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Interview with Jacques Bertin
by Juan C. Dürsteler [message nº 116]

Jacques Bertin is one of the fundamental gurus of Information Visualisation since he was the first in articulating a coherent and reasoned theory for the analysis of quantitative graphic representation.

Jacques Bertin.

Source: Roberto Gimeno 

His book “Semiologie Graphique” edited in 1967 is a monumental work, based on his experience as a cartographer and geographer. It represents the first and widest intent to provide to a part of what we call today Information Visualisation of a serious theoretical foundation.

The digital magazine of InfoVis.net wants to make a small homage to this long trajectory devoted to the study of graphics with this interview.

Jacques Bertin has used some parts of his last reflections written in 2001 about the "Semiologie Graphique", to answer our questions. For this reason the basic contents of this interview corresponds to the images and contents of said document. (You can see the document at "La Graphique" in several languages) .


Mr. Bertin, you have more than 70 years of cartography behind you, a considerable amount of experience that maybe began when you were 10 when you received the first prize of cartography at primary school. Your vocation really began so early?.


I never had problems with drawing. I doubted between architecture, the teaching of drawing and cartography. Finally fate…fate made that things work out as well as they did. 


Your book “Semiologie Graphique” was published well before the boom of personal computing and computer graphics. Nevertheless the avalanche of data present in Internet and the impulse that computers have provided to visual communication mean that many people associate Information Visualisation with computers. In your opinion, what is the role that computers have to play in this context?

J. Bertin: 

The use of computers shouldn’t ignore the objectives of graphics, that are:

  • Treating data to get information.

  • Communicating, when necessary, the information obtained.

Computers are able to multiply useless images without taking into account that, by definition, every graphic corresponds to a table. This table allows you to think about three basic questions that go from the particular to the general level. When this last one receives an answer, you have answers for all of them. Understanding means accessing the general level and discovering significant grouping (patterns). Consequently, the function of a graphic is answering the three following questions:

  1. Which are the X,Y, Z components of the data table? (What it’s all about?)

  2. What are the groups in X, in Y that Z builds? (What the information at the general level is?

  3. What are the exceptions?

These questions can be applied to every kind of problem. They measure the usefulness of whatever construction or graphical invention allowing you to avoid useless graphics.

The orderable matrix answers all these questions. It’s the basic construction of graphics. It organises the reflection, gives a sense to automatic manipulation and provides the key that allows you to classify graphics, and choose the most appropriate construction.

MatrixTFig_18.gif (10706 bytes)
Meat production in 5 countries. Table (15) indicates the elementary data about meat production (question 1). But it's interesting to integrate the global information (question 2). 
The answer is provided by construction  (16) the orderable matrix that re-orders rows and columns showing that the data  (15), i.e., 25 numbers, can be reduced to 2 groups: A and B, of opposite structure. 
Country C is an exception (question 3). It doesn't belong to any group. 
The constructions in (17) show that only the orderable matrix (16) answers all the questions. This matrix is the fundamental construction in graphics. It constitutes the optimal application of the properties of images and resumes the chain of logical operations: data - matrix - reduction - exceptions - discussion - decision -communication

Las construcciones (17) ponen en evidencia que solamente la matriz ordenable (16) responde a todas las preguntas.
La matriz ordenable es la construcción fundamental de la gráfica. Constituye la aplicación óptima de las propiedades de la imagen y concretiza la cadena de las operaciones lógicas: datos - matriz - reducción - excepciones - discusión - decisión - comunicación

Source. La Graphique , text and images courtesy of Roerto Gimeno.

In order to avoid erroneous representations it’s sufficient, both in cartography as in statistics:

  • Equalling or neutralizing the computing classes (or categories). An operation that can be mathematical (ratios, densities. %, indices), or graphical (reticules or contour levels)

  • Using the variation in size, This variation along with the use of the natural range of progressive sizes avoids the insoluble problem of the choice of degrees of intensity and erroneous images. This is a generalized problem due to the use of computer programs that provide only an apparent solution (insufficient degrees of intensity, too finer grids that confound each other, incomplete analysis of the objectives…)
  • Varying the level of the cut-offs. Effectively, representing the quantities in Z means answering to two questions: which are the distribution’s characteristic degrees of intensity? and in which level does the useful image appear?: eliminating small “islands”, showing the similarities with another, covering a particular surface, setting a cut-off…? The possibility of easily varying the level of cut-off thanks to computer science, constitutes an efficient solution.


Before as well as after your work the interest in a theory of graphics has been traditionally low. In fact today Information Visualisation is still more a practice than a science, with a great amount of creativity but little serious work towards the integration of all this effort into a theoretical framework beyond “Semiologie Graphique”. Is this true and if so, why ?

Jacques Bertin: 

In France this happens due to lack of interest. On the other hand, the comments of the Americans, English or Germans… are abundant…

The problem that still remains to be solved is that of the orderable matrix, that needs the use of imagination…When the two components of a data table are orderable, the normal construction is the orderable matrix. Its permutations show the analogy and the complementary nature that exist between the algorithmic treatments and the graphical treatments.  


Probably the true value of graphics, more than just for communicating known facts or results, resides in the discovery of patterns, of knowledge hidden in the mountains of available data that well worked out graphics have the potential of discovery in a simple and intuitive way. What do you think about this?

Jacques Bertin: 

Data is transformed into graphics to understand. A map, a diagram are documents to be interrogated. But understanding means integrating all of the data. In order to do this it’s necessary to reduce it to a small number of elementary data. This is the objective of the “data treatment” be it graphic or mathematic. 

As we have said, the fundamental question is: which are the groups that the data builds in X, and in Y. The construction that responds to this question is the orderable matrix, that re-orders rows and columns and shows the exceptions at the same time. 

These two pieces of information (the groups in X and Y and the exceptions) are invisible in any other construction.
Nevertheless, this is the information that has to be shown. Mathematical and graphical treatment precede, then, the writing of the comments and conclusions and determine the relevance of the latter. 


¿Cuál es, según su criterio, el futuro próximo de la Visualización de Información como ayuda para comprender el ingente volumen de datos que la tecnología vierte sobre nosotros?

Jacques Bertin:

We shouldn’t forget that the three dimensions of the image make the visual perception our most powerful perceptive system. But images have only three dimensions and the consequences of this limit are important.

In that sense, interdisciplinary studies will always be difficult, since the geographer puts the space, the historian, time, psychologists the individuals, sociologists the social categories. What is, the,n the “synthesis science” when each academy, each discipline, each research center is defined by their own X, Y, Z components that characterize their information domain?. 

This way is how you can show the limits of rationality . A particular treatment is justified only within the boundaries of a well delimited set: the data table. But there is an infinite number of well delimited sets. Our rationalization efforts, whatever they may be, will inevitably drown in the infinitude of the irrational. 

We are grateful to J. Bertin for being so kind to let us interview him. The interview was made by e-mail during January 2003. Special thanks to Roberto Gimeno professor of the Institut d’Études Politiques de Paris, cartographer, that was kind enough to put us in contact with Mr. Bertin, handling our e-mails and translating the answers of Mr. Bertin into Spanish.

More articles about Jacques Bertin

The reflections on "Semiologie Graphique" can be found at the interesting web site maintained by Roberto Gimeno and Patrice Mitrano (In French, Spanish and Italian)

Links of this issue:

http://www.infovis.net/printRec.php?rec=llibre&lang=2#SemiologieGraphique   The book Semiologie Graphique by Jacques Bertin
http://www.sciences-po.fr/cartographie/cartographie_html/5_page5theorie/graphique_bertin2001/index.html   Web site about "la Graphique"
http://www.sciences-po.fr/cartographie/cartographie_html/5_page5theorie/graphique_bertin2001/04_niveaux_perception/04_niveaux_de_percept.html   Perception Levels (from "La Graphique")
http://wwwusers.imaginet.fr/~bplanque/bertin.html#Points%20forts   Article in French about Bertin by Bernard Planque and Serge Bonin
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