I don't understand the meaning of the word "symbols" in the abstract, without a brain to interpret them with and map them onto reality.

Think in terms of LISP gensyms - objects which themselves support only one operation, ==. The only thing we can say about (rg45t) is that it's the same as (rg45t) but not the same as (2qox), whereas we think we know what (forall) means (in the game of set theory) - in fact the only reason (forall) has a meaning is because some of our symbol-manipulating rules mention it.

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.)