THE FLETCHER’S PARADOX
Imagine a fletcher (i.e. an arrow-maker) has fired one of his arrows into the air. For the arrow to be considered to be moving, it has to be continually repositioning itself from the place where it is now to any place where it currently isn’t. The Fletcher’s Paradox, however, states that throughout its trajectory the arrow is actually not moving at all. At any given instant of no real duration (in other words, a snapshot in time) during its flight, the arrow cannot move to somewhere it isn’t because there isn’t time for it to do so. And it can’t move to where it is now, because it’s already there. So, for that instant in time, the arrow must be stationary. But because all time is comprised entirely of instants—in every one of which the arrow must also be stationary—then the arrow must in fact be stationary the entire time. Except, of course, it isn’t.
While it may be true that the arrow doesn’t change its position ‘during’ the instant it does definitely still have a velocity, only you cannot observe that by just looking at a snapshot. But that doesn’t mean it’s not there.
An explanation might be that “moving” is not defined very clearly. If you rephrase the word “moving” and use the word “velocity” instead, the paradox immediately breaks down:
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