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# Knowledge and Uncertainty

via Brilliant

### Overview

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.

### Syllabus

• Introduction: Meet a new way of thinking about uncertainty!
• Guess Who: What is the fastest way to learn?
• Find the Counterfeit Coin: Apply information theory to solve a classic puzzle.
• What's the Fastest Language?: See how Information Theory even governs the way we speak.
• 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.
• Measuring Uncertainty: Learn why a 'bit' is the perfect unit for measuring your uncertainty.
• Information Decreases Uncertainty: How much does this hunch decrease your uncertainty?
• Entropy: What is the true meaning of entropy?
• Compression: What has Information Theory got to do with computers and the byte sizes of your files?
• A Trit of Information: How do we convert from bits to another unit of information?
• 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?
• A Medical Examination: Should you believe that you have a rare and terrible disease if your test says so?
• Bayes' Rule: How to update your beliefs when you learn something new.
• The Monty Hall Problem: See how Bayes' Rule sheds light on this perplexing probability problem.
• The Problem with P-values: Bayesian statistics can make up for shortcomings in how research is reported.
• The Cause of Bayes' Rule: Thinking about the causes of things gives us an alternative (and more natural) way to understand Bayes' rule.

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