This overhyped Zone 2 must not be discrete

Natural distribution of heart rates vs that from modern life.

Heart rates must be Lognormal in distribution. Simply, it is not possible to have a negative heart rate and at low variance (and a mean > 6 standard deviations away from 0), the lognormal behaves like a normal.

Incidentally I failed to understand from San-Millan’s paper(s) the 2 mmol lactate threshold claimed in the podcast with Petter Attia and elsewhere. I don’t see a threshold. Even for athletes (top graph below) there is a mix outside asymptote (Lactate >5 mmol becomes 0 fat oxidation).

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Detecting BS in Correlation Windows

S&P 500 and 10-year US Treasury Bond Rolling Correlation of Monthly Returns

Financial theory requires correlation to be constant (or, at least, known and nonrandom). Nonrandom means predictable with waning sampling error over the period concerned. Ellipticality is a condition more necessary than thin tails, recall my Twitter fight with that non-probabilist Clifford Asness where I questioned not just his empirical claims and his real-life record, but his own theoretical rigor and the use by that idiot Antti Ilmanen of cartoon models to prove a point about tail hedging. Their entire business reposes on that ghost model of correlation-diversification from modern portfolio theory. The fight was interesting sociologically, but not technically. What is interesting technically is the thingy below.

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