# Problem solving, biases, etc.

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I've got some commentary on the explanation, but it has spoilers, so perhaps I'll post it later.  8)

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Very nice, I tested 9 different sequences before guessing

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I got it right from the first guess but only because I already read about it in some book...

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So, this is spoilery:

I don't know that I love this example -- there's a good justification for being "tricked" here (see <a href="http://web.mit.edu/cocosci/Papers/nips99preprint.pdf">this paper</a> for a technical explanation of why). Basically, given the actual "rule" they have selected, you are unlikely to see that particular sequence of numbers if they had just picked a random sample. Much more often than not, given the sequence they presented, the rule that people guess when they're "tricked" is the rule that is statistically most likely given the sequence they've presented.

They're framing the behavior they are observing as "confirmation bias" but I could just as easily give the same example to argue that people are rational b/c they are doing the mathematically correct inference. I think the counter argument they are making is kind of absurd -- yes, disconfirming evidence is often stronger than confirming evidence, but in practice we face an absolutely massive number of inferences like this every day. "Bias" makes it sound like a bad thing.

(not to argue that that the type of reasoning they suggest is a bad thing -- just pointing out that they present this particular example through a very specific lens that supports a pre-determined argument, which is ironic)

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I mean, I've taught that example to make the exact opposite point.

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TheAIGuy,

I completely agree with you. Especially since I got it wrong!

Boiler

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My spoiler'ish comment:

(Don't read before doing the puzzle)

One thing that the explanation does not mention is that examples can only disprove something, they cannot prove anything. And actually, both "nos" and "yes"es can disprove a theory. In this particular case, both "nos" and "yeses" are useful.

Ultimately though there are infinite number of nos and infinite number of yeses, so we can never know the rule by just doing experiments.

The right way to approach this problem is to throw a large number of random experiments at it and only then make a theory.

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