Dear Eckhard Blumschein,
You mentioned that all ten FQXi contests offered opportunity for learning. I have watched your essays become clearer and cleaner (or perhaps I just understood them better as we went along) and I suspect this last essay topic is ideal for you. It's difficult to find the correct word, but I believe that wisdom best describes your understanding expressed in the current essay, which reveals:
"Why models may look as if they were reality even if logical discrepancies are undeniable, while on the other hand decisive imperfections of some mathematical metaphors are stubbornly ignored."
Many people have trouble thing with this reality, but you take it in stride! Somewhat relevant to this is David Hestenes' comment:
"Everything we know about physical space-time is known through its representation by some model, so when we're thinking about space-time and its properties, we're actually thinking about the model" ... "However we attribute an independent existence to space-time which might not be accurately represented by our model... so we must keep the distinction clear when considering the possibility that the model is wrong."
As you further note on page 7: "Physicists are always responsible for their models.... They have to be careful with models that calculate down to r=0 as if any conductor was a line and charge a point."
Your excellent example: "Be careful. Don't interpret all calculated results as if they did apply in physics too. Instead of accepting that the calculated infinite field strength around a line-shaped conductor approaches infinity, one should use a realistic model with the radius of the conductor larger than zero." As you note: "there are theoreticians who do not accept that they are just operating with mere fictions."
You point out "the formal remedy offered by Leibniz: a kind of "as if", the relative infinity. This fiction replaced rigorous logic by feasible mathematics." How well stated!
I very much enjoyed your remarks in #8 on the complex number in QM. Whereas many physicists do not appear to understand the points you make in this essay, I find them fascinating and agree with you as I understand them.
I have, for several years now focused on the propensity of physicists to project mathematical structure onto physical reality, and then appear to believe that reality exhibits and is constrained by such structure, with "symmetry" being a key example.
I hope that in the back of your mind, you have thought of writing a book encompassing the material in your essays.
My very best regards,
Edwin Eugene Klingman