lotsofplants: (dendrobium)
[personal profile] lotsofplants
You may have seen this "stumper" before: if the area of a pond covered by lily pads doubles ever day, and it takes 48 days to cover the entire pond, how long does it take to cover half the pond? It's a popular example in books on the science of thought, to demonstrate how people tend to take mental shortcuts that lead us to incorrect results; the shortcut answer is: half the area must be half the time = 24 days. But clearly the answer is 47; if it doubles each day, to cover half the pond you go back one day from full coverage.

However, something about this question has been bothering me--it clearly does not consider the real-world scale of this exponential growth, and none of these authors have ever asked, while editing their clever examples "just how big is this pond, anyway?" Let us assume, for the sake of argument, some radiation-addled lily pads capable of supernatural growth rates. If we assume a normal-to-small 4-inch diameter lily pad, and begin on day 1 with a single lily pad (area pi*r^2 = a bit over 12 square inches), by day 48 we have lily pads covering an area of 1.76766E+15 square inches or 440,321 square miles (sq mi). To put this number in perspective, Lake Superior, the largest freshwater lake in the world, is not quite 38,000 sq mi. If our super lilies can thrive in salt water, we could put them in the Caspian Sea, the world's largest land-locked body of water, but at 143,200 sq mi we'd need more than three of them for all the vegetation. Really, we're talking a pond nearly the size of Hudson Bay (475,800 sq mi), but without any ice cover. If tempted to say that's a Texas-sized pond, you'd mean it would swallow Texas (268,580 sq mi) whole. It could be contained by Alaska, at 663,267 sq mi, but the lily pads would probably prefer the climate in the Mediterranean Sea; they'd cover about 2/5 of it on day 48; if not stopped, by day 57 they'd overflow the 71% of the earth covered in water (including the area occupied by polar ice.)

What I'm saying is that "pond" may be a poor choice of terms here. And my professional recommendation is to avoid creating super-fast growing, salt-resistant lily pads capable of surviving in extreme climates.

Date: 2013-01-25 05:25 am (UTC)
From: [identity profile] randomdreams.livejournal.com
I've seen a similar absurdity related to illustrate Malthusian catastrophe: if human population continues increasing at the rate it is currently, within 2000 years we'll be expanding from the planet at greater than the speed of light from pressure of new human bodies being created. Obviously there are piles of problems with that scenario but it is evocative.

Date: 2013-01-25 05:25 am (UTC)
From: [identity profile] randomdreams.livejournal.com
also lily pads freak me out because the last one I picked had a leech on the underside.

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