Depth Confusion

post by Richard Henage (richard-henage) · 2023-10-17T06:06:01.292Z · LW · GW · 1 comments

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I noticed I was getting confused about exponential growth scenarios. I'll try to put down my reasoning here, although it seems like a very obvious mistake when typed out. 

Should I give to charity, or be a teacher and inspire multiple other people to give to charities? Like, isn't the teacher better? No, because I can give to an efficient charity that will spread information and convince even more people to give to charity than being a teacher would^[1]. But if I was a teacher, I could convince people to give to that charity and therefore make an even bigger impact! 

And on and on. Where's the flaw? 

I'm skipping down the pyramid as if the level number doesn't matter. Sure, being a teacher could inspire X students to give to charity, but giving to an information-spreading charity would inspire 2X^[1] students to give to charity. Going down the pyramid once further, in the teacher scenario, those X students could, at best, give to the information-spreading charity and cause 2(X^2) people to give to charity, but in the charity scenario, the 2X information-readers could give to the information-spreading charity and cause 4(X^2) people to give to charity.

Depth confusion, a bit like accidentally skipping down the page to the next line and getting a garbled sentence.

1. ^{^}

   I don't actually think it's that simple

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