Your “harmfulness” criteria will always have some false negative rate.
If you incorrectly classify a harmful plan as beneficial one time in a million, in the former case you’ll get 10^44 plans that look good but are really harmful for every one that really is good. In the latter case you get 10000 plans that are actually good for each one that is harmful.
This would imply a fixed upper bound on the number of bits you can produce (for instance, a false negative rate of 1 in 128 implies at most 7 bits). But in practice you can produce many more than 7 bits, by double checking your answer, combining multiple sources of information, etc.
Combining multiple source of information, double checking etc are ways to decrease error probability, certainly. The problem is that they’re not independent. For highly complex spaces not only does the number of additional checks you need increase super-linearly, but the number of types of checks you need likely possibly also increases super-linearly.
Your “harmfulness” criteria will always have some false negative rate.
If you incorrectly classify a harmful plan as beneficial one time in a million, in the former case you’ll get 10^44 plans that look good but are really harmful for every one that really is good. In the latter case you get 10000 plans that are actually good for each one that is harmful.
This would imply a fixed upper bound on the number of bits you can produce (for instance, a false negative rate of 1 in 128 implies at most 7 bits). But in practice you can produce many more than 7 bits, by double checking your answer, combining multiple sources of information, etc.
Combining multiple source of information, double checking etc are ways to decrease error probability, certainly. The problem is that they’re not independent. For highly complex spaces not only does the number of additional checks you need increase super-linearly, but the number of types of checks you need likely possibly also increases super-linearly.
That’s my intuition, at least.