Incidentally, my (possibly naive) answer to Heraclitus is that he can't see the wood for the trees. I of course agree that you don't literally step into the same river twice, but I don't agree that you can say nothing useful about the river as an ensemble. The analogy I am instantly reminded of in physics is Statistical Mechanics, or Thermodynamics in general, ie "how do we describe a gas, made from countless trillions upon trillions of tiny particles constantly interacting?" The answer is to care less about what the individual particles are doing, about which you can never have complete knowledge, and start focusing on what the gas is doing as a whole. You can measure its pressure, its volume, over average properties, and it turns out that way so much useful information lies.
Or, in your analogy, the individual ping-pong ball's time to travel tells you little, but there's nothing to stop you dropping dozens or hundreds, and measuring the average journey time (and then repeating the experiment in different seasons, before or after rainfall, etc).
Don't disagree that studying ancient Greek philosophers is interesting, though. Thanks for the video!