Basically try to answer: "Is it true what they say about that whole infinity thing?"
I have no idea how you'd do this, but if you could somehow trace the path of lot of subatomic particles and map them into a computer program, you'd do two things with them:
1) Find two separate particles that moved
in the same path and "drew" a similar squiggle and see how long they did the same thing.
2- Over time, find if you get two particles that, through their random movement created something looking like an object. Any object, this would be random and compared to a datebase of all the objects in the universe. A daisy, a smiling face, whatever.
3- Make a timeline of how long it might take to draw something more advanced, like a monkey and how many particles might draw that monkey before breaking down into random squiggles.
4- Determine if anything cohesive might EVER be drawn at random or if the reset to chaos would never be overcome.
Kind of a study of infinity. Would probably need numbers way bigger than Googleplexes to get any useful results. Some future computer might even say "Working on it, doing three trillion calculations a nanosecond should have a reasonable answer for you in about one billion trillion googleplex years give or take a few. Would you like to watch some funny cat videos in the meantime?"
Something like this might have been suggested but I'd have no idea what to search for to see it it's been thought about or not.
Also, a fish powered toaster.