Lx=d: SundayResearch

I have a Japanese version of this page . There was a good question on my last article. ``What happen if the vending machine (a function) is broken?'' First of all, we need to define what broken means. Some of you would say, ``Broken is broken, what else?'' But, this answer does not make any sense for mathematicians. Are there no common sense in the head of mathematician? Maybe, yes. But, there is a reason. I am a Sunday mathematician/programmer. Mainly I program a code to solve some of my problems. To tell my computer to solve my problem, I need to interpret my problem to a code which my computer can execute/understand. Many of mathematics formulation is really formulated, which means you do not need to understand what it is, they are just a procedure. Then my computer can execute to solve my problem. I formulate some problem since after that is done, I do not need to think about that. Rest of the problem is solved automatically. This is fun for me. ``Computer, search s

Japanese version My colleague told me this realtime raytracing demo with photon mapping (caustics). My machine has not enough power to run the demo. But it is quite impressive that just 4k bytes demo program can do this in realtime. Unfortunately, the code is not published. The rendering time in a movie sometimes took 8 hours to render a frame. Which means it takes more than 8 days for one second movie. But these people usually has a render farm that contains 1000 or more computers. So, after they start render images, 1000 frames will be ready. For this demo we can take video directory. When you visit to YouTube, there are higher quality movie. http://www.youtube.com/watch?v=LWx2HjvFzHw http://www.pouet.net/prod.php?which=51443

( Japanese version ) The word lambda calculus itself has ``calculus,'' so it can also calculate numbers. But, when I started to learn the lambda calculus, I want to know that what is ``calculate'' means. Then I also think about ``what is the number?'' If I want to teach ``what is the number'' to small children, I do not know how to teach it. Also I did not recall how to learn that. But, I think I know what numbers are. I can tell that there are some properties about numbers. First, it does not matter how to read it. In the hitchhiker's guide, there was a planet called Earth. The people on the planet have a lot of languages. For example, English, German, Latin, Japanese, and so forth. Interestingly enough, every language seems to have a concept about numbers. There are many representations for numbers, for example, (1, 2, 3, ...), (one, two, three, ...), (ein, zwei, drei, ...), (ichi, ni, san, ...), and so on. But no matter how you read them, there s

lambda calculus and Hitchhiker's guide One day, I hit on to want to know about lambda calculus, and looked up Wikipedia. There are nice entry about that, but I could not understand some examples of calculation. It took a week to figure out. Maybe this is trivial, but I would like to brag myself about that. There is a common saying, ``they brag most who can do least.'' I am not familiar with lambda calculus. If I encounter something not familiar, I usually lookup some kind of guide book. I went to some city, I usually have a book called ``Chikyu no aruki kata (How to walk on the earth (in Japanese)),'' or Hitchhiker's guide to the Galaxy. This article could be a tiny version of a Hitchhiker's guide to lambda calculus. According to the Hitchhiker's guide to the Galaxy, the Hitchhiker's guide to the Galaxy is the most successful book in the universe. However, it seems no one knows the book is written in which language. If that is the most successful boo