The OG Nick Bostrom argument [1] makes an argument for simulation theory with some reasonably simple math you can see in the paper with only a few variables:
- `f_p` - Fraction of all human-level technological civilizations that survive to reach a posthuman stage
- `f_I` - Fraction of posthuman civilizations that are interested in running ancestor-simulations
- `N_I` - Average number of ancestor-simulations run by a posthuman civilization
- `H` - Average number of individuals that have lived in a civilization before it reaches a posthuman stage
And then the formula for the fraction of observers with human-type experiences (after simplifying) is just: f_sim = (f_p * f_I * N_I) / (f_p * f_I * N_I + 1).
By first arguing that `N_I` is likely to be very large (because, pretty much, why not) -- you can thus conclude that one of these three conditions are met:
1. `f_p ~= 0` -- or the human species is very likely to go extinct before reaching a “posthuman” stage;
2. `f_I ~= 0` -- or any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof);
3. `f_sim ~= 1` -- or we are almost certainly living in a computer simulation.
It's all feels pretty similar to the Fermi paradox to me -- which I'm also suspicious of for reasons I can't justify properly. Something about point estimates for variables like `f_I` is... weird? Idk. I'm honestly not good enough at math to disagree - but it also feels like folks who are too good at math might be using `f_I` in equations in a way that isn't legitimate.
Like, assuming the "existence" of `f_I` as a concept to reason with -- doesn't it feel like more might be sneaking in with this assumption?
One of Aaronson's arguments in the article boils down to the idea that running a full universe simulation (without cheating) on a universe with the same physics as ours may just not be possible computationally; it seems physically plausible that you need a universe to compute a universe.
If that's true, then the simulators would need to be running in a different kind of universe than ours... in which case "ancestor simulation" doesn't really make sense.
Well, yes, quantum physics says that's true. Our universe is the minimal requirements necessary to run our universe. There could be tricks, for instance maybe you only simulate at fine grain the universe near an observer. But still, to simulate our granularity you need a simulation of equal (or greater) granularity. There's the trick, it's conceivable that the simulator exists in a universe with more dimensionality.
- `f_p` - Fraction of all human-level technological civilizations that survive to reach a posthuman stage
- `f_I` - Fraction of posthuman civilizations that are interested in running ancestor-simulations
- `N_I` - Average number of ancestor-simulations run by a posthuman civilization
- `H` - Average number of individuals that have lived in a civilization before it reaches a posthuman stage
And then the formula for the fraction of observers with human-type experiences (after simplifying) is just: f_sim = (f_p * f_I * N_I) / (f_p * f_I * N_I + 1).
By first arguing that `N_I` is likely to be very large (because, pretty much, why not) -- you can thus conclude that one of these three conditions are met:
1. `f_p ~= 0` -- or the human species is very likely to go extinct before reaching a “posthuman” stage;
2. `f_I ~= 0` -- or any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof);
3. `f_sim ~= 1` -- or we are almost certainly living in a computer simulation.
It's all feels pretty similar to the Fermi paradox to me -- which I'm also suspicious of for reasons I can't justify properly. Something about point estimates for variables like `f_I` is... weird? Idk. I'm honestly not good enough at math to disagree - but it also feels like folks who are too good at math might be using `f_I` in equations in a way that isn't legitimate.
Like, assuming the "existence" of `f_I` as a concept to reason with -- doesn't it feel like more might be sneaking in with this assumption?
[1] https://simulation-argument.com