2008-10-04

Introducing lambda.

Japanese version

Standard mathematics books explain mathematical stuffs as definition, theorem, proof, definition, theorem, proof, .... This is quite simple and enough abstracted. Therefore, we can also explain lambda calculus in the standard way. But Marvin will sure complain that is so depressed. More abstracted theory could be more applicable to many things. It becomes less unnecessary stuffs, then, it becomes simpler and also more beautiful in a sense. The theory is to the point when more abstract.

Japanese sword seeks for the beauty in the sword itself, it never decorates with some kind of jewels. Because a sword maker/master thinks the beauty comes from the sword itself. They shamed if they need to cover a sword with non-sword component. We can find many swords, staffs, ... are decorated with gold or some jewels. I can also see some kind of gorgeousness in that, however, I prefer beauty in these kind of simpleness. A French pilot said ``A designer knows he has achieved perfection not when there is nothing left to add, but when there is nothing left to take away.'' I sympathize with this word. Also, I like the story about a ship called Vasa, which sank in the sea. The story about a project manager (a Swedish King) requested too many features to his ship. Any software comes from Sirius Cybernetics coop. has too much features and hard to use, because the project managers believe that the customers want to have new features instead of a simple and stable software. (Kode Vicious Pride and Prejudice (The Vasa) CASM Vol.51, No.9)

The beauty of mathematics is in the simpleness and abstraction. I could understand that a mathematician wants to discuss more simple and more abstract entity. But then the mathematics becomes more difficult to the usual people like me. I see here some kind of closeness. If only a few people who knows mathematics well can enjoy the mathematics, that's a bit sad for me.

When I discover some beauty, I sometimes want to keep it to only myself. If I discover some beauty which nobody doesn't know, I feel some privilege. Because I need a lot of effort to find out something beauty in mathematics, it is a kind of reward for me. If I explain them to many people and people also find the beauty, that's nice. On the other hand, I sometimes feel some kind of loneliness. Like it is not only mine anymore. Someone who loves mathematics seeks for more beauty in that, then she/he may search for more abstract form. The result becomes more substance, all the background, history, etc. will be lost. That's also the reward for mathematicians. It is pure substance, however, it is not familiar with me anymore. I do not feel that I understand that anymore.

I also prefer abandoned extra part of mathematics. Why lambda calculus is created? How it is created? What was the first attempt of that? These may be not so important after constructed the lambda calculus. ``What can lambda do?'' becomes more important. Usually ``what is it?'' is not so important in mathematics like operators are more important than some kind of substances like numbers.

Vogons in the guide are extremely officious, their relationship is dry. Only important thing is what others can do for them. ``Who'' did is no matter at all. For them, even relative is only a relationship which people knows whom. Even if their grandmother ask to help her children, they do nothing unless there is a contract. A family may be worse than bureaucracy. A dry software company only asks employees to implement a new feature. This is important of course for business. But, who did it is not so important. This means, it does not matter who did that. It is just a function of the company. However, if a company does not applicate or does not matter the people, the people usually leave such kind of company. So, Vogonism is hardly work in the human society. But it seems Vogonism is working in mathematics theory.

The important thing of lambda is also what the lambda calculus can do. However, this is a Hitchhiker's guide. Let's talk about not-so-important things, like, why lambda is created. lambda calculus is also made by a person. Therefore, there must be some kind of motivation. Marvin is the most depressed existence in the universe, he (she/it?) has no motivation at all. He is always depressed, but he even has no motivation to suicide... But, the designer of Marvin from Sirius Cybernetics coop. did not want to make a depressed robot (I think). The designers just thought if they can combine a few hundreds of genius brains, such thing should be super-genus. However they are enough to smart to design Marvin, but they are not enough smart to imagine that such super-genius is usually insane. There is a purpose of lambda. Let's talk about the motivation of lambda next time.

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