In 1910, Ripley's Believe It or Not claimed, "If all the Chinese in the world were to march four abreast past a given point they would never finish passing, though they marched forever and ever." Try for yourself to see if this is true, adjusting country, rank size and spacing, and marching speed.

This Demonstration uses Mathematica's built-in function CountryData for the current population estimate and the annual fractional growth estimate. It estimates how long it would take the entire population of a country to march past a given spot.

The number of people passing per year is a function of the marching speed, rank spacing, and number of people per rank. For marching speed, a slow march is 60 steps per minute, a quick march is 120, and a double march is 180. Rank spacing in the US military is 40 inches with a 30-inch step length. The number of people passing per year, r, is thus: .

The number of people marching who have yet to pass a given spot at time in years is .

is the country's initial population. We assume that people passing in the parade no longer contribute to population growth. The instantaneous change is given by the growth rate multiplied by the initial population, less :

.

If is is zero, then

, and the population passes by in years.

Otherwise, the remaining population is given by the exponential function:

, and the population passes by in years.

The idea of a country's entire population marching has stuck in the public imagination, and served as partial inspiration for Cyril Kornbluth's 1951 science-fiction story "The Marching Morons".

Reference

[1] https://en.wikipedia.org/wiki/Military_step

[2] C. M. Kornbluth, "The Marching Morons," Galaxy, 2(1), 1951 pp. 128–158.