Extrapolating beyond the point where you have a leg to stand on

In the November issue of The American Statistician the Editor published this comment by David J. Finney, Professor Emeritus of Statistics at the University of Edinburgh: “On a day in 1919 or 1920…I murmured silently to myself: ‘David, you are becoming a clever boy…you have learnt to stand on one leg. What next?’…I showed creditable numerical ability in saying to myself ‘2-1-0.’ I willed myself to make…an effort to lift the foot. I rapidly became aware of a sore bottom…I never tried again but memory of the pain has given me a prejudice against any form of extrapolation from particular to general.”

In 1798, Thomas Malthus created one of the most controversial extrapolations in history in An Essay on the Principle of Population. Based on the sketchy statistics of the time, he assumed that population grows geometrically (exponential), whereas food supplies increase at an arithmetic rate (linear). No wonder he became known as “Gloomy” Malthus! Fortunately, due to development of new agricultural regions and improvements in productivity from these lands, the mass misery of his projections did not happen...yet.

In 1972, I read a book called Limits to Growth by the Club of Rome think tank. They presented a series of Malthusian projections with consumption increasing exponentially relative to linear expansion of resources. I found it terribly depressing. It seemed certain to me from all the graphs that mankind would not last beyond 2000. As subsequent developments averted what seemed sure disaster, I became ever more wary of extrapolation, especially ones that predict doom and gloom.

“Human history becomes more and more a race between education and catastrophe.”
-- H. G. Wells

On the other hand, I’ve seen forecasts fizzle and become forgotten that turned out true -- albeit much delayed. For example, in the spring of 1989 I co-taught a DOE class in the San Francisco Bay Area. One night my top-floor room shook so hard that it woke me up – it was an earthquake that registered a bit above 5 on the Richter scale. The next morning another earthquake rocked our training room – built on stilts just off shore on the Bay. It measured near 6. That led to a forecast that by week end there was a 20 percent probability of a really major quake. It did not materialize. However, in October, San Francisco suffered the devastating Loma Prieta earthquake – nearly 7 points on the Richter scale.

So, whereas little Finney took a fall from misguided extrapolation, Bay Area residents found themselves floored from what turned out to be a prophetically forecasted tremblor. I suppose one way of dealing with scenarios for the future is to expect, and plan, for the worst, but hope for the best, that is, hedge your bets. For example, try to keep two feet on the ground as often as possible, keep a hold on the bannister and look before you leap.