Dear Anthony DiCarlo,
Thank you for putting in the effort to grasp my essay, and then giving me your opinion.
Your first problem seems to be with my 'starting rules', which are: 'don't go outside of reality' for your building blocks and/or concepts, specifically God, a mathematical (Platonic) universe, 'laws' of physics, or more than four dimensions. Had I known the trend that has developed in this contest, I would have included 'digital-computers-in-the-sky' (or in some other dimension).
You then say that this would have precluded imaginary numbers. But imaginary numbers are a two dimensional concept, and it is 'representational reality' that is at question, not physical reality. Having explained (briefly in my essay, at length in referenced work) why I 'allow' mathematics (as evolved inside our physical universe) then I am comfortable with the use of infinite Hilbert spaces and 'imaginary' numbers if their use facilitates representation and/or 'solution' of physical problems, which they clearly do.
On the other hand, I do reject belief that imaginary number is physical; it is simply a shorthand for 'orthogonal'. And I do reject that an 'infinite series of wave-functions' is physical. It is simply a way to decompose complex shapes, which are mathematically intractable, into sine waves.
So I disagree that 'no one should ever think such thoughts' even though the consequence in reality is often a period of confusion, as is the case today with 'qubits'.
Your next potential problem is that the 'scaled function G' is not explained 'physically', and doesn't give a picture of what's happening. This is a fair complaint. It's really hard to see what's happening. An earlier criticism of my theory was that it had no time dependence, although this accusation was leveled against the derived Newton equation and not my Master equation. When Ray Munroe made me aware of Nottale and scale invariance I saw that my Master equation (not Newton's equation) is scale invariant, and Nottale shows, motion invariant. This is mathematically easy to show, but initially physically confusing. What it means to me is that the physical universe, as long as it is validly described by the Master equation is scale invariant, and this means that even if the scale is changing, the Master equation is still the proper description. It is only when symmetry breaks, 'releasing' the hitherto suppressed C-field, that the equations evolve. I believe this is a physical explanation, not just mathematical, but it may take some mental effort before this becomes clear.
You next attempt to map my theory into your theory, or vice versa, in terms of equating 'curvature that creates mass' (Calabi's phrase) with 'curvature of the mirrors'. My theory is complex, and so is yours, and you have spent more time on this equivalence than have I, so you may be correct, but it is not clear to me at this moment, as I do not understand what the 'mirrors' represent in my model, and I am not a believer in a 'holographic' universe. This is to me a (mis-)application of Cauchy's integral formula which relates the value at any point on a surface to the integral around a closed contour surrounding the point. But that is valid for conservative potentials, and does not, in my opinion, extend into the non-linear regions implied by Yang-Mills. This is not to deny that reflections play a huge role in the physical universe, and are often appropriately modeled by a 'box'.
When you 'step outside the box' and see muons implied, you have lost me. You clearly seem to have a picture in mind that ties it together, but I don't yet have the picture.
Now I will go out on a limb and conjecture that you are working not so much in four dimensional reflections but in a Hilbert space of reflections, and this might be mathematically fruitful. I am still confused about the physical meaning of the mirrors.
Finally, although Jill's experience is the essence of reality, and is key to understanding consciousness in the universe, any reasonable discussion of this is beyond a comment. I have written another essay, several books, and many comments on this aspect of reality, and the gist of these is that topology is far more basic to conscious awareness of global connectivity, and metric distance is merely a 'utilitarian overlay' which is necessary for local intelligent 'operation' in the universe.
I feel somewhat disappointed that I am not able to respond as well to your comment as I would like to, but the effort required to map your theory of the universe into my theory of the universe exceeds my immediate resources. I sincerely thank you for the serious effort that you have expended on understanding my theory and congratulate you on an original and interesting theory with two truly excellent pictures or diagrams that support your explanation. The entire purpose of fqxi, in my opinion, is to provide a forum for such ideas. For any who have not yet read Tony's essay, I recommend it.
Best wishes,
Edwin Eugene Klingman
