Kelsey Houston-Edwards on percolation

"The question that scientists struggle to answer is: When? What is the equivalent, for any given network, of the zero degrees Celsius at which ice melts or the 100 degrees C at which water boils? 

"At what point does a meme go viral, a product dominate a market, an earthquake begin, a network of cell phones achieve full connectivity or a disease become a pandemic? 

"Percolation theory provides insight into all these transitions.

"Mathematicians typically study idealized networks —symmetric in geometry and infinite in extent —because they are the ones amenable to theoretical calculations. 

"Infinite networks are generally the only ones with truly sharp phase transitions. Real-world networks are limited in extent, are often messy and require challenging calculations —but they, too, have transitions, albeit more rounded ones. 

"As the world becomes increasingly connected through complex layers of links that transport people, provide them with energy by means of electrical grids or connect them via social media —and sometimes spread disease among them —percolation theory becomes ever more pertinent."