The greatest shortcoming of the human race is our inability to understand the exponential function. This was Al Bartlett's mantra. His catchphrase. The alpha and omega of the lectures he gave on overpopulation before his death in 2013.
Bartlett was a physics professor. He understood natural phenomena often outstrip our brain's gronkulatory machinery. The very small (quantum mechanics). The very fast (relativity). But also exponential growth. So he spent his emeritus years educating the public. Breaking it down for the layperson. You may know some of his examples. Wheat and chessboards. The bacteria bottle. Doubling rates. If you don't, you should (Bartlett's lectures are available on YouTube).
The crux of our misunderstanding is the power of the exponential. If a process grows exponentially and its constraint does not, exponential growth will win every time. What kind of process? Human population growth, yes. But also the adoption of technology. The spread of rumors. Compound interest. Nuclear reactions. The transmission of disease. Tolian Soren notwithstanding, exponential growth is the fire in which we burn.
Which brings us to COVID.
We are currently getting a harsh lesson in exponential growth, and the teacher is COVID-19. An infectious disease spreads exponentially for the simple reason that each new infected infects others. As such, the rate of new infections is proportional to the current size of the infected population. They fell two friends, and they fell two friends, and so on, and so on. This is the definition of exponential growth.
Health care professionals keep warning this is not over. The people in charge beg to differ. Some only seem to care about their own fortunes, be they political or literal. But some have good intentions. If your constituents are staring down the barrel of financial ruin, of course you want this nightmare to be over. Fear leads to the dark side and all that (although I would point out the tax cuts Republicans handed to their billionaire friends would fund COVID unemployment relief for several decades. Maybe remember that come November).
Alas, the only relief I can offer is illumination.
A reasonable argument seems thus: Let's go back to work. If things go sideways, we'll close down again.
Such a proposal perilously pokes the power of exponential growth. The mind fails to grasp how fast things can go from good to bad and bad to worse. With exponential growth, one can catnap in Eden and wake up in Megiddo. Even if you realize the tides are turning, if the tides are turning exponentially, you're too late.
To demonstrate this, I made a Javascript.
My app puts you in charge of containing a COVID outbreak in your community. The red expanding circle represents the outbreak, growing (wait for it) exponentially. You attempt to contain the outbreak by clicking the "lockdown" button. This has the effect of removing individuals from the infected population so they can't infect others.
But there's a catch.
The black circle defines how long you wait to respond. A threshold resurgence before you realize COVID has returned. This is set by the slider. Bigger circle = longer delay. The app will ignore your clicks until the infections pass this line in the sand. The sim halts after 200 days or when your hospitals are overwhelmed, whichever comes first.
Pick a delay, select start, and begin your career in public health management:
(short) --- delay --- (long)
What you should have discovered is the job is harder the longer you wait. The growth rate is proportional to the current number of infected. As such, a click later is worth "less" than a click now, because, proportionally, a later click removes a smaller -- and eventually a much smaller -- proportion of infecteds. You get diminishing returns for your efforts. Wait long enough, and your efforts are for naught. Because the growth rate is proportional to population size, the number of infecteds increase no matter how fast you click. This demonstrates our present dilemma.
If things go sideways, we'll close down again. That doesn't work. Like kudzu or rap, once COVID escapes into the countryside, it's very difficult to eradicate. A genie that won't go back in the bottle. A bell that can't be unrung. Yes, the infection will eventually burn itself out, but like the Number 4 reactor eventually burned itself out at Chernobyl.
This is why we need to keep the brakes on and the chocks in. The financial pain doesn't matter because the financial pain would happen anyway. Slightly later maybe, but worse. Much worse. Our options have been reduced to bad options, but one of the bad options risks catastrophe.
Think of COVID as an upturned broomstick balanced on our fingertips: Easy to control when upright. Harder when the deviation from upright is small. Impossible once it gets away from you.
That is the power of exponential growth.
Bartlett was a physics professor. He understood natural phenomena often outstrip our brain's gronkulatory machinery. The very small (quantum mechanics). The very fast (relativity). But also exponential growth. So he spent his emeritus years educating the public. Breaking it down for the layperson. You may know some of his examples. Wheat and chessboards. The bacteria bottle. Doubling rates. If you don't, you should (Bartlett's lectures are available on YouTube).
The crux of our misunderstanding is the power of the exponential. If a process grows exponentially and its constraint does not, exponential growth will win every time. What kind of process? Human population growth, yes. But also the adoption of technology. The spread of rumors. Compound interest. Nuclear reactions. The transmission of disease. Tolian Soren notwithstanding, exponential growth is the fire in which we burn.
Which brings us to COVID.
We are currently getting a harsh lesson in exponential growth, and the teacher is COVID-19. An infectious disease spreads exponentially for the simple reason that each new infected infects others. As such, the rate of new infections is proportional to the current size of the infected population. They fell two friends, and they fell two friends, and so on, and so on. This is the definition of exponential growth.
Health care professionals keep warning this is not over. The people in charge beg to differ. Some only seem to care about their own fortunes, be they political or literal. But some have good intentions. If your constituents are staring down the barrel of financial ruin, of course you want this nightmare to be over. Fear leads to the dark side and all that (although I would point out the tax cuts Republicans handed to their billionaire friends would fund COVID unemployment relief for several decades. Maybe remember that come November).
Alas, the only relief I can offer is illumination.
A reasonable argument seems thus: Let's go back to work. If things go sideways, we'll close down again.
Such a proposal perilously pokes the power of exponential growth. The mind fails to grasp how fast things can go from good to bad and bad to worse. With exponential growth, one can catnap in Eden and wake up in Megiddo. Even if you realize the tides are turning, if the tides are turning exponentially, you're too late.
To demonstrate this, I made a Javascript.
My app puts you in charge of containing a COVID outbreak in your community. The red expanding circle represents the outbreak, growing (wait for it) exponentially. You attempt to contain the outbreak by clicking the "lockdown" button. This has the effect of removing individuals from the infected population so they can't infect others.
But there's a catch.
The black circle defines how long you wait to respond. A threshold resurgence before you realize COVID has returned. This is set by the slider. Bigger circle = longer delay. The app will ignore your clicks until the infections pass this line in the sand. The sim halts after 200 days or when your hospitals are overwhelmed, whichever comes first.
Pick a delay, select start, and begin your career in public health management:
---
(short) --- delay --- (long)
What you should have discovered is the job is harder the longer you wait. The growth rate is proportional to the current number of infected. As such, a click later is worth "less" than a click now, because, proportionally, a later click removes a smaller -- and eventually a much smaller -- proportion of infecteds. You get diminishing returns for your efforts. Wait long enough, and your efforts are for naught. Because the growth rate is proportional to population size, the number of infecteds increase no matter how fast you click. This demonstrates our present dilemma.
If things go sideways, we'll close down again. That doesn't work. Like kudzu or rap, once COVID escapes into the countryside, it's very difficult to eradicate. A genie that won't go back in the bottle. A bell that can't be unrung. Yes, the infection will eventually burn itself out, but like the Number 4 reactor eventually burned itself out at Chernobyl.
This is why we need to keep the brakes on and the chocks in. The financial pain doesn't matter because the financial pain would happen anyway. Slightly later maybe, but worse. Much worse. Our options have been reduced to bad options, but one of the bad options risks catastrophe.
Think of COVID as an upturned broomstick balanced on our fingertips: Easy to control when upright. Harder when the deviation from upright is small. Impossible once it gets away from you.
That is the power of exponential growth.
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