Chains, Bottlenecks and Optimization
Consider an idea consisting of a group of strongly connected sub-ideas. If any sub-idea is an error (doesn’t work), then the whole idea is an error (doesn’t work). We can metaphorically model this as a metal chain made of links. How strong is a chain? How hard can you pull on it before it breaks? It’s as strong as its weakest link. If you measure the strength of every link in the chain, and try to combine them into an overall strength score for the chain, you will get a bad answer. The appropriate weight to give the non-weakest links, in your analysis of chain strength, is ~zero. There are special cases. Maybe the links are all equally strong to high precision. But that’s unusual. Variance (statistical fluctuations) is usual. Perhaps there is a bell curve of link strengths. Having two links approximately tied for weakest is more realistic, though still uncommon. (A group of linked ideas may not be a chain (linear) because of branching (tree structure). But that doesn’t matter to my point. Stress the non-linear system of chain links and something will break first.) The weakest link of the chain is the bottleneck or constraint. The other links have excess capacity – more strength than they need to stay unbroken when the chain gets pulled on hard enough to break the weakest link. Optimization of non-bottlenecks is ~wasted effort. In other words, if you pick random chain links, and then you reinforce them, it (probably) doesn’t make the chain stronger. Reinforcing non-weakest links is misallocating effort. So how good is an idea made of sub-ideas? It’s as strong as its weakest link (sub-idea). Most ideas have excess capacity. So it’d be a mistake to measure how good each sub-idea is, including more points for excess capacity, and then combine all the scores into an overall goodness score. Excess capacity is a general feature and requirement of stable systems. Either most components have excess capacity or the system is unstable. Why? Because of variance. If lots o