The Ex­plorer in the Cave

by Roberto

Imag­ine, if you will, you are an ex­plorer. Cu­ri­ous. Fas­ci­nated, en­chanted even, by the nat­ural world, in all its rich­ness and beauty. Now, you find your­self ex­plor­ing a won­drous cave whose walls are stun­ning; stud­ded with shin­ing crys­tals. Crys­tals you be­gin to col­lect for their sheer beauty. No doubt, you also ap­pre­ci­ate their enor­mous value. Sell­ing them will bring unimag­in­able riches.

The Ex­plorer in the Cave. Source

As you pluck each gem you no­tice drops of wa­ter seep­ing out from the tiny ori­fices left be­hind. But there's some­thing odd go­ing on. "That's in­ter­est­ing," you think out loud, "every time I pull out one lit­tle rock from the wall, twice as much wa­ter comes out." You go on pick­ing, obliv­i­ous to the tiny pud­dle slowly form­ing at your feet. Yet, with every gem you col­lect, the vol­ume of wa­ter ooz­ing out from the cave's huge wall dou­bles.

You be­gin to re­al­ize your time to col­lect gems is get­ting short, so you fran­ti­cally in­crease the speed at which you col­lect. At first you took your time, care­fully in­spect­ing each one, ap­pre­ci­at­ing their in­di­vid­ual beauty. But af­ter ex­tract­ing so many you've got­ten much faster; you're now pluck­ing out one gem per sec­ond, no longer even glanc­ing at them. The wa­ter reaches your waist, yet you keep at it. "There's still plenty of time be­fore I have to leave. The cave is huge and there still so much to pick from these leaky walls. I'll be sure to exit with plenty of time; it'll only take me a few min­utes to find my way out."

You con­tinue to pick at this now fren­zied pace un­til the cave is half full, your feet barely touch the bot­tom. It is time to head out. Reach­ing for one more shiny, beau­ti­ful, price­less bit of rock you turn to­wards the exit.

 ...

But in one more sec­ond, the cave is full.

 ...

Why? It's ex­po­nen­tial growth (more next week). 

 

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