> There is a mathematical theorem that forbids you from writing down a discrete version of certain quantum field theories.
> (...)
> You know, if you take this theorem at face value, it’s telling us we’re not living in the Matrix. The way you simulate anything on a computer is by first discretizing it and then simulating. And yet there’s a fundamental obstacle seemingly to discretizing the laws of physics as we know it. So we can’t simulate the laws of physics, but it means no one else can either. So if you really buy this theorem, then we’re not living in the Matrix.
I don't buy this reasoning.
I can encode the continuous function f(x) = x^2 on a computer.
Then I can calculate this function for any number up to any digit, if I allocate enough memory.
I don't need to allocate a discrete domain up-front and then stick to it at all times. I can increase and decrease the accuracy as needed.
In a similar fashion I could simulate a continuous universe encoded with continuous operators. I could simulate it on a discrete lattice with certain precision as long as nobody inside the simulation builds equipment that can measure things "in-between" the lattice points. And when somebody does, at that moment, I can simply pause the simulation, calculate the values of my operators using a locally-denser lattice, then unpause. The observer with their equipment wouldn't notice anything because the simulation was paused, they would just get the correct measurement.
> (...)
> You know, if you take this theorem at face value, it’s telling us we’re not living in the Matrix. The way you simulate anything on a computer is by first discretizing it and then simulating. And yet there’s a fundamental obstacle seemingly to discretizing the laws of physics as we know it. So we can’t simulate the laws of physics, but it means no one else can either. So if you really buy this theorem, then we’re not living in the Matrix.
I don't buy this reasoning.
I can encode the continuous function f(x) = x^2 on a computer. Then I can calculate this function for any number up to any digit, if I allocate enough memory.
I don't need to allocate a discrete domain up-front and then stick to it at all times. I can increase and decrease the accuracy as needed.
In a similar fashion I could simulate a continuous universe encoded with continuous operators. I could simulate it on a discrete lattice with certain precision as long as nobody inside the simulation builds equipment that can measure things "in-between" the lattice points. And when somebody does, at that moment, I can simply pause the simulation, calculate the values of my operators using a locally-denser lattice, then unpause. The observer with their equipment wouldn't notice anything because the simulation was paused, they would just get the correct measurement.