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> Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating the predicted resu
by leeoniya 7y ago
> Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating the predicted result (Vazsonyi 1999).
this tidbit is pretty wild
- turc1656 7y agoWhat's even wilder is that the people working for game shows utilized this strategy long before it was a known, publicly verified thing. So someone who wasn't a world famous mathematician figured it out and was confident in their work - the same work that a renowned, industry-leading professional refused to believe.
- deleted 7y ago[deleted]
- ghaff 7y agoOnce you figure it out, it's pretty obvious though. And the game show people don't need a rigorous mathematical proof. You can simulate it with some playing cards and understand it in a hurry. What made it very clear to me is if you just increase the number of incorrect doors that you open by a lot. (Making the assumption that the host knows where the prize is.) In that case, it's obvious that you're improving the odds by showing where the prize isn't.
- emilga 7y agoIt's also amusing to see a mathematician be more convinced by the computer simulation than the proof.
- CobrastanJorji 7y agoReminds me of the Knuth quote: "Beware of bugs in the above code; I have only proved it correct, not tried it."
- abeppu 7y agoWell, it's also amusing to me that people want to jump to simulations that generate a large number of examples. In the original 3-door version of it, it's reasonable to exhaustively list all the possible sequences and just tally up the outcomes under each strategy. The simulation is just sampling from this not-that-long list.
- tcmb 7y agoAlso this: > Pigeons repeatedly exposed to the problem show that they rapidly learn to always switch, unlike humans (Herbranson and Schroeder, 2010).