywhere denote questions like these as ‘interesting’, but I find that an odd word for problems like that. Real-world people don’t find those kinds of questions interesting; We don’t want to know how alike two coffee machines are, we want coffee!

Anyway, about studying the behavior of two systems: There are several ways to do this. You can look at the program inside the machine, and compare the programs letter by letter, and only if the programs are identical, you’ll say that the machines are comparable. But maybe that’s not what you care about, maybe you just want to know if they behave the same. That is: If I put a quarter in, I want coffee. I don’t care what the machine does on the inside, I don’t care how many electrical signals it sends across its wires, as long as I get my coffee. That’s a reasonable thing to say, after all you’ve just put in a quarter so it’s only fair that you get something in return. We can compare systems by looking at their observable behavior, and comparing that. So, suppose we have two machines and we put a quarter in each. If their behavior is similar, they will both give coffee. If not, then they will not. You can consider all sorts of extra things, like: How long does it take to give coffee? What happens if it’s out of coffee, will I get my quarter back? Can one of the machines also give you tea? If so, is their behavior still similar?

My assignment is to study a very very very general way of looking at various kinds of systems. So, let’s say also systems with chances, i.e. there is a **chance** that the machine gives me coffee. What if two machines have different chances of giving coffee – one gives you coffee half the time, the other always gives coffee – is their behavior then still similar? And also systems that may have branching behavior, i.e. the machine **either** gives coffee **or** it gives tea when you put a quarter in. There are already many ways to compare the behavior of certain systems. My goal is to examine a **new type** and see if we can figure out a way to compare two systems of that new type. I’m not describing that new type here, it has far too little to do with coffee to be of interest to regular folks ðŸ˜‰

Some other things:

- I’ve found a piano! As some of you may now, I’ve had 1,5 years of piano lessons, but quit because the style of teaching was rather classical (I think I’ve only played two songs I knew, that’s it). Maybe I can figure out some pop songs? I’ve asked Jan if he has some sheet music somewhere, he once sent me a bunch of them but I didn’t bring them to Japan.
- Saturday, there’s a get-together day at the international student house I’m staying at and also there’s a barbecue of a Belgian girl that my internship supervisor got me in touch with.
- On www.kyotoguide.com, you can see what kinds of activities there are in Kyoto. During Golden Week, which is April 29th and 3-5 May the university is closed and there’s a lot to do in town.
- I’ve added a page that contains all photo’s of my internship, for those interested. You can find it in the menu bar above.