Super-accurate Innumeracy

A.K. Dewdney

Between 1984 and 1991, A.K. Dewdney authored numerous articles in the section on Mathematical Games of Scientific American. He was one of the successors to Martin Gardner, most famous contributor of that section. Dewdney is also the author of an amazing book, The Planiverse (1984), which belongs to the same genre of mathematical fantasy as Edwin Abbott's Flatland, published just a century earlier.

In the previous post I offered a few examples of innumeracy taken from A.K. Dewdney’s book 200% of Nothing. In this book, Dewdney points out, among many others, two very frequent mathematical mistakes. The first consists in giving so few digits of a number that it loses all usefulness (he calls those numbers nums, to indicate that they are not full numbers, as they are not complete). The second mistake is the opposite: giving too many digits of a number, beyond what is necessary or makes sense. He calls unnecessary digits dramadigits, as they only serve to give the particular number a more dramatic look.

Let's look at an example from Dewdney's book:

The following caption appears below the photo of a rare bird in a magazine: its average weight is 226.8 grams. What accuracy! Did they weigh a certain number of specimens to the tenth of a gram and then took the average?

Then someone noticed that 226.8 grams is exactly one half of 453.6 grams (an English pound). Obviously, the original weight indicated was half a pound, and then someone translated it into grams, but in doing so the translator forgot that, when one says that a bird weighs half a pound, one does not want to be exact, just gives an approximate value. The correct translation would have been just over 200 grams.

An example I have found in the December 6, 2021 issue of Science News:

News headline: Climate change could make Virginia's Tangier Island uninhabitable by 2051.

And the text adds: As of 2020, 436 people lived on the island. According to Schulte and Wu’s analysis of population, that number could drop to zero by 2053.

Do they need to be so exact? Shouldn't both texts say around 2050? In this case, 1 and 3 are dramadigits.

Let's look at another example, proposed by Dewdney and taken from the famous science fiction series Star Trek: in a certain episode, Captain Kirk and Mr. Spock were hiding in a camp of Klingons, the deadly aliens, enemies of the human species. Kirk wonders aloud if they will manage to escape alive, and Spock answers:

The probability of our escape is 0.000162.

It would have been more reasonable if Spock had said one in 6000, although the value is obviously false, as in all the chapters of the series Kirk and his crew managed to escape from terrible dangers without too much difficulty. Obviously, offering a probability to six decimal places in such a case is unnecessary and useless. Note that, although Spock's estimated survival probability is small, it’s over 16 times greater than the probability that you will hit the first prize in the Spanish Christmas lottery after buying a single number (one in 100,000).

Finally, let's look at another example, which I have taken from Science News (dated October 26, 2021), which echoed the Emissions Gap Report 2021: The Heat Is On:

News headline: Earth will warm 2.7 degrees Celsius based on current pledges to cut emissions.

And the text adds: Current pledges to reduce greenhouse gas emissions and rein in global warming still put the world on track to warm by 2.7 degrees Celsius above preindustrial levels by the end of the century.

Taking into account the many uncertainties in these forecasts, it is clear that at least the second figure of the given number is a dramadigit. If they had said between 2 and 3 degrees Celsius, the statement would have been more reasonable.

The same post in Spanish

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Manuel Alfonseca