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#5608·Benjamin Davies, about 16 hours agoIn #5555, you say that adding an arbitrary component to an explanation makes it worse. Consider these two explanations of winter:
A: Winter happens because a god repeats a spell seven times.
B: Winter happens because a god repeats a spell seven times, and the spell only works if the god wears a red hat.
Suppose neither story explains why the number must be seven. We could substitute eight, nine, or any other positive whole number while the story still accounts for winter. In B, we could also change the required hat colour without affecting its ability to account for winter.
Both explanations therefore have infinitely many working variations. Your program declares them equally hard to vary.
But B has an additional arbitrary requirement: the hat colour. It is explicitly part of the supposed mechanism, not an unrelated detail added to the wording.
Removing that requirement removes an arbitrary part of the explanation. Yet your program cannot register the improvement, because the variation count remains infinite.
Okay, this is a great additional point that continues along the dealing-with-infinities path.
In #5598, I discussed the case where two explanations both have an infinite number of variants. I also said:
I don't think we need to get into comparing different sizes of infinity here.
In revision #5604, I explicitly added the ability to deal with infinite variations. Nevertheless, your point stands that the current program would treat A and B as equally hard to vary.
I think there's a pretty simple remediation. Rather than only comparing the number of variants, the program can also keep track of how many independently variable parameters have an infinite number of possible values.
So in your example, A has one infinitely variable parameter whereas B has two, so the program would rank A as harder to vary than B.
I think this is a good extension because it captures the improvement you're pointing out. I submitted a revision accordingly: #5609