When I say this I’m expressing that I see no practical reason to distinguish between 1 in a trillion and 1 in a googol because the rest of my behavior will be the same anyway. I think this is totally reasonable because quantifying probabilities is a lot of work.
I mean more or less the same thing, but I think I’m lazier <3
I’ve noticed myself say epsilon as a placeholder for “that is not in an event space I’ve thought about and so I was probably acting like the probability was 0%”...
...then I think rigorously for an hour and end up with a probability as high as 10% or 7% or so. So for me I guess one hundred and one trillion are “roughly equally too big to really intuit without formal reasoning”?
Part of the challenge is having a habit that works with a range of possible situations and audiences.
Some people say 100% (or 0%) and are wrong about 25% of the time in such cases.
This is so common that if I just say “100%” near another person who is probabilistically numerate and calibrated on normal humans, they might hear “100%” as “75% (and this person cannot number real good (though they might human very well))”.
Some people say 99.999% as a way to say they are “as absolutely sure one can be, while pragmatically admitting that imperfect knowledge is impossible”…
...but they usually don’t think that they’ve just said that “in 49,000 tries the thing would probably never be observed, and with 100,000 tries ~1 case would occur, and if you were searching for true cases and each person was a case, then ~70,000 people (out of ~7 billion) are actually probably like this, and if they exist equally among the WEIRD and non-WEIRD then ~3500 people who are positive cases are in the US, and therefore an ad campaign could probably find 100 such people with only a small budget”.
For these reason, I try to say “1 in 50” and 98% roughly interchangeably, and for probabilities more extreme than that I try to stick to a “1 in N” format with round number N.
Like “1 in a trillion” or “1 in 5000″ or whatever is me explicitly trying to say that the main argument in favor of this involves some sort of “mass action” model based on known big numbers and imaginable handfuls of examples.
A person has ~500M “3 second long waking thoughts” per life. There are approximately ~50k municipalities in the US. There are ~10M people in the greater LA region (and in 2010 I could only find ~4 people willing to drive an hour on a freeway to attend a LW meetup). And so on.
Example: There are ~10k natural languages left (and I think only Piraha lacks a word for “four” (Toki Pona is an edge case and calls it “nanpa tu tu” (but Toki Pona is designed (and this is one of the worst parts of its design))). So “based in informed priors” I tend to think that the probability of a language having no word for “four” is roughly 1 in 5000. If betting, I might offer 1 in 500 odds as a safety margin… so “99.8%” probability but better to say “between 1 in 500 and 1 in 15,000″ so that if someone thinks it is 1 in 100,000 they can bet against me on one side and if someone else thinks it is 1 in 100, then I can think about taking both bets and arb them on average :-)
If I say “epsilon” in a mixed audience, some people will know that I’m signaling the ability to try to put high quality numbers on things with effort, and basically get sane results, but other people (like someone higher than me in a company hierarchy who is very non-technical) might ask “what do you mean by epsilon?” and then I can explain that mathematicians use it as a variable or placeholder for unknown small numbers on potentially important problems, and it sounds smart instead of “sounding ignorant”. Then I can ask if it matters what the number actually might be, and it leads the conversation in productive directions :-)
My guess is that the work of quantifying small probabilities scales up with how small probability is, given the number of rare events that one has to take into consideration. I wonder if this can be estimated. It would be some function of 1/p, assuming a power law scaling of the number of disjunctive possibilities.
When I say this I’m expressing that I see no practical reason to distinguish between 1 in a trillion and 1 in a googol because the rest of my behavior will be the same anyway. I think this is totally reasonable because quantifying probabilities is a lot of work.
I mean more or less the same thing, but I think I’m lazier <3
I’ve noticed myself say epsilon as a placeholder for “that is not in an event space I’ve thought about and so I was probably acting like the probability was 0%”...
...then I think rigorously for an hour and end up with a probability as high as 10% or 7% or so. So for me I guess one hundred and one trillion are “roughly equally too big to really intuit without formal reasoning”?
Part of the challenge is having a habit that works with a range of possible situations and audiences.
Some people say 100% (or 0%) and are wrong about 25% of the time in such cases.
This is so common that if I just say “100%” near another person who is probabilistically numerate and calibrated on normal humans, they might hear “100%” as “75% (and this person cannot number real good (though they might human very well))”.
Some people say 99.999% as a way to say they are “as absolutely sure one can be, while pragmatically admitting that imperfect knowledge is impossible”…
...but they usually don’t think that they’ve just said that “in 49,000 tries the thing would probably never be observed, and with 100,000 tries ~1 case would occur, and if you were searching for true cases and each person was a case, then ~70,000 people (out of ~7 billion) are actually probably like this, and if they exist equally among the WEIRD and non-WEIRD then ~3500 people who are positive cases are in the US, and therefore an ad campaign could probably find 100 such people with only a small budget”.
For these reason, I try to say “1 in 50” and 98% roughly interchangeably, and for probabilities more extreme than that I try to stick to a “1 in N” format with round number N.
Like “1 in a trillion” or “1 in 5000″ or whatever is me explicitly trying to say that the main argument in favor of this involves some sort of “mass action” model based on known big numbers and imaginable handfuls of examples.
A person has ~500M “3 second long waking thoughts” per life. There are approximately ~50k municipalities in the US. There are ~10M people in the greater LA region (and in 2010 I could only find ~4 people willing to drive an hour on a freeway to attend a LW meetup). And so on.
Example: There are ~10k natural languages left (and I think only Piraha lacks a word for “four” (Toki Pona is an edge case and calls it “nanpa tu tu” (but Toki Pona is designed (and this is one of the worst parts of its design))). So “based in informed priors” I tend to think that the probability of a language having no word for “four” is roughly 1 in 5000. If betting, I might offer 1 in 500 odds as a safety margin… so “99.8%” probability but better to say “between 1 in 500 and 1 in 15,000″ so that if someone thinks it is 1 in 100,000 they can bet against me on one side and if someone else thinks it is 1 in 100, then I can think about taking both bets and arb them on average :-)
If I say “epsilon” in a mixed audience, some people will know that I’m signaling the ability to try to put high quality numbers on things with effort, and basically get sane results, but other people (like someone higher than me in a company hierarchy who is very non-technical) might ask “what do you mean by epsilon?” and then I can explain that mathematicians use it as a variable or placeholder for unknown small numbers on potentially important problems, and it sounds smart instead of “sounding ignorant”. Then I can ask if it matters what the number actually might be, and it leads the conversation in productive directions :-)
My guess is that the work of quantifying small probabilities scales up with how small probability is, given the number of rare events that one has to take into consideration. I wonder if this can be estimated. It would be some function of 1/p, assuming a power law scaling of the number of disjunctive possibilities.