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Knowledge and Uncertainty

Learn the math behind uncertainty — and how to get rid of it!

Can you put a number on how much you don't know? (Sure you can!) When you learn something new, how should it change your beliefs about how the world works? (It depends!) Is there some formula for that? (Why, yes, there is.)

This course gives you tools for managing uncertainty and interpreting information. You will learn cutting edge mathematics like Information Theory, Bayesian Networks and Causal Inference, but without calculations getting in the way. The emphasis is on applying these ideas to deal with the uncertainty in your life.



Concepts and

  1. 1


    Meet a new way of thinking about uncertainty!

    1. Guess Who

      What is the fastest way to learn?

    2. Find the Counterfeit Coin

      Apply information theory to solve a classic puzzle.

    3. What's the Fastest Language?

      See how Information Theory even governs the way we speak.

  2. 2

    Information Theory

    Learn how to put a number to how uncertain you are about anything, from 'who did it?' to the bits and bytes on your computer.

    1. Included with
      Brilliant Premium

      Measuring Uncertainty

      Learn why a 'bit' is the perfect unit for measuring your uncertainty.

    2. Included with
      Brilliant Premium

      Information Decreases Uncertainty

      How much does this hunch decrease your uncertainty?

    3. Included with
      Brilliant Premium


      What is the true meaning of entropy?

    4. Included with
      Brilliant Premium


      What has Information Theory got to do with computers and the byte sizes of your files?

  3. 3

    Bayesian Thinking

    To have a scientific mindset we need to change our opinions when new information comes in. But should we weigh new evidence against what we already know?

    1. Included with
      Brilliant Premium

      A Medical Examination

      Should you believe that you have a rare and terrible disease if your test says so?

    2. Included with
      Brilliant Premium

      Bayes' Rule

      How to update your beliefs when you learn something new.

    3. Included with
      Brilliant Premium

      The Monty Hall Problem

      See how Bayes' Rule sheds light on this perplexing probability problem.

    4. Included with
      Brilliant Premium

      The Problem with P-values

      Bayesian statistics can make up for shortcomings in how research is reported.