Incautious Extrapolation

I saw this error referenced in two books:

• Standard Deviations, by Gary Smith
• How Not to Be Wrong, by Jordan Ellenberg

and so I thought to jot a quick summary.

Incautious Extrapolation, a term used by Smith refers to how human beings are prone to using data without theory and draw inaccurate conclusions.

He has a few examples:

1. Abraham Lincoln, the man himself(!), incautiously extrapolated the population of the US in 1930 to be 251 million people (he did this from Census Data collected from 1790 to 1860). The actual population in 1930 was 123 million (less than half his prediction!). Smith says, "If we have no logical explanation for a historical trend and nonetheless assume it will continue, we are making an incautious extrapolation that may well turn out to be embarrassingly incorrect".

2. Another one that was quite funny was the average sentence length uttered by British speakers over the last 350 years. The sentence length was found to have fallen from 72.2 words per sentence for Francis Bacon to 24.2 for Winston Churchill. At this rate, we will soon arrive at 0 words per sentence and then go negative some years later!

Another example is "We will all work for IBM" in which analysts studied IBM's explosive stock growth in the 1970s and plotted these points on a graph and fitted a curve showing exponential growth; they based their future estimates on this graph and turned out to be quite wrong. Such growth could simply not be sustained. This is what happens when you blindly follow data without having theory. The other point in this example is that incautious extrapolation doesn't just happen with straight lines. You can do this with curves of any kind.

Ellenberg uses the example of a journal article on Obesity which extrapolated that All Americans will be obese by 2048. Again, the researchers took data points and applied linear regression to come up with this future state prediction. Again, this is applying a technique to data without theory. Is the phenomena we are looking at linear? As with the IBM example (which assumed that growth would just keep happening without considering that already big companies cannot sustain such growth indefinitely; there are factors such as labor force and productivity that will constrain it), as the number of overweight people grows, it *must* slow down, because there are fewer and fewer people to make obese; these are the skinny people remaining and we will always have such a population. A little theory / common-sense goes a long way, but I suppose it is easier / sexier and provocative to make outlandish statements.

On a final note, both authors use Mark Twain's example of incautious extrapolation of the length of the Mississippi River and how based on measurements, if we look backwards, it used to be upwards of 1,300,000 miles long and in 742 years, it will be 1.75 miles long. "There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact."