Physics and Mathematics Research

Does a model of Mathematics help Science?

I started on this line of thought almost forty years ago. First I thought Information was out there, and I decided to add it as a substance to be found an analyzed by Physics in a reductionist way. Also it appeared to me that to know how we know, would help. Recently I have added the social dynamics of the scientific community as another important element.

Always some scientists have considered meta issues, from the simple introspection of figuring out how they came to a particular idea, or solution, to a full fleshed philosophical inquiry; that in itself is not new. What is new is called Neuroscience. The scientific study of the mind has led to insights; I hope these insights will improve my ability to do science.

I have chosen Lakoff and Núñez's model of where mathematics come from. It comes from the brain, as individual mathematicians socially engage other mathematicians, until they get to an agreement. Personally, I don't believe in "truth," I believe in "fit." As a physicist I am concerned with the quality of the fit between my mathematical steps, and experimental steps, usually measured with smaller and smaller errors, both in calculation, and measurement, and of course, between the predicted number and the observed one.

Today the European Space Agency released pictures of one object in "21 Lutetia," , you can see the animated gif in this blog here., just click the picture and you'll get animation.

As you can see, the object is not spherical, therefore one expects like in the case of Hypeia, also shown in this blog, through an animation here, that Lutetia has some kind of chaotic motion. I wonder if the Rosetta probe can confirm that. Is Lutetia's motion chaotic?

Professor Peale from Santa Barbara, succeeded in two mathematical predictions, volcanoes on Io, and Hypeia's chaotic motion. Both required numerical work, even though the predictions may seem merely qualitative. I know that Stan was not concerned with how is it that he knows; because I was at UCSB in the 70s. That is not what he was doing, and as far as I know, is not what he is doing now.

Another person that was there then, is Terry Sejnowski; he was not doing that then, but I know he is doing that now.

In any case, I want to use these new ideas for research.

The field could be called: Computational Mathematical Physics ; a Neuroscience approach.

This is a first attempt to define the discipline.

Mathematical steps are fed to a computer which produces steps representing behavior; sometimes of the brain, and sometimes of a physical phenomenon. Results have to fit: Brain produced behavior, and physical object's behavior; in a more advanced version, the artificial brain will correctly predict physical phenomena.

I know this definition is wordy and long; I hope though, that some readers, definitively myself, should be able to understand what I mean.

My computer language of choice is Scheme, a dialect of Lisp.