If someone tells you they are trying to save the planet, you should normally treat that with considerable scepticism.
Well, yes, but if someone tells you they are the tallest person in the world, you also should treat that with considerable scepticism. After all, there can only be one person who actually is the tallest person in the world, and it’s unlikely in the extreme that one random guy would be that person. A one-in-six-billion chance is small enough to reject out-of-hand, surely!
The guy looks pretty tall though. How about you get out a tape-measure and then consult the records on height?
“Considerable scepticism” is not an argument against a claim. It is an argument for more evidence. What evidence makes John Baez’s claims that he is trying to save the world more likely to be signalling than a genuine attempt?
If someone I met told me they were the tallest person in the world, I would indeed treat that with considerable scepticism. I would count my knowledge about the 7 billion people in the world as evidence weighing heavily against the claim.
Your 7 billion people are just your prior probability for him being the tallest before you actually examine his size. Once you have seen that he is somewhat tall, you can start developing a better prior:
If he’s taller than any of the people you know that puts him in at least the top three hundredth—so less than 24 million people remain as contenders. If he’s taller than anyone you’ve ever seen, that puts him in at least the top two thousandth—so less than 3.5 million of that 7 billion are actually potential evidence he’s wrong.
So now our prior is 1 in 3.5 million. Now it’s time to look for evidence. At this point, the number of people in the world is irrelevant: it’s already been factored into the equation. What evidence can we use to find our posterior probability?
A cool thing about Bayesian reasoning is that you can cut extreme numbers down to reasonable sizes with some very cheap and very quick tests. In the case of possible ulterior motives for claiming to be saving the world, you can with some small effort distinguish between the “signalling” and “genuine” hypotheses. What tests—what evidence—should we be looking for here, to spot which one is the case?
Well, yes, but if someone tells you they are the tallest person in the world, you also should treat that with considerable scepticism. After all, there can only be one person who actually is the tallest person in the world, and it’s unlikely in the extreme that one random guy would be that person. A one-in-six-billion chance is small enough to reject out-of-hand, surely!
The guy looks pretty tall though. How about you get out a tape-measure and then consult the records on height?
“Considerable scepticism” is not an argument against a claim. It is an argument for more evidence. What evidence makes John Baez’s claims that he is trying to save the world more likely to be signalling than a genuine attempt?
If someone I met told me they were the tallest person in the world, I would indeed treat that with considerable scepticism. I would count my knowledge about the 7 billion people in the world as evidence weighing heavily against the claim.
Your 7 billion people are just your prior probability for him being the tallest before you actually examine his size. Once you have seen that he is somewhat tall, you can start developing a better prior:
If he’s taller than any of the people you know that puts him in at least the top three hundredth—so less than 24 million people remain as contenders. If he’s taller than anyone you’ve ever seen, that puts him in at least the top two thousandth—so less than 3.5 million of that 7 billion are actually potential evidence he’s wrong.
So now our prior is 1 in 3.5 million. Now it’s time to look for evidence. At this point, the number of people in the world is irrelevant: it’s already been factored into the equation. What evidence can we use to find our posterior probability?
A cool thing about Bayesian reasoning is that you can cut extreme numbers down to reasonable sizes with some very cheap and very quick tests. In the case of possible ulterior motives for claiming to be saving the world, you can with some small effort distinguish between the “signalling” and “genuine” hypotheses. What tests—what evidence—should we be looking for here, to spot which one is the case?