[Lee Jong-gil's Autumn Return] The Principles of Mathematics Embedded in Human Culture

Herv? Lehning 'All the Mathematics in the World'

Movie 'Avengers: Infinity War' still cut

In the movie "Avengers: Infinity War (2018)," Thanos (Josh Brolin) eliminates half of all life in the universe. He believes that the balance of the universe and nature has been disrupted by overpopulation. The foundation of his firm belief is "Malthusianism," a social mathematical model proposed by the British demographer Thomas Robert Malthus (1766?1834).

Malthus viewed population change as following an exponential growth model in each territory, meaning that the population each year in a given territory is equal to the previous year's population multiplied by a certain rate. In contrast, he believed that the increase in food resources follows an arithmetic growth model, meaning that the resources each year are equal to the previous year's resources plus a fixed amount.

The exponentially increasing population per territory inevitably surpasses the resources produced in that territory at some point. Therefore, Malthus advocated for birth control. However, the results of mathematical models need to be contrasted with reality. The exponential growth model Malthus used to describe long-term population changes lacks realism. All exponential growth eventually reaches a limit, just as trees do not grow endlessly.

"The Mathematics of the World," written by French mathematics educator Herv? Lehning, thoroughly explores the principles of mathematics embedded in human culture. It focuses on historical anecdotes and puzzles rather than complex formulas to facilitate quick understanding. When explaining the errors of "Malthusianism," it uses the relationship between the field vole and the stoat as an example.

The population of field voles sharply declines every four years. Unlike other predators such as foxes, seagulls, and snowy owls, stoats exclusively hunt field voles. Due to this high predator dependence, when the number of field voles decreases, the stoat population also significantly drops. This allows the surviving field voles to have the opportunity to increase their numbers again.

Italian mathematician Vito Volterra (1860?1940) quantitatively described the oscillating population of field voles and proposed the Volterra model. "The Mathematics of the World" explains as follows:

"All mathematical models generally reflect the interdependence among various factors, initial conditions, and coefficients adjusted according to the past. By calculating these, predictions about the future can be inferred. However, such predictions respond sensitively depending on the values chosen for the coefficients. Therefore, results obtained through calculations must always be regularly compared with reality."

This also applies to predicting infectious diseases such as the novel coronavirus disease (COVID-19). In September 2014, the World Health Organization (WHO) announced that the number of new Ebola virus cases in West Africa had doubled every month since May of the same year. For example, if there were 250 new cases in May, then 500 in June, and 1,000 in July.

If this trend had continued, the number of new cases in September 2015 would have reached 16 million. However, such a catastrophe did not occur. While WHO's response played a significant role, above all, infectious diseases do not follow an exponential growth model.

The first scholars to describe how diseases operate on a large scale were Scottish mathematician William Kermack (1898?1970) and epidemiologist Anderson McKendrick (1876?1943). To apply differential systems like the Volterra model, they divided the population into three major groups: those at risk of infection, those already infected (and contagious), and those who have recovered or died from the disease. Based on this, they calculated the probability of a person exposed to the virus becoming infected, and the probability of survival or death after infection.

As a result, if the potential number of disease victims was below a certain threshold, the disease did not spread. Conversely, if it exceeded that threshold, it became a pandemic. Whether an infectious disease outbreak occurs depends not on the number of infected individuals but on the number of people at risk of infection. This justifies vaccination policies. In the case of Ebola, since there was no vaccine, the only options were isolating patients and protecting medical staff. Even now, as COVID-19 spreads, the situation remains similar. There are still countless people at risk of infection.

This content was produced with the assistance of AI translation services.