Small errors in position/velocity are amplified exponentially at each collision. Air molecules collide on average about once every 200 picoseconds. So, an er

Small errors in position/velocity are amplified exponentially at each collision. Air molecules collide on average about once every 200 picoseconds. So, an error of one part in 10^1000 will build up to an O(1) difference in about O(log 10^1000) collisions, or maybe ~1 microsecond (the "less than a millisecond" claim was being very conservative.) It's a testament to the power of exponential growth.