Basically, this cannot happen if I am updating rationally. You say, “Worse, each additional step is novel; the additional five steps you discovered after completing step 6 didn’t add anything to predict the additional twelve steps you added after completing step 19.” But in fact, it does add something: namely that this task that I am trying to accomplish is very long and unpredictable, and the more such steps are added, the longer and more unpredictable I should assume it to be, even in the remaining portion of the task. So by day 30, I should be expecting about another month, not another 5 days. And if I do this, at some point it will become clear that it is not worth finishing the task, at least assuming that it is not simply the process itself that is worth doing.
I will repeat what I have already repeated several times: Assume that you’re correctly updating.
Your calculation is worthless because it fails to consider the probability that you’re incorrectly updating. The solution is to consider the probability that you’re incorrectly updating.
If you are required to assume that you’re correctly updating, but it’s a real life situation where you aren’t, then there is no solution because you have assumed something false.
I will repeat what I have already repeated several times: Assume that you’re correctly updating.
That assumption may be such an unreasonable assumption in a real-life situation that it makes the conclusion worthless to use in real life.
Okay. You decide your calculations are worthless. How do you decide how to proceed?
Your calculation is worthless because it fails to consider the probability that you’re incorrectly updating. The solution is to consider the probability that you’re incorrectly updating.
If you are required to assume that you’re correctly updating, but it’s a real life situation where you aren’t, then there is no solution because you have assumed something false.