From the Foot of Hercules: Extrapolation and Predictive Power

John Cousins
February 7, 2023
3 min read
Ex pede Herculem

From the Foot of Hercules

I love finding out about cool antique ideas. This one is about extrapolation (which is also the name of a great album by John McLaughlin). Extrapolation is the estimating technique of concluding something by assuming that existing trends will continue or a current method will remain applicable.

Predictive Power

This idea also has to do with the basis of statistics and making estimating the whole from a partial sample set. We have experienced the limitations of this kind of estimating in attempts to predict recent election results but it still has lots of value when you can’t readily aggregate up all the data or need to make predictions about the future.

from his foot, we can measure Hercules

Ex pede Herculem, “from his foot, we can measure Hercules”, is a maxim of proportionality inspired by an experiment attributed to Pythagoras:

“The philosopher Pythagoras reasoned sagaciously and acutely in determining and measuring the hero’s superiority in size and stature. For since it was generally agreed that Hercules paced off the racecourse of the stadium at Pisae, near the temple of Olympian Zeus, and made it six hundred feet long, and since other courses in the land of Greece, constructed later by other men, were indeed six hundred feet in length, but yet were somewhat shorter than that at Olympia, he readily concluded by a process of comparison that the measured length of Hercules’ foot was greater than that of other men in the same proportion as the course at Olympia was longer than the other stadia. Then, having ascertained the size of Hercules’ foot, he made a calculation of the bodily height suited to that measure, based upon the natural proportion of all parts of the body, and thus arrived at the logical conclusion that Hercules was as much taller than other men as the race course at Olympia exceeded the others that had been constructed with the same number of feet.” (translated by John C. Rolfe of the University of Pennsylvania for the Loeb Classical Library, 1927)


In other words, one can extrapolate the whole from the part.

Ex ungue leonem, “from its claw we can know the lion,” is a similar phrase. This is what we do with dinosaur bones and fossils.

from its claw we can know the lion


The principle was raised to an axiom of biology; it has found dependable use in paleontology, where the measurements of a fossil jawbone or a single vertebra, offer a close approximation of the size of a long-extinct animal, in cases where comparable animals are already known. Paleontologists call these comparable animals alive today Analogs. The studies of proportionality in biology are pursued in the fields of morphogenesis, biophysics and biostatistics.

Caveats and Limits

There are limits to relying on extrapolation and proportionality. Here is a quote by the renown data scientist:

Forming your worldview by relying on the media would be like forming your view about me by looking only at a picture of my foot.

― Hans Rosling, Factfulness

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John Cousins
Author, Entrepreneur, & Teacher

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