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063 Jordan Ellenberg: Shape

The hidden geometry of shapes is fundamental to understanding how the world works.

Jordan Ellenberg: Shape


Jordan Ellenberg explores how the hidden geometry of shapes is fundamental to understanding how the world works. From the way we interpret data and make decisions to the way organisms evolve and interact with their environment, geometry plays a crucial role in shaping our world. Ellenberg uses examples from fields as diverse as mathematics, biology, politics, and finance to show how understanding the geometry of shapes can help us solve problems, make better decisions, and gain new insights into the nature of reality.


Title: "Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else"

Author: Jordan Ellenberg

Publishing Year: 2021

Publisher: Penguin Press

Length in Hours: 14 hours and 23 minutes

5 main ideas

  1. Geometry is not just a branch of mathematics, but a fundamental aspect of the way the world works.
  2. The shapes of things can reveal important information about their properties and behaviors.
  3. Understanding the geometry of shapes can help us solve problems and make better decisions.
  4. Geometry plays a crucial role in fields as diverse as biology, politics, and finance.
  5. The study of geometry can help us gain new insights into the nature of reality and the way we perceive the world.
Jordan Ellenberg: Shape

5 funny quotes

  1. "Geometry is like a secret code that the universe uses to communicate with itself."
  2. "Shapes are like fingerprints – each one is unique, and they can tell us a lot about the things they belong to."
  3. "Geometry is like a treasure map – it can lead us to hidden treasures of knowledge and insight."
  4. "Shapes are like puzzle pieces – when we put them together, they can reveal a bigger picture that we didn't see before."
  5. "Geometry is like a magic wand – when we wave it, we can make invisible connections between things visible."

5 thought-provoking quotes​

  1. "Shapes are the language of the universe, and understanding their geometry is the key to unlocking its secrets."
  2. "The geometry of shapes can reveal hidden patterns and connections that are invisible to the naked eye."
  3. "Geometry is not just a branch of mathematics, but a way of seeing and understanding the world around us."
  4. "The shapes of things can tell us a lot about their properties and behaviors, and can help us make better decisions and solve problems more effectively."
  5. "The study of geometry is not just about measuring angles and distances, but about gaining a deeper understanding of the nature of reality itself."

5 dilemmas

  1. How can we use geometry to create better visualizations of complex data and information?
  2. How can we apply the principles of geometry to solve real-world problems, such as climate change and economic inequality?
  3. How can we balance the benefits of using geometry to gain new insights with the risks of oversimplifying complex phenomena?
  4. How can we teach geometry in a way that is engaging and accessible to people of all ages and backgrounds?
  5. How can we ensure that the study of geometry remains relevant and impactful in a world that is increasingly driven by technology and data?

5 examples

  1. Fibonacci sequence – a mathematical sequence that appears in many natural shapes and patterns.
  2. Fractals – geometric shapes that repeat at different scales, found in everything from coastlines to tree branches.
  3. Game theory – a branch of mathematics that uses geometry to model strategic decision-making.
  4. DNA – the double helix shape of DNA molecules contains important information about how genetic information is stored and replicated.
  5. Stock market trends – understanding the geometric shapes of stock market trends can help investors make better decisions about when to buy and sell.

Referenced books

  1. "The Wealth of Nations" by Adam Smith
  2. "Thinking, Fast and Slow" by Daniel Kahneman
  3. "The Elements of Style" by William Strunk Jr. and E.B. White
  4. "The Structure of Scientific Revolutions" by Thomas S. Kuhn
  5. "Geometry and the Visual Arts" by Dan Pedoe

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"Geometry is not just a branch of mathematics, but a way of seeing and understanding the world around us."

Jordan Ellenberg: Shape
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