As you can clearly see…
Before and after Feynman
(image 5/5 of diploma series)
You are on a river rowing a boat upstream and suddenly, unbeknownst to you, your hat falls in the water and floats away. Forty-five minutes later, you realize it is missing and execute the instantaneous, acceleration-free about-face such puzzles depend on. Rowing back, you try to calculate exactly how long it will take to recover your hat. Your speed against the current is 4.25 km/h, but your speed against the land is only 2km/h.
Assume you lost your hat at point H. When you discovered it was missing, you turned around at point T, 1.5km upstream from point H. However, within the time you spent rowing away, your hat had floated 1.6875km downstream, changing position to point H’. Currently, it is 3.1875km from point T to point H’, which means it will take you 0.49038462 hours (that is 29.4230772 minutes) to reach point H’ at your total speed of 6.5km/h. By the time you row from point T to point H’, unfortunately, the hat will have floated another 1.103365395km downstream to point H’’. A wave of vertigo sweeps over you with the thought of an H followed by an infinite number of primes building up, the decimals getting longer, mistakes multiplying, as you constantly overtake the point where the hat was just a little while ago, though, within that time, it has advanced a bit further. Momentarily, you have the impression that all motion is impossible; displacement from point A to point B, no matter how close, forces you to pass through an infinite number of distances in a finite time – first halfway, then half of the remaining distance, then half again and so on… an infinite amount of calculation is required to reach the hat.
After exactly 45 minutes of intense mental calculation, you catch up with your hat. There is obviously a simple solution to the problem, so you must be the protagonist of a trick question. Was it your mathematics professor friend who did this to you? It certainly seems like the kind of bad practical joke she likes to play on her students.
In a bright flash of inspiration, you realize that the river's motion is irrelevant – as irrelevant as the earth's motion through the solar system or the solar system's motion through the galaxy. In fact, all the velocities are just a distraction, a ruse, an illusion, a bad practical joke. Imagine the situation from the perspective of the hat: floating passively, your speed is the same as that of the river, therefore, the velocities cancel each other out. Consider then, that the turbulent river is nothing more than a quiet lake. You watch the boat, and you see at once that it will return in the same forty-five minutes it spent rowing away.