An electron is a quivering ripple in the fabric of space. A more intricate ripple is a proton, as is a neutron. An assembly of them, like a carbon atom, is an incredibly intricate quivering bundle. And you, for an extreme example, are an inconceivably intricate one. It took about four and a half billion years of persistent tweaking, give or take a few hundred million, to get you going and quivering for about fifty years, give or take a few decades. You embody evanescent vibes built up over eons from intricate--but still relatively rudimentary--ripples that, astonishingly, replicate themselves. (By the way, Biology is trying to demystify rudimentary replication to understand how life arises, but I doubt if that effort will be successful until such replication becomes a precise part of Physics, or at least Chemistry.) The most rudimentary kind of ripple is the electromagnetic field, first understood and articulated by Michael Faraday in prose. His ideas eventually led James Clerk Maxwell to accurately model that field in mathematics (the very first such model in a discipline now pervaded by field models). Maxwell's exploratory models were whimsically concrete, but his final one was bafflingly abstract, yet unexpectedly accurate. (About it Heinrich Hertz asserted that "It is impossible to study this remarkable theory without experiencing at times the strange feeling that the equations somehow have a proper life, that they are smarter than we, smarter than the author himself, and that we somehow obtain from them more than was originally put into them.") Then Paul Adrian Maurice Dirac built a model of the electron even more abstract and accurate, that Richard Feynman, Julian Schwinger, Sin-itiro Tomonaga and Freeman Dyson enhanced. With those successes, others built even better models of other ripples in the fabric of space. These visionaries were limited by the modeling tools available: Maxwell was saddled with Cartesian coordinates augmented by the perplexing quaternions of Hamilton. The others had the expressive-but-clumsy vector calculus of Gibbs and Heaviside, augmented by the slightly less perplexing complex numbers and matrices of them. Fortunately, a more coherent and elegant modeling language is now available, namely the transparent Geometric Algebra envisioned by Grassmann, partially amalgamated by Clifford, and polished by Hestenes et al. Its amalgamation and polishing, accidentally and unfortunately, focused on the free algebra exclusively, and neglected the bound one. The bound algebra is the most expressive part of Grassmann's creation because it directly articulates locus, and--best of all--automatically generates the free algebra as a sub-language. If you are interested in that full algebra, take a look at the free–bound distinction displayed here before linking to its explication. (Click on the image. Important hint: dashed lines in this image represent addition.) My hope is that future visionaries will be able to use this language to make even better models of ripples in the fabric of space ("field theories"). Make such good models, in fact, that the mysteries of the quantum evaporate. Toward that dream, the full algebra presented in the preceding link is being converted into an algorithmic language. Here are some preliminaries: (coming up, but when? I wonder.) When that dialect becomes available, I hope to use it to build my own quivering model of the electron, more concrete than those now available; more in Maxwell's exploratory spirit. I hope that endeavor will provide a taste of the challenges a visionary faces, and might just teach me a lesson, namely why there are so very few Maxwells. That effort is nascent: (also coming up, and when oh when?) |