That sounds like a ridiculous thing to say and I can’t really steelman it.
Do you have a reliable source for this quote? The Wikipedia talk page for the Rutherford article contains this exchange:
Now that we have dealt with the statistics quote, let’s move on to the next quote, which is purportedly: You should never bet against anything in science at odds of more than about 1012 to 1. The number 1012 seems oddly precise, although the cited collection of quotes supports it, and yesterday editor 134.225.100.110 changed it to 10-12, which was reverted a few hours later by Gadfium. I suggest that what he really said was not 1012 (one thousand and twelve), and not 10-12 (ten to twelve), but rather 1012 (ten to the twelfth), which seems a much more likely thing for a physicist to say. A brief Google search turned up evidence for all 3 hypotheses (!), all in what appear to be not very reliable quote collections. Can anyone find a more reliable source, such as a book about Rutherford, to check what he actually did say? Dirac66 (talk) 19:35, 12 October 2012 (UTC)
I reverted because the source given didn’t support the change. Now that you’ve raised the matter, I see that all three variants do appear in Google, and I agree finding an authoritative version is desirable
The quote itself, while still on the page, references this site which is an unsourced quote collection.
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.
Ernest Rutherford
That sounds like a ridiculous thing to say and I can’t really steelman it.
Do you have a reliable source for this quote? The Wikipedia talk page for the Rutherford article contains this exchange:
The quote itself, while still on the page, references this site which is an unsourced quote collection.
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.