Number 01/Failure & fragility/Systems
The Mismatch Ratio
The ratio of a system's response time constant to the timescale of its dominant driver. Where it exceeds one, lag accumulates into debt; where it approaches ten, correction becomes abrupt.
01Why it matters
It predicts the shape of the response rather than its size, and it is dimensionless, so the same number should predict abruptness in ecosystems, institutions and machines alike.
02Expected value
Most systems that fail abruptly should sit between one and ten; systems below one should track their drivers smoothly.
03How it would be measured
Estimate the time constant from response to a step change, and the driver timescale from its spectrum. Both are measurable from existing records.
04What would refute it
If abrupt and smooth systems have indistinguishable ratios, the number predicts nothing.