Evan Soltas
Jun 20, 2012

The Math Behind The Culture

From John Milton's Paradise Lost to YouTube, there is beautiful math behind cultural phenomena.

Consider the long s, that archaic letter which looked like an f or integral sign. It once appeared in words where an s fell at the beginning or middle of a word.

Using Google's N-gram tool, we can pinpoint the moment that the long s fell out of style: 1800. It was then when "ſaid" became "said," when "Paradise Loſt" became Paradise Lost -- and when, more broadly, modern English as we mostly know it today came into form.

What is so striking, even beautiful, about the demise of the long s is that, as seen the time series documenting the disappearance of "loſt" and its replacement by "lost" look exactly like a pair of logistic functions.

Here is a graph of the time series from 1750 to 1850, with a "smoothing" of 3:


The results repeat themselves for most other examples.

Compare that to an example of modern culture -- the YouTube video of President Obama speaking at this year's White House Correspondents' Dinner:

Again, if you look at the statistics for many other YouTube videos, the logistic function appears again and again, after any major link-to a video received.