how many times did the explanation just “work out” for no apparent reason
From the examples later in your post, it seems like it might be clearer to say something more like “how many things need to hold about the circuit for the explanation to describe the circuit”? More precisely, I’m objecting to your “how many times” because it could plausibly mean “on how many inputs” which I don’t think is what you mean, and I’m objecting to your “for no apparent reason” because I don’t see what it would mean for an explanation to hold for a reason in this case.
Yes, that’s a clearer way of putting it in the case of the circuit in the worked example. The reason I said “for no apparent reason” is that there could be some redundancy in the explanation. For example, if you already had an explanation for the output of some subcircuit, you shouldn’t pay additional surprise if you then check the output of that subcircuit in some particular case. But perhaps this was a distracting technicality.
From the examples later in your post, it seems like it might be clearer to say something more like “how many things need to hold about the circuit for the explanation to describe the circuit”? More precisely, I’m objecting to your “how many times” because it could plausibly mean “on how many inputs” which I don’t think is what you mean, and I’m objecting to your “for no apparent reason” because I don’t see what it would mean for an explanation to hold for a reason in this case.
Yes, that’s a clearer way of putting it in the case of the circuit in the worked example. The reason I said “for no apparent reason” is that there could be some redundancy in the explanation. For example, if you already had an explanation for the output of some subcircuit, you shouldn’t pay additional surprise if you then check the output of that subcircuit in some particular case. But perhaps this was a distracting technicality.