Hello again,
As I am completely unfamiliar with Cabibo-Snot theory, I want to steer things back to the topic of your essay, and try to relate it back to things I do know about. FYI - the result from CDT and Quantum Einstein Gravity, that reality is 2-d near the Planck scale, is very satisfying to Loop Quantum Gravity and Spin Foam folks. When numerous theories all converge on a similar result, I take this as evidence that there is something special worth examining there.
You should note that I apply this rule to the Fractal Universe paradigm, as well. As you point out in your essay, there are a bunch of theories under serious consideration, all of which point to a universe that is fractal. And as I pointed out both here and on Richard Easther's essay page, folks would rather talk about a 'multiverse' than admit that things are fractal even up to the ultra-large scale beyond observability. I find this curious and somewhat disturbing, as calling it a fractal makes far more sense, in my view.
In my own essay, I point out that I too feel there has been an over-dependence on Math, sometimes at the expense of good logic and clear conceptual thinking. But I am a constructivist through and through. I am firmly of the belief that the existence of the universe is clear evidence that it could be constructed from earlier constituents and ultimately from first principles. That is; there had to be some process or procedure by which the form we see could come into existence, for it to exist at all. But I hold Math to the same standard, even while believing that the shape of Mathematics may be a 'mold' or 'template' for physical reality.
For the sake of understanding how your approach is similar to - or different from - other theories with which I am familiar, I would like to summarize and ask you to make a comparison or clarification. As I remember, your Discrete Scale Relativity results in a modified Planck Scale, but I'm not sure how this works.
First; it seems that all the related ideas describe a reality whose dimension is resolution dependent. I find this idea satisfying as it links up with the view from Constructive Math that a space has no definite dimensionality, apart from what is observable, measurable, or computable. What does DSR say about this?
Nottale's Scale Relativity describes a fabric of reality that is continuous but non-differentiable, like the Peano curve. It appears as a solid membrane, because it fills space. In Connes' approach from NCG, the resolution-dependent aspect arises in a manner similar to the situation on a flower like a daisy, where a tiny bug is constrained to walk around each petal and a larger insect can walk across them and travel a much shorter distance. In ElNaschie's Cantorian Space approach, it is as though the petals are separable as well, so that gaps appear between them. This translates the Math into a conceptual framework.
How does your Discrete Scale Relativity fit with these examples, if at all, and why does it result in a modified Planck Scale?
Regards,
Jonathan
