"Because of gravity" is only sensible if it refers to that mathematics.

Well, that's where we disagree (I'd agree with "useful" instead of "sensible"). The mathematical description is just a more precise way of describing what we see, of describing what a thing does. It is not providing any "justification". The experimental result needs no justification. It just is. And we describe that result, the conditions, the intermediate steps. No matter how precise that description, no matter what language we clad it in, the "mechanism" always remains "because that's what gravity does". We have no evidence to assume that there are "souls" which generate consciousness. However, that is an explanation for consciousness. Just not one surviving the Razor.

To preempt possible misunderstandings, I'm pointing out the distinction between "we have no reason to assume this explanation is the shortest (explains observations in the most compact way) while also being accurate (not contradicting the observations) -- and -- "this is not an explanation, it just says 'souls do consciousness' without providing a mechanism". The first I strongly agree with. The second I strongly disagree with. All our explanations boil down to "because x does y", be they Maxwell's or his demon's soul's, or his silver hammer's.

Turing machines do not perform arbitrary computations instantly.

I wasn't previously aware you draw distinctions between "concepts which cannot exist which are useful to ponder" and "concepts which cannot exist which are over the top". ;-) Both of which could be called magical. While I do see your point, the Computer Science-y way of thinking (with which you're obviously familiar) kind of trains one to look at extreme cases / the limits, to test the boundary conditions to check whether some property holds in general; even if those boundary conditions aren't achievable. Hence the usefulness of TMs.

But even considering a reasonably but not wholly unconstrained model-builder, it seems sensible to assume there would be fewer intermediate layers of abstractions needed, as resources grow. No need to have as many separate concepts for the macroscopic and the microscopic if you have no difficulty making the computations from a few levels down (need not be 'the base level'). Each abstracted layer creates new potential inaccuracies/errors, unless we assume nothing is lost in translation. Usually we don't need to concern ourselves with atoms when we put down a chair, but eventually it will happen that we put down a chair and something unexpected happens because of an atomic butterfly effect which was invisible from the macroscopic layer of abstraction.

That's rather a barrage of questions, but they are intended to be one question, expressed in different ways. I am basically not getting the distinction you are drawing here between "base-level things" and "computational hacks", and what you get from that distinction.

Let me try one way of explaining what I mean, and one way to explain why I think it's an important distinction. Consider two model-builders which are both unconstrained to the maximum degree you'd allow without dismissing them as useless fantasies. Consider two perfectly accurate models of reality (or as accurate as you'd allow them to be). Presumably, they would by necessity be isomorphic, and their shortest representation identical. However, since those shortest representations are uncomputable (let's retreat to more realism when it suits us), let's just assume we're dealing with 2 non-optimally compressed but perfectly accurate models of reality. One which the uFAI exterminating the humans came up with, and one which the uFAI terminating the Alpha-Centaurians came up with. So they meet over a game of cards, and compare models of reality. Maybe the Alpha-Centaurians -- floating sentient gas bags, as opposed to blood bags -- never sat down (before being exterminated), so its models don't contain anything easily corresponding to a chair. Would that make its model of physics less powerful, or less accurate? Maybe, once exchanging notes, the Alpha-Centauri AI notes that humans (before being exterminated) liked to use 'chairs', so it includes some representation of 'chair' in its databanks. Maybe the AI's don't rely on such token concepts in the first place, and just describe different conglomerates of atoms, as atoms. It's not that they couldn't just save the 'chair'-concept, there would just be no necessity to do so. No added accuracy, no added model fidelity, no added predictive power. Only if they lacked the oomph to describe everything as atoms-only would they start using labels like "chairs" and "flowers" and "human meat energy conversion facilities".

What I get from that distinction is recognizing pseudo-answers such as "consciousnessness is an emergent phenomenon and only exists at a certain macroscopic level" as mostly being a confusion of thinking macroscopic layers to be somehow self-contained, independent of the lower levels, instead of computationally-friendly abstractions and approximations of lower levels. When we say "chairs are real, and atoms are real, and the quarks are real, and (whichever base levels we get down to) is real", and hold all of those as true at the same time, there is a danger of forgetting that chairs are only real because atoms are real, which are only real because elementary particles are real, which ...", there is a dependency chain going all the way down to who knows where. All the way down to the "everything which can be described by math exists" swirling color vortex. "Consciousness is an actual physical phenomenon which can only be described as a macroscopic process, which only emerges at a higher level of abstraction, yet it exists and creates conscious experience" is self-contradictory, to me. It confuses a layer of abstraction which helps us process the world with a self-contained "emergent" world which is capable of creating conscious experience all on its own. Consciousness must be expressable purely on a base-level (whatever it may be), or it cannot be.

Of course it's not feasible to talk about consciousness or chairs on a quark level (unless you're Penrose), and "emergent" used as "we talk about it on this level because it seems most accessible to us" is perfectly fine. However, because of the computational-hack vs. territory confusion, "emergent" is used all too often as if it was some answer to some riddle, instead of an admission of insufficient resources.

That's rather a barrage of text with only a single pass of proof-reading, if you have enough time to go through it, please point out where I've been unclear, or what doesn't make sense to you.