User:Rgdboer
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My great-grandparents lived in the land of Herman Boerhaave and Hendrik Lorentz, most of my grandparents were born there. When I was a boy I took an interest in coin collecting, especially the Lincoln cent. In a local library I read about meterology, a perpetual spur to understanding. A schoolmate showed me how chess was played; it captured my attention; like Philidor I was enchanted with the power of the pawn.
I was amazed that my crystal radio worked without batteries -- the power to drive the earphone was "in the air". At that time there was no internet, but shortwave communications offered a window on the world. I studied morse code, took up amatuer radio practice and obtained a FCC license (or two). A fascination with electronics began before my real schooling.
I put some of my physical energy into learning to ride a unicycle. After junior high school I started studying through the summers, taking a course to typewrite the first summer. I participated in interscholastic debate as a high school student, an activity that encourages research and criticism. The space race brought learning opportunities; for example before grade 11 the NSF sponsored a summer school where I listened to talks on the Rydberg formula and the Bohr model of the atom. Each of my parents had a cousin in academia, so that was my career goal. First I needed to get the necessary academic degrees and become the kind of scholar that can read French, German and Russian mathematics.
At the University of Michigan in 1966 I enjoyed a course from Irving Copi using his textbook on logic. The next year my interest in Foundations of mathematics was aroused by Raymond Wilder's course and text. I took my bachelor's degree from Michigan and a masters on integral geometry at the University of Alaska Fairbanks, reading Luis Santaló. Both schools taught me some ring theory. Nevertheless, the national presumption (at the time) of conscription forced me out.
When I came to Canada, it was the theory of relativity that I was reading up. In Halifax, Nova Scotia in 1972 I attended a conference on differential geometry and relativity where I heard F. A. Kaempfer of UBC speak on an extension of the Lorentz group to a “Conformal Group of Spacetime”. The concept goes back to work by Harry Bateman, and compares symmetries in geometry with symmetry in physics. I became a registered student, a teaching assistant, and had opportunities to become a candidate for the Ph.D. and to write up a dissertation on inversive ring geometry and relativity. I relied upon biquaternions, and referring to a book by Walter Benz, I made extensive use of split-complex numbers in building up a mathematical model of spacetime and its conformal transformations. A change in reference libraries in the 1980s (Vancouver’s UBC), brought me into contact with the works of Isaak Yaglom. Intensive library work over many years showed me the significant insights of pioneers like James Cockle, Alexander MacFarlane, and Ludwik Silberstein. After all, I see a 12-parameter conformal group of spacetime as projectivities on the ring of coquaternions. Admittedly this group is conformal in the generalized sense; nevertheless, this structure provides a covariant theory of perpendicularity and hyperbolic-orthogonality. Indeed, the pan-orthogonality in the coquaternion ring underpins both simultaneity and ordinary perpendicularity in space.
Christoph Riedweg's book Pythagoras (2005) has me thinking; anyway I have been a Vegetarian for 20+ years, relying on whole grains in the form of Brown rice, Quinoa, and Millet along with Legumes. I also enjoy roasted peanuts and fresh vegetables, especially those in the leaf and root categories. I ride bicycle in Vancouver or kayak the Strait of Georgia. Further physical exercise comes in playing Matkot.
