When I was a child, my grandfather blew my mind with a bit of basic probability and statistics. If you play the lottery, he explained, you might as well just play the numbers 1, 2, 3, 4, 5, 6. Your chance of winning will be exactly the same as with any other particular combination of numbers. I was astonished and incredulous at first, but then I thought it through, and had to admit, of course, that he was right.
Now, years later, I am not so sure anymore.
Have you heard of the Dunning-Kruger effect? It’s an interesting psychological insight about how people’s actual knowledge and skill aligns with their perceived knowledge and skill.
People who are not very skilled at a particular task find it very hard to understand the level of skill needed to do that task well. As a consequence, they fail to recognise a truly skilled practitioner when they see one, and they tend to overestimate their own skill. As a people get better at a particular skill, they also get better at accurately estimating how good they are at it. This is true for a wide range of skills and knowledge areas, including grammar, logical thinking, and even humour. It was first described in a 1999 paper by Kruger and Dunning entitled Unskilled and Unaware of it.
Now, here is the problem.