Guest essay by Thomas P. Sheahen
We all learned in elementary school that “you can’t divide by zero.”  But what happens when you divide by a number very close to zero, a small fraction?  The quotient shoots way up to a very large value.
Pick any number.  If you divide 27 by 1, you get 27.  If you divide 27 by 1/10, you get 270. Divide 27 by 1/1000 and you get 27,000.  And so on.  Any such division exercise blows up to a huge result as the denominator gets closer and closer to zero.
There are several indices being cited these days that get people’s attention, because of the big numbers displayed.  But the reality is that those big numbers come entirely from having very small denominators when calculating a ratio.  Three prominent examples of this mathematical artifact are: the feedback effect in global warming models; the “Global Warming Potential”; and the “Happy Planet Index.” Each of these is afflicted by the enormous distortion that results when a denominator is small.
A.     The “Happy Planet Index” is the easiest to explain:  It is used to compare different countries, and is formed by the combination of