Tom,
I consider my old-fashioned training in EE at TU Dresden from 1960 to 1966 excellent. Among my teachers was "Nabla Jot" Lehmann, an early pioneer of small computers. During my whole carriere as a teacher myself, I used complex calculus and designed a lot of problems for students.
Why do you assume I was scandalized by something quite normal?
If a function of time is continuous, then the corresponding complex function of frequency must of course be discrete and vice versa.
Complex integral transformation is not metaphysical but necessarily unphysical.
Hermitian symmetry is not a physical phenomenon but relates mathematically to algebraic continuation of what is called a semigroup into the void "half"-plane.
Mirroring just creates redundancies.
The complex representation is not a richer one if it originates from a real-valued one.
Well, this statement of mine is at odds with putative essentials of quantum mechanics and most of its trouble with itself.
I published more than 50 papers. Some of them dealt with dualities in particular in power electronic circuits.
I uttered the conjecture that a check of duality may help to reveal imperfections in theory. So far this seems to be true. Cantor's paradise fails the check. I collected mounting indications that confirm my suspicion: Cantor was wrong.
Well, I was shocked when I read how Schroedinger impressed his 14 years old pupil Itha Junger by telling her to expect getting the Nobel price, made she his lover, promised care but refused to divorce from his wife when Itha got pregnant.
I was also shocked when it got more and more obvious to me how carelessly Schroedinger, Heisenberg, and others dealt with the innocent complex calculus.
Instead of hand-weaving, you might look at the results of some simulations:
http://home.arcor.de/eckard.blumschein/M283.html
http://home.arcor.de/eckard.blumschein/M284.html
http://home.arcor.de/eckard.blumschein/M285.html
I apologize for not yet providing the due explanations there. Experts should nonetheless be in position to understand my argument.
My basic insight is: The reality of any physical process is restricted to elapsed time. I derive serious consequences from that restriction.
Read again: fqxi.org/community/forum/topic/369
To those physicists who are interested I will make already available
"A still valid argument by Ritz" (8 pages).
Non-physicists, in particular physicians, might rather look at the attached file.
Regards,
Eckard