Consider any property of any box of matter. Or consider any signal generated by a finite computer. Assume physics has true RNG. I claim that eventually either
this signal will stop changing, or
the system will reach a prior state and the signal will oscillate, or
the system will reach irrecoverably high entropy and the signal will be noise.
You won’t see eg a never-ending mandelbrot zoom because the computer will run out of bits.
Steady state is just oscillation with a time period of 0, so really there’s only two possible long term outcomes.
Is this of any use? I already know that my shoe will stay shoe and that the radio plays static if nobody is broadcasting. However, McDonald’s is not steady state or noise at a very detailed level. There aren’t really any isolated finite boxes of matter unless you take the whole lightcone to be one.
Perhaps a weaker & less formal version is of some use:
Consider any property of any person, organization, music genre, dog, rock, friendship, computer network, star, or body of water. Eventually that property will either oscillate, stop changing, or become noise.
So you have a way to categorize your goals and things. You can ask yourself eg “This job is alright now. In one year will this job max out (be great) or min out (suck) or will there be cycles or will things keep meaningfully changing (like going further on the mandelbrot zoom)?” Maybe this is somehow useful.
Or the short version you’ve heard before:
There are no constant nonzero derivatives in nature.
What’s wrong here? What’s right? Is this a nothingburger or is it useful? Who said all this already?
Fixed point or oscillate or noise
Consider any property of any box of matter. Or consider any signal generated by a finite computer. Assume physics has true RNG. I claim that eventually either
this signal will stop changing, or
the system will reach a prior state and the signal will oscillate, or
the system will reach irrecoverably high entropy and the signal will be noise.
You won’t see eg a never-ending mandelbrot zoom because the computer will run out of bits.
Steady state is just oscillation with a time period of 0, so really there’s only two possible long term outcomes.
Is this of any use? I already know that my shoe will stay shoe and that the radio plays static if nobody is broadcasting. However, McDonald’s is not steady state or noise at a very detailed level. There aren’t really any isolated finite boxes of matter unless you take the whole lightcone to be one.
Perhaps a weaker & less formal version is of some use:
Consider any property of any person, organization, music genre, dog, rock, friendship, computer network, star, or body of water. Eventually that property will either oscillate, stop changing, or become noise.
So you have a way to categorize your goals and things. You can ask yourself eg “This job is alright now. In one year will this job max out (be great) or min out (suck) or will there be cycles or will things keep meaningfully changing (like going further on the mandelbrot zoom)?” Maybe this is somehow useful.
Or the short version you’ve heard before:
There are no constant nonzero derivatives in nature.
What’s wrong here? What’s right? Is this a nothingburger or is it useful? Who said all this already?