Think of it this way: if you take a single particle in the world changing course, when it eventually collides with another, it will be with a different particle

Think of it this way: if you take a single particle in the world changing course, when it eventually collides with another, it will be with a different particle that it would originally have collided with. Once that happens, two particles now have a different course. Eventually, it'll be four, then eight, and so on, until pretty much every particle's course is shifted. This global shift is almost certain to happen eventually, and relatively quickly. At a macroscopic scale, though, that won't look like much at all. Air currents, temperature, and so on don't really depend on what specific microstate the atmosphere is in. It's like shifting every object in a room at random by a tenth of a millimeter, for all intents and purposes it doesn't change anything. Usually. From time to time, some microscopic details can snowball into macroscopic effects. Well, pretty much any small change anywhere in the world is going to shuffle all of these, everywhere in the world, a few years down the road. This means that, perhaps counter-intuitively, the more time passes, the more likely a small change is to have an effect. First it will shift everything a tenth of a millimeter, but eventually one of these shifts will snowball into a one-millimeter shift... which will propagate everywhere, setting the stage for a ten-millimeter shift, and so on. You'd be unlikely to notice, though, because the proximal cause for a big change will almost always be a medium-sized change, not a tiny one. Furthermore, it could take a very long time for the effects to really ramp up: large scale natural processes are very robust. Still, if a process has any kind of sensitivity to noise, it's just a matter of time before it shifts.