I think that ideas can have a bottleneck effect, but that isn’t the only effect. Some ideas have disjunctive justifications. You might have genetic evidence, and embryological evidence, and studies of bacteria evolving in test tubes, and a fossil record, all pointing towards the theory of evolution. In this case, the chains are all in parallel, so you can add their strength. Even if all the fossil record is completely discounted, you would still have good genetic evidence, and visa versa. If, conditional on the strongest line of evidence being totally discounted, you would still expect the other lines might hold, then the combination is stronger than the strongest.
If I have 10 arguments that X is true, and each argument is 50⁄50 (I assign equal probability to the argument being totally valid, and totally useless) And if these arguments are totally independant in their validity, then P(not X) < 1/1000. Note that total independance means that even when told with certainty that arguments 0 … 8 are nonsense, you still assign 50% prob to argument 9 being valid. This is a strong condition.
Disjunctive arguments are stronger than the strongest link.
On the other hand, Cojunctive arguments are weaker than the weakest link. If I have an argument that has 100 steps, and relies on all the steps holding for the argument to hold, then even if each step is 99% certain, the whole argument is only 37% certain.
For those of you looking for a direct numeric analogue to resistors, there isn’t one. They have similar structure, resistors with x+y and 1/x, probabilities with x*y and 1-x, but there isn’t a (nice) function from one to another. There isn’t f st f(x+y)=f(x)*f(y) and f(1/x)=1-f(x)
I think that ideas can have a bottleneck effect, but that isn’t the only effect. Some ideas have disjunctive justifications. You might have genetic evidence, and embryological evidence, and studies of bacteria evolving in test tubes, and a fossil record, all pointing towards the theory of evolution. In this case, the chains are all in parallel, so you can add their strength. Even if all the fossil record is completely discounted, you would still have good genetic evidence, and visa versa. If, conditional on the strongest line of evidence being totally discounted, you would still expect the other lines might hold, then the combination is stronger than the strongest.
If I have 10 arguments that X is true, and each argument is 50⁄50 (I assign equal probability to the argument being totally valid, and totally useless) And if these arguments are totally independant in their validity, then P(not X) < 1/1000. Note that total independance means that even when told with certainty that arguments 0 … 8 are nonsense, you still assign 50% prob to argument 9 being valid. This is a strong condition.
Disjunctive arguments are stronger than the strongest link.
On the other hand, Cojunctive arguments are weaker than the weakest link. If I have an argument that has 100 steps, and relies on all the steps holding for the argument to hold, then even if each step is 99% certain, the whole argument is only 37% certain.
For those of you looking for a direct numeric analogue to resistors, there isn’t one. They have similar structure, resistors with x+y and 1/x, probabilities with x*y and 1-x, but there isn’t a (nice) function from one to another. There isn’t f st f(x+y)=f(x)*f(y) and f(1/x)=1-f(x)
I replied at https://www.lesswrong.com/posts/qEkX5Ffxw5pb3JKzD/comment-replies-for-chains-bottlenecks-and-optimization