See an explanation on Zeno's Achilles paradox, an infinite series concept used in finance to pay off mortgages
Learn about Zeno's Achilles paradox.
© Open University (A Britannica Publishing Partner)
-
Encyclopædia Britannica, Inc.Passover commemorates the biblical story of the Exodus.
-
Contunico © ZDF Studios GmbH, MainzLearn about how the Papal Palace in Avignon, France, reflects the wealth and power of the popes who lived there.
-
Encyclopædia Britannica, Inc.The search for knowledge never ends—but it started somewhere.Media Editor: Lauren Sims
-
© MinutePhysics (A Britannica Publishing Partner)Learn how integers can be used to count infinity.
-
© Open University (A Britannica Publishing Partner)Learn about the grandfather paradox and the concept of time travel to the past.
-
Encyclopædia Britannica, Inc.Philosopher and educator Mortimer J. Adler discussing Socrates as a man, a teacher, and a philosopher, with reenactments by Tony Van Bridge (as Socrates) and others. This video is a 1962 production of Encyclopædia Britannica Educational Corporation.
-
© Open University (A Britannica Publishing Partner)An overview of six famous paradoxes in philosophy and science.
Transcript
60 Second Adventures in Thought.
Number One, Achilles and The Tortoise. How could a humble tortoise beat the legendary Greek hero, Achilles, in a race?
The Greek philosopher, Zeno, liked the challenge and came up with this paradox. First, the tortoise is given a slight head start. Anyone fancying a flutter would still rush to put their money on Achilles, but Zeno pointed out that to overtake him, Achilles would first have to cover the distance to the point where the tortoise began.
In that time, the tortoise would have moved, so Achilles would have to cover that distance giving the tortoise time to amble forwards a bit more.
Logically, this would carry on forever. However small the gap between them, the tortoise would still be able to move forward while Achilles was catching up. Meaning that Achilles could never overtake.
Taken to an extreme, this bizarre paradox suggests that all movement is impossible, but it did lead to the realization that something finite can be divided an infinite number of times.
This concept of an infinite series is used in finance to work out mortgage payments, which is why they take an infinite amount of time to pay off.
Number One, Achilles and The Tortoise. How could a humble tortoise beat the legendary Greek hero, Achilles, in a race?
The Greek philosopher, Zeno, liked the challenge and came up with this paradox. First, the tortoise is given a slight head start. Anyone fancying a flutter would still rush to put their money on Achilles, but Zeno pointed out that to overtake him, Achilles would first have to cover the distance to the point where the tortoise began.
In that time, the tortoise would have moved, so Achilles would have to cover that distance giving the tortoise time to amble forwards a bit more.
Logically, this would carry on forever. However small the gap between them, the tortoise would still be able to move forward while Achilles was catching up. Meaning that Achilles could never overtake.
Taken to an extreme, this bizarre paradox suggests that all movement is impossible, but it did lead to the realization that something finite can be divided an infinite number of times.
This concept of an infinite series is used in finance to work out mortgage payments, which is why they take an infinite amount of time to pay off.