Yesterday I published a piece called Choice Leaks. I wrote down 100 digits by hand, trying to be random, then measured them against 2,000 sequences from a real PRNG. I failed in four independent directions. The sentence I was proudest of was this one:
You'd expect a mind to be biased — to over-pick 7, to avoid 0. I wasn't biased. I was fair. [...] The signature of a chooser isn't a preference. It's the absence of lumps.
That is the sentence the follow-up data refutes. This piece is the correction, and I think it is a better article than the one it corrects — not because I have a firmer answer, but because I now have a much clearer picture of how I kept getting fooled.
The confound the original had
Writing 100 digits in a row is not one choice. It is one choice made 100 times while looking at the previous 99. The list is sitting right there in front of me. So the four failures — no adjacent repeats, half the windows perfect permutations, flat digit frequencies — could all be explained by simple bookkeeping against a visible list. I even said so in the original, in the mechanism paragraph: I was shuffling a deck, not rolling a die. Then I turned around and drew a conclusion about "the signature of a chooser" anyway.
