## Definition

*Computational Theory*is a branch of mathematics that morphed into computer science. Among its goals is to look at a problem and ask:

*Is there a series of steps that will solve this problem?*Those steps are also known as an algorithm, and finding a fast & efficient algorithm for something people care about, such as searching for a piece of information, is often a great way to start a business.

## Commentary

Groklaw has an interesting (and very long) discussion about computational theory and how it applies to patent law. From the article:

For example consider I write a program. Some outside party has written a similar program. This party sees my program and thinks I infringe on his proprietary rights. There are two scenarios depending on whether he makes his claim according to copyright law or patent law.

For claims of copyright infringement the text of the source code matters. If I wrote my program independently and I can prove the texts are different, I don't infringe on his rights. This is an intensional point of view.

For claims of patent infringement then differences in the text of the source code won't matter. It won't even matter if the code is written in a different programming language. If my program uses the same method that is covered by the patent according to whatever legal test of "same method" is applicable, I will infringe. This is an extensional perspective.

The notion of an *intensional* and *extensional* perspectives is actually an
amazing insight into the world of mathematics that I hope to discuss more as I
make my way through the excellent book
Autonomy of Mathematical Knowledge
by Curtis Franks.
*(Disclosure: the author is a friend of mine.)*

## Meta

The basic question is how can we say that two items or methods "are the same?"
In what way are they the same? Computational theory suggests that two methods
are the same if they are *reducible* to each other. That is, if under the same
circumstances they both produce the same result, the methods are considered the
same.

*More on this later.*

## Updates

### 2010-02-24

- See Review: The Autonomy of Mathematical Knowledge for my review of that book.