Achilles and the Tortoise

The Paradox:

In this thought experiment, Achilles, a swift warrior, is racing against a slow-moving tortoise. To make it fair, the tortoise is given a head start. The paradox argues that Achilles can never overtake the tortoise, no matter how fast he runs.


Here’s how the paradox is laid out:

  1. Initial Position: The tortoise starts ahead of Achilles.
  2. Achilles Moves to the Tortoise's Initial Position: By the time Achilles reaches the point where the tortoise started, the tortoise has moved forward a small distance.
  3. Achilles Moves to the Tortoise's New Position: Achilles then moves to the new position of the tortoise, but by the time he gets there, the tortoise has moved even further ahead.
  4. Repetition: This process continues indefinitely, with Achilles always reaching where the tortoise was, but the tortoise always being a little bit ahead.

The paradox suggests that Achilles will never be able to overtake the tortoise because there are infinitely many points he must reach where the tortoise was before he can catch up.

Resolving the Paradox:

If you sum the infinite series of times Achilles takes to cover these increasingly smaller distances, the sum converges to a finite value. This means that, mathematically, Achilles will indeed overtake the tortoise after a finite amount of time, despite the infinite steps involved in the paradox.

A mindfulness message:

The Achilles paradox offers us a profound lens through which to view time, suggesting that within every fleeting moment lies an infinite series of experiences.

 FIVE THOUSANDTHS of a second the margin Noah Lyles won the 100m Olympic Final - the difference between triumph and defeat.

This emphasises the incredible value of even the smallest moments in our lives.  They are the building blocks of our experiences, shaping our journeys in ways we might not always notice.

When we say life is short, it's easy to overlook the infinite number of moments that fill even a single second. The Achilles paradox reminds us that within the span of what seems like a brief life, there are endless opportunities, choices, and experiences—each as valuable as the last.

So, rather than seeing life as fleeting, we can embrace the idea that every moment, no matter how tiny or "insignificant," is infinite in its potential. Just like in that Olympic race, where a fraction of a second made all the difference, every moment in our lives holds the power to shape our future. 

Life may be finite in years, but it's infinite in moments—each one a precious opportunity to live fully and meaningfully.

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