Achilles and the Tortoise
A perfectly logical false conclusion. (The Bus 5.12)
Welcome aboard The Bus!
THURSDAY ARCHIVE EDITION - FIRST PUBLISHED (1.8) 2 MAY 2022
The Stop
'Achilles and the Tortoise’ is Zeno of Elea’s most famous paradox.1 Zeno attempts to show that logic doesn’t always work: in fact, it can result in a completely incorrect outcome.2
Here’s the paradox:
Achilles and a tortoise decide to race, but because Achilles can run twice as fast as the tortoise, he gives her a long head start. But this causes a problem as by the time Achilles reaches the tortoise’s starting point, she will have moved ahead by half the distance of her lead. And by the time Achilles reaches that point, the tortoise will have moved on by half of that distance again. This continues ad infinitum: for at each point in the race, by the time Achilles covers the distance between them, the tortoise will already have moved ahead of him by half of the distance of her lead. So, logically Achilles cannot catch up and can never overtake the tortoise. The (far) slower opponent wins.
Of course, this is ridiculous as Achilles would certainly win the race and everyone (including Zeno) knows it. But that’s not the point.
The paradox is designed to demonstrate that even an impeccably logical argument can lead to a false conclusion. ‘Achilles and the Tortoise’ shows that it is possible to start from reasonable - and unobjectionable - premises and then move by faultless logical steps to a wholly untrue conclusion. In the words of Brian Magee, this realisation ‘threatens with chaos all our attempts to reason about the world around us’ - and some people find that rather unsettling.3
For a short video explaining the paradox, check this out on YouTube from the Open University: Achilles and the Tortoise
The Detour
Today’s Detour is to an article about the ‘second life’ of The Simpsons. For the first several years I was a huge fan, but my admiration for the show faded after the first ten or so series. Even if you’re not a fan - or don’t think it should have ended long ago - this article is an eye-opening attempt to get to the bottom of why this show continues to endure and engage.
The Inside Story of the Simpsons' Remarkable Second Life
The Recommendation
Today’s book suggestion is Tom Standage’s A History of the World in Six Glasses (2005) Tracing human history through six of its most iconic beverages - beer, wine, spirits, coffee, tea and Coca Cola - the author weaves a story connecting these drinks to the eras in the development of civilisation they represent. A great read.
Reviews:
New York Times
The Sounds
Today’s playlist is a fun combination of rap, dance, pop and a dash of surrealism. Plus you get to sing about getting ‘a little bit Genghis Khan’ while enjoying B.I.G’s ‘triple beam/lyrical dream’: ‘Dance Wiv Me’ (Dizzee Rascal, 2008), ‘Genghis Khan’ (Miike Snow, 2016), ‘Mo Money Mo Problems’ (The Notorious B.I.G., 1997), ‘Work It Out’ (Jurassic 5, 2006) and ‘Birdhouse in Your Soul’ (They Might Be Giants, 1990). Enjoy!
The Thought
Today’s Thought is from Professor Barbara Tversky (Professor of Psychology and Education, Columbia Teachers College; Professor Emerita of Psychology, Stanford University).4
“How do the limits of the mind limit our understanding?”
If you have a thought on this Thought - or on any part of today’s issue - please leave a comment below:
And that’s the end of this stop - I hope you enjoyed a brief diversion from your regular journey!
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Until the next stop …
A paradox is a ‘situation or statement that seems impossible or is difficult to understand because it contains two opposite facts of characteristics’ (Cambridge Dictionary). There are many, many paradoxes - a lot of which are worth a look. You can find 10 here: 10 Paradoxes.
Zeno of Elea was a pupil of the pre-Socratic philosopher Parmenides, who lived during 5th Century BCE. Despite only one bit of his writing surviving - fragments of a metaphysical poem usually referred to as ‘On Nature’ - Parmenides is generally considered to be early Greek philosophy’s ‘most profound and challenging thinker’. It is also notable that in Plato’s dialogue Parmenides, he (Parmenides) meets a much-younger (about 20 years old) Socrates. It is thought that both Parmenides and Zeno’s paradoxes influenced what later became known as the Socratic Method. So, there are some serious connections here. For a biography of Parmenides, see: Parmenides
Preserved in Aristotle’s Physics, Zeno’s paradox was intended to support Parmenides’s argument that motion is nothing but an illusion. It can also be used to show how any finite value can be divided an infinite number of times. However, I think the way it reveals how perfect logic can result in an impossible answer has more relevance today.
Magee, Brian. The Story of Philosophy. London: DK Books, 1998; page 19. Magee (1930-2019) was a British philosopher, politician and broadcaster known for popularising philosophy by bringing it to a mainstream audience. His obituary: Magee Obituary
Jesus Bryan, just when I think this is one of your recycled early pieces and I read that article on the Simpsons and I know why your Substack remains one of the few that I read every single time. Doh!