The mathematics of information disorder



It is necessary to remove from platforms the power to decide what can be posted or not, according to their diffuse and opaque “terms of use”.


In recent years, a large part of society and its responsible political and intellectual leaders have had their attention drawn to an apparent new problem that some call “disinformation”, others “informational disorder”, the majority just call “fake news“. It is the dissemination, through so-called “social networks”, of lies, conspiracy theories, hate speech, obscurantist or anti-scientific manifestations of all kinds, which in addition to promoting increasing anti-social behavior, the worst of which is violence against individuals for any trivial reason, mainly affecting women and more vulnerable groups, are profoundly affecting the present and future of democratic societies.

The real cause of this whole problem is the tearing apart of the social fabric and, with it, of a certain hegemonic political and cultural ordering until a few years ago in liberal-democratic capitalist societies, due to the neoliberal reordering, promoted and sponsored, paradoxically, by these same democracies, a reordering that led to the fragmentation of the world of work and the emergence of social resentments catalyzed, through “networks”, by billionaire financiers and opportunist agitators affiliated with fascist, obscurantist, retrograde ideologies.[1] Having understood this, “social networks” are not a “cause” but just a very efficient means used by this neo-right to enlist and mobilize resentment and hatred in favor of their Nazi-fascist and fundamentalist causes.

They are efficient means because they are technically, politically and economically organized in such a way that they serve as a glove for reactionary causes.[2] Controlled by financial capital and able to operate globally, from the United States, outside of any effective regulation,[3] These “networks”, owned by corporations like Alphabet, Meta, Telegram, make billions of dollars in profit annually, thanks in large part. the promotion of hate or obscurantist speeches. Until measures are adopted – which can only be of a regulatory nature – that directly affect the business models of these corporations, other measures will be nothing more than dipyrone in the treatment of sepsis: undoubtedly, reducing the fever is necessary, but insufficient.

This article, however, does not aim to debate the more general problem, but a specific point. Recently, a new expression has emerged in the semantic confusion that characterizes the debate: “information integrity”. This concept seems to have been born at the beginning of this century, in the field of Engineering, as we can deduce from an article published on the IEEE website – Institute of Electrical and Electronic EngineersIn 2003.[4] The definition of the concept is very engineering:

“Information integrity is the reliability or credibility of information. More specifically, it is the accuracy, consistency and reliability of the content, process and information system. This is an issue that concerns all business, government and social organizations. Information failures have until now been seen as a universal and widespread problem, despite costing the economy many billions of dollars. The concept space considers several perspectives, including: prevention, monitoring and correction of information errors; security audit and control; design, development and operation of information systems for greater integrity; and information integrity requirements of specific industries, such as financial institutions, healthcare, defense and transportation.”

Although we are here dealing with problems that are basically social and cultural in nature, as well as political, this concept has recently been assumed as key to confronting the global pandemic of misinformation and lies. As Kamya Yadav and Samantha Lai note, “misinformation is just a symptom of a much larger problem” – and that problem is found in the social contexts where information is produced and circulated.[5]

Bringing it to these contexts, that concept not only contains the many vices of concepts originating from the so-called “Global North” (once understood as “imperialist countries”…) from where they spread as new paradigmatic truths for the “Global South” (once understood as “colonized or dependent countries”…), as it lacks greater rigor, or any rigor at all. The fact is that, suddenly, from 2023 onwards, the “world” started talking about “information integrity” as if it were something as natural as the sun or rain…

In September 2023, Canada and the Netherlands launched a Declaration on the integrity of information on networks (“online”), immediately signed by around 20 other countries, including Brazil. According to this document:

“The term 'information integrity' is defined in this Declaration as an information ecosystem that produces accurate, reliable and reliable information, meaning that people can trust the accuracy of the information they access while being exposed to a variety of ideas. By using the term 'information integrity', we want to offer a positive vision of a broader information ecosystem that respects human rights and supports open, safe, secure, prosperous and democratic societies.”[6]

It seems obvious that we continue to have the problem of defining what “accurate, trustworthy and reliable information” is. Let us cite a limitless example: “Does God exist?” For an atheist, it is nothing more than belief; for a religious person, it is truth, it is trustworthy and reliable information.

The debate on “information integrity” gained greater dimension at the pre-G-20 meeting, held in São Paulo, on April 30th and May 1st. Promoted and organized by the Secretariat of Digital Policies of the Secretariat-Ministry of Social Communication of the Brazilian government, with support also from the Internet Steering Committee in Brazil (, the “G20 Dialogue – Information Integrity”, adds to other events that are happening right now, preparatory to the big G-20 meeting in Rio de Janeiro, next November. It was undoubtedly a large meeting with a very likely impact on future debate, given the quality and quantity of academics and activists present. Brazil put both feet into this discussion.

Having said all this, this article is only focused on the debatable concept of “information integrity”. Since it is not clear what it might mean and, most likely, it has different meanings for different actors or formulators, this article only intends to contribute to the search for greater conceptual rigor, if possible.


Since the concept was born in Engineering, let's take it from there: let's better examine the Information Theory applicable to the case, through very didactic examples.

To start a football match, the judge proposes a game of “heads and tails” to the captains of the two teams. The currency only allows these two choices. It doesn't matter if, when falling to the ground, the coin shows the “heads” side or the “tails” side: out of two possible choices, a result was obtained. When, between two possible choices, a result is obtained (it doesn't matter which one), Information Theory says that 1 bit of information has been obtained.

Now, let's consider a traffic light. In principle, its objective is to give drivers and pedestrians two options: “stop” or “walk”. These two messages could be expressed by just one light bulb: on (“stop”) or off (“walk”). A bit of information. However, the chances of errors in such a system, considering its purpose, are high. If the lamp is off because of a breakdown in the electrical system? To avoid mistakes, three lamps with different colors are introduced and a basic rule: only one lamp can light at a time (L – on), while the other two remain off (D - to switch off). It doesn't matter, in this case, which lamp is on and which are off: each of them provides 1 bit of information, therefore, at each instant, or with each new message, the traffic light provides 3 bits of information: L/D/D; D, L [D; D/D/L.

This system, however, contains more possible states than those it actually transmits: three lamps completely off (D/D/D), all three lamps on (L/L/L), three different combinations of two lamps on, and one off (L/L/D; D/L/L; L/D/L). Any of these other combinations will transmit a single message: error. In other words, to guarantee the security of the message to be transmitted, or if you want the “integrity of information”, it was necessary to introduce an excess of possible messages over those that were actually necessary or, in fact, valid (“stop”/”go”) . This excess is called redundancy.

Common sense tends to confuse redundancy with duplication. This is just one of the possible forms of redundancy. Also, for this reason, redundancy is confused with something somewhat useless; waste. Nothing more wrong. Redundancy is absolutely necessary to guarantee the “integrity”, or “reliability”, or “accuracy”, of any code through which information is intended to be transmitted. The language through which we communicate, for example, is full of redundancies, delimited by syntax, semantic and stylistic rules. Information without redundancy is like a broken traffic light…

In the case of the traffic light, a driver, upon seeing the red light with two off, received 3 bits of information. After a few minutes, the system status changes, it lights up yellow, two other lamps go out: another 3 bits. In a few seconds, yellow turns green, always with two other lamps off: 3 more bits. The driver, in total, in the time he spent receiving and obeying the traffic light messages, processed 9 bits of information. However, as we have seen, the semaphore could transmit more information than is actually valid, in total it would transmit 24 bits (3 x 8 possible states). This would be the total information contained in the system.

Knowing that the redundancy rate R of any code is given by the formula R = (Hm - Hr)/Hm for Hm = maximum information; Hr = real information, in the case of the traffic light, replacing Hm by 24 and Hr by 9 we will get a redundancy rate of 62,5%. Thanks to this redundancy rate, the semaphore code can guarantee the “integrity”, “reliability”, “accuracy” of messages that, in total, must only contain 9 bits of information.

Let us admit, however, that due to some sudden electro-mechanical failure, the traffic light would madly fire all its lamps, turning them all off at the same time, in the next instant turning them all on, or combining two on and one off, also the three valid combinations. It's easy to imagine the confusion that would ensue in traffic, at this intersection with such a crazy traffic light...

Mathematically, applying the above formula, we would have R = (24 – 24)/24 = 0/24 = 0. If the redundancy is zero, or if the information could be total, we would be in a chaotic state, as practice confirms.

There is no valid information that does not contain some greater or lesser rate of redundancy. Redundancy results from constraints imposed on codes, thanks to which we can identify and distinguish valid, or “reliable”, messages from invalid, or inaccurate ones. If we are talking about technological systems, these coercions, according to some well-defined programming, are of a physical or chemical nature: an electrical signal that should, or should not, be activated; organic molecule that may or may not interact with others. But if we are talking about social systems, coercion is also necessary in any human society, even the original ones.

Well-known taboos, such as incest or the prohibition, among Semitic peoples, of pork as food, are examples of social coercions that proved to be necessary for the process of humanization of the human being, whether for humanity as a whole or for any of its many diverse cultural groupings, given the challenges they have faced throughout our evolution as social beings.


We can define informational disorder in society as a social state in which the redundancy rate of socially valid information tends to zero.

By socially valid information we will define that which the social system, through its legitimate institutions, defines as valid. It is obvious that we could enter into a huge and inconclusive discussion here about “legitimate institutions”, “validity” etc. Revolutionary groups question the legitimacy of institutions and, if or when victorious, determine other and distinct rules of “validity”. We are dealing here with formal or even informal institutions whose legitimacy was gained through the cultural and political revolutions that spread from Europe to the rest of the world, from the 17th and 18th centuries onwards, without ignoring the important theoretical, political and artistic contributions arising from from Latin America, Africa and Asia, often critical, transformative, enriching of those institutions, but without denying, ultimately, those roots.

An obvious example, but not by far the only one, is Marxism, including the political regimes it engendered, originating in the European Enlightenment left but greatly transformed and enriched by thinkers and political leaders whose theoretical and political practices took place in Latin America, Africa or Asia.

In a simple and very symptomatic example, until a few decades ago no one would dispute that the Earth was a spherical planet, regardless of the political, ideological, social, ethnic, even religious condition of different groups of individuals; It didn't matter if they were European, South or North American, Asian or African, as long as they had a minimum level of education and culture, no matter how great their other differences were. This is information that organizes not only the scientific institution as such, but based on it, basic education, everyday culture, including beliefs, even religious ones, for some centuries now.

Suddenly, social groups appear arguing that the “earth is flat”. Now, from an informational point of view, such a statement and efforts made to prove it (so far, obviously, fruitless and even with tragic results) would be like traffic light bulbs that must remain off for social codes to function safely and validity. If the redundancy rate decreases, cases begin to occur, as we know, of teachers being challenged in primary schools by children or their parents contesting, often with verbal violence and physical threats, the validity of the spherical shape of the Earth, hence all the validity of scientific teaching as our Civilization conceives and validates it since at least the times of Columbus and Galileo.

For social or cultural reasons already suggested above, which we cannot delve into in this text, but which cannot be ignored, it is a fact that, for two or three decades now, a broad set of basic codes that organized our social life, and therefore also repressed how redundant (in the concept presented above) a wide range of other possible messages began to be questioned. A new informational regime emerged, however in latere of what we define as civilized, which has been calling into question not only formal democratic-liberal political institutions, but civilizational achievements that seemed to be consolidated forever, from the principles of human rights to advances in science and their impacts on education, public health and in our everyday lives.

For example: universal vaccination, a social behavior (social code) that seemed consolidated (in Brazil, for sure!), became the target of massive attack by other beliefs, the result of which, from an informational point of view, as we have seen, it would be comparable to drivers and pedestrians starting to ignore, disregarding confusion and risks, the valid traffic light messages, even if the legitimate authorities did not authorize such behavior that denies the legally established redundancy.

The process of informational disorder that we are experiencing was favored, in large part, by the leniency of liberal democracies themselves, perhaps too confident in the definitive solidity of their institutions. However, to this end, without a doubt, a decisive contribution was made by the “informational agora” that was created on the internet infrastructure. It is always necessary to distinguish the internet itself, a socio-technical system organized according to logical engineering determinations, from the layer that operates on it, organized by large corporations with financial background, to distribute content according to the logic of the capitalist market. Although the two layers may have overlapping links, it is in this upper layer that the major and serious political and cultural problems are concentrated.

It was hoped that the “networks” would serve to deepen the Enlightenment debate, to finally consolidate the ambition of a popular “public sphere”, but committed to reason, justice and democracy: the only lamps that should light up in society’s traffic light . However, what we saw was the widespread release, through the “networks”, of resentments, frustrations, idiosyncrasies, anger, until then with no spaces to express themselves beyond the socially very limited ones in conversations in bars, family gatherings, barber or hairdresser chats. . “The internet gave a voice to millions of imbeciles”, cried Umberto Eco. It revealed to each and every one of us, an “other world”, not the one we wished possible according to the slogan of the World Social Forum, but one that seemed impossible, until unthinkable.

From an informational point of view, “networks” have made it possible to reduce social redundancy rates to zero. All the institutions that we have been building over the last hundred, or two hundred, or even three hundred years are called into question. It is therefore a matter of knowing whether we will continue to allow this process of destruction of Civilization to advance, or whether we will reaffirm, perhaps even harden, the social redundancies that allowed our society to advance to the stage in which we find ourselves.

It is worth remembering Karl Popper: “one cannot be tolerant of intolerants”.


Any word is relatively polysemous. The word “coercion” is usually understood in a negative sense, as some unwanted, imposed obligation. But, we have seen, there is no society, not even the original ones, that are not organized thanks to coercions, explicit or tacit laws, that allow us to live with each other.

To drive our leisure or work vehicles, we obey the constraints of traffic laws, including obtaining a special license that authorizes us to drive vehicles. Medicines do not arrive at pharmacies without first undergoing coercive investigations by regulatory bodies, complying with the constraints of specific laws. Companies large or small are subject to fiscal and monetary coercion, also those related to the environment and social justice, labor rights, etc., always in accordance with laws debated, approved and implemented by legitimate political institutions, such as Congress and other democratic powers. The list would not cease.

From its generic social use, the word “coercion” gained a precise meaning in Cybernetics: it deals with the rules that organize any code. Our language only works as a means of communication because it is subject to many syntactic, semantic and stylistic coercions. It is the constraints that determine what can be valid information and what is redundancy indicative of error, in any information system.

The internet, due to its history, has expanded throughout the world without major coercion, other than those that are strictly technical. Not even the constraints determined by the jurisdictional borders of each country were respected in its initial expansion. From the United States, it was assumed that the messages that would travel through it should not be subject to greater coercion (in the cybernetic sense), beyond those naturally inherent to elastic linguistic codes.

For the first time in the history of electro-electronic media, a technological system of commercial and cultural employment, with wide penetration in the daily life of the entire society, was set aside from public regulatory coercion already in its origins. Regarding content traffic, it was assumed that the redundancy rate should be within the limit of zero.

It should be noted that, no matter how broad the conditions of freedom of expression in the press and broadcasting are, they are always, in any democracy, subject to coercive codes spelled out in law or tacitly accepted in the behavior of their professionals: journalists, artists, communicators etc. A simple example: practically no journalist or interview guest, speaking into a television camera or radio microphone, will use any profanity. An unwritten but socially established code imposes this limit.

Social communication organizations themselves, with their professional hierarchies and their behavioral habitus, constitute coercive systems that, however, for this very reason, are systems that reproduce legitimate information, in that concept defined above. Even so, it is far from a highly redundant system through which only a single message pattern would pass. Yes, we are aware of the many legitimate criticisms that are made to certain informational standards prevalent in these organizations, determined by their political and economic interests.

It is true that certain fields of messages, mainly those of the Left, although also valid in the concept presented above, find it very difficult to cross the channels of dominant organizations. But, staying with the Brazilian examples and without making a value judgment, it is also not possible to ignore the differences in informational standards between a Globo ou Band, or between a radio CNN and a Young pan. On the contrary: it is worth asking, despite your hierarchical filters, whether Band, Young pan and similar ones would also not be located closer to the field of informational disorder than the Globe ou CNN. It implies saying, as critical movements have claimed since the 1988 Constitution came into force, that a regulatory project cannot also ignore the regulation of “traditional” media.

The organizations that established themselves on the internet had no interest in determining formal or informal coercions that were closely similar to those that condition activities in the “traditional” press and broadcasting. This absence of greater redundancies resulted in this scenario that now motivates investigations and debates about “informational disorder” or “information integrity”.

Please allow me to refer to a personal example. Once, in a post on Twitter, I used the word “suicide”. The post was immediately blocked from being sent, and my account was immediately suspended. Twitter claimed that I had violated its “terms of use.” Obviously, I used that word in some metaphorical sense, in a context of political debate, not in its denotative meaning, much less directed at any person. But the algorithm does not notice these subtleties. I literally had to acknowledge the “error” to get my account back, or I would need to enter into an administrative dispute, the duration of which and the outcome were, for me, completely uncertain (almost zero redundancy).

This episode reveals that (i) the platforms' algorithms can, in a time limit of zero, block messages that would not comply with the platform's codes; (ii) these codes, that is, these particular systems of coercion, are determined by a private company, eventually, but not necessarily, based on broader social codes. They are not determined by any legislation of a public nature, nor are they transparent in any way.

It is therefore a matter of establishing, by law and regulations, principles that will determine redundancy rates relating to content that may or may not be posted on platforms. Obviously, here, the expression “redundancy rate” is a metaphor: no mathematics can measure this... What will measure this is the society project we want to build and the need to defend it from another project that wants to destroy us.

It is necessary to remove from platforms the power to decide what can be posted or not, according to their diffuse and opaque “terms of use”. On the contrary, these must comply with laws and regulations established by legitimate public authorities. However, it is extremely necessary to make platforms a politically and culturally healthy environment for democracy and civilization. The necessary coercions must not be timid in the face of the need to send back to the space of redundancies, the informational events that intend and are, unfortunately, managing to disorganize the entire society: obscurantism, denialism, racism, xenophobia, various intolerances, hate preaching, etc. They are also possible messages like the three lights off on a traffic light. However, in the face of the codes of liberal democracy and Civilization, they are nothing more than an error. As such, let them return to the socially inevitable redundant sociocultural surplus from which they should never have had the chance to manifest themselves.

It's time to fix the social traffic lights so that only the lights of reason shine again!

*Marcos Dantas He is a retired full professor at the School of Communication at UFRJ. Author, among other books, of The logic of information capital (Counterpoint).


[1] Nancy Fraser, “The End of Progressive Neo Liberalism”, Dissenter, 2/01/2024,; Marcos Dantas, “Two years of misgovernment – ​​Bolsonarism and lumpen capitalism”, the earth is round, 19/04/2024,

[2] Giuliano da Empoli, The Chaos Engineers, São Paulo, SP/Belo Horizonte, MG: Vestígio, 2019; Max Fisher, The chaos machine: how social networks reprogrammed our minds and our world, São Paulo, SP: However, 2023.

[3] Marcos Dantas, “To unblock the debate about blocking profiles on the internet”, GGN newspaper, 3/08/2020, available at

[4] E. Geisler, P. Prabhaker and M. Nayar, “Information integrity: an emerging field and the state of knowledge,” PICMET '03: Portland International Conference on Management of Engineering and Technology Technology Management for Reshaping the World, 2003., Portland, OR, USA, 2003, pp. 217-221

[5] Kamya Yadav e Samantha Lai, “What Does Information Integrity Mean for Democracies?”, lawfare, 22/03/2024,

[6] Canada and the Netherlands launch the Global Declaration on Information Integrity Online,

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