wedrifid comments on Pascal's Mugging: Tiny Probabilities of Vast Utilities - Less Wrong
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That's not the point. None of those probabilities are as strong as 3^^^3. Maybe big, buy not THAT big.
The point is that no more than 1/3^^^3 people have sole control over the life or death of 3^^3 people. This improbability, that you would be one of those very special people, IS big enough.
(This answer fails unless your ethics and anthropics use the same measure. That's how the pig example works.)
I was about to express mild amusement about how cavalier we are with jumping to, from and between numbers like 3^^^^3 and 3^^^3. I had to squint to tell the difference. Then it occurred to me that:
3^^3 is not even unimaginably big, Knuth arrows or no. It's about 1/5th the number of people that can fit in the MCG.
Being cavalier with proofreading =/= being cavalier with number size.
But that is indeed amusing.
Well, I didn't want to declare a proofreading error because 3^^^3 does technically fit correctly in the context, even if you may not have meant it. ;)
I was thinking the fact that we are so cavalier makes it easier to slip between them if not paying close attention. Especially since 3^^^3 is more commonly used than 3^^^^3. I don't actually recall Eliezer going beyond pentation elsewhere.
I know if I go that high I tend to use 4^^^^4. It appeals more aesthetically and is more clearly distinct. Mind you it isn't nearly as neat as 3^^^3 given that 3^^^3 can also be written and visualized conceptually as 3 -> 3 -> 3 while 4^^^^4 is just 4 -> 4 -> 4 not 4 -> 4 -> 4 -> 4.