Innumeracy

Douglas Hofstadter

Douglas Hofstadter, the author of the book Gödel, Escher, Bach, an Eternal Golden Braid, coined the word innumeracy, by analogy to the word illiteracy, to mean the lack of mathematical knowledge affecting a large part of the population.

Let's look at an example of innumeracy proposed by A.K. Dewdney in his book 200% of Nothing:

A man finds a $5 bill, puts it in his pocket and thinks: "As I have a $10 bill in my other pocket, I just won 50%." When he arrives at home, he discovers that he has lost the $5 note he had found. He then thinks: “As I had $15 and have lost $5, I have suffered a 33% loss. As previously I had won 50%, overall I have won 17%.”

Reading this, one tends to think: this situation is so absurd, that it cannot actually happen. However, on May 30, 2008 I heard the following news on the Spanish National Radio:

The fishermen complain about the rise in the price of diesel. Five years ago, it cost them 320% less.

I suppose they were paid whenever they filled the tank. What actually happened is that the price of diesel had risen by 320%. What used to be worth 100, now cost 420. Therefore 5 years ago, fishermen had to pay 76% less (320/420), rather than 320% less (320/100).

I can’t see any difference between this news and the anecdote invented by Dewdney. It is evident that the person who prepared the news in question for the Radio station suffered an acute attack of innumeracy.

A.K. Dewdney

Let's look at another example, also real, mentioned in Dewdney's book. In California, during the craze to replace incandescent bulbs by fluorescent bulbs, with a saving of energy for the same illumination, a magazine ran a full-page ad for Northeast Utilities, a local power company, stating that those who used the new bulbs would save 200% energy.

A Californian who did not suffer from innumeracy called the electric company and asked if the company planned to pay him a monthly amount if he used those bulbs. After all, if the energy savings were 200%, the bulbs must inject energy into the electrical grid whenever they are turned on. The company employee answered with a terse "No" and hung up the phone.

The Californian then called the advertising company that had placed the ad and tried to explain what a 200% savings would mean, but the employee who answered him replied that "we know by good authority that the math is correct." And there was no way to convince him.

Why did they come to that conclusion? Let's imagine that the energy consumption of the incandescent bulbs was equal to 100. Assume that fluorescent bulbs had an energy consumption equal to 33. The savings would be equal to 67 (that is, 67%). But those who did the calculations, instead of comparing 67 with the initial expense (100), as they should have done, compared it with the final expense (33), and of course, they got 200%. But this result does not make practical or mathematical sense.

Let's look at another example of innumeracy that I heard on Radio 5 News on May 29, 2008:

The CPI has risen 4.7%. Last year it was up 2.3%. Therefore, prices are twice as high as last year.

The CPI measures the variation in prices. A double CPI means that the price increase has been double, not that the prices are double.

I end with another example from Dewdney's book: We know that a googol is equal to 10¹⁰⁰ (a one followed by a hundred zeros). An advertisement from the National Security Agency offering jobs for computer scientists, wrote the value of the googol (one followed by a hundred zeros) in the middle of the advertisement and explained:

We are showing you the googol [because] to consider the National Security Agency you need to think big.

And it added:

Counting 24 hours a day, you would need 120 years to reach a googol.

Is this true? Let's think: 120 years is equivalent to about 3,786,831,130 seconds. Then to count a googol in 120 years, you must count 10¹⁰⁰ / 3,786,831,130 = 2.64 × 10⁹⁰ units every second. It seems that the authors of the ad did not have a very clear idea of ​​ what a googol means. In other words, they suffered from innumeracy.

I could add many more examples, but this is enough for today.

The same post in Spanish

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Manuel Alfonseca