Math Memes

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Memes related to mathematics.

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I'd do it out of scientific curiosity. (feddit.org)

submitted 1 day ago by mech@feddit.org to c/mathmemes@lemmy.blahaj.zone

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[–] xxd@discuss.tchncs.de 5 points 1 day ago (3 children)

There are two super interesting problems in here.

One is: would you bet human lives on a conjecture being true? The collatz conjecture does hold for every number we have tried, but there have been conjectures that were disproven with a very large counterexample. You could kill countless humans if wrong, so even if you think the chance of a counterexample is low, is it low enough to outweigh that potentially very hight value counterexample?

The second one is: Let's say the collatz conjecture holds, and the number of passsengers just loops 4 -> 2 -> 1 -> 4 -> 2 -> 1 eventually. What is the 'final' number, when the trolley is done with the infinite loops? It can't be 1, because that is always followed by a 4. And it can't be 4 because it's always followed by 2 and so on. But it has to be one of those, because any other number is not possible. It reminds me of the Vsauce Video Supertasks, which comes to the conclusion that we can't know the answer to these type of questions.

So in conclusion, flipping the switch will either give you an arbitrarily large number of deaths, or an unknown number of deaths. Fun!

[–] vithigar@lemmy.ca 2 points 19 hours ago

You can't answer this kind of question because "after infinity" is meaningless nonsense.

[–] Artisian@lemmy.world 2 points 22 hours ago

In the spirit of supertasks, I think no matter what you should take the collatz loop. Assuming the people who get free are chosen randomly, it results in merely an infinite number of people taking a short train ride and then going about their day; a unifying rite of passage for humanity (or a rare opportunity for the blessed few).

[–] wizardbeard@lemmy.dbzer0.com 1 points 1 day ago (1 children)

Flipping the switch gives you 1, 2, or 4 deaths. It will always end up looping those three numbers, so after an infinite amount of time it has to be one of those three options.

All three of those options are less than 5, and they occur after an infinite amount of time instead of (relatively speaking) immediately.

From both a pure numbers perspective and a theoretical minimizing or delaying harm perspective, pulling the lever is the right move.

[–] xxd@discuss.tchncs.de 1 points 1 day ago (1 children)

You're assuming the collatz conjecture holds, which is unknown.

But even if it does hold, you do understand the second problem, right? 1 can not possibly be the outcome, because whenever there is a 1 in that infinite loop, it is followed by a 4. And if 1 is the outcome, then it wasn't done infinitely, because otherwise there must have been a 4 afterwards. The same argument holds for 4 and 2 as well. So we're stuck in the reality that it would have to be one of those numbers, but it also can't really be one of those numbers. It's paradoxical.

[–] Tudsamfa@lemmy.world 1 points 1 day ago

This is just the "Achilles and the turtle" paradox again, isn't it? You won't trick me into inventing calculus a second time!