The Fletcher Paradox

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WanderingGaze22
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Joined: June 9th, 2021, 12:39 am

The Fletcher Paradox

Post by WanderingGaze22 »

Imagine a fletcher (i.e. an arrow-maker) has fired an arrow 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. Is this also an example of superposition?
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LuckyR
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Re: The Fletcher Paradox

Post by LuckyR »

WanderingGaze22 wrote: January 23rd, 2022, 3:35 am Imagine a fletcher (i.e. an arrow-maker) has fired an arrow 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. Is this also an example of superposition?
The red sentance by my reckoning is where your train of thought breaks down. Time, as you describe it, is a human made analogy to make the concept of time make sense to us, yet is not a true description of "time".
"As usual... it depends."
Ecurb
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Re: The Fletcher Paradox

Post by Ecurb »

This is a standard Greek philosophy question: Is time a measure of motion, or is motion a measure of time. Heralitus said, "You cannot step into the same river twice."

When he told his wife, he explained that by the time you step into the river a second time, the river will have run downstream, so it would not be the same river.

"Don't be an ass, Heraclitus," rejoined his wife. "YOu can step into the same rive twice if you run downstream."

So Heraclitus went down to the Ilisus. He threw a twig into the river (to measure the speed of the current). Then he stepped in, and ran down stream and stepped again. But the river was flowing swiftly, and by the time he stepped again, the twig had raced ahead of him. So he stepped and ran, stepped and ran, stepped and ran, until he ran into the Agean Sea and drowned.

So much for Heraclitus.
ernestm
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Re: The Fletcher Paradox

Post by ernestm »

More conventionally the problem is cited as Zeno's paradox.
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IreneJohnson
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Re: The Fletcher Paradox

Post by IreneJohnson »

If zero time has passed, the arrow cannot exist because zero time has zero space. Therefore, the arrow is moving at all times even in a “snapshot”.
Good_Egg
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Re: The Fletcher Paradox

Post by Good_Egg »

ernestm wrote: January 24th, 2022, 6:08 pm More conventionally the problem is cited as Zeno's paradox.
It is like Zeno's paradox in that it relies on dividing time into a set of intervals in such a way that they don't add up again to the whole of time.

It is mathematically different.

Zeno's intervals were each half as long as the interval before (in the version where the hare runs twice as fast as the tortoise). That set of intervals never quite adds up to the point in time where the hare catches the tortoise.

The fletcher's intervals are of zero length (in order that the arrow is stationary in that interval) and thus never add up to any length of time at all. It's a form of infinity paradox, infinity being the reciprocal of zero.
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