This analysis also quite reasonably assumes zero transfer time between donkeys, perfect knowledge to run donkeys to exactly their limit (which are identical bet

This analysis also quite reasonably assumes zero transfer time between donkeys, perfect knowledge to run donkeys to exactly their limit (which are identical between all donkeys), and zero overhead in general. That's all fine, it's an upper limit analysis. But the overhead will be biting you in the exponential regime, unfortunately. Another thing to remember about "the old days" is that they may not have computers and they may not have the Internet, but they have LOTS of time to think about more efficiency compared to an Internet commenter for whom this is merely a momentary side diversion for a few moments, and a lot more motivation. I feel satisfied with some of the answers to things like "How was Stonehenge built?" that have been found in the last couple of decades (or, if you prefer, "Can you show at least one method that could have been used to build Stonehenge?"), but I think one of the other lessons that was learned (at least by me) is that "take a modern person, give them one try in their busy lives to try the first thing that comes to their mind, and declare the task impossible when that doesn't work" isn't a very good way to understand the ancient world. They had time. Would an ancient have described the "harmonic transfer technique" in this way? Heck no. Could they have worked their way to it through trial, error, and much simpler thinking? Absolutely. Finding that solution doesn't require calculus. Calculus just supplies a very nice analysis framework and a fantastic communication tool between the post author and us readers.