Doubling time

“Exponential growth leads to surprisingly large numbers in a short time,” Professor Kenneth E.F. Watt wrote in chapter 1 of his book The “Titanic” Effect: Planning for the Unthinkable (Dutton, 1974).

An environmental scientist and zoologist on the University of California-Davis faculty, Watt explained that exponential growth resulted from increases by a fixed percentage year over year, in contrast to linear growth which increased by a constant amount. The example was compound interest on savings; you can make a lot more money over time by putting your dollars in an account that earns 2% annually than you can by putting the same amount of dollars in your sock drawer. Watt wrote: “Exponential growth is often described in terms of ‘doubling times.’ . . . doubling occurs in a remarkably short time when exponential growth rates are high.” (pp. 8-9)

The chapter was included in the transcripts of a series of hearings on “Growth and Its Implications for the Future” held before the Subcommittee on Fisheries and Wildlife Conservation and the Environment of the House of Representatives Committee on Merchant Marine and Fisheries in 1973 and 1974. As chair of the subcommittee, Congressman John D. Dingell (D-Michigan) wrote the foreword to the transcript of the first hearing, in May 1973, where he discussed the significance of the findings reported in The Limits to Growth, which had been published the year before. Dennis Meadows, who led the research team at MIT whose work resulted in the publication of the book, gave testimony at the hearing and the entire text of the book was included in the appendix to the transcript.

The book, aimed at an audience of policy makers and other educated readers, explained exponential growth for an audience whose literacy was solid but whose numeracy might not be. The book’s lead author, Donella Meadows (she and Dennis were married to each other), used “a French riddle for children” to illustrate the concept; the riddle was repeated in the French edition of the book.

As Watt said, “doubling occurs in a remarkably short time,” and, as Meadows wrote, the suddenness of the end, the 29th day when the limit is reached, takes us by surprise.

Doubling time applies not only to population growth, resource depletion, and other elements discussed in The Limits to Growth but also to the current pandemic.

For example, in Arizona, in July 2020, covid19 cases are doubling about every four weeks.

Having my own numeracy issues, I found an online calculator to gauge when Arizona might reach the limit of infections, the limit here referring to the point where there isn’t a single Arizonan left for the virus to infect. I input the current number of cases, according to the Arizona Department of Health Services, the doubling rate of 28 days (4 weeks), and the total population estimated at 7.4 million.

The calculator shows that it will take 163 days for the number of cases to equal the number of Arizonans, and during the last bleak month, December, everyone who doesn’t already have covid19 will get it.

Clearly, I’m going for shock value here. It’s highly unlikely we’ll reach that point because other factors are at play and they will slow the rate of exponential growth. The factors include mask wearing, social distancing, handwashing, quarantining, and all-around getting with the program, people. What we might want to aim for is such a long doubling time that most of us can remain virus-free long enough to get to a time when vaccinations grow at exponential rates that outrun the infection rates.

Although the 1972 edition of The Limits to Growth is outdated (although still influential, but more about that later), at least one truism from its production and reception persists: most politicians and policy makers still don’t understand exponential growth or its implications and the ones who do don’t have the power or the will to overcome resistance and denial.

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