## 2008-12-10

### Three guests in a restaurant... meaning of computation (1)

Japanese version

Several weeks ago, one of my friends visited me. We told about lambda calculus and the meaning of computation. Lambda calculus tried to define the computation only in a formal way without thinking its meaning. On the other hand, it is usually important what I am computing in every day life. Interestingly, I started to think about the meaning of computation more deeply when I think about how-to-not-to-think-about-the-meaning. I think something I start to understand when it was missing.

There is a film called ``Paper moon''. In the film, there are several cheating methods which are good examples of using misunderstanding of meaning of the computation. If I remember correctly, a classic Japanese Rakugo, ``Tubozan'' has the same tricks. There is also a good example of how a physicist connects the meaning and computation in a book, ``Surely You're Joking, Mr. Feynman!.'' In this article, ''three guests in a restaurant''is a famous story, but even my friend still needed some time to understand what the problem is

There are three guests in a restaurant. They took a course menu and it costs 300 Euro. A waiter collected money from the guests and backed to the kitchen, then the master said, ''Today is the anniversary day of the restaurant, so the course costs 250 only.'' The waiter came back to the table, but, he thought, ''50 Euro is hard to divide by three persons.'' Then, he said ''Today is our restaurant's anniversary day, so 30 Euro back. Each can get 10 Euro.'' The guests thanked the waiter and left the restaurant. The waiter felt a bit guilty, but, he decided to forget it. However, he realized a bit odd. ''Each paid 90 Euro, so the sum was 270, I have got 20 Euro from them. But the sum is 270 + 20 = 290 instead of 300Euro. Where is the 10 Euro?''

I actually thought this works only in Japanese. But, that worked in German. Later I tried another friend with in English, it seemed working. You might figure out what is wrong here. Even so, it is hard to make a good explanation. If you did not know this story, please think though it.