UncleEbenezer wrote:XFool wrote:Well, at some level I would consider her correct! But perhaps four times would not really be adequate for drawing that conclusion.
Q. How many throws would it take to convince you?
None.
Why? "None" in the sense that no number would convince you it was unfair? Or none in that you accept it was defined as fair?
UncleEbenezer wrote:You could pose a hypothesis that it is not a fair die, and then test it statistically. But you need to test your hypothesis using new data, not past data that led you to formulate the hypothesis in the first place.
Not sure I understand - you could form the hypothesis with NO past data. Possibly raising the question of why you would consider it not a fair die etc. But then, starting from scratch, even if you could see no reason for it not being fair, you could just be setting out to test if it really IS fair.
UncleEbenezer wrote:Stoppard's Rosencrantz and Guildenstern throw a coin, and get Heads 92 consecutive times.
I wasn't counting when I saw it! OTOH, perhaps the number was mentioned in the script, it was a long time ago.
UncleEbenezer wrote:Is it a fair coin? The chances of that happening with a fair coin are one in 4951760157141521099596496896 (about five million million million million). But if you toss a fair coin an infinite number of times, the chance of 92 consecutive heads happening at some point is 1.0, and the chance of it never happening is zero. This is the principle that's sometimes referred to in terms of infinite monkeys.
But you can't toss a coin an infinite number of times... Even in principle, only the number of times a coin could have been tossed (thermodynamic effects?) since the start of the universe. (The difference between mathematicians & philosophers and physicists & applied engineering?)
UncleEbenezer wrote:The practical effect is that you can say it looks as if it's most unlikely to be a fair coin. But to test that statistically you have to discard the 92 tosses you already know, and start again with a carefully-designed experiment.
You mean you have to account for its characteristics changing over time?
Perhaps, outside philosophy, it's best to simply thoroughly examine the device and reasonably conclude it has no current inherent bias and is not plausibly likely to develop any over time. Then to monitor its output over time to see if there is any detectable bias. Good enough for the Premium Bonds. Well, apart from the more paranoid holders!
UncleEbenezer wrote:With a complex topic like climate change, there's a lot of misinformation and misrepresentation. Not all those who get funded have a clue what they're doing, and journalists who report them talk nonsense more often than not. Result: lots of ammunition for Denialists, who see bogosity and extrapolate from that to claim it's all tainted. The principle that one rotten apple spoils the barrel.
(I'm sure didds and other Fools with a bit of maths and/or stats in our background understand this).