Intuition pump: my theory says that the sequence of coinflips HHHTHHTHTT-THHTHHHTT-TTHTHTTTTH-HTTTHTHHHTT, which I just observed, should happen about once every 7 million years.
Intuition pump: if I choose an interesting sequence of coinflips in advance, I will never see it actually happen if the coinflips are honest. There aren’t enough interesting sequences of 40 coinflips to ever see one. Most of them look completely random, and in terms of Kolmogorov complexity, most of them are: they cannot be described much more compactly than by just writing them out.
Now, we have a good enough understanding of the dynamics of tossed coins to be fairly confident that only deliberate artifice would produce a sequence of, say, 40 consecutive heads. We do not have such an understanding of the sort of things that appear in the news as “should only happen every N years”.
There aren’t enough interesting sequences of 40 coinflips to ever see one.
Every sequence of 40 coin flips is interesting. Proof: Make a 1 to 1 relation on the sequence of 40 coin flips and a subset of the natural numbers, by making H=1 and T=0 and reading the sequence as a binary representation. Proceed by showing that every natural number is interesting.
Intuition pump: if I choose an interesting sequence of coinflips in advance, I will never see it actually happen if the coinflips are honest. There aren’t enough interesting sequences of 40 coinflips to ever see one. Most of them look completely random, and in terms of Kolmogorov complexity, most of them are: they cannot be described much more compactly than by just writing them out.
Now, we have a good enough understanding of the dynamics of tossed coins to be fairly confident that only deliberate artifice would produce a sequence of, say, 40 consecutive heads. We do not have such an understanding of the sort of things that appear in the news as “should only happen every N years”.
Feynman on the same theme.
Every sequence of 40 coin flips is interesting. Proof: Make a 1 to 1 relation on the sequence of 40 coin flips and a subset of the natural numbers, by making H=1 and T=0 and reading the sequence as a binary representation. Proceed by showing that every natural number is interesting.