Exponential Growth and Limits to Growth
"The greatest shortcoming of the human race is the inability to understand the exponential function."
- Al Bartlett, professor, University of Colorado, Boulder
Double Double
If a hypothetical epidemic caused a doubling of cases every week, from 1 case on January 1, the total number of infections would reach the entire world population in mid-July. (33 doublings). Fortunately, we are all too distributed to contract that result, but exponential growth is an alien concept to an innumerate society.
The Limits to Growth, 1972
The 1972 Limits to Growth study was an early computer model of where civilization was headed if we continued to overconsume everything. The conclusions were not precisely timed, but a general estimate of consequences. Increasing the estimate of available resources only changed the shape of the curves by a few years. The results included a prediction that peak pollution would come after peak resource usage -- which is confirmed by unconventional energy such as fracking and tar sands. |
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Grains of Wheat on a Chessboard
https://www.theguardian.com/commentisfree/2020/mar/20/er-doctor-coronavirus-exponential-growth
I'm an ER doctor. Please take coronavirus seriously
Most people don't understand exponential growth. If they did, they'd be far more frightened
Clayton Dalton
Fri 20 Mar 2020
Why is it so difficult for us to appreciate the scale of what an unchecked global pandemic could do? The answer may have something to do with how difficult it is to intuitively understand abstract concepts like exponential growth.
This difficulty has been appreciated since at least 1256, when an Islamic scholar recorded what is known as the wheat and chessboard problem. The problem appears in a parable about the inventor of chess, whose king demands to purchase the new game. The inventor names his price, to be paid in wheat. He suggested that one grain of wheat should be placed on the first square of the chessboard, two grains on the second, and so on, with the sum doubling in this way over 64 squares. The king thinks this a great bargain, and is stunned when his treasurer informs him that the sum would bankrupt the kingdom. The total number of grains comes to 18,446,744,073,709,551,615.
Here's another example. If you took 30 steps from your front door, with each step twice as large as the last, how far could you get? The answer might surprise you – it's 26 times the Earth's circumference.
[note: that distance is also more than going to the Moon and back]
Chris Martenson, PeakProsperity.com: the Crash Course
Al Bartlett (1923-2013): Arithmetic, Population and Energy
https://www.albartlett.org/presentations/arithmetic_population_energy.html
Professor Al Bartlett began his one-hour talk with the statement, "The greatest shortcoming of the human race is our inability to understand the exponential function."
Audio of presentation:
Global Public Media
(If not available, you can listen to our archive)
Audio transcripts:
English
Français - French
Español - Spanish
Courtesy Global Public MediaHe then gave a basic introduction to the arithmetic of steady growth, including an explanation of the concept of doubling time. He explained the impact of unending steady growth on the population of Boulder, of Colorado, and of the world. He then examined the consequences steady growth in a finite environment and observed this growth as applied to fossil fuel consumption, the lifetime of which is much shorter than the optimistic figures most often quoted.
He proceeded to examine oddly reassuring statements from "experts", the media and political leaders - statements that are dramatically inconsistent with the facts. He discussed the widespread worship of economic growth and population growth in western society. Professor Bartlett explaind "sustainability" in the context of the First Law of Sustainability:
"You cannot sustain population growth and / or growth in the rates of consumption of resources.
The talk brought the listener to understand and appreciate the implications of unending growth on a finite planet, and closed noting the crucial need for education on the topic.
https://www.albartlett.org/presentations/arithmetic_population_energy_transcript_english.html
https://www.youtube.com/watch?v=DZCm2QQZVYk
The Most IMPORTANT Video You'll Ever See FULL LECTURE AlBartlett org Download
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