Imagine a tortoise: Mud-green; hard-shelled; sad-eyed. Possibly, the tortoise in your mind is chewing sedately on a lettuce leaf, as it plods its way down the inner lane of a race track in a ruined amphitheatre.
Now, imagine the fastest runner you’ve ever seen. To the Greeks, this would have been been Achilles (a strange conceit, for he was known to have weak heels). To use a slightly more contemporary image, let’s imagine Usain Bolt – smiling that beatific smile of his – as he sprints towards the tortoise.
Usain Bolt and the tortoise are in a race; as a gesture of good sportsmanship from the fastest man in the world, the tortoise has been given a 50 metre head start.
If you were a betting sort of person, you’d probably put your money on Usain Bolt winning. But what if I told you that Usain Bolt could never overtake the tortoise?
Before Usain Bolt can overtake the tortoise, he must first catch up to it. While our tenacious runner covers the gap between himself and the tortoise, the tortoise plods along, still in motion. When Usain Bolt covers the first gap, he finds that the tortoise has created a new gap, smaller than the first, but one that must still be surmounted. To his frustration, he crosses the second gap, only to find that the damnable creature has created a third, even smaller gap.
Well, you can probably see where this is going. Imagine Usain’s trademark grin turning into a pained grimace, as he struggles to surmount increasingly smaller numbers of infinite distances, stuck in a never-ending race.
For your pleasure and bemusement, here’s another tale relating to infinite testudine. Bertrand Russell, the esteemed philosopher and scientist, was giving a public lesson on astronomy. He regaled his audience with how the earth revolves around the sun, just one of a myriad stars in our infinite universe.
Most of the audience was suitably impressed. But a little old lady stood up at the back of the auditorium and started to boo. “Bollocks,” she scoffed. “Everyone knows that the world is a flat disc that lies on the back of a turtle.”
Perhaps he was being kind, or perhaps the esteemed philosopher was merely being patronising, for he engaged with the old lady’s point of view.
“That’s an interesting notion, good woman,” he said. “But pray tell, what is the tortoise standing on?” he asked.
The little old lady’s eyes flashed with brief bewilderment, and then sparked with conviction.
“You’re very clever, young man…very clever. But you can’t bamboozle me. It’s turtles all the way down.”
The first of these turtle stories originated two millennia ago, one of several paradoxes created by the pre-Socratic philosopher, Zeno of Elea.
Zeno was attempting to prove that one of the most commonsensical of phenomena – the concept of motion – could not logically occur. Or perhaps he was just trolling.
The second, apocryphal story is more recent, a patronising anecdote that was perhaps meant to illustrate the contrast between the rational Western mind and superstitious Eastern beliefs.
When confronted with concepts that we do not fully comprehend, we can tend towards two opposing approach. On one extreme, there is the approach of extreme skepticism: To question the veracity of every iota of knowledge, to the point of paralysis.
On the other hand, there is the approach of conviction: To believe, in the face of logic and empirical evidence, that our worldview is infallible, and it is indeed turtles all the way down.
Stories move a lot faster these days. They move, not at the placid velocity of a turtle on a race course, but at the speed of thought and fibre optics.
At its height, The Library of Alexandria contained half a million scroll of ancient knowledge; in the modern day, we could bit torrent the sum of it in less than a second.
We live half in reality, half in the world of the Internet: A phantasmic space where digital avatars tweet and twitch and regram; where a million Towers of Babel are built of hashtags and clickbait, crumbling to dust with every weekly news cycle; a world of subreddit tribes, online enclaves and a thousand conflicting stories.
When knowledge move at the frenetic speed of thought, there seems to be little time for ancient stories about turtles. Both these stories have been debunked by scientists, mathematicians and philosophers, but they provide us with important questions to ask ourselves: How do we question? How do we believe?