I recognize that my map is a different portion of the territory, that portion of the territory which resides inside my head and which is merely correlated to the actual territory outside of my head.
But the actual-territory is not (or at least, need not be) causally influenced by the territory inside your head that's implementing the map.
But tsn't that the opposite of what you and Tegmark IV are saying: namely that the maps we call "equations" represent something ontologically basic about the whole of the territory?
I can't speak for Tegmark, of course, but what I'm saying is that "equations" are the territory, and the stuff that looks to us like rocks and trees and people and the Moon is just a map.
I'd be careful what I'd call "nonsensical" when your argument instead must lead to the conclusion that things must exist even when they don't exist...
On the contrary, the conclusion is that things must exist even when they don't "exist" - where that quotation refers to some silly little savanna-concept we have in our brains, about rocks and trees and people and the Moon. Which don't exist.
Epiphenomenalism is usually referring to something conceptual or cognitive (e.g qualia or consciousness or subjective experience) that doesn't have an influence on physical states.
You're instead talking about physical existence not having an influence on conceptual entities (namely the mathematical equations).
That's because (in my model) the conceptual entities are the bedrock of the hierarchy, and physical existence is strongly analogous in this model to qualia in a physical-realist model. After all, "{equations}" and "rocks following {equations}" both give the same result for "value of X at time T", so the existence of rocks is epiphenomenal to the equations.
once you have the physical reality of a mouth and a keyboard (which happen to require mass-energy) to be able to say to the equations, you can just say "equations"
But a simulated me, existing only as information represented by electrons in a computer, could say "equations" just as loudly. So why couldn't a purely informational me, existing as unrepresented information, say "equations" too? Physical reality is a burdensome detail which doesn't add any explanatory power to your model; the claim that information needs to be represented in order for conscious entities contained within that information to exist seems to me to have no evidence backing it up, nor indeed to be capable of having such evidence, and therefore Occam demands that we frame our model in such a way as to make that claim inexpressible. It's rather like moving from configuration space to relative configuration space; unmeasurable claims become unreal.
But it still doesn't conclusively explain how the territory came to be.
It doesn't need to "come to be"; 'time' and 'causality' are parochial notions, concepts we can use to model things within our universe. Expecting the multiverse to obey them seems to me to be a Mind Projection Fallacy. A block universe just is.
Thanks for the insightful critique, by the way - it's helping me to understand the arguments better and see weak points that I wouldn't have noticed myself. I'm still not sure whether my theory is circular, nor whether I should care if it is.
Follow-up to: Syntacticism
I wrote:
In my experience, most people default1 to naïve physical realism: the belief that "matter and energy and stuff exist, and they follow the laws of physics". This view has two problems: how do you know stuff exists, and what makes it follow those laws?
To the first - one might point at a rock, and say "Look at that rock; see how it exists at me." But then we are relying on sensory experience; suppose the simulation hypothesis were true, then that sensory experience would be unchanged, but the rock wouldn't really exist, would it? Suppose instead that we are being simulated twice, on two different computers. Does the rock exist twice as much? Suppose that there are actually two copies of the Universe, physically existing. Is there any way this could in principle be distinguished from the case where only one copy exists? No; a manifest physical reality is observationally equivalent to N manifest physical realities, as well as to a single simulation or indeed N simulations. (This remains true if we set N=0.)
So a true description requires that the idea of instantiation should drop out of the model; we need to think in a way that treats all the above cases as identical, that justifiably puts them all in the same bucket. This we can do if we claim that that-which-exists is precisely the mathematical structure defining the physical laws and the index of our particular initial conditions (in a non-relativistic quantum universe that would be the Schrödinger equation and some particular wavefunction). Doing so then solves not only the first problem of naïve physical realism, but the second also, since trivially solutions to those laws must follow those laws.
But then why should we privilege our particular set of physical laws, when that too is just a source of indexical uncertainty? So we conclude that all possible mathematical structures have Platonic existence; there is no little XML tag attached to the mathematics of our own universe that states "this one exists, is physically manifest, is instantiated", and in this view of things such a tag is obviously superfluous; instantiation has dropped out of our model.
When an agent in universe-defined-by-structure-A simulates, or models, or thinks-about, universe-defined-by-structure-B, they do not 'cause universe B to come into existence'; there is no refcount attached to each structure, to tell the Grand Multiversal Garbage Collection Routine whether that structure is still needed. An agent in A simulating B is not a causal relation from A to B; instead it is a causal relation from B to A! B defines the fact-of-the-matter as to what the result of B's laws is, and the agent in A will (barring cosmic rays flipping bits) get the result defined by B.2
So we are left with a Platonically existing multiverse of mathematical structures and solutions thereto, which can contain conscious agents to whom there will be every appearance of a manifest instantiated physical reality, yet no such physical reality exists. In the terminology of Max Tegmark (The Mathematical Universe) this position is the acceptance of the MUH but the rejection of the ERH (although the Mathematical Universe is an external reality, it's not an external physical reality).
Reducing all of applied mathematics and theoretical physics to a syntactic formal system is left as an exercise for the reader.
1That is, when people who haven't thought about such things before do so for the first time, this is usually the first idea that suggests itself.
2I haven't yet worked out what happens if a closed loop forms, but I think we can pull the same trick that turns formalism into syntacticism; or possibly, consider the whole system as a single mathematical structure which may have several stable states (indexical uncertainty) or no stable states (which I think can be resolved by 'loop unfolding', a process similar to that which turns the complex plane into a Riemann surface - but now I'm getting beyond the size of digression that fits in a footnote; a mathematical theory of causal relations between structures needs at least its own post, and at most its own field, to be worked out properly).