The 29th Day

Project:Explaining exponential growth
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Project wiki:Explaining exponential growth

In the video "Are Humans Smarter than Yeast", an example is given of some lilly pads doubling every day and covering a lake on the 30th day. The 29th day, the lake is only half covered and most people wouldn't notice a problem.

I just notice that Lester Brown wrote a book called The Twenty-Ninth Day (1978)
It seems that the title refers to the same problem (exponential growth and carrying capacity).

I wonder: who invented this allegory first?
Where else did you see this allegory (in one form or another) ?



I'm not sure where the lily pad metaphor emerged. On page 29, "Limits to Growth" (1972), Donella Meadows uses the metaphor, calling it "A French riddle for children...." She also uses exponential growth of a colony of yeast cells in a different example. -- Dan Chay


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moving to proper queue.


This riddle is an effective first-introduction to multiple critical math and science concepts and understandings - which should be LISTED and discussed following the riddle. Items for such a list? (Exponential growth vs. Linear or "Arithmetic" growth), the Power of exponential progressions, the extremely Deceptive and Misleading nature of exponential progressions (e.g., - "by the time you realize that it is about to hammer you, it has already hammered you"), J-curves in populations (and their classical climb-and-collapse population outcomes) versus s-curves in populations, and the rapidity and seeming sudden-ness of change in exponential populations.

The riddle also facilitates discussion of a second set of real-world concepts such as ecological, environmental, and planetary "carrying capacities" (which are not just about "running out of" suppositions such as food, water, oil, etc., but are also about wastes and levels of sheer damage, destruction, and eradication of the only planetary life-support machinery so far known to exist anywhere in the universe).

Lastly, in a follow-up session, after reviewing the above riddle, an additional discussion should be considered: In the classical lily-pad / 29th day riddle, calamity is ASSUMED to unfold when the pond becomes completely "filled." This, unfortunately, is a far more optimistic supposition than multiple, classical, quintessential, and calamitous REAL-WORLD population-environment examples would recommend. An article accessible at for example, outlines THREE such classical examples, all three of which were characterized by 99% die-offs and/or mass mortalities in environmental surroundings that remained approximately 99.998% UNOCCUPIED and which visually-appeared to remain almost entirely 'empty.'

( A downloadable image to depict such 2/1000ths of 1% or 99.998% "too late" conditions is accessible at http://www (dot) flickr (dot) com/photos/Pali_Nalu )

If the lily pad riddle is modified to reflect the classical REAL-WORLD examples cited above, the "too late" conditions in the pond would not take place on day thirty when the pond becomes completely "filled" - instead, the actual REAL-WORLD "too late" population-environment tipping point would be approached, reached, and breached under 99.998% unoccupied conditions. (Note that even the most educated, intelligent, and thoughtful members of a sentient species would find it difficult, if not impossible, to imagine either the degree or the proximity of the calamity that is about to overtake their populations, so that if the scholars and leaders of such a population WAIT until the depicted conditions develop (2/1000ths of 1% occupied / 99.998% unoccupied), they will have already WAITED TOO LONG.