This is certainly a very interesting essay, however, I find myself a bit baffled by a certain recurring theme that I consider disturbing, and that is the implicit anthropocentricity of some of the ideas.
To exemplify my concern let us focus on a topic that appears prominently in the essay:
Gödel's lesson, regarding the undecidability of the truth values of certain statements within an axiomatic ( mathematical) system . What Gödel showed is that there are certain true statements that cannot be proven by following the ``axiomatic-logical path", but there is no issue at all regarding the truth of those statements. However, here the author seems to give a dramatically strong role to an aspect of the question that seems rather anthropocentric: The fact that there are meaningful statements for which no man could ever ascertain their truth value, is somehow taken as casting doubts about the statement having a truth value in itself. Furthermore, in fact, the very possibility of producing Gödel's result relies on a notion of the "truth value" of a statement ( within an axiomatic system) that is independent of the notion of proof .
This is taken further regarding computability: the fact that nor man or man-made machine ( for which a Turing Machine is an idealized characterization) can compute in a finite time ( a criteria further reduced to take into account the finiteness of the time made available by cosmology) a certain number, is somehow taken to mean that such number does not exist. Thus, existence is made strongly dependent on men (or similar thinking organisms). This is , in my view, a step back from the lessons, that are often considered as starting with N. Copernicus, having shaken our conception of being at the center of the universe, and further enhanced by Darwin's theory of evolution that shook our conviction that we were the center of creation [with newly adapted versions of the idea, in my view equally erroneous, which somehow see us, humans as the ultimate goal of evolution : i.e. to create the simple cells and take live into more and more complex forms so that the world might end up with beings like us].
Here physical laws are required to be such that their predictions are computable.
This posture seems rather problematic to me. This is even so when taken in the realm of mathematics: should we take the view that say existence proofs, say of solutions to differential equations with given initial data, are meaningless unless they are constructive? We are often content to know the solution exist and is unique, while the question of
actually finding the solution is taken as one of quite a different nature.
To adopt Landauer's view of physical laws as necessarily tied to the capacities of a computer, even the most conceivably versatile version thereof ( say a superefficient universal Turing Machine or even a quantum version of it) is to place us humans at the center once again. This time not merely at the center the universe, but at the basis of the very essence of existence. I think we can all imagine a world where there are no sentient beings, no computers, and nothing like that. In fact, our own theories of cosmology indicate that for a very long time that was precisely the state of the universe. Thus, unless one adopts a teleological posture, it seems that we must accept that the emergence of the conditions that made beings like us possible (i.e. the formation of galaxies, stars, solar systems, life and the emergence intelligence as a successful adaptation) are mere contingent facts, and that the universe could easily be conceived as having gone into a different path.
I think it is hard to dispute the notion that physical laws can limit what is, in principle, computable, but, one must recognize that the notion itself of what is computable ( say in terms of Turing Machines and the like) has a very strong anthropocentric component ( what the machines we can device can compute), and thus the posture that computability limits physics is in a sense, going back to placing ourselves at the center.
It is natural to expect that the extent of the things we might be able to know, be strongly anthropocentric, it is quite different to claim that the same applies to the world out-there itself.
I should say, however, that in certain aspects what is considered here resonates with one idea I considered in my own essay, but I think, we part ways dramatically at considerations like " ...reality is the total sum of what sentient beings can actually measure or observe (e.g. classical bits of information and rational numbers)...". Similarly, information is a notion that acquires meaning in the context where we have taken for granted the existence of sentient beings, who might store it in devices which in idealized terms they describe, using the notion of bits, but it seems hard to give a meaning to information in the absence of such beings. Placing information at the center like in Wheeler's " it from bit" catchy phrase, is again returning to an admittedly more sophisticated than older ones, but nonetheless, clearly anthropocentric world view.
As I said I am convinced there is a world out-there and there is a question of the extent to which we can, through our own very human theoretical constructions, produce accurate descriptions thereof. Here the posture seems to make the very existence of world out-there dependent on us.
