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Dear Constantinos,
While I'm really just an uneducated, highly experienced information systems analyst (retired) who can't do the math, I very much enjoyed much of what I understood of your essay. I particularly liked: "energy propagates continuously but interacts discretely"; Ptolemy's epicycles: "...we can write bad physics using good math"; "We can't fault Math for the failings of Physics". I had previously been struck by Ptolemy's equations predicting the motions of planets through the sky as an example of a correct but invalid mathematical proof - are the quotes original?
I was compelled to delve into physics in 2008 when, recovering from a long illness, "Most of our Universe is Missing" was on TV and happened to hear astronomer Vera Rubin explain the observations leading to the establishment of dark matter saying (paraphrased): "...we had expected that they [stars in spiral galaxies] would rotate [orbit] just like planets in the Solar system." I've spent much of my time since trying to learn how to explain that she had meticulously applied standard analytical processes to the first survey of spiral galaxy rotational characteristics to produce a simply incorrect assessment - establishing the requirement for dark matter in physics! I think that the simple answer to that whole debacle is that, in all cases, galaxies are not planetary systems.
I really can't do the math, but I'd very much appreciate if you could read last year's brief (2 page) essay: "Mass Distribution Characteristics Invalidate the Galaxy Rotation Problem". I think you'll see why I particularly liked your essay.
Thanks,
Jim