Ask HN: Good Counter-Intuitive Arguments? | Hacker News Reader

Ask HN: Good Counter-Intuitive Arguments?

1 pointkeepamovin8 comments

I'm looking for a collection of such, or maybe this Q will make one here. Any topic area.

You might get a better response by providing an example of one such counter-intuitive argument that you find good.

Unfortunately all the ones I have in mind are too controversial and would only elicit a negative response. Or in the very least cause upset to some, which would only be counter productive haha! :)

Yeah it's just difficult to determine what one views as "counter-intuitive".

I guess the birthday paradox is one such example (https://en.wikipedia.org/wiki/Birthday_problem) but if you've taken a course in probability theory then it doesn't really seem counter-intuitive.

There's quite a few veridical paradoxes in probability theory

Oh good thinking! :) Yes, that reminds me of one. The "two random choice" thing, which I think is connected to the "Pick a Door" problem, of famous Math Lady Column infamy. I'm not familiar with it if anyone can give a good, Here is the problem, here is the regular intuition, and here finally is the counter intuition that's actually correct about it.

But haha I was just thinking about math stuff at all. More like sociological, biological, systems, anything!

think the trolley problem. but now there is the same number of people on both tracks. is changing the course of the trolley worse than doing nothing at all? why or why not? i think that's a nice one to think about...

Monty Hall problem is a classic one, if that's the sort of thing you mean?

Haha cool! I wasn't asking for people to read my mind, and wasn't thinking math specifically, just trying to open it up to all areas. But I will check this out now! :) Do you have a good 'glib' statement, like: 1) the problem, 2) the regular (but incorrect) intuition, 3) the counter-intuition, that's actually correct ? :)

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Regular intuition: switching doors doesn't matter, you have a 50/50 shot either way.

Counter-intuition: probably just check out the wikipedia article, there's a few different approaches.

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