For the Monty Hall problem in particular, I like to imagine more doors. Imagine 1 car and 99 goats. You choose a door with a 1/100 chance it is car, and 99/100 chance the car is one of the other 99 doors. Then, Monty reveals 98 goats, chucking out all the noise, and squashing all that 99/100 goodness down into 1 door. Switch!
I find it helps me. But, when I use this model to try to help other people, it doesn't. They still cannot see why it does not become 50:50. Barbie was right, math is hard.
That's a great idea! I really like it, and it follows the pattern of good thought experiments by taking a real phenomenon and exaggerating it so our fast brain can get some intuitive traction (bad thought experiments take something impossible and assume it is real).
I would really expect this argument to work, and yeah, that it doesn't illustrates even more powerfully how hard this stuff it.
The first time I heard this was from a math teacher at the old Malaspina College. He was telling it to prove that Liberal Arts students couldn't understand science and math properly and were easily fooled by real life situations. He told the instructions incorrectly (everybody does), but I didn't know that until I read the Wiki, which does a great job of explaining the instructions. Nor is it a simple straightforward problem that everyone will understand if they just have enough math. Really, it's a verbal problem. Almost no one (including me) understands what's going on without a diagram (like the "simple solutions" part of the WIki). In fact, I'd say that without a diagram like the "simple solutions" diagram, there's no way you could answer this. In that sense, it's like the word problems that my daughter brings home from school. Even in Grade 4, there are questions so complex that I need a diagram to answer. But maybe that's your point.
That is indeed my point. I'm an expert at this stuff. I was fairly expert when I first encountered the problem. It still took me DAYS to understand what was going on with it, and it's a simple problem! This stuff is just hard, but we need to get way better at it if we're ever going to have a society that doesn't keep tripping over its own feet and doing all kinds of damage in the process.
For the Monty Hall problem in particular, I like to imagine more doors. Imagine 1 car and 99 goats. You choose a door with a 1/100 chance it is car, and 99/100 chance the car is one of the other 99 doors. Then, Monty reveals 98 goats, chucking out all the noise, and squashing all that 99/100 goodness down into 1 door. Switch!
I find it helps me. But, when I use this model to try to help other people, it doesn't. They still cannot see why it does not become 50:50. Barbie was right, math is hard.
That's a great idea! I really like it, and it follows the pattern of good thought experiments by taking a real phenomenon and exaggerating it so our fast brain can get some intuitive traction (bad thought experiments take something impossible and assume it is real).
I would really expect this argument to work, and yeah, that it doesn't illustrates even more powerfully how hard this stuff it.
The first time I heard this was from a math teacher at the old Malaspina College. He was telling it to prove that Liberal Arts students couldn't understand science and math properly and were easily fooled by real life situations. He told the instructions incorrectly (everybody does), but I didn't know that until I read the Wiki, which does a great job of explaining the instructions. Nor is it a simple straightforward problem that everyone will understand if they just have enough math. Really, it's a verbal problem. Almost no one (including me) understands what's going on without a diagram (like the "simple solutions" part of the WIki). In fact, I'd say that without a diagram like the "simple solutions" diagram, there's no way you could answer this. In that sense, it's like the word problems that my daughter brings home from school. Even in Grade 4, there are questions so complex that I need a diagram to answer. But maybe that's your point.
That is indeed my point. I'm an expert at this stuff. I was fairly expert when I first encountered the problem. It still took me DAYS to understand what was going on with it, and it's a simple problem! This stuff is just hard, but we need to get way better at it if we're ever going to have a society that doesn't keep tripping over its own feet and doing all kinds of damage in the process.