Error Propagation

Error propagation is CF’s account of why a flaw in a low-level idea does not stay local: it spreads upward into every idea built on it, and its destructive effect increases with distance. Using the knowledge skyscraper metaphor, an error on floor 5 damages floor 6 a little and floor 15 catastrophically. The structure cannot rise more than roughly ten floors above its first major error, because higher floors put more weight on the faulty support. CF stresses that ideas scale exponentially, not linearly — treat each floor as twice as heavy as the one below — so even a modest base flaw compounds fast.

This drives CF’s central practical claim: the more you intend to reuse an idea or build on it, the higher its quality must be. An idea good enough to support one layer can be far too weak to hold ten. CF also notes that propagation rarely produces “medium” damage — most errors either limit you to 0–10 further floors or allow thousands, a near-binary split linked to the jump to universality. The dangerous cases are major yet subtle errors: they let you build a few more layers before progress stalls, by which point the original cause is buried several layers down and hard to connect to the current symptom.

The remedy is reviewing earlier floors for the earliest major error rather than grinding on the current one — and front-loading error-checking before practice automatizes a flaw into the subconscious. This connects to CF’s error-rate concern: a small per-step rate, compounded across many dependent layers, predicts failure at the top.