Terry,
Like your practice of numbering responses by paragraphs. and a useful analytic. Had not thought of approaching my reading in that manner. Like that free acrobat permits highlighting and commenting.
Many interesting thoughts in your responses. Skipping beyond a few of them to
(4) Euler's identity - yes, apparent deepness of connection between math and matter befuddles. re inversion, i did try to work with conductance early in exploration of impedance quantization. Shoulda been trivial. Seemed more sensible to work in terms of what goes easy rather than what resists. Simple thing in mathcad (left a link for you to pdf of an early mathcad file in our thread on my essay) to work either way. Was very puzzling. Gave it a lot of attention, as somehow it seemed a philosophical item of importance, to opt for conductance rather than resistance. Could not make any sense of it, still don't understand why. Couldn't get the numbers to work. One has to calculate to figure anything out. Couldn't calculate. Had to give up, switch back to impedances. Can't believe there is anything fundamental in the modeling that would cause this. Wish i had a student to chase it.
(5) renormalization - you are calling conductance 'the primary fraction'? Like that, but of itself it is not enough to result in finiteness if i understand correctly. Impedance has both capacitive and inductive components with pi/2 phase shift between them in 'free space', a consequence of how wave function of interest excites the eight-component 3D Pauli vacuum wavefunction. Capacitive impedance is zero at the singularity, inductive is infinite. Going from ohms to mhos doesn't get rid of the singularity, just shifts its phase. However either extreme results in an infinite mismatch.
(5a) Regarding applications of quantum impedance matching in amo/condensed matter, agree there are possibilites as yet unimagined. Been humping on that for years. Only way to understand the inertia of mainstream is to experience it. Would seem obvious. The computer holding me a willing captive at this very moment is chock full of impedance matches. How could a quantum computer be any different? So far in our investigation of impedance quantization it seems the concept is firmly grounded in reality. Computers require impedance matching. Quantum computers require quantum impedance matching. Have a Buddhist friend that likes the phrase 'not no mind'. Me, i go with compassion for ignorance, otherwise would hate my not no self and go lusting for the not no gold mines' kitty kats. What a funny world we live in. Mortgages and back taxes.
(6) dude! We got got gravity. That was our black hole info paradox paper/poster for the 2013 Rochester Conference on Quantum optics, information, and measurement. Vetted by Optical Society of American, world guardian of quantum information theory/experiment. Poster is perhaps quickest click. http://vixra.org/pdf/1306.0102v1.pdf
(7a) excellent. You know math better, perhaps i have found a teacher please. The uniqueness of 3D space is an area pretty new to me, and i've never seriously looked at quaternions. When trying to model particle physics one picks and chooses what to learn very carefully, as there is infinity of beauty and complexity in every direction. For the purposes of tying together loose ends it seldom suffices to simply chase down the ends and knot them, unless one agrees to be satisfied with the tangle that connect them. Lacking that the universal PhD path dives in and start untangling. The village idiot just tracks down the ends and ties the knot. and poof fairy tale tangle vanishes and he steps in a cow pie. So it goes. Michaele and i are more modelers than typical theorists, and def not math types. Calculators.
(7b) thanks for link to Traill, Peter Jackson also recommended him and I took a look but was not able to wrap the mind around it, will try again.
re intuition, i think much of it has to do with what one experiences in life, what the Buddhist might call dependent arising. For me it was working with my brother, designing/building/operating vibratory piledrivers, synchronized spinning eccentric weights. Standing next to them, feeling the energy transfer,... Made one want to laugh, to dance and sing. That and dad was an electronics guy, we build the electronic analog and ran it on the bench. Mechanical and electrical impedances. Quantization comes easy once one gets that.