Dear Michael,
This is very nice and well argued essay you have proposed here. I learnt many things, I did not know about conservative logic for example, and will for sure come back to it multiple times in the coming months.
You are perfectly correct that noise should not, and maybe cannot, be discarded. And the reference to the 3 Kelvin CMB is pot on about this.
A small issue I have with one of the theses you develop however, is that you say that because a computer ultimately relies on external resources (whatever they are for: memory, energy etc...), once this storage somehow runs out the programme will halt. This is perfectly true but I would not consider this as being the same as saying that the halting problem does not apply. If the programme is terminated before it terminates on its own then it is still a major problem and this is not, I believe, what the original Halting problem was about.
So, to me, if anything, you actually put forward, like Paul Davies does in his essay, an additional limitation to computation.
So, instead of dispelling these undecidability and incompatibility problems, I think you actually add to them by considering more realistic scenarios.
Another interesting point you mention is that mathematics can only go as far as the tools of mathematics, themselves governed by the laws of physics, enable them to go.
I would venture to object that the very laws of physics we have developed are equally prone to the same critic. So I am not sure how one can be used to undermine the other.
This reminds me of Penrose's claim that the proof of Godel's first incompleteness theorem could not be checked by a Turing machine and out of which he would conclude that our brains go beyond such idealised machines. Do you have any thoughts about this?
Many thanks again for this inspiring essay.
Best of luck for the contest.
Fabien