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Lumifer comments on Dr. Jubjub predicts a crisis - Less Wrong Discussion
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Everything can be broken. It's a misleading approach to think of robust systems as breakable and resilient systems as not breakable.
Both kinds of systems will break with sufficient damage. Ceteris paribus you can't even say which one will break first. The difference is basically in how they deal with incoming force: the robust systems will ignore it and resilient systems will attempt to adjust to it. But without looking at specific circumstances you can't tell beforehand which kind will be able to survive longer or under more severe stress.
There is also the related concept of graceful degradation, by the way.
I think that model works quite well for a lot of practical intervention where people do things to increase robustness that cost resilience.
But you are right that not every robust system will break earlier than every resilient one.