But suppose that rather than a expressing a scientific theory in the form of words (which can result in excessive philosophising about what those words actually mean) or as a system of equations, one expressed it in the form of a computer program. This allows students to try out all sorts of 'what if?' ideas. They can try different inputs to the program. If they are more advanced then they can try altering the program. Of course this might not produce sensible results, but I feel that it is much less likely to produce nonsense than playing with a theory expressed in words - computers are unforgiving of a lack of rigor.
The purpose of this website, therefore, is to explore the possibility of using computer programs as the basis of mathematical proofs and scientific theories. This will be done as a series of open source projects, which I hope that other people will become involved in. It is my intention that these programs will be easy to download and use, with graphical frontends and straightforward installation. The proposals for the first two projects are listed below. If you are interested in taking part in these projects then please contact me at
Gödel's incompleteness theoremGiven a set of axioms for arithmetic, Gödel tells us that there is an arithmetical statement which can neither be proved or disproved from those axioms. The purpose of this project is to write a computer program which will take the axioms and use them to generate an statement which is undecidable in that axiom system. Details
Bell's theoremBell's theorem says that any model which reproduces what happens in quantum theory has to satisfy one of two rather strange constraints. The first is that it allow faster than light transmission of information. The second is sometimes referred to as defying realism, but I would replace this by the model having to include the minds of experimenters. The aim of this project is to produce a framework in which such models can be tried out, to see how such constraints arise. In particular, it is planned to investigate the model described in Disproof of Bell's Theorem by Clifford Algebra Valued Local Variables by Joy Christian
The simulation to investigate this can now be seen here