Fixed point or oscillate or noise

There’s a saying about investing which somewhat applies here. “The market can stay irrational longer than you can stay solvent”. Another is “in the long run, we’re all dead.”

Nothing is forever, but many things can outlast your observations. Eventually everything is steady state, fine. But there can be a LOT of signal before then.

Note that your computer doesn’t run out of bits when exploring the Mandelbrot set. Bits can encode an exponential number of states, and a few megabytes is enough to not terminate for millennia if it’s only zooming in and recalculating thousands of times per second. Likewise with your job - if it maxes or mins a hundred years out, rather than one, it’s a very different frame.

I think what you're pointing at is adjacent to many interesting or useful things. For instance, poincare recurrence and how predictions of boltzmann brains can be a death-knell for any model of the world. Or the technique of solving for equillibrium, which if everyone internalized would probably prevent us from shoving ourselves even further away from the pareto frontier. Or the suprising utility of modelling a bunch of processes as noise and analysing their affects on dynamics. 

But the idea that everything either reaches a steady state, a periodic sequence of states, or becomes noise seems useful only insofar as it lets us see if something is noisy/periodic/steady-state by checking that it isn't the other two. (I'm not sure that this is true. The universe may well have negative curvature and we could get aperiodic, non-noisy dynamics forever.) 

Okay my computer right here has 10^13 bits of storage and without too much trouble I could get it to use all that memory as a counter and just count to the highest value possible, which would be 2^(10^13) or in other words much much longer than the age of the universe even at a fast clock speed.

Now technically yes, after it got to that 2^(10^13) value it would have to either halt or start over from 0 or something... but that seems not so practically relevant to me because it's such a huge integer value.