You can calculate how long a pencil can stand on its tip before falling using quantum physics.

Basically a version of this was on our freshman accelerated physics final, and no one got it right so our professor happily explained it to us the next day.

It was pretty much the same as is described here.

https://thephysicsvirtuosi.com/posts/old/how-long-can-you-balance-a-quantum-pencil/