The Beautiful Math Behind Cultural Phenomena

06/25/2012 01:59 pm ET | Updated Aug 25, 2012

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.

Note: This post was originally published on Evan Soltas' blog,