On this site I have gathered together my writings on various topics in physics and mathematics.
An Introduction To Lie Theory Through Path Geometry (my book – a big, ongoing project)
Of most interest to me are optics (my professional field), general relativity and geometry in physics, thermodynamics from an informational theoretical standpoint and especially on its implications for evolution of life on Earth, quantum mechanical foundations and mathematics as a language for describing our physical World. The mathematical fields I am keenest on are Lie theory and geometry.
We are all animals of the Neogene Wet Savannas of Africa and have evolved to ken and understand the patterns we met in that world. There is no reason, therefore, why we should, or even why we can understand patterns arising in the World that are far removed from our Wet Savanna home. To reach out to logic and mathematics is maybe one way we can put aside the prejudices and limitations that have inevitably beclouded our World view by dint of our evolution. The Mathematical Universe Hypothesis of Mark Tegmark resonates strongly with me.
Keeping mindful of our Wet Savanna origins perhaps teaches us humility in approaching the gathering of knowledge about our World. Certainly greater humility in the application of technology on our limited and beautiful Earth home is something that we sorely need.
But in keeping mindful of our humble beginnings there also springs the hope that maybe, just maybe, the secrets of the World are within our grasp someday. What evolutionary advantage could possibly be given us by an ability to grasp, say, the spin statistics theorem, or the Einstein field equations? Most decidedly, no obvious advantage arises from this ability. Why then do we have this ability? Maybe, then, it is a by-product of a meta-ability that does beget an evolutionary advantage: the ability to speak and do mathematics and grasp logic, useful in the working out solutions to the challenges our Wet Savanna Forebears came up against. The fact that experimentally we find this selfsame logic that our forebears used and indeed many other animal species use (with varying degrees of conscious awareness of their own mathematical abilities) in overcoming everyday challenges affords us insight into the workings of a neutron star is perhaps experimental evidence that the underlying laws of the Universe may indeed indeed be simple and ultimately graspable.
Will we grasp these laws? Hope is not foresight, after all. We may and we may not. But it is surely fun finding out: there is a joy in being, as Carl Sagan says, the Universe contemplating itself.