In a hypothetical, extremely simple Cloud Ark consisting of only two arklets, only one calculation needed to be performed: namely, the calculation that answered the question "Will Arklet 1 bang into Arklet 2 if both stay on their current courses?" In a three-arklet cloud, it was also necessary to figure out whether Arklet 1 would collide with Arklet 3, and whether 2 and 3 were going to collide. So, that was a total of three calculations. If the cloud expanded to four arklets, six calculations were needed, and so on. In mathematical terms these were known as triangular numbers, a kind of binomial coefficient, but the bottom line was that the number of calculations went up rapidly with the number of arklets in the cloud.
( Neal Stephenson )
[ Seveneves ]
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