4 ms·

It could be that our universe's state can be described by the initial input '1234567', 1 page of differential equations, and an amount of time T to simulate. A

It could be that our universe's state can be described by the initial input '1234567', 1 page of differential equations, and an amount of time T to simulate. An inner universe's state could have an initial input of some string describing all of human history up to T in the outer universe, the same differential equations, and the same amount of time T to simulate. One might say that the inner universe contains more information, because the smallest unambiguous description of it is larger than the smallest description of its parent universe. However, the outer universe is able to simulate the inner universe.

drdeca 10y ago
But you can specify the information of state of the simulation by specifying 1234567, the differential equations, T, and something to identify the machine that you mean, and that you want the information it stores. This gives you the same info, and would presumably be shorter than "some string describing all of human history up to T" . It would still describe all the info though.
- MichaelBurge 10y ago
  The purpose of 'Some string describing all of human history' is to have something irreducibly dependent on the first machine. It's extremely unlikely that you'd be able to find an alternate way to describe it that didn't involve describing the outer machine in some way. You could mark a time and an algorithm for accumulating information, but you now have 2 more pieces of information in the inner machine than the outer one. So the outer machine has somehow managed to simulate the inner machine even though it has less information. Although... the moment you actually carry out this experiment, it falls apart: Instead of using T, you can just look at time T + U, where U is the amount of time needed to simulate the inner machine. This is because we're sitting here talking about the experiment and eventually carrying it out, so those initial conditions encode the conclusion of the experiment. This is subtle enough I'd have to look at the math. I can't think through it.
  - Razengan 10y ago
    Do we know if it's possible (or impossible) to run a perfectly accurate, 1:1 simulation of our universe inside a computer? If yes, then can we add something to that simulation, like an extra type of particle?

drdeca 10y ago

But you can specify the information of state of the simulation by specifying 1234567, the differential equations, T, and something to identify the machine that you mean, and that you want the information it stores. This gives you the same info, and would presumably be shorter than "some string describing all of human history up to T" . It would still describe all the info though.

MichaelBurge 10y ago
The purpose of 'Some string describing all of human history' is to have something irreducibly dependent on the first machine. It's extremely unlikely that you'd be able to find an alternate way to describe it that didn't involve describing the outer machine in some way. You could mark a time and an algorithm for accumulating information, but you now have 2 more pieces of information in the inner machine than the outer one. So the outer machine has somehow managed to simulate the inner machine even though it has less information. Although... the moment you actually carry out this experiment, it falls apart: Instead of using T, you can just look at time T + U, where U is the amount of time needed to simulate the inner machine. This is because we're sitting here talking about the experiment and eventually carrying it out, so those initial conditions encode the conclusion of the experiment. This is subtle enough I'd have to look at the math. I can't think through it.
- Razengan 10y ago
  Do we know if it's possible (or impossible) to run a perfectly accurate, 1:1 simulation of our universe inside a computer? If yes, then can we add something to that simulation, like an extra type of particle?