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.
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.