Arquivo para a ‘Matemática’ Categoria

A worldview beyond time

09 Sep

Aristarchus of Samos (320 BC – 250 BC) organized a cosmology far ahead of his time, what was known to date was the studies of Pythagoras (571-390 BC) and Heraclides (390-310 BC), who claimed that the stars were immobile that the earth was the center of the universe, only Mercury and Venus would orbit around the sun. While flourishing Euclid’s Geometry (300 BC – ?).
Aristarchus which also had works on optics, music and mechanics, astronomy and astrology, invited by Ptalomeu I will compose the famous Academy of Alexandria, and his influence on the Renaissance will in particular influence his studies on proportions and projections, and although others are cited, Piero dela Francesca (1415-1942) is the great success of Euclidean geometry in the Quattrocent Renaissance.
Aristarchus’ view far ahead of his time was that the earth revolved around the south, and the moon revolved around the earth, thought of two experiments to measure Earth’s radio and the distance from Earth to the Sun.
The experiment thought was to build a tower facing the sea and knowing the height of the tower and the angle between the sea horizon (where there is less distortion thinking the earth as a sphere), can similarity of triangles calculate the radius of the Earth, the The error was small for the measurement difficulties of the time, very close to the 6 378 km of the equatorial radius.
If an object is 1 ° from some measurement point, that object is necessarily 57 times its size, because the tangent of 1 ° is about 0.01745 (see figure) see figure and so Aristarchus calculated the radius of the earth.
The second experiment, knowing the radius of the earth was to find the distance to the sun, he knew that during the full moon, under the average 31 minute angle of the arc (half of 1) tells us that this measurement will be 115 times its diameter, and we can find the distance from the earth to the moon, using again the tangent (he found an angle of 87º) one can measure the distance to the sun that gave 7 million and 300 thousand kilometers, in fact the angle was 89º853´, and the distance between the earth and the sun is 150 million km.
Carl Sagan makes a beautiful presentation and Aristarchus of Samos and his worldview beyond his time:

Source: Costa, J. R. V. Aristarco de Samos e a distância Terra-Sol. Astronomia no Zênite, jul 2000. Disponível em:


Michel Serres dies

03 Jun

I get the news in the morning of the 1st. of June working at home, Michel Serres passed away, I remember several things of him that I gave in class for having appreciated by the new technologies and to make analyzes less pessimistic of this aspect.
I also remember his words about Hiroshima, who affirmed it as the sole objective of his philosophy, in the sense of peace, of course, he said that he had no influence from thinkers, but he was guiding nothing less than Bachelard, he lived with Jacques Monod, and did a published interview with Bruno Latour.
In this interview she stated: “it is carnally formed in this atrocious environment and has remained, since then, removed from all politics: power continues to mean only corpses and tortures to it”, the problem of violence has always been its main problem and hence its work .
He did not follow the traditional French epistemology that in his view is based on the separation between “sciences” and “humanities”, his perspective was to create a bridge between one field and another, the primacy of the course on the discourse (see that there is difference) , in short the search for a generalized theory of the place.
He wrote in The Leibniz System: “Through the most distant regions there is often an underground relationship that intuition alone can not attain, nor can immediate knowledge or discursive knowledge, but which can be attained, by a pure and refined formalism … The aptitude to the diverse is proportional to the initial purity.”
Alongside Michel Foucault, in the early days of the University of Vincennes (Paris-VIII) in 1968, he formed a generation of researchers and thinkers who had him as a great teacher.
Among the faceted ones of Serres, the one of historian of the sciences, in “Elements of History of Sciences” (1989) was revealed. Under his direction worked Authier, Isabelle Stender, Bruno Latour and Pierre Lévy, just to mention what is best known in Brazil.
He saw in the new technologies not a curse that cushioned relations, they were dampened by modernity and non-originating knowledge, he affirmed that a new Pedagogical Society is yet to be born.
He said in a prophetic tone, that our communications world is aging, giving birth to a pedagogical society, that of our children, where continuing education will continue for the rest of our lives, an increasingly rare work.
The universities at a distance, everywhere and always present, will replace campuses, closed ghettos for rich adolescents, concentration camps of knowledge … “(SERRES, 1995, p 56).
SERRES, M. The legend of the Angels (in Portuguese), São Paulo: Aleph, 1995.


The crisis of Science and Knowledge

22 May

The quantum physics that dismantled the building of mechanistic physics, which was the idea of ​​an increasingly mathematical knowledge, and this would be rigor and not philosophy, in the sense of thinking, is a crisis established in the beginning of the last century, studies of the Vienna Circle and Husserl’s statement of the crisis of the European sciences were the initial contours of this crisis.

On the crisis in European culture caused by the orthodox view of science as a privileged discourse of appropriation of the world being, pointed out in the original idea of ​​Edmund Husserl in “The Crisis of the European Sciences and the Transcendental Phenomenology” (2002), Heidegger points to a crisis in European culture caused by the orthodox view of science as the privileged discourse of appropriation of the being of the world.

Heidegger later wrote of it: “The decisive development of the character of modern enterprise of science, therefore, also wed another species of man. The scholar disappears. It is rendered by the researcher (researcher) who is in his research endeavors. These, and not the care of a erudition, give to their work the fresh air. The investigator no longer needs any library at home. He is constantly on the move. Discusses in colloquies Discusses in colloquiums and is informed in congresses. “(HEIDEGGER, 2002, p.108).

It was pointed out correctly by the Brazilian researcher, Cintia Struchiner, that “this is not a crisis of the sciences as such (it is quite obvious that the sciences continue to progress and produce knowledge), but it is basically a crisis of sense. The neutrality of the world of science leaves out fundamental human questions (values, culture, ethics), so that between the world of science and the life-world a process of detachment is gradually being established. Husserl’s point is that science, so constituted, has very little to offer us regarding the most fundamental issues for humanity: its values, its culture and the sense of individual and collective existence” (STRUCHINER, 2007)

The contours of this crisis lie in the vision and thought of science, but extrapolate these and emerge in a culture of obscurity, ignorance as thought, the immediacy of the being of the world, and the emptying of being-in-the-world produces only a weariness, an absence of essentiality, a superficial criticism that does not leave the technician and does not discuss technique as an essential knowledge, but does not exhaust itself, because it does not contemplate Being.

These changes continue to occur in the 21st century, a European work explains this through phenomenology itself, showing the digitization and opening of this knowledge:


HEIDEGGER, H. Caminhos de floresta. Lisboa: Fundação Calouste Gulbenkian, 2002.

HUSSERL, E. A Crise das Ciências Europeias e a Fenomenologia Transcendental, São Paulo Ed. Forense Universitária, 2012.

STRUCHINER, Cinthia Dutra. Fenomenologia: de volta ao mundo-da-vida. Rev. abordagem gestalt., Goiânia , v. 13, n. 2, p. 241-246, dez. 2007 .


The informational impact

08 May

Society, information abundance, information turnaround and other appeals to the novelty that arose not with the internet, but with the computer and the possibility of handling the data in volume (Big Data) certainly brought a new perspective.

Anyone who wanted to understand eighteenth-century society should study the industrial revolution and its impact on manpower and the production of serial products, today anyone who wants to analyze contemporary society cannot lose sight of the volume of data they are produced to try to make this volume accessible to society.

But it is not so, because together with this volume came by previous process, it is only to check with history, not the romantic dreamed by idealists, but the real one and to realize that the problem of both Information in volume and depth, made it difficult to digging and knowing what is essential.

We have already posted here Karl Kraus, who complained to journalists in the midst of the threat of a second world war because of misunderstood news highlighting only interests. In an interview with the newspaper El Pais, Peter Sloterdijk also warned that “it is difficult to think of contemporary society,” Byung Chul Han his disciple alert to “active vita” (Chul-Han)

The phenomenon we witnessed in which information became practically a commodity, started with the digital model of Shannon (photo) and the Turing machine in the 1930s, and accelerated with the construction of modern computers.

What we witnessed and did not always participate in an “active” and reflexive way, able to elaborate thinking about information, is the fragmentation of knowledge accelerated by new gadgets, but which was initiated by a crisis in the thinking of Western society, which only deepened over the years, its initializing in modernity.

The Movie The game of imitation (2015) illustrates the life of Alain Turing and his theory:




Mathematics woman wins Abel award

21 Mar

Niels Henrik Abel was born on August 5, 1802 in Finnoy, Norway, and died on April 16, 1829 in Froland, when he went to visit the bride on a sleigh, and died days later in 1829, his main work Recherches sur les fonctions elliptiques was published in 1827 in the first volume of Crelle’s Diary, a mathematics-only diary.
The Abel Prize was established in Norway in 2002, and now for the first time a woman wins the award, the American Karen Keskulla Uhlenbeck, who according to the Norwegian Academy of Literature and Sciences held “pioneering achievements in differential equations in Gauge Theory and integrable systems; and for the fundamental impact of his work on analysis, geometry, and mathematical physics.”
The Gauge Theories, or Caliber´s Theories, formalize a class of physical theories based on the idea that the symmetry transformations, which can be either local or global. These ideas apply not only to field theories, but to so-called finite-dimensional systems, as are those modeled by ordinary differential equations.
It is an important model in the generalization of the General Relativity Theory and curious that arises at the same time from the proof of the non-objectivity of science (see the post), although there is no immediate relationship, the fact that local results are not objective is interesting for a mathematical theory shows that they are both important, how would the composition of the two results be?
The Nature magazine on March 19 dedicated a special note to Karen.
This vídeo of the Spring River shows the Gauge Theory: