A few years ago I was at a congress in Odessa, a beautiful Ukrainian city on the shores of the Black Sea. The climate was pleasant, there were beautiful buildings and except for the scientists with whom the rest of the people spoke, they did not understand English almost at all. And I the Russian, or rather the Ukrainian, nothing at all.
I don’t know if it happened, butIt is hard to go down the street and have no idea what the street signs say. When he wanted to buy something, he made a questioning face, made the universal symbol of how much it cost with his thumb and index finger and handed them a paper and a pen so that they could write down the price. A decent meal cost about 150,000 Ukrainian coupons, about 400 pesetas at the time. The moral of this anecdote is thatAlthough we do not know many languages, there is one that is universal: mathematics. Everybody understands the numbers. Mathematics is universal.
In this regard, there is a curious anecdote about one of the most important chemists of this century: Josiah Willard Gibbs. Gibbs was a quiet and withdrawn member of the university community at the prestigious Yale University. About him it is said that during the thirty years he was there he only made one speech. It is said that his unrepentant silence was broken during a heated discussion in a café about which discipline, classical languages, modern languages, or science, best trained the mind. Gibbs, with his usual parsimony, got up and said:
– Gentlemen, mathematics is a language.
And he sat down again.
Certainly mathematics is a language. And a universal language. That is why scientists are able to communicate with each other even if they do not understand the language with whom they share their information. But the most mysterious of all is that mathematics is the only way we have to understand the world around us. The language with which nature is expressed is that of mathematics and whoever wants to read that book must learn it. We don’t really know why this is so. Furthermore, it is not clear to us that Nature knows mathematics. Perhaps it is the means that we use to interpret the facts of the world.
Now, it is not difficult to hear phrases like “math was never my strong suit” or “don’t talk to me about math; I am of letters ». Sometimes we can even hear our interlocutor boast that he has no idea about mathematics, that adding and subtracting is enough for him. This behavior is part ofa certain social trend where it is well seen to declare oneself illiterate in any matter related to science. Something surprising, because no one would think of feeling proud of not knowing who Cervantes was.
Unfortunately,the consequences of mathematical anumerism are serious. Everyday life is full ofsituations where an elementary knowledge of mathematics is essential to make an appropriate decision. This is especially exaggerated in our perception of probability. An example we have in the call“Gambler’s fallacy”. Let us suppose that in a casino roulette wheel the color red has appeared six times in a row. Players often think that in the next game there is a greater chance that black will come out when in reality there is the same as before, 50%.
Probability
This blindness tooddsit is even more marked when we want to analyze risk situations. We know how to distinguish between what does not involve any risk and what does. However, we are unable to differentiate between an act that has, for example, a 1 / 10,000 risk of another with a 1/100. What concerns us is not whether the risk is high or low, but rather that there is risk. And even more serious: while we refuse to perform certain acts because they involve risk, we assume others where the percentage of risk is higher. An example is in the case of plane accidents. Phobias aside, some people don’t want to fly for fear of an accident. But that does not prevent them from taking the car when the probability of dying in a traffic accident is much higher. The maximum irony appears when, to justify themselves, they say that «well, yes, but if it’s your turn? it’s your turn ”, as if that didn’t happen with cars. These examples show us that humans do not know how to estimate probabilities intuitively; we need to learn how to do it. Our brain has a habit of making us believe that an event is very likely to occur, not based on neat probabilistic calculations, but for a much more mundane reason: the easier it is for us to imagine it mentally and the more it impresses us emotionally.
Someone once said thatin this life there are only two things certain: death and taxes. And it’s true. The rest of the things may or may not happen to us. Anyway, whatour life is governed by probability.
Knowing this, what is most shocking is that we do not really care to understand what probability is. We do not even feel the slightest need to know how to estimate it, and that taking into account that the human being has an innate inability to interpret it. Sometimes I think it is genetic. But,I challenge you to do the following experiment with your friends.
To a group of them, propose the following problem. Imagine that the government is preparing a remedy for the famous flu A. Your friends are part of the team that must decide between two treatments. Out of 600 people, treatment A will surely save 200. From B there is a one-third probability that all 600 will be saved, and therefore two-thirds that none will be saved. Now choose which treatment you would choose. If the average is met, when this question was asked to a group of people 72% chose program A. Now pose this problem, but with another approach, to another group of friends. Tell them that with program A, 400 people will surely die and with program B, no one will die with a one-third chance and 600 with two-thirds will die. Again, if the average is met, 78% of the people who were asked this question chose program B.
How is it possible that, being the problem identical, two different programs are chosen simply because it has been presented differently?
Even worse. In the long term, both programs have the same result: 200 are saved and 400 die, then it is indifferent to opt for one or the other.
Miguel Angel Sabadell
