you can see where a cannonball will land without simulating the cannonball.
To predict with any degree of accuracy where a cannonball will land, I'm going to need to know the muzzle velocity, angle, and elevation of the cannon, and then I'm going to need to mathematically simulate the cannon firing. If I want to be more confident or more accurate, I'm also going to need to know the shape, size, and mass of the cannonball; and the current weather conditions; and I'm going to need to simulate the cannon's firing in more detail.
If I wanted to predict anything about a chaotic system, like the color of an arbitrary pixel in a gigapixel rendering of the Mandelbrot Set, I'd need to do a much finer-grained simulation--even if I'm just looking for a yes/no answer.
To get an answer from a particular decision theory, Omega is going to have to do the functional equivalent of lying to that decision theory--tracing its execution path along a particular branch which corresponds to a statement from Omega that is not veridical. I don't think we can say whether that simulation is detailed enough to be consciously aware of the lie, but I don't think that's what's being asked.
To predict with any degree of accuracy where a cannonball will land, I'm going to need to know the muzzle velocity, angle, and elevation of the cannon, and then I'm going to need to mathematically simulate the cannon firing.
No, you really don't. LCPW please. The cannonball is flying unrestricted through the air in an eastwardly direction and will impact a giant tub of jello.
Just developing my second idea at the end of my last post. It seems to me that in the Newcomb problem and in the counterfactual mugging, the completely trustworthy Omega lies to a greater or lesser extent.
This is immediately obvious in scenarios where Omega simulates you in order to predict your reaction. In the Newcomb problem, the simulated you is told "I have already made my decision...", which is not true at that point, and in the counterfactual mugging, whenever the coin comes up heads, the simulated you is told "the coin came up tails". And the arguments only go through because these lies are accepted by the simulated you as being true.
If Omega doesn't simulate you, but uses other methods to gauge your reactions, he isn't lying to you per se. But he is estimating your reaction in the hypothetical situation where you were fed untrue information that you believed to be true. And that you believed to be true, specifically because the source is Omega, and Omega is trustworthy.
Doesn't really change much to the arguments here, but it's a thought worth bearing in mind.