Personal and social problems of innumeracy

The innumeracy, or inability to comfortably handle the fundamental concepts of number and chance, gives issues to many people who, on the other hand, can be regarded as well-educated.

Plus, at social level, the innumeracy gives rise to societies that

  • Overestimate the frequency of matches. They are people who generally attach a lot of importance to all kinds of correspondences and, on the other hand, give little importance to less glamorous but absolutely conclusive statistical evidence. 
  • Have a strong tendency to personalize. People for whom the image of reality is distorted by their own experiences, or by the attention mass media provide to individuals and dramatic situations.
  • They believe in pseudoscience. To the question of why he does not believe in astrology, the logical Raymond Smullyan responds with irony that he is Geminis and that the Geminis do not believe in astrology.

As an anecdote about innumeracy, the general inability to comfortably handle number and chance concepts, the one day that in the news was said that for the next weekend, rain was expected for Saturday with a 50% probability and the same for Sunday, and the person next to me concluded that the probability of rain during the weekend was 100%.

The effects of innumeracy, affect many areas of our lives.

Sometimes with innocuous consequences as staying at home because we are convinced that the probability that it will rain the weekend will be 100%. Others of less innocuous such as not correctly estimating the probability of car accidents and not reasonably preventing the risk.

And let’s not say how serious it is in the medical field.

I once heard a doctor who made three statements about a treatment that demonstrated his total mathematical ignorance:

  • It presents a risk of between one million
  • It is safe at 99%
  • Normally it goes out perfectly

In general, we do not understand the odds and we do not have a large mental representation of magnitudes such as one million items, one billion items, …

Let’s see that explain in the following story:

In a column on innumeracy in the Scientific American, computer scientist Douglas Hofstadtercites the case of Ideal Toy Company that, in the Rubik’s cube wrapper, stated that the cube admitted more than 3,000 million different configurations, that is, a 3 followed by 9 zeros.

If we make the calculations, we will see that the possible configurations are 4 followed by 19 zeros, that is, 40,000,000,000,000,000,000, 40 millions of billions, a number much higher and not comparable to the 3,000 million advertised in the wrapper.

The phrase of the envelope is true but is very inaccurate, and therefore it is not relevant and even gives place to disinformation.

Look at it in that way. It is as if at the entrance to Barcelona there was a sign that said: “Barcelona, ​​more than 6 inhabitants.”

In order to be able to make comparisons and know how to handle large numbers, especially now that we are in the era of the Big data, it would be nice for us to think (and calculate) in the school for how long it takes a million seconds, namely eleven days and a half. And how long do they last one billion seconds, that is, 32 years.

With a knowledge of the magnitudes we could be more aware of the extent of environmental disasters and everything that affects our state budgets.

It would be very interesting to put the boys and girls questions like the following, and teach them to solve them and put the result in context (*):

  • At what speed human hair grows in qm/hour
  • How many cigarettes are smoked annually in Catalonia?
  • Total volume of existing human blood in the world
  • Relationship between the supersonic velocity of the concord and that of the snail
  • Relationship between the speed in which an average computer adds ten digits and the speed of human calculation
  • When it would take to make disappear an isolated mountain as the Fujiyama transported it in trucks.
  • Assume Shakespeare’s account is accurate and Julius Caesar gasped “You too, Brutus” before breathing his last. What are the chances you just inhaled a molecule which Caesar exhaled in his dying breath? The surprising answer is that, with probability better than 99 percent, you did just inhale such a molecule. Do you want us to do the calculation?

(*) Whoever wishes to know the answers can request customized training or be aware of our next regular trainings in Statistics and Probabilities and in Data Literacy.

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