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The psychology of probability
It is natural to suspect some causative dependence among events: for example, when listening to clicks from one's Geiger counter one is tempted to think that if there has been a long silence then another click is bound to be imminent. On the other hand, it is easy to get into the habit of risking a very low probability event as it agreeably keeps on not occurring.
I thus wonder if the Geiger counter fallacy is useful: if we have some sense of a cosmic book-balancing that resists being pushed far either way then, even if the trials in the latter example are as independent as in the former, perhaps we are nonetheless appropriately disinclined to push our luck unduly. Our poor judgment in one wise may help to counter our poor judgment in another.
I thus wonder if the Geiger counter fallacy is useful: if we have some sense of a cosmic book-balancing that resists being pushed far either way then, even if the trials in the latter example are as independent as in the former, perhaps we are nonetheless appropriately disinclined to push our luck unduly. Our poor judgment in one wise may help to counter our poor judgment in another.