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Issue 172

From Issue #172
August 2008

Aug 01, 2008  By John Knight
 in
Hilbert II (www.qedeq.org)

Here's one for the mind-bending category. In this age of shared information and decentralization comes another cool addition to the realm of shared consciousness. Hilbert II attempts to resurrect and build on the ideals of a near dead project, QED (check the link at the end for a copy of QED's manifesto). Hilbert II's goals are:

...decentralised access to verified and readable mathematical knowledge. As its name already suggests, this project is in the tradition of Hilbert's program....Hilbert II wants to become a free, world-wide mathematical knowledge base that contains mathematical theorems and proofs in a formal correct form. All belonging documents are published under the GNU Free Documentation License. We aim to adapt the common mathematical argumentation to a formal syntax. That means, whenever in mathematics a certain kind of argumentation is often used, we will look forward to integrate it into the formal language of Hilbert II. This formal language is called the QEDEQ format.

Hilbert II provides a program suite that enables a mathematician to put theorems and proofs into that knowledge base. These proofs are automatically verified by a proof-checker. Also, texts in “common mathematical language” can be integrated. The mathematical axioms, definitions and propositions are combined to so-called QEDEQ modules. Such a module could be seen as a mathematical textbook that includes formal correct proofs. Because this system is not centrally administrated and references to any location in the Internet are possible, a world-wide mathematical knowledge base could be built. Any proof of a theorem in this “mathematical web” could be drilled down to the very elementary rules and axioms. Think of an incredible number of mathematical textbooks with hyperlinks, and each of its proofs could be verified by Hilbert II. For each theorem, the dependency of other theorems, definitions and axioms could be easily derived.

The Complex World of Mathematical Collaboration through Hilbert II

Installation

First things first, Hilbert II is a Java-based program. We generally try to avoid Java-based projects because this is Linux Journal, not “Platform-Neutral Java Webstart Journal”, but the cooler projects are definitely worth examining, and besides, it does have a Linux-specific version. For the lazy, there is a webstart version that can be launched from your browser (see the link at the end of this section), which requires you to have the Java browser plugins installed. For the Linux version, the precondition for a working prototype is a Java Runtime Environment, at least version 1.4. Hilbert II uses LaTeX for a lot of its functions, and there are some potential bugs that frequent users may run into, so check the Web site for further information on possible LaTeX requirements.

Head to the Download section of the Web site and download the Linux tarball. Extract it to your directory of choice, and open a terminal in the new qedeq directory.

At the console, enter: 

$ ./qedeq_se.sh

Or, if that doesn't work, enter: 

$ sh qedeq_se.sh

Usage

Hilbert II works around XML files, and you'll need some of these XML files to get started. If you choose File→Load from web, a default file is provided from which you can begin to experiment. If you look in the main window, there's a tab called QEDEQ. Clicking on any entry on the left displays its nuts and bolts in this tab. Under Tools→LaTeX to QEDEQ, you can start playing around with your own formulae, and under Check→Check Mathematical Logic, you can make sure that your syntax and so on check out. To export your work for the world to see, going to Transform→Create LaTeX output creates a new LaTeX .tex file in the generated folder under qedeq.

But from here, you're on your own, because I haven't got a clue what I'm talking about in this world of advanced mathematics and formulae (and I've probably said something wildly inaccurate in the process of writing this section). However, I'm keen to see the results of this academic collaboration, where ideally knowledge should keep advancing and continue to be built upon, and I hope to see more of these mind-bending shared-consciousness projects.

______________________

John Knight is the New Projects columnist for Linux Journal.

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