American Journal of Physics April 2020April 2020 Issue,

Volume 88, No. 4


The Persian Immortals: A classical case of self-organization

We present an example from classical history that perfectly illustrates the concept of a self-organizing system, namely, the “Persian Immortals” described by Herodotus. Their name refers to the fact that their number was always kept constant (at 10 000) by instantly substituting every warrior who fell during a battle. One evident advantage of this was to undermine the morale of the enemy troops. Here, we focus on a second major benefit, namely, that the Immortals—thanks to the replacement tactics—were actually becoming a stronger unit in the course of the battle. Modeling the substitution of the fallen ones by a plausible set of replacement rules, and using Order Statistics to analyze the evolution of the unit's fitness, we show that the distribution of fighting skills will ripen to a robust and favorable equilibrium state.



The Persian Immortals: A classical case of self-organization by Giorgos Kanellopoulos, Dimitrios Razis and Ko van der Weele. DOI: 10.1119/10.0000834

Seven formulations of the kinematics of special relativity by W. N. Mathews Jr. DOI: 10.1119/10.0000851

Two-penny physics: Teaching 2D linear momentum conservation by Lorenzo Galante and Ivan Gnesi. DOI: 10.1119/10.0000518

Angular momentum in the fractional quantum Hall effect by S. J. van Enk. DOI: 10.1119/10.0000831

The motion of a conical pendulum in a rotating frame: The study of the paths, determination of oscillation periods, and the Bravais pendulum by José A. Giacometti. DOI: 10.1119/10.0000374

Incorporating the Stern-Gerlach delayed-choice quantum eraser into the undergraduate quantum mechanics curriculum by William F. Courtney, Lucas B. Vieira, Paul S. Julienne and James K. Freericks. DOI: 10.1119/10.0000519

Geodesy on surfaces of revolution: A wormhole application by Lorenzo Gallerani Resca and Nicholas A. Mecholsky. DOI: 10.1119/10.0000464

Single photon beat note in an acousto-optic modulator-based interferometer by Renaud Mathevet, Benoit Chalopin and Sébastien Massenot. DOI: 10.1119/10.0000299

Stirling engine operating at low temperature difference by Alejandro Romanelli. DOI: 10.1119/10.0000832

The negative flow of probabilityby Anthony Allan D. Villanueva. DOI: 10.1119/10.0000856


A zeroth power is often a logarithm yearning to be free by Sanjoy Mahajan. DOI: 10.1119/10.0000841


Erratum: “Reliable determination of contact angle from the height and volume of sessile drops” [Am. J. Phys. 87(1), 28–32 (2019)] by F. Behroozi and P. S. Behroozi. DOI: 10.1119/10.0000387


Chaos and Dynamical Systems by John L. Bohn. DOI: 10.1119/10.0000678


American Journal of Physics 88, 256 (2020);

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