Knowledge and Confidence

Experts are experts precisely because they have more information, they’ve absorbed the relevant theories, and they’ve had their ideas critically analyzed by other experts. They have cultivated a deeper understanding than laypeople. Consequently, they are more entitled to their opinions than laypeople are. Continue reading

Entitled to Your Opinion

“There is no royal road to geometry”, said Euclid to King Ptolemy. The King was trying to learn mathematics from Euclid, but he found it too difficult and had asked Euclid for an easier way to learn it. And of course, Euclid was right. There are no oracles, no shortcuts to knowledge, no quick trick for telling a truth from a lie. There is no substitute for an actual understanding of a subject. And an understanding is what entitles one to an opinion. Continue reading

Fighting for Your Beliefs

When someone disagrees with you it can feel like they’re attacking you, so it’s a natural tendency for humans to think of debates as a conflict. This is a most unfortunate human tendency. If you think the goal of debate is to defeat the people who disagree with you, then debating is not an attempt to determine who is correct, but merely a contest of argumentative skill. Continue reading

Bayes’ Formula Made Easy

Scientists often use Bayes’ formula when they test their scientific theories, but the formula doesn’t just apply in the realm of science. Bayes’ formula can also be useful in thinking about many situations encountered in daily life. Even if you can only make educated guesses about the probabilities involved, Bayes’ formula can improve the accuracy and consistency of those guesses. We’ll look at one of the simplest ways to use Bayes formula. Continue reading

Belief and Expectation

Your beliefs are your mental model of the world. When you see something happen in the world, your beliefs can often give you a way to explain it. You see water droplets turn sunlight into a rainbow. But having a good mental model of the world isn’t just about being able to explain things. Just as important – perhaps more important – are the things your beliefs can’t explain. In other words, your beliefs should narrow down the list of possible things you expect to observe. Continue reading

Three Ingredients

Imagine that I claim to have invented a new test for diagnosing some disease. Unlike many other tests, my test never gives false positives. In statistics we say the test is 100% specific; if you don’t have the disease, my test always correctly says you do not have the disease. This may seem like quite a remarkable achievement. Assuming my claims are true, would you rely on this test to diagnose you? Continue reading

Probability and Scientific Values

Science is often described as having a set of values or rules that guide the scientist in their quest for knowledge. Through history the great figures of science, from Aristotle to Bacon, Galileo and Descartes, to Einstein, Feynman and Sagan, have championed these values. These are used to justify the methods and reasoning that scientists use to understand the world, but this leads to the question: what is the justification for these values themselves? Continue reading

Considering the Alternative

If you were faced with a choice, and receiving $100 was one option, would you choose it? If the other choice was to receive $1000, you probably wouldn’t; if the alternative was getting kicked in the shin, you’d probably take the hundred bucks. In decision making, different options can not be rationally evaluated on their own, only compared to each other. What’s important are the differences between the expected outcomes of the choices. The best choice is the one that tends to produce the best outcome relative to the other options. Continue reading