How the triumph of Liverpool in the Premier League highlights the Fibonacci series, one of the most famous numbers sequences in history

Something extraordinary happened recently in English football. The Liverpool FC was crowned for the second time champion of the Premier League. In addition to his 18 titles prior to the Premier League, he matches Manchester United record of being England champion 20 times.

But while the club’s followers celebrated this moment of triumph, another amazing facet aroused the attention of mathematicians.

And it is that the conquest of the title by the Liverpool completed the opening of an exceptional series of numbers that have been taking place for 33 years. The sequence arises when we classify Liverpool with the other clubs that have won the Premier League since its creation in 1992, listing them by the number of titles won, starting with the lowest.

As can be seen in the following table, the number of Premier League titles is as follows: 1, 1, 2, 3, 5, 8, 13.

For an inexperienced eye, this sequence may not seem significant. But it will be enough to excite many mathematics fans. They will recognize it as the Fibonacci sequence, in which each number (after the first two) is the sum of the previous two of the sequence.

This sequence is in an amazing variety of places: from the spirals of the seeds of the sunflowers and the bracts of the pineapples to the patterns of the genealogical trees of some animal species.

The Fibonacci sequences (plural sequences because if it is based on a couple of different initial numbers and the rule of adding consecutive numbers is followed to generate the following a different sequence is obtained, but related) were first introduced into European science in 1202 by Leonardo de Pisa, also known for his nickname Fibonacci (which means son of Bonaccio).

However, long before Fibonacci popularized the sequences in his book “Liber Abaci”, the Indian mathematicians already knew them. They had resorted to the sequences to help them list the number of possible poems of a certain length, using short syllables of a duration and long syllables of two units of duration.

The Indian poets/mathematicians knew that a poem in length n could be made taking a poem in length N-1 and adding a short syllable or a poem in length N-2 and adding a long syllable. Therefore, they deduced that to calculate the number of poems of a certain length, it was enough to add the number of poems that had a less syllable and the number of poems that had two less syllables, the exact rule that we used today to define a fibonacci sequence.

In the sequences another important and related mathematical pillar is hidden: the golden proportion.

As the terms of a fibonacci sequence increase, the relationship between each term and the previous one is increasingly close to the golden proportion, approximately 1,61803 by the first places of its decimal expansion.

It is believed that the golden proportion governs the arrangement of the leaves in the stem of some species of plants and, supposedly, produces aesthetically pleasant results when applied to art, architecture and music.

Mathematicians usually present Fibonacci sequences as examples of the beauty of mathematics. They can provide vivid visual examples of mathematics written in real world patterns, without which many non -mathematics can have difficulty understanding the elegance we see in our matter.

However, in our excess proselytism, there is the temptation to present the sequences of Fibonacci or the golden proportion as a kind of omnicomprehensive natural law that governs phenomena of several orders of magnitude, from the spiral forms of the nautilos shells to the vortices of hurricanes or the curved arms of the galaxies.

Actually, although these natural characteristics are aesthetically pleasant, very few of them conform to the rules of the Fibonacci sequence or present the golden proportion.

We must be careful not to try to put all beautiful patterns in the delicate patterns in the delicate fibonacci glass shoe, to suggest causality and impose meaning where there is no.

It is extraordinary that the Fibonacci sequence appears in a place as unexpected as the Premier League. When, as scientists, we observe that a sequence as well known as it appears apparently from nothing, we should start asking if it tells us something important about the process generated by the sequence.

Is there any surprising and invisible process that underlies the battles for the title of the Premier League or is it nothing more than a beautiful coincidence? We see a fibonacci sequence in something does not mean that it is there for some reason.

However, detecting this type of apparent coincidences can be very useful for the scientific discovery process. In 1912, for example, Alfred Wegener observed the apparently strange coincidence that the Coast of Western Africa and the Eastern Coast of South America seemed to fit the pieces of a puzzle.

Despite the predominant opinion at the time, according to which the huge land masses of the continents were too great to move, Wegener proposed the only theory that reconciled his observations.

Continental drift suggested that the earth masses were not rooted in their place, but that they could, very slowly, change their relative positions on the earth’s surface.

When Wegener posted his theory in 1915, he became everyone’s laughing.

The geologists rejected their extravagant idea, claiming the lack of a mechanism to move so huge pieces of the earth’s surface, and the apparently adjusted tessellation of the continents.

However, in the 1960s, the theory of plate tectonics – the movement of the solid mantle and the cortex on the earth’s surface – gave credit to Wegener’s theories, now widely accepted.

Although coincidences can point out the way to new scientific discoveries, they can also assume an obstacle to scientific progress when they seem to confirm an incorrect theory.

At the beginning of the 19th century, German anatomist Johann Friedrich Meckel made an error of this type. Meckel believed in the natural scale (The staircase of nature), according to which the human being is above the rest of the animals in an orderly but static hierarchy.

The simplest and most primitive ways of life were supposed to be located on the lowest steps on the stairs, while the most complex and advanced beings resided in the highest.

His views were not surprising, since this “great chain of being” was the predominant theory of the time. The theory of “common offspring”, today generally accepted, according to which multiple species descend from a single ancestral population, was then an incipient idea.

Meckel used the natural scale to formulate a conjecture about your specialty: embryonic development.

Known as recapitulation theory, it postulated that, as they developed, the embryos of higher order animals (such as mammals) progressed successively through forms that looked a lot like the “less perfect” animals, such as fish, amphibians and reptiles, located on lower steps of the scale.

A surprising, but apparently unlikely prediction, of this theory was that, as humans advanced by the “fish stadium”, their embryos would have gill gangs.

In 1827 it was discovered that human embryos really have clefts that resemble gills at an early stage of development. This extraordinary finding seemed to confirm Meckel’s prediction and corroborate his recapitulation theory.

Until almost 50 years later, in the 1870s, the development recapitulation theory was not definitively ruled out and the idea of ​​common offspring began to impose itself.

The common offspring is the basis of what we know today as modern evolutionary theory. He made it clear that, far from going through a “fish stage” in the uterus, the gill clefts were a consequence of the fact that, by sharing a common ancestor with the fish, we also share much of its DNA and its first development processes.

Sometimes coincidences can lead scientists by bad way, because they seem to aim at a conclusion when, in reality, there is an alternative explanation for the observations that relies better in the facts.

So what means for the king sport the fact that the beautiful and almost mystical sequence of Fibonacci has appeared in the data on the number of titles of the Premier League won? Without any plausible mechanism that may have given rise to the sequence, the answer is almost certainly.

It is wonderful to have discovered this mathematical sequence in such an unusual place, which gives us the opportunity to reflect on the importance of Fibonacci numbers. But a pattern does not always mean causality: a coincidence is sometimes just a coincidence.

And, like Meckel’s gill slit, its appearance in the Premier League records is nothing more than that: nothing more than a spectacular coincidence but, ultimately, misleading.

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