Unreasonable effectiveness of numbers
P.C. CHANDRASEKHARAN
WHEN THE nineteenth century physicist Lord Kelvin famously remarked: "When you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind," he had probably in mind numerical quantification of scientific knowledge. However in today's world Kelvin's aphorism has taken on an altogether different meaning and almost every walk of human activity is dominated by numbers.
Whether it be GDP growth, infant mortality rate or spread of communicable diseases, the fact that these entities are expressed in terms of numbers confers on them an aura of authenticity. In the midst of all this euphoria about numbers it is worth remembering that on occasions they do hide much more than they choose to reveal.
A classic example of the trivialisation of the number game is witnessed every day on our TV channels where questions of concern to the citizens are posed and immediate answers sought from the viewing public. They are supposed to come up with instant `yes' or `no' answers and the consolidated responses `for' or `against' are announced the same night with much fanfare. The answers are supposed to reflect the `sense' of the nation.
This is at best an exercise in futility and at worst an act of deception. How can one give instant `yes' or `no' answers to issues which are serious and amenable to multiple interpretations? Sometimes the questions posed are themselves trivial and worded in such a way that any right thinking person can come out with only one answer. Even from a statistical viewpoint the method does not make sense because those who respond to these questions are limited to a minuscule minority, possessing cell phones.
Mode of selection
To cite yet another example illustrating the unreasonable effectiveness of numbers, consider the mode of selection of the best sportsperson in the country in a particular field via opinion polls. The methodology adopted is to make known in advance the essential attributes to be considered for the particular game along with their respective weightages. The figure of merit is to be arrived at using the well known weighted average method which by itself is a perfectly legitimate tool.
However, the snag here is in the arbitrary assignment of weights. Clearly, by tampering with the weights the figure of merit could be altered at will. Such a procedure is patently unjust on those who are pushed out of the race, the more so because these ratings are commercially exploited for monetary gain by interested parties.
It is not only the lay public who are victims of such gimmicks. Surprisingly, even the scientific community has occasionally fallen into this trap. A few years back, the Institution of Higher Education at Shanghai Jiao Tong University in China conducted a survey to obtain the overall ranking of world-class universities (not ranked discipline-wise). Among other things they based their assessment on criteria such as citation indices, the number of Nobel laureates working in the institution and publications in reputed journals. Different weightages were allotted to each of the items.
The results from this study were on expected lines with Harvard, Stanford, Cal Tech., U.C. Berkeley and Cambridge occupying the first five slots. Even in this case the ratings do not give a true picture as no special weightage was assigned to departments in universities, some of them with outstanding track record and reputation.
As in all scientific matters so also in real life, the level of precision that one may choose to employ to arrive at specific conclusions should be commensurate with the task in hand. It is not always possible to give precise answers to imprecise questions. It looks as though in certain matters it is far better to be vaguely right than precisely wrong.
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