Linear vs exponential: suppose we shut down the city for 2 days. That takes away 2 days of business. On the other hand, if we stay open, then for months to come, we will have twice the number of covid-19 cases in Chicago. @chicagosmayor @chicago
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While the number of cases is small, twice as many isn’t much more. But that factor of two lives in perpetuity. 20,000 cases is a lot more than 10,000.
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(Reported cases in Illinois are doubling approximately every 2 days)
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Replying to @math_wilkinson
It's strange and frustrating how hard it is to convey to the mathematically traumatized the difference between (1.2)^10 and (2.1)^10. And it's stunning how many of us are mathematically traumatized. Henry Briggs understood this sort of thing in his bones, more than 400 years ago.
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The consequences of grossly ineffective mathematics pedagogy, especially K-12, may soon come to seem far more alarming than ever before. If the differences between exponential and linear (indeed, even polynomial) growth were obvious to most, we would all be vastly safer now.
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