OK, maybe the quote isn’t legit, but after all quite a lot of our favorite quotes are misquotations—that’s not the point. It’s an interesting thought even if no Nobel laureate ever said it. Is it ridiculous? It makes a lot of sense to me.
It’s ridiculous if taken literally as a universal prior or bound, because it’s very easy to contrive situations in which refusing to give probabilities below 1/10^12 lets you be dutch-booked or otherwise screw up—for example, log2(10^12) is 40, so if I flip a fair coin 50 times, say, and ask you to bet on every possible sequence.… (Or simply consider how many operations your CPU does every minute, and consider being asked “what are the odds your CPU will screw up an operation this minute?” You would be in the strange situation of believing that your computer is doomed even as it continues to run fine.)
But it’s much more reasonable if you consider it as applying only to high-level theories or conclusions of long arguments which have not been highly mechanized; I discuss this in http://www.gwern.net/The%20Existential%20Risk%20of%20Mathematical%20Error and see particularly the link to “Probing the Improbable”.
But it’s much more reasonable if you consider it as applying only to high-level theories
Yes, that’s how I read it. Obviously it doesn’t literally mean you can’t be very sure about anything; the message is that science is wrong very often and you shouldn’t bet too much on the latest theory. So even if it’s a complete misquote, it’s a nice thought.
In addition to gwern’s reply, if you read it as 10-to-1 to 12-to-1 odds, or even 1012-to-1 odds, and not 10^12-to-1 odds, then obviously there are lots of physical theories that deal with events that are less likely than 1/1012. And lots of experiments whose outcome people are more than 1012-to-1 sure about, and they are right to be so sure.
You quoted the most ridiculous figure, that of 10-to-1 or 12-to-1. I’m quite legitimately more than 12-to-1 sure about some things in physics, and I’m not even a physicist! The Wikipedia talk quote makes the point that all three possible quotes are to be found on the internet.
OK, maybe the quote isn’t legit, but after all quite a lot of our favorite quotes are misquotations—that’s not the point. It’s an interesting thought even if no Nobel laureate ever said it. Is it ridiculous? It makes a lot of sense to me.
It’s ridiculous if taken literally as a universal prior or bound, because it’s very easy to contrive situations in which refusing to give probabilities below 1/10^12 lets you be dutch-booked or otherwise screw up—for example,
log2(10^12)is 40, so if I flip a fair coin 50 times, say, and ask you to bet on every possible sequence.… (Or simply consider how many operations your CPU does every minute, and consider being asked “what are the odds your CPU will screw up an operation this minute?” You would be in the strange situation of believing that your computer is doomed even as it continues to run fine.)But it’s much more reasonable if you consider it as applying only to high-level theories or conclusions of long arguments which have not been highly mechanized; I discuss this in http://www.gwern.net/The%20Existential%20Risk%20of%20Mathematical%20Error and see particularly the link to “Probing the Improbable”.
Yes, that’s how I read it. Obviously it doesn’t literally mean you can’t be very sure about anything; the message is that science is wrong very often and you shouldn’t bet too much on the latest theory. So even if it’s a complete misquote, it’s a nice thought.
In addition to gwern’s reply, if you read it as 10-to-1 to 12-to-1 odds, or even 1012-to-1 odds, and not 10^12-to-1 odds, then obviously there are lots of physical theories that deal with events that are less likely than 1/1012. And lots of experiments whose outcome people are more than 1012-to-1 sure about, and they are right to be so sure.
You quoted the most ridiculous figure, that of 10-to-1 or 12-to-1. I’m quite legitimately more than 12-to-1 sure about some things in physics, and I’m not even a physicist! The Wikipedia talk quote makes the point that all three possible quotes are to be found on the internet.