Humans don’t have good intuition for exponentials: we often underestimate them. Start with a group of 50 people, and grow membership 10% per week – you’ll have 7,100 at the end of the year. Keep up that rate, and next year you’ll hit 1 million. Viruses infect populations exponentially, explaining why governments take extraordinary measures to limit the spread. The same phenomenon explains why Venture Capitalists are willing to invest millions in early stage start-ups when 9 out of 10 will fail: thanks to exponential math, one big success can return the entire fund. Memes follow the same math, as they jump from brain to brain via word of mouth or on social media like a virus – as Richard Dawkins made the analogy – “viruses of the mind”.
Memes with a viral coefficient greater than 1 – each person spreads the idea to more than one other – grow exponentially. This is a function of participation rate (how many hosts share), branching factor (how many they share it to) and infection rate (how many exposed get infected). Taken together this describes a meme’s “fecundity”, or how much they replicate. To do so memes first to be remembered, much like a virus needs to stay alive long enough to induce its host to sneeze and pass it on, so “longevity” or memorability is important. Related is the meme’s “fidelity”, or how accurately it can be copied when being spread from person to person. If in a game of Chinese whispers the meme’s essence gets lost, it doesn’t persist over time, and it’s essential properties get mutated out of existence. Also important is cycle time – how much time it takes for all this to happen – spreading in days not weeks has a dramatic effect on growth. When a celebrity or influencer shares something to a wide audience, we often mistakenly say it has “gone viral”, but that’s not technically true, unless the viral coefficient of those they share with is greater than 1. The initial one-to-many “super spreader” event will certainly cause rapid short term growth, but it’ll die just as quickly if the audience doesn’t then start sharing with others. If you have true virality you only need a small seed audience and compound growth will take care of the rest.
Exponential growth can’t continue indefinitely: 10% growth sustained over 4 years is 20 billion members, more than Earth’s population. Viruses eventually run out of hosts to infect, because more of the people they encounter are immune, less ‘connected’ (i.e. less likely to spread), or already infected. Exponential ‘hockey-stick’ growth is just the first part of the logistic ‘S-curve’ shape, where growth flattens out as the population gets saturated, with diminishing marginal returns from each transmission. These curves are incredibly valuable to predict, because getting in and out at the right moment can make you millions of dollars, and yet accurate forecasts remain extremely illusive. Until you’ve reached at least 95% of the peak value, you can’t easily predict where the curve flattens, by which time the prediction is far less valuable. What follows is a long, slow decline as the meme is forgotten: memes that are memorable, or get documented by their hosts, will survive longer. Only technological change can reverse the decline: mature memes jump to a new medium, riding a higher S-curve, and the cycle continues.