INFINITY
IS
NOT
A
BIG
N U M B E R
63
higher rainfall than years I and 2. Keep on going and we see that the expected number of record rainfalls in the first N years of record keeping is 1 + '/2 + !/3 +
%+
Vs + . . . + lM
To find the number of records expected per century if conditions are random just put N — 100 and add up the terms. The answer is 5.19. Certainly in the United Kingdom at the moment there are a lot more record rainfall years — and other climatic records — than the 5 per century that this simple harmonic series predicts. This implies that the weather variations are not random, and that there is a systematic change underlying the observed variations, similar to that expected from so called 'global warming'. Notice that the infinite value of the sum of the series reflects the intuitive fact that there is always a chance of a new record in an infinite sequence of observations.
3/4-^
<—11/12
<
>
25/24
Fig 4.4 A never-ending stack of books. An infinite number of books can be supported so long as the centre of gravity of the stack never lies beyond the edge of the bottom book. This is possible in principle, not in practice.