If I flip a coin 100 times and get all heads, there are many, many hypotheses that suddenly get a lot more plausible. Perhaps the coin is strongly biased. In fact, a weak prior of slight bias will, post-update, seem much more plausible than the fair coin. Perhaps it’s a double headed coin, and in my inspection I failed to notice that. It seems vanishingly unlikely that I would miss that on repeated inspection… but I’m still more inclined to believe that, than a mathematically fair coin coming up heads every time. Perhaps I’ve unconsciously learned how to predictably flip a coin. Perhaps I’ve failed horribly at counting, and actually only flipped the coin 10 times. Perhaps any of the above are combined with my not noticing a tails or ten appear in the result string.
In other words, exceedingly unlikely events will make me doubt my sanity before they make me start doubting math.
I assumed you did. I just thought it worth explicitly adding to the discussion that considering only some extraordinarily weird ideas when discussing extraordinarily weird events is a form of bias that seems to run rampant in hypotheticals around here. It’s not just the one aspect you mentioned where our confidence should be shaken by such a result.
If I flip a coin 100 times and get all heads, there are many, many hypotheses that suddenly get a lot more plausible. Perhaps the coin is strongly biased. In fact, a weak prior of slight bias will, post-update, seem much more plausible than the fair coin. Perhaps it’s a double headed coin, and in my inspection I failed to notice that. It seems vanishingly unlikely that I would miss that on repeated inspection… but I’m still more inclined to believe that, than a mathematically fair coin coming up heads every time. Perhaps I’ve unconsciously learned how to predictably flip a coin. Perhaps I’ve failed horribly at counting, and actually only flipped the coin 10 times. Perhaps any of the above are combined with my not noticing a tails or ten appear in the result string.
In other words, exceedingly unlikely events will make me doubt my sanity before they make me start doubting math.
Agreed with all of that. (Not sure if you think we disagree on any of it.)
I assumed you did. I just thought it worth explicitly adding to the discussion that considering only some extraordinarily weird ideas when discussing extraordinarily weird events is a form of bias that seems to run rampant in hypotheticals around here. It’s not just the one aspect you mentioned where our confidence should be shaken by such a result.
Ah, gotcha… sure, agreed on all counts.