The main advantage NumPy brings is speed…although it also makes dealing with arrays easier and has lots of built-in functionality, saving you time having to write your own functions!
I find it impossible to believe that someone with a phD in math would argue this wrong. It's like problem #1 in Chapter #1 of any undergraduate text on probability. In fact I'd be surprised if a high schooler taking AP statistics got this wrong honestly.
Thanks for writing the article though. This really is a litmus test on whether someone has a basic understanding of probability and should required learning in high school imo. So many great lessons in this simple thought experiment.
But the main point for me is one I briefly mention in the conclusion: humans don't have an innate intuition for statistics. Even the best statisticians, if they go on intuition, would get many outcomes wrong. I think I recall reading this view in Daniel Kahneman's book, too
I think it says more about the over-confidence of people who think they know best and are always right. This was from a pre-social media era (early 1990s, I believe), but they're the same kind of people who live on social media today and who confidently state rubbish because they fail to think, or are too blinded by something or other…
The craziest thing about all those people bashing her was these were supposed to be people with phD's. Any one of them could have provided a proof of why she was wrong if they were correct. That is literally the protocol for any mathematical argument.
In the field of mathematics, especially postgraduate level, it is disturbing to see that many 'academics' skip the part of proving their statement or even providing some sort of logical counterargument of hers.
Thanks again for posting this article. I learned a lot here. I sincerely thought the Monte Hall problem was just a canonical problem in probability mainly used to show the failure of intuition even in the simplest bayesian example. Similar to the problems where you can show 99% effective is misleading...
Arguing from a point of authority is a very dangerous thing.
Or, in some cases, are so used to being legitimately right most of the time that they become blind to the possibility of ever being wrong. A major trap for smart people.
I didn't use np, but I did generate an array:
tries = []
for n in range(n_times+1):
____doors = [goat, goat, goat]
____doors[randint(0,2)] = 'car'
____tries.append(doors)
(I really wish Substack had better a comment interface!)
The main advantage NumPy brings is speed…although it also makes dealing with arrays easier and has lots of built-in functionality, saving you time having to write your own functions!
Oh, no doubt. I rarely need it in my dabbling, so it’s just not my first go-to. 😀
Just as an aside:
dpick = randint(0,2)
dopen = door_with_a_goat(dpick)
dswap = 3 - (dpick + dopen)
I find it impossible to believe that someone with a phD in math would argue this wrong. It's like problem #1 in Chapter #1 of any undergraduate text on probability. In fact I'd be surprised if a high schooler taking AP statistics got this wrong honestly.
Thanks for writing the article though. This really is a litmus test on whether someone has a basic understanding of probability and should required learning in high school imo. So many great lessons in this simple thought experiment.
But the main point for me is one I briefly mention in the conclusion: humans don't have an innate intuition for statistics. Even the best statisticians, if they go on intuition, would get many outcomes wrong. I think I recall reading this view in Daniel Kahneman's book, too
Wow. I was totally unaware of the backstory about Marilyn Vos Savant. That is disturbing. Again thanks for the article.
I think it says more about the over-confidence of people who think they know best and are always right. This was from a pre-social media era (early 1990s, I believe), but they're the same kind of people who live on social media today and who confidently state rubbish because they fail to think, or are too blinded by something or other…
The craziest thing about all those people bashing her was these were supposed to be people with phD's. Any one of them could have provided a proof of why she was wrong if they were correct. That is literally the protocol for any mathematical argument.
In the field of mathematics, especially postgraduate level, it is disturbing to see that many 'academics' skip the part of proving their statement or even providing some sort of logical counterargument of hers.
Thanks again for posting this article. I learned a lot here. I sincerely thought the Monte Hall problem was just a canonical problem in probability mainly used to show the failure of intuition even in the simplest bayesian example. Similar to the problems where you can show 99% effective is misleading...
Arguing from a point of authority is a very dangerous thing.
Or, in some cases, are so used to being legitimately right most of the time that they become blind to the possibility of ever being wrong. A major trap for smart people.