Response to Zeno’s Arrow Paradox

1 10 2010

“The Arrow.  Does the arrow move when the archer shoots it at the target? If there is a reality of space, the arrow must at all times occupy a particular position in space on its way to the target. But for an arrow to occupy a position in space that is equal to its length is precisely what is meant when one says that the arrow is at rest. Since the arrow must always occupy such a position on its trajectory which is equal to its length, the arrow must be always at rest. Therefore motion is an illusion.”

I don’t know about you but I had to read this eight times to “figure it out” and I’m still not sure I understand it because it is poorly written.  It says “a position in space that is equal to its length”.  A position is a portion of space occupied by something, or a point/location.  He’s equating a three-dimensional space or a point to a line (length).

After proving to myself this is not correct, I Googled Zeno’s paradoxes and found all kinds of lame reasons why this is incorrect, including the arrow can be in motion at an instant, but not in and instant.  Suddenly, I may see why Clinton under testimony questioned, “It depends on what the meaning of is is.”  This is a bunch of hair splitting by people who don’t understand physics.

Here is my answer in less than 50 words:

For anything to start, stop, accelerate or decelerate there is deflection of the object even though it may be infinitesimal.  Therefore, the arrow DOES NOT take up precisely the same space or maintain its exact length.

End of answer.

When the archer lets go of the string, the energy transferred to the arrow compresses it linearly.  The string continues to exert force on the arrow but when the arrow departs from the string it lengthens like a spring.  On its way to the target I guarantee it is vibrating along the length of shaft at least for some period of time.

Throw a water balloon; it will clearly deflect possibly to the point it bursts.  Throw a baseball and it will deflect as well and so will your fingers.  You can find plenty of snapshots of golf balls being smushed.  If the object that is acted upon cannot absorb all the energy, it breaks or splits, but it will move first.  Even putting something in motion by gravity will change shape.  Anything stationary sitting on the floor, roof, or table is deflecting to some extent under its own weight.  Roll an egg off a table sometime and watch it deflect on the floor.

written by Jeffrey L. Ihnen, P.E., LEED AP

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