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Friday, Jan. 28, 2005 - 11:59 a.m.

The boy has this theory, that after the first girl, he can never give the same amount of lovefaithhope to any of the other girls in his life. He has thought about this in a mathematical way, because as it turns out, quantities of lovefaithhope can only be described by a geometric progression.

This is a series of increasing or decreasing numbers, where there is a multiplicative relationship between any two consecutive numbers. Take the series 0.1, 0.09, 0.081, 0.073 ... ; the next number is obtained by always multiplying the preceding number by a constant of 0.9, or 90%.

This series quantifies the decreasing lovefaithhope that can be given to all the subsequent girls, either because the boy always keeps ten percent to protect himself, or because a little part of him dies with each girl.

It is obvious that the series can go on forever: the boy takes the smallest number he can think of, and then he takes ninety per cent of that. The numbers that make up a geometric series - are infinite, like all the permutations of girls that the boy will meet in his lifetime. But the sum of all these infinite numbers is a single finite number, given by the equation:

s = a / (1 - r)

where s is the sum to infinity, a is the first number in the series, and r is the multiplicative constant.

Using our example, with a = 0.1 and r =0.9, we find that the sum to infinity,

s = 0.1 / ( 1 - 0.9) = 1

The boy cannot argue against the math. The number '1' stands like a monolith. In summing all the girls that he has met and all the girls he will ever meet to infinity, he finds irrevocably that the first one, was the one.



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