For those of you who aren’t familiar: Achilles and a Tortoise race, however the tortoise is given a leading start. Achilles is at Point A, whereas the tortoise is ahead at point B. The race begins, and by the time Achilles makes it to point B, where the Tortoise used to be, it has reached point C. Then Achilles arrives at point C with the Tortoise at point D. So on and so forth, with Achilles never catching up to the Tortoise as per the paradox.
But he definitely catches the Tortoise eventually, right? The tortoise has a lower velocity, hence the head start, so after a certain amount of time the distance between points is smaller than Achilles and the Tortoise’s difference in speed. What, if anything, is paradoxical about the world’s most famous paradox?
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The reason this is a “paradox” is that the logic seems irrefutable although our common sense tells us otherwise. It isn’t a true paradox because it isn’t a logical contradiction but rather the reasoning seems to go against common sense.
To actually show why this isn’t a true paradox involves understanding infinite series. We can build an infinite series out of the sequence 1, 1/2, 1/4, 1/8… Now every term of the sequence is positive. “Logically” adding all the terms would result in “infinity” as there are an infinite number of positive numbers added together.
It actually isn’t obvious to a person not familiar with infinite series, why this “logic” isn’t true.
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