The Achilles and tortoise paradox

July 6, 2020
by Noriyuki Morimoto

The impossibility of Achilles to catch up with the tortoise, or the arrow to reach its target, represents a well-known paradox in the history of philosophy.

A tortoise is in front of Achilles, and there is some distance between the two. However fast Achilles may be, it takes a certain amount of time for him to travel that distance. During that time, however slow the tortoise may be, it moves forward a little. Again, as Achilles takes some time to cover that distance, the tortoise moves a little ahead. As this situation keeps repeating itself, even as the distance between the tortoise and Achilles shrinks infinitely, Achilles will never catch up with the tortoise.

The arrow shot by the archer passes the midpoint between the archer and the target. It then passes the midpoint between the first midpoint and the target. Since such midpoints exist infinitely toward the target, given that the arrow has to pass all of them, it may come infinitely close to the target but never reach it.

The paradox is caused by setting a distance to the target object, dividing it into infinite parts, then integrating time and space, and dividing time into infinite divisions in accordance with the infinite division of space. Therefore, if the distance to the target is removed, the paradox will not hold.

When this paradox is applied to issues of human society, it would mean that if we keep aiming towards a goal, we may approach the goal but never reach it. What breaks the paradox is the way Achilles runs and the way archers shoot.

Achilles does not run in order to catch up with a tortoise. His unique way of running happens to result in passing the tortoise. If his aim is to pass the tortoise, he will be restrained by the tortoise and cannot beat it. The same holds if the tortoise is changed to a leopard. It is the freedom without goals or standards, and the rigor and loneliness of that freedom, that are the essence of growth, leap and innovation.

As for the flying arrow, it does not stop motion at the moment it touches the target. The arrow is released with a power to reach far beyond the target. The target is not the arrival point of the arrow, but only a point in the course of the arrow. Therefore, the arrow pierces the target with force. That is a matter of fact.


[Category /Investment Philosophy]

Noriyuki Morimoto
Noriyuki Morimoto

Chief Executive Officer, HC Asset Management Co.,Ltd. Noriyuki Morimoto founded HC Asset Management in November 2002. As a pioneer investment consultant in Japan, he established the investment consulting business of Watson Wyatt K.K. (now Willis Towers Watson) in 1990.