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.
There’s some subtlety here about exactly what “zooming” means. In standard implementations, zooming recalculates a small area of the current view, such that the small area has higher precision (“zoomed”), but the rest of the space (“unzoomed”) goes out of frame and the memory gets reused. The end result is the same number of sampled points (“pixels” in the display) each zoom level.
Memory-efficient mandelbrot zooms are an interesting rabbit hole apparently. But I think that with any of them you must store at least one number in full precision. If you zoom 2x/sec then you use minimum 1 bit more ram per second pretty sure. Not certain.
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.
Interesting, I thought that zooming at a constant speed increased RAM usage at a constant rate but I hadn’t checked.
There’s some subtlety here about exactly what “zooming” means. In standard implementations, zooming recalculates a small area of the current view, such that the small area has higher precision (“zoomed”), but the rest of the space (“unzoomed”) goes out of frame and the memory gets reused. The end result is the same number of sampled points (“pixels” in the display) each zoom level.
Memory-efficient mandelbrot zooms are an interesting rabbit hole apparently. But I think that with any of them you must store at least one number in full precision. If you zoom 2x/sec then you use minimum 1 bit more ram per second pretty sure. Not certain.