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Blink 3 of 8 - The 5 AM Club
by Robin Sharma
Listen to the Intro
Shape summary
Jordan Ellenberg
The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else
26 mins
Topics
Table of Contents
Shape
Summary of 9 key ideas
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Key idea 1 of 9
Anywhere there’s a notion of distance, there’s geometry.
In Greek, the word “geometry” means “measuring the Earth.” When we examine the geometry of something, that’s precisely what we’re doing – although not always literally.
A patch of land, a set of people, a team of horses – we can assign a geometry to each of them. All we have to do is define our metric – that is, the number we’re using to signify the distance between any two points. Whatever metric we choose results in different geometry.
For instance, we might look at two points on a map through the “crow-fly” metric, in which distance is the length of a straight line connecting those points. Or your metric could be the distance between two places on an alphabetical list of all US cities. By this metric, Los Angeles is closer to New York than it is to San Francisco.
The key message here is: Anywhere there’s a notion of distance, there’s geometry.
It’s not just places that can have a geometry. People can, too – say, actors. To study the geometry of actors, we just need a metric to measure how “far apart” they are.
In fact, there’s already a metric for this called the costar distance. Two actors form a link when they appear in a movie together. The distance between any two actors is the smallest number of links that joins them.
So, for instance, the distance between George Reeves and Keanu Reeves is 2. How? Well, George appeared in From Here to Eternity with Jack Warden, who was in The Replacements with Keanu.
What about the geometry of a deck of cards? It’s just like the geometry of movie stars, except on a much bigger scale. The “points” are all the different ways a standard fifty-two card deck can be arranged – which is a huge, sixty-seven-digit number written as 52!, or 52 factorial.
Now we’ve defined the points in our deck of cards. Next, we need a way to think about the distance between them. That’s where shuffling comes in, specifically a riffle shuffle, where you cut the deck into two stacks of any size and then recombine them. If you can riffle shuffle the deck once to get to another, specific ordering, those two orderings are linked. The distance between them is the number of riffle shuffles it takes to get from one ordering to the other.
Cities, actors, decks of cards – what else do you think has a geometry?
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What is Shape about?
Shape (2021) is a love letter to geometry, addressed to those who have – or thought they had – sworn off math forever. Accessible and fascinating, it shows how geometry underpins not just objects in the physical world, but also things like games, pandemics, artificial intelligence, and even American democracy. When we understand geometry, we understand a bit more about almost everything.
Who should read Shape?
- Math haters convinced that geometry is boring
- Math lovers interested in how geometry intersects with other subjects
- The perennially curious
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