Con-C.2.3 — Michaelis-Menten Credibility Does Not Transfer to N=1 System#

Severity: C (Serious) | Sphere: Se1, Se2 | Target: RiskyMADorMAP (th8 evidence)

Formal mathematical equivalence between models does not transfer epistemic credibility. Michaelis-Menten kinetics is credible because of its empirical track record, not its mathematical structure:

  1. Replication: >105 independent experiments across hundreds of laboratories.

  2. Controlled conditions: substrate concentration, pH, temperature, and enzyme purity systematically controlled.

  3. Large-N statistics: billions of enzyme and substrate molecules per experiment.

RiskyMADorMAP has none of these:

  1. N=1. One Earth. No ensemble to average over. Variance of a single CTMC realization can be enormous.

  2. Rate estimated from 4 data points. The 95% confidence interval for a Poisson rate from 4 events in 40 years is approximately [0.027, 0.256]/year — the true rate could be 3x lower or 2.5x higher.

  3. The 1/3 transition probability is unmeasured. In Michaelis-Menten, \(k_{\text{cat}}\) is measured from product formation. In RiskyMADorMAP, the MAD → Dead probability is a subjective estimate. If the true probability is 1/10 instead of 1/3, median time to extinction triples.

  4. Cold War stationarity assumption. Using 1949–1989 data to predict 21st-century risk involves an unexamined assumption that rates have not changed.

  5. Survivorship bias. We observe only the conditional distribution (survived), biasing rate estimates in unknown directions.

Academic support: Kaplan and Meier (1958) on right-censoring bias. Jaynes (2003), Probability Theory, ch. 18: posterior uncertainty from N=4 events is enormous. Taleb (2020), Statistical Consequences of Fat Tails: small-sample rate estimates for fat-tailed distributions are systematically unreliable.

(Source: C2.3 from OOv1 Critique Round 2.)