How To Build Knowledge Skyscrapers

In a simplified model, some trait currently has a value of 40, and it causes failures for the whole system/goal when less than or equal to 10. It has random variance of +/- 3.

A small error reduces it to 38, causing no failures.

A big error reduces it to -50, causing failure.

A medium error reduces it to 11, which leads to sporadic failures due to random variance.

To get failures sometimes, instead of always or never, the error has to get the trait within 3 of 10. You can see why that’d be rare compared to errors that don’t get near 10 or go way past 10. The target range is small. In general, breakpoints and the areas near them are small and rare compared to all numbers. It’s a lot more common to be far from a (relevant, important) breakpoint than near one.

This is one simplified model. It’s sometimes useful and sometimes doesn’t fit well. It is not a universally correct way to look at things.

Note: People tend to focus on non-randomly selected traits which are nearer to breakpoints than average. Their intuitions often assume being near a breakpoint because they tend to look at things that are and ignore things that aren’t. This is often reasonable or practical, but it’s misleading when understanding abstract theory about how things work. It’s sort of like how a ton of people are used to cities and spend most of their time in cities but most land isn’t in a city and you need to get away from a city-biased perspective if you want to be a good geographer.