COVID-19 has brought home the term “exponential growth” in a visceral, gut-wrenching way.
Its spread is an exponential trend appearing on every screen, every day, everywhere in the world. Despite that exponential’s profound impact on every human on the planet, it remains devilishly deceptive. Let’s try to tame exponentials with practical simplicity, in 200 words or less.
We can’t Visualize Exponentials
A simple exponential relationship is y= 2x. x increases 1, y doubles.
- Look at your phone. Imagine a stack of 15 phones. Pretty easy (1×15 is linear).
- Imagine it doubled: 2 phones. Imagine doubling your phone 15 times. You have to use the phone’s calculator just to get the total: 32,768 phones. You can’t visualize them.
- Practice barely helps. Humans are wired for linear, not exponential.
Be Vigilant With Small, Exponentially-Growing Events
- Don’t ask “How many?” Ask, “How fast is it doubling?”
- January 23, Hubei: 654 COVID-19 cases. Calm in America: only 654? Meh. But cases were doubling every two days. How fast might that become One Billion cases? Yikes! (Answer’s below.)
- Time from one billion to all humanity at that rate? 6 days.
- Exponentials tricked even the New York Times, which reported that while reaching the first million COVID-19 cases took 4 months, the second million took only 13 days. The important data was a slowing: the two previous doublings took 6 days.
When encountering an exponential, check your intuition with your phone’s calculator. Tiny tweaks to exponential growth rates can make forecasts say whatever their creators want.
Answer: 654 needs to double just slightly over 20.5 times to surpass 1,000,000,000. If doubling happens every two days, that’s 41 days.