Dear Michael
Thanks for your kind comments.
Regarding p-adics, I am reminded of a paper I once read by Herman Bondi who said that if children we were taught special relativity in primary school, as adults we would not find things like length contraction and time dilation the least bit strange or unusual. Similarly, I expect, if we were taught p-adic arithmetic in primary school, we would not find p-adic numbers strange or exotic as adults. Peter Scholze, who won the Fields Medal last year, is quoted as saying that he has got so used to p-adics that now he finds the real numbers really strange and exotic!
Your letter raises a really interesting and important issue - the role of irreversibility. The fractal attractors I am considering have zero volume and hence zero measure relative to the measure of the Euclidean space in which they are embedded. The classical dynamical systems which generate these attractors asymptotically must therefore be irreversible: start with a finite volume and it shrinks to zero asymptotically.
What is the origin of this irreversibility? In terms of the attractor geometry, the irreversibility could be localised to some small region of state space, such that when the state of the system goes through this region, state-space volumes shrink a bit. In this way, it is possible for the dynamics to be Hamiltonian almost everywhere. But it cannot be strictly Hamiltonian everywhere. It is tempting to suppose that such irreversibility is associated with space-time singularities, but this is merely a conjecture.
Regarding your essay, I think I am in agreement with your perspective. Although I am claiming that the universe as a whole has these properties of uncomputability, I don't think it makes sense to think of sub-systems of the universe as approximating the properties of the full system in any way at all. In my essay I refer to the inability of the full system to be fully emulated by a sub-system of the full system as Computational Irreducibility - a phrase that I think Stephen Wolfram coined.
Of course it is worth noting that in many practical cases, noise can and should be treated as a positive resource. Personally, I think human creativity arises because the brain has been able to harness noise in this way - please see:
https://www.mdpi.com/1099-4300/22/3/281
Best wishes
Tim