A ball and a bat cost a total of $1.10. The bat costs $1 more than the ball. How much does the ball cost?
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The first time I heard the story of the ball and the bat, it was from a friend who was studying cognitive science at Princeton. She had just read Kahneman’s book and wanted to do the test with me.
Like most people, I gave an instinctive response. I listened to my System 1 without knowing it was called System 1. Without thinking, without doing any calculations, I gave the first answer that popped into my head: “5¢.”
I felt that my answer annoyed my friend but I didn’t immediately know why. She took the time to explain what was up. I was supposed to answer “10¢,” or at least take a few seconds before answering “5¢.” At any rate, there was no way I was supposed to answer “5¢” immediately, without taking the time to think about it. That was simply not allowed. A guy had even won the Nobel Prize for showing it was impossible.
The author is a mathematician and has automatized some math skills such that he could get the correct answer intuitively.
The article is about how it’s possible to train your intuition.
Nothing is counterintuitive by nature—something is only ever counterintuitive temporarily, until you’ve found means to make it intuitive.
This quote fits with this article by Elliot: Rational Confidence and Standards for Knowledge. No topic is inherently difficult or counterintuitive, it’s about your knowledge and skill. A society with better math education could have almost every adult answer the ball and bat question intuitively and get it right.
If people are universal knowledge creators then the variations of skills and personalities people can have are infinite. When psychologist do studies they aren’t really testing human nature, but some specific culture. A possible type of person or society is one that can answer the ball and bat question intuitively and get it right. The same should apply to every single bias that might be claimed is part of human nature.
My numeric intuition isn’t all that remarkable. I wouldn’t be able to do the calculation if the ball and bat together cost $2,734.18 and the bat cost $967.37 more than the ball.
If people were asked this question they wouldn’t answer using their intuition. But with 1 dollar and 10 cents they have faulty confidence in their intuition. They’re not operating on proper knowledge. Judging when your intuition is reliable is an important skill.
A nice quote from the article on error correcting your intuition:
Nothing’s more exciting than a big glaring error: it’s always a sign that I’m not looking at things in the right way, and that it’s possible to see them more clearly. When I’m able to put my finger on an error in my intuition, I know it’s good news, because it means that my mental representations are already in the process of reconfiguring themselves.
I don’t think I would’ve detected the error without being primed either. And I don’t detect as many errors like Elliot does:
Which means I’m not good enough at logic! Otherwise I would’ve detected more like Elliot does. So knowing Elliot’s perspective on the commonality of logic errors, I’m more interested in learning formal logic and automatizing it.