Computers are ubiquitous in science. From elementary scientific education to cutting edge research it is likely that a computer will have a significant role. I feel, however, that there is a gap - which this website is intended to fill. Scientific writing is often difficult to understand, but attempting to present it to students in a simpler form is likely to result in less rigor. This may not matter if the intention is for the students simply to learn what has already been done, but if their intention is to become fully involved in the science then there is a problem. Such involvement means asking 'what if' questions - if you changed part of the theory, what would the result be? The trouble is that if the students start from a less that rigorous exposition of the theory, then the result is likely to be meaningless nonsense - a collection of jargon words strung together.

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 stephen at domain name

Gödel's incompleteness theorem

Given 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 theorem

Bell'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

Cosmology and Expanding space

I have doubts about the usefulness of the concept of expanding space in cosmology, and this section will contain calculations relating to this. The first of these concerns how an object moving through space is affected by the expansion of the universe and can be found at cosmology1.html

Landauer's principle and the second law of thermodynamics

Landauer's principle states that you can do computations with an arbitrarily small amount of energy, but that getting rid of the data that is generated has a specific energy cost. The idea of this project is to investigate this by modelling thermodynamic systems at the scale of individual elements, but with enough of them to see thermodynamic effects arising. As well as looking at Landauer's principle, it is intended to look at the idea that interesting things happen on 'the edge of chaos', in certain kinds of dissipative systems.

Quantum Chromodynamics

There are a number of open-source programs to perform lattice calculations in quantum chromodynamics. This project aims to construct a graphical front end for such software and to look into ways of using it to perform significant calculations on a personal computer rather than a supercomputer.
My other websites
Take a look at Chronon Critical Points which has scientific reviews, articles and applets, and at which has reviews and articles of a non-scientific nature. Also, which questions whether Einstein's battle with quantum theory was really as futile as people say.
Recent changes to my websites

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