As I understand it ec429’s intuition goes a bit like this:
Take P1, a program that serially computes the digits in the decimal expansion of π. Even if it’s the first time in the history of the universe that that program is run, it doesn’t feel like the person who ran the program (or the computer itself) created that sequence of digits. It feels like that sequence “always existed” (in fact, it feels like it “exists” regardless of running the program, or the existence of the Universe and the time flow it contains), and running the program just led to discovering its precise shape.(#)
Now take P2, a program that computes (deterministically) a simulation of, say, a human observer in a universe locally similar(##) to ours, but perhaps slightly different( ###) to remove indexing uncertainty. Applying intuition directly to P2, it feels that the simulation isn’t a real world, and whatever the observer inside feels and thinks (including about “existence”) is kind of “fake”; i.e., it feels like we’re creating it, and it wouldn’t exist if we didn’t run the program.
But there is actually no obvious difference from P1: the exact results of what happens inside P2, including the feelings and thoughts of the observer, are predetermined, and are exclusively the consequence of a series of symbolic manipulations or “equation solving” of the exact same kind as those that “generate” the decimals of π.
So either: 1) we are “creating” the sequence of decimals of π whenever we (first? or every time?) compute it, and if so we would also “create” the simulated world when we run P2, or 2) the sequence of digits in the expansion of π “exists” indifferently of us (and even our universe), and we merely discover (or embody) it when we compute it, and if so the simulated world of P2 also “exists” indifferently of us, and we simply discover (or embody) it when we execute P2.
I think ec429 “sides” with the first intuition, and you tend more towards the second. I just noticed I am confused.
(I kind of give a bit more weight to the first intuition, since P2 has a lot more going on to confuse my intuitions. But still, there’s no obvious reason why intuitions of my brain about abstract things like the existence of a particular sequence of numbers might match anything “real”.)
(#: This intuition is not necessarily universal, it’s just what I think is at the source ec429’s post.)
(##: For example, a completely deterministic program that uses 10^5 bit numbers to simulate all particles in a kilometer-wide radius copy of our world around, say, you at some point while reading this post, with a ridiculously high-quality pseudo-random number generator used to select a single Everett “slice”, and with a simple boundary chosen such that conditions inside the bubble remain livable for a few hours. This (or something very like it, I didn’t think too long about the exponents) is probably implementable with Jupiter-brain-class technology in our universe even with non-augumented-human–written software, not necessarily in “real-time”, and it’s hard to argue that the observer wouldn’t be really a human, at least while the simulation is running.)
(###: E.g., a red cat walks teleports inside the bubble when it didn’t in the “real” world. For extra fun, imagine that the simulated human thinks about what it means to exist while this happens.)
I think ec429 “sides” with the first intuition, and you tend more towards the second. I just noticed I am confused.
No, I'd say nearer the second - the mathematical expression of the world of P2 "exists" indifferently of us, and has just as much "existence" as we do. Rocks and trees and leptons, and their equivalents in P2-world, however, don't "exist"; only their corresponding 'pieces of math' flowing through the equations can be said to "exist".
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).