Who does the future belong to? To science, to mathematics—it offers us some forms of prediction, mostly through probabilities. A classic example is the coin toss: when tossing a coin a hundred times, half the time it is expected to land heads up (and the other half, tails, it is clear).
It is known, however, that this prediction is not very accurate. If the coin were actually tossed a hundred times, maybe the heads side would show up 46 of the times. Or in 58. This variation does not escape mathematics either: it is analyzed by the so-called normal distribution. The concept is well illustrated by a graph—the Gaussian curve—which shows, in this example, the most likely swings of the coin (eg, forty heads and sixty tails) and the most unlikely (like eighty heads and twenty tails).
But predicting the apparent face of the coin is not so difficult, after all there are only two options. How to predict the behavior of more complex systems, which depend on many variables, such as the human organism or a colony of bacteria? This is the question that guides the research of mathematician Dirk Erhard.
Passionate about probability, Erhard himself escapes the Gauss curve: mathematicians who have won medals in trampoline jumping are rare. Born and raised in Berlin, at age seven he was discovered by an Olympic gymnastics talent scout. After almost a decade of intense training, the young man realized that the dream of being world champion on trampoline would forever be a dream. “I wasn’t bad, but I knew I wasn’t good enough to get to the top,” recalls the German. Between the ages of eleven and seventeen, he became five-time champion of the sport in Germany — he says, however, that the youth category does not reveal much about the athlete’s potential.
With low odds of becoming a successful gymnast, he bet his chips on math. Erhard is so unlikely that, in his early years of graduation, he didn’t like probability. At the time, he even had an affinity with functional analysis — a discipline that deals with the study of functions. On an exchange program in Paris, the boy got lucky: he had classes with a great teacher, who explained, precisely, the intersections between functional analysis and probability. “It was the best course I had in my life, taught in an easy to understand way”, recalls the mathematician, who chose to pursue an academic career in the area.
Between master’s, doctoral and postdoctoral programs, Erhard passed through Germany, France, Holland and England, until finally reaching the current job of professor at the Federal University of Bahia — the idea was to be closer to the family of his Bahian wife, for whom fell in love with the European wanderings. Even living in several countries, the mathematician dedicated himself to the same investigation: to make predictions simpler, mainly of complex systems. Instead of analyzing coin flips, Erhard focuses on systems with multiple particles that interact with each other and behave differently at different points in time and space.
The research still has a theoretical character, but shows its potential when applied to practical situations, even if hypothetical. An example would be a wide and deep lake, where fish breed and, for that, they need an ideal temperature. At each point of the lake, the temperature will be a little different, influenced by variables such as depth, incidence of the sun, presence of shoals. Erhard works on the creation of a mathematical model that facilitates the prediction of the temperature in the different regions of the lake.
While the German is investigating the movement of particles, at least one more concrete possibility of applying his studies has already been on the agenda. “A few months ago, I had a conversation with a group of physicists who are looking to understand more about the human brain,” says Erhard. Whether it will be possible to predict brain behavior remains to be seen — but if it depends on the mathematician, the probability is high.
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Murilo Bomfim is a journalist.
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