Arquivo para a ‘Matemática’ Categoria

Unitas multiplex, networks and the beatitudes

03 Nov

Among the main concepts developed by Edgar Morin are cosmic Dasein (similar to Heidegger’s Dasein but expanded to the cosmic and similar to Teilhard Chardin’s Cosmic Christ), hominization and human identity, which is also linked to anthropolytic, but a fundamental and new is Unitas Multiplex.

According to Jean Ladriére Unitas Multiplex is “a system is a complex object, made up of distinct components joined together by a certain number of relationships”, and this both combines with the concept of social networks (not media) and Morin’s complexity, and Here we will establish a set of relationships with the biblical virtues of the beatitudes.

In a complex system, a certain number of relationships may be broken, what in social networks are called “structural holes” (Burt, 1992), weak ties (Granovetter, 1973) and small worlds of Duncan Watts (1998)

A system represented as a social network is a structure that connects nodes (forms a mathematical graph), generally each of these nodes are people, and links between nodes, representing relationships between these people (GRANOVETTER, 1973).

For Granovetter, bridges are links that enable weak ties, those that are on the periphery of the network or that are only reached by some nodes.

But neither the network theory nor the unitas multiplex theory establish the virtues that enable greater contact between these nodes, and as all these nodes can be reached, talking about empathy and bonds of solidarity is little, the biblical beatitudes can help.

Jesus climbs a mountain and speaks to a crowd of people, not just the disciples but everyone who wants to hear him (Mt 5:3-12):

“Blessed are the poor in spirit, for theirs is the Kingdom of Heaven. Blessed are the afflicted, for they will be comforted. [the weak ties]

Blessed are the meek, for they will possess the earth. Blessed are those who hunger and thirst for righteousness, for they will be satisfied. [the strong ties]

Blessed are the merciful, for they will obtain mercy. Blessed are the pure in heart, for they will see God. [empathy]

Blessed are those who promote peace, for they will be called children of God. Blessed are those who are persecuted for the sake of righteousness, for theirs is the Kingdom of Heaven!

Blessed are you when people revile you and persecute you and falsely say all kinds of evil against you because of me. Rejoice and be glad, for your reward will be great in heaven” [keeping the net united to the mystical body or “cosmic dasein”].

It seems heroic, or utopian, but if we want a peaceful Homeland, it’s a good recipe.


BURT, R. S. The social structure of competition. In: NOHRIA, N.; ECCLES, R. G. Networks and organizations: structure, form and action. Boston: Harvard Business School, 1992.

GRANOVETTER, M. S. The strength of weak ties. American Journal of Sociology, Chicago, vol. 78, no. 6, p. 1360-1380, May 1973.

WATTS, D. J.Strogatz, S. H. (1998). “Collective dynamics of ‘small-world’ networks” (PDF), NATURE, VOL 393, 4 June.


Mass over the world

06 Sep

Teilhard Chardin’s writing turned 100 years old on September 3, 2023, it ended in the Ordos desert in Mongolia, the writing started in 1919 when he worked as a porter in the First World War, it was remembered by the pope who was in Mongolia on this date.

For years the writings of Teilhard Chardin were banned, but little by little they were removed and were published revealing a spirituality and an updated and real worldview, it was Chardin who popularized the word Noosphere by Volodymyr Vernasky.

This mass reads: “Lord, since once again, no longer in the forests of France, but on the steppes of Asia, I have no bread, no wine, no altar, I will rise above symbols to the pure majesty of the Real , and I, your priest, will offer you, on the altar of the whole earth, the work and suffering of the world “.

Chardin had completed his thesis on paleontology and was in Mongolia to collect fossils when he finished the work, as he was unable to hold a conventional mass there (pictured with Émile Licent, in the Ordos desert, Mongolia).

His best-known work is “The Human Phenomenon”, controversial because he develops his theology within an evolutionary conception, which infuriated the theologians of the time and which is still fought today in more fundamentalist Christian sectors, it is good to remember that Jesus used parables to explain things complex and that the evidence for the existence of man in primitive periods is already a fact and many biblical allegories are clear, such as those used in the Apocalypse.

In the mass written by Chardin there is the desire for a single humanity, attached to the love of incarnation and revisited in the holy Host of each mass: “Receive, Lord, this total Host that Creation, moved by Your call, presents to You in the new dawn. This bread of our effort is, in itself, I know, nothing more than an immense disintegration. Unfortunately, this wine of our pain is still nothing more than a dissolving drink. But at the bottom of this formless mass, you have placed — I am sure, because I feel it — an irresistible and sanctifying desire that makes us all cry out, from the impious to the faithful: “Lord, make us one!” “.

The desire to see all creation as one and linked to life and Love is the Creator’s deepest desire.

CHARDIN, P.T. La Messe sur le Monde. (in portuguese), 1923.




Small worlds and closed circles

05 Aug

Small groups can potentiate their effects on a network, not only due to the ability to influence or cohesion, but also due to the degree of connectivity between nodes, which in technical language is called clustering, has nothing to do with closed circles, but the few connections are called Small Worlds.

This model of Social Networks (seen as a mathematical model of graphs and not just as media) observes a curious phenomenon called Small Worlds that was first proposed by Duncan J. Watts and Steven STrogatz in an article published in the journal Nature in 1998, the The model establishes that in a network there is a degree of separation between the points (network nodes) called six degrees of separation.

Albert L. Barabasi’s book “The New Science of Networks”, which expanded and corrected this model for larger scales, called scale-free, is thus described on pg. 47 of the book:

““The surprising discovery of Watts and Strogatz is that a few extra links are enough to drastically reduce the average separation between nodes…thanks to extensive bridges…connect nodes on the opposite side of the circle…”.(Barabasi, 2009).

So this is not the same as closed circles, since despite few connections, there must be bridges with nodes on the opposite side of the circle, so this “opening” is necessary, as mentioned for us on the opposite side of the circle.

This explains how many cultures and information expand or close according to the types of connectivity they have (the issue of clustering, in the graph p=0 to p=1) and due to the wider possibility of information today due to technology, the factors become more psychopolitical than geopolitical.

But it is also possible to explain the expansions of previous periods that depended on mobility and the “opening” of circles to other different cultures, Christianity for example, the book by Barabasi quotes, depended on the strategy of Paul of Tarsus which was to speak to the “Gentiles ” and to peoples who did not have Jewish culture, and from there it expanded into a network.

But they were a small group (12 apostles and then 72) but who traveled through the western world at the time, this idea of ​​small worlds is still present in Christianity until today, although numerous, the precepts of Love and Solidarity are not always observed, and this reduces it to closed circles.

The future is also expressed in Christian culture (Lk 12:31): “Do not be afraid, little flock, for it is the Father’s good pleasure to give you the Kingdom”, then the parable of the administrator is told. they do not know the time that will arrive and must always act waiting for you to arrive and find them attentive, in this case it refers to true treasures that we have already dealt with in previous posts.



Being, Pain and Easter

15 Apr

This is a time that did not abolish Pain, because as we developed in previous posts it is inherent to existence, but we condemn it to oppose it to Being and Happiness, the philosopher Byung Chul Han wrote: “Just in the palliative society hostile to pain , silent pains multiply, crammed into the margins, which persist in their absence of meaning, speech and image”. (HAN, 2021, p. 57).

Nothing is more paradoxical in post-modernity than Pain, so the Cross is imagined as a symbol of liberation and of life, one could even say: absurd, but Paul the Apostle warns: “For both Jews ask for signs, and Greeks seek wisdom; but we proclaim Christ crucified, who is a stumbling block to Jews and foolishness to Gentiles.” (Corinthians, 1:23).

It is in this perspective that racial violence, various forms of exploitation and what Byung Chul Han calls “self-exploitation” are explained, we no longer need others to exploit us, we do it voluntarily, incitement to a daily life with the mark of counting and not of Being.

The Pandemic could be an occasion for solidarity pain, but it was another impulse for exclusion, for isolation, for the strengthening of barriers and individual anxieties, which exploded in an anxiety crisis, in various ways of ignoring the pain of others, the point of denying it altogether.

It took a while, but in the final battle against the Pandemic we gave in to fatality, to the delirium of public parties out of time, the desire to overflow and try to ignore the pain for the ecstasy of public parties.

What appears on the horizon of this delusion are even more hellish wars, desires for domination and more power, lives are ignored with almost always absurd justifications: it was inevitable, there is no way to stop them without weapons, etc. more wars, more deaths, more suffering and market crashes.

Apparently, ignoring the divine Passion, we are making great strides towards a civilizing, humanitarian “passion” (of suffering) and a greater abyss than that which would be to live and manage the pains of a sick civilization and postmodernity with a horizon dingy.

There remains the hope of those who believe in the solidarity overcoming of a dormant humanity, of a balanced civilization center that recovers not only the process of hominization but also its solidarity with nature and the universe we live in.

This is a possible reading for the Divine Passion of the one who for love endured human pain, only a “passage” through Pain can make us understand a new possible humanity.

HAN, Byung-Chul. (2021) A sociedade paliativa: a dor hoje (The palliative society: pain today). trans. Lucas Machado. Brazil, Petrópolis: Vozes.


The complexity and its genesis

21 Sep

As we penetrate into the increasingly studied man-machine relationship, it is necessary to understand what has been theorized about nature so far, which means forming a model for nature, and in turn, making human and non-human collectives and individuals, composed in a culture, or in a tradition, or in a more general scope, what is articulated and what is only configured.

That is, the model may be subject to error or failure according to the areas implemented and can be determined by them, but by re-articulated it within its own history of creation, not naturalization but the culturalization of concepts, we understand the model that we have a priri, and that it is not always nature itself.

The one who penetrated deeper into this idea was Edgar Morin and from there conceived his method and developed complexity, conceiving nature requires ultimately preserving the network from which he conceptually emerged and correcting where the concepts were separated, identifying a network.

So it’s about identifying the culture that developed around nature, Morin puts it in lowercase to differentiate it from Nature itself in capital letters which is all that was said here and so the complex develops, which means what was “fabric together”.

What we then say about nature is the culture that developed around the idea that we could dominate it, but one of Francis Bacon’s maxims is that “we can’t dominate it if we don’t understand”, modern quantum physics, Modern astrophysics have shown how naive the models of Newton, Galileo and Copernicus were, but they were woven together to arrive at the new models proposed today.

Edgar Morin explains the “disorder of order” starting with two quotes to say that the order: “simplified laws invented by the wise” (Brillouin, 1959, p. 190), abstractions taken by the concrete (Whitehead, 1926)” (MORIN, 1977 , p. 76).

It is now, according to Morin, squeezed “between microphysical chaos and the diaspora”, and it matters to know how it was born: “How did it develop from scratch? How to conceive of it despite, with and in disorder? How can she appear to us as the sole sovereign of the universe if it is now so difficult to justify her existence? (idem).

What is the genesis? “the concept of order, in classical physics, was Ptolemaic. As in Ptolemy’s system, where suns and planets revolved around the Earth, everything revolved around an order”. (MORIN, 1977, p. 82).The Copernican revolution, however, was not the final word: “Hubble took away the entire astral or galactic center. And here is the great Meta-Copernican and Meta-Newtonian revolution, which went underground from Carnot and Boltzmann to Planck, Bohr, Einstein and Hubble. There is no longer a center of the world, whether it is the Earth, the sun, the galaxy or a group of galaxies” (idem)

And he continues: ”There is no longer an unmistakable axis of time, but an antagonistic double process that emerged from the same and single process. The universe is, therefore, simultaneously polycentric, centered, decentered, disseminated, diasporizing…” (ibid.).



Language beyond logic

21 Jul

In the entire history of philosophy and even science, there are three concepts that surpass in many aspects the concepts of logic, among them, the truth, the good and the justice are the most common, already in

Plato go beyond being logical principles, they embody cosmological principles and as such must resort to metaphysics, analogy and metaphor.

Thus, in Book VI of the Republic, the great metaphysical analogy falls on the idea of ​​good, homonymous to justice and truth: the sun is the son and progeny of good itself, and is still its visible analogue, there it is placed in the shadows of shapes in the cave, the contrast with the real and perfect world of shapes and the analogy of the sun to “lighten” objects.

In the absence of knowledge, they confuse mere shadows with reality, and philosophy is for Plato the pedagogical bridge that serves to pass from complete obscurity to the light of knowledge.

The use of language can also be only logical, in the 1930s, Wittgenstein said that as we know that in language there are only propositions, and surprises only occur in the world, so there are no surprises in mathematics: mathematics is totally “grammatical”, right -se-ia today is just syntactic.

In the context of semantics, and of meaning, language acquires other properties and in them that the metaphor makes sense, when saying José is brave as a lion, the analogy serves to increase what it means brave, giving new semantics to the syntax: José is very angry.

But the metaphor is also contextual, the beautiful poem by Fernando Pessoa “The poet is a pretender” is only understood if we know that “rope train” refers to a child’s play in the 20s and 30s of the last century and that “wheel rails” refer to the tracks, there:

And so on the wheel rails

It turns, to entertain the reason,

that rope train

Which is called the heart.

There is also the penetration of the metaphor into the mystery, the ineffable as we have already posted, and being able to affirm it.



The pandemic plateau remains

06 Jul

The data observed in the last week of deaths by the corona virus, which are reliable data, since the curve of infected people depends on testing, which is done by companies and is still low, indicate that the plateau remains and the pandemic is internalized in the Brazil (see graph), we have already stressed the importance of making the logarithm to better visualize the slope of the curve, which is exponential.

What the policy would be for this moment is to continue maintaining social isolation, personal hygiene, and social distancing habits, in addition to precautions in relation to municipal policies.

Any prospect of a peak, at least the data indicates, seems meaningless, the number of infections remains around a thousand daily deaths, and a #lockdown is no longer viable, as the virus has already spread and regional isolation does not mean pandemic control.

We will navigate through uncertainties, already tired of a long period of isolation and with an open and close policy that does not have much effective results, except to contain a greater contagion, without meaning any effective result of controlling the pandemic at the federation level.

The economic costs that would be great in the case of a #lockdown period, will now be higher because both the commerce and the services that effectively need face-to-face contact would not be justified to keep them disabled, and few services are non-essential.

The plan is to continue the so-called “social isolation”, whose more certain name in the Brazilian case we have already said, is “social distance” which is compatible with some open services.

The essential is therefore to maintain personal care and hope that the curve falls “naturally”. 


It is not a cIt is not a crisis of thought alone

02 Jul

The crisis may seem like something too intellectual, thinking would be far from the concrete reality of science, and thus from ordinary life, but its extension reaches the everyday science from statistics to medicine, from bibliometrics to biology and this can affect confidence in science and in In the spiritual field there is an immense openness to quackery and the manipulation of good faith.

This criticism questioned, for example, the fact-value dichotomy, emphasizing the social construction of facts, and can be traced back to the works of philosophers like Friedrich Nietzsche and Edmund Husserl, with their rejection of science as a metaphysical substitute.

Stephen Toulmin was very articulate in his criticism of the Cartesian idea of ​​rationality (1958), while the essence of the scientific method has been the subject of writings (and disputes) by authors such as Karl Popper, Thomas Kuhn, Paul Feyerabend and Imre Lakatos.

The essence of the scientific method has been the subject of writings (and disputes) by authors such as Karl Popper, Thomas Kuhn, Paul Feyerabend and Imre Lakatos, the echo of these disputes reaching the world of physics as the debate about string theories and their physical reality.

An interesting literature on the current crisis was the work of Derek of Solla Price “Little Science, Big Science” of 1963, he states that there is a point of saturation and senility, which was the result of the exponential growth he experienced in the 20th century.

Another more interesting work is the book by Jerome Ravetz “Scientific knowledge and its social problems”, which offers a critique of the myths of objectivity (it is our main object of this blog), and which asks about the solution of practical problems, that is , social.

In a recent work he recently argued Ravetz (2016) that “Applying a” scientific “methodology to science governance tasks leads directly to corruption, as any system can be at stake”, in another article, Ravetz (2011) defines the issue in terms of the “maturation of the structural contradictions of modern European society”.

The pandemic showed the inefficiency of both the medical field where “specialists” defend medicines that have not been proven effective and generate collateral problems, such as hydroxychloroquine and others (according to the magazine Veja (in section Saude), 69 medicines are tested: 18 are anticancer, 14 immunosuppressants, 13 antihypertensive drugs, 12 antiparasitic drugs and 12 anti-inflammatory drugs, and statistical treatment also hide the real results, as are the analyzes of the evolution of the pandemic in Brazil


De Solla Price, D. J. (1963). Little science big science. Columbia University Press.

Ravetz, J. R. (1971). Scientific knowledge and its social problems. Oxford University Press.

Ravetz, J. (2008). Faith and reason in the mathematics of the credit crunch. The Oxford Magazine. Eight Week, Michaelmas term 14–16, Available online at http://www.

Ravetz, J. R. (2011). Postnormal Science and the maturing of the structural contradictions of modern European science. Futures, 43, 142–148.

Ravetz, J. R. (2016). How should we treat science’s growing pains? The Guardian 8 June 2016.

Toulmin, S. E. (1958) The Uses of Argument, UK: Cambridge University Press. 






The development of science and the epistemic crisis

01 Jul

Several ideas and news spread among the peoples and become dogmas and legends since the origin of humanity, however it was the organization of knowledge that organized the episteme, the doxa its a single opinion.
The first great scientific question raised by Boethius in the seventh century, was whether or not there are universal or just private categories, this question gave rise to a dispute between nominalists like Duns Scotto and William Ockham who argued that “names” were universal, and realistic. like Thomas Aquinas, who said the real be.

Roger Bacon (1220-1292) defended experimentation as a source of knowledge, and together with Duns Scotto and William de Ockham they create the empiricist basis of thought, and so knowledge does not depend only on faith, but also our senses.

With his philosophical operation called “methodical doubt”, René Descartes ended up instituting a philosophical paradigm that was identified as conceptual pragmatism, and John Locke, representative of the empiricist current, and René Descartes, founder of the Cartesian method, converged in their theories when they stated that the valid knowledge comes from experience and the senses, as they are innate to the soul.

Kant’s idealism will create 12 categories separated into 4 groups, that of Quantity (Unit, Plurality and wholeness), Quality (Reality, Denial and Limitation), the relationship (Substance, Causality and Community), Modality (Possibility, Existence and Necessity), and in them the phenomena fill the empty forms.

Thus, the phenomena can only be considered within the categories, differently from the phenomenology that directs consciousness to the thing itself, that is, it returns to the beings, and this will open a new possibility for metaphysics.

Despite strong signs of a crisis in thought, mathematics changes with the emergence of non-Euclidean geometries, the fourth dimension, physics with the uncertainty principle where the theory of relativity and quantum physics came from, the logical paradoxes presented in Vienna circle and mainly a crisis in humanist thought, showed an early 20th century in crisis, but two wars and the cold war were not avoided.

The fall of the Berlin wall, an apparent end to the ideological struggle, has given rise to new crises now in the world of culture, the war in Iran, Afghanistan and the permanent one in many Arab countries have now shown an East vs. West tension.

The pandemic should solidarize the peoples, in fact it created a more serious ideological polarization, the danger of totalitarian regimes emerging with greater force, it is necessary to have hope and fight for a more solidary world and a humanism worthy of the name


Beyond idealism, new logic and pandemic

29 Apr

Kant’s simplification led to abstract formulations so complicated that it would be inappropriate to call them complex since he intended the opposite, but the attempt to reduce 12 categories and three central ideas: the psychological (soul), the cosmological (the world as a whole) ) and the theological (of God).
This will produce an ingenious, rational but very complicated construct, which are the three judgments that would link Subject (A) to predicates (B), the judgments: analytical, synthetic a priori and a posteriori, the idea of a priori judgments was the most controversial because it sees the mind as having a natural memory.
Edmund Husserl and Gottlob Frége, who had a strong arithmetical logic formation, looked at this Kantian theme, imagining that logic could not be reformulated based on action, that is, we do not change our mind because our way of acting changes, this is based on all who seeing the change in the logic of everyday life caused by the pandemic, they imagine that the mind does not change.
Husserl’s departure from mathematical logic to the world of experiences, under the strong influence of Franz Brentano who worked on intentionality (see the previous post, the other eidos), made him formulate a new world of experiences, from human emotions to total life of the world (Lebenswelt).
While the Logical Investigations date back to 1900 and 1901, their idea of intentionality formulated in their phenomenology as the return to things themselves, or how they appear to consciousness through phenomenological reduction, their epoché, which is to place our concepts and thoughts in parentheses, a clear disagreement with the Cartesian cogito.
On its return to the Greek eidos, it will promote eidetic variation, which can be explained as from the phenomenological epoché (putting concepts in parentheses) it produces an eidetic variation on the idea we had of the thing (concepts, thoughts or objects) and it can produce in the end new “horizons”, a fundamental category for the dialogue about the new.
Our pandemic phenomenon produced an “colletive” epoché, a new look at a deadly virus, we had to produce an eidetic variation, what we think of this “little flu”, and this should produce new “horizons” about the concepts of how to live the day to day: attitudes health, economic solidarity and total reformulation of family life: spaces, time, food and relationships and the use of technology.
Idealists continue to imagine that everything will be as it was before, they did not do the epoché pandemic.