@cicerone imposter,
Quote:Because all of the particles are always in flux, there's no possibility of predicting any future outcome.
This may be true. Since it might be impossible to get a snapshot of all the particle positions and velocities. And that snapshot would act like the initial conditions of an n-body like problem. So you might be right there. But not being able to predict the future doesn't really say anything about whether the world is determined or not.
We could not anticipate the 3-body problem from the video without a computer bigger than the one that was originally used. That's if we could get the snapshot. So we are already behind in the race, since we do not have the benefit of knowing where stuff is and how fast its moving.
Quote:It's not a matter of n-body factors; it's about future unpredictability of what the particles will do. The earth goes through climate change; we couldn't predict this winter and summers weather patterns only 12 months ago.
It's about more than just one thing. It's about being faster than the largest computer that can ever exist - the universe. It's about crunching numbers using machines that are made out of the things you are doing the number crunching about. It may be an impossible task to make exact predictions for these reasons.
Quote:There's no way to predict the flux/change.
There actually are mathematical ways to predict the way things change. Velocity is the rate at which positions change. Acceleration is the rate at which velocities change. These rates of change are known as derivatives. And you can keep taking derivatives to find new ways the particles change in time. Once you know the positions in time you can find any rate of change. All you have to do is take a derivative. So if we had the equations for an n-body problem we could predict where the particles would be and how those positions, and the derivatives would change with time.
But for the other reasons I think you are right. It might be impossible to completely predict a complex outcome like the weather 6 months from now.