# Design of causal diagrams: Barr art chart, Lombardi diagrams, evolutionary trees, Feynman diagrams, timelines

December 1, 2003  |  Edward Tufte
19 Comment(s)

It is easy to draw a linking line or an arrow of implied causality, but very hard to make credible causal inferences.

Linking lines, arrows, and influence trees bring with them many implicit but powerful assumptions. Suppose we take the arrows seriously—how are we to evaluate the evidential quality of influence diagrams? The answer is clear, at least to the open and skeptical mind: by the usual standards for evidence of causality. A good start on what it takes to make causal inferences is found in A. Bradford Hill’s classic paper on making causal inferences (in Hill’s case, about the link between smoking and lung cancer), posted here. The principles of making sound causal inferences favor no particular ideology or point of view, except that of wanting to find out what is actually going on.

Below is a discussion of the famous art chart of Alfred Barr. The analysis applies to evolutionary trees, Lombardi diagrams, and a good many timelines. The last two paragraphs are particularly important with regard to the assumptions involved in linking lines.

The material below is from a draft of my book, Beautiful Evidence.

• Mark Hineline says:

In my dissertation (“The Visual Culture of the Earth Sciences,” 1993), I made this claim about the explanatory block diagrams of William Morris Davis, a leading geographer of the early 20th century: His diagrams were not pictures of his theories. The diagrams were his theories. I see no reason to disagree with myself ten years later.

But visual language is the strangest of language games, because it is considerably less rule-driven than verbal or numerical language games. Thus, diagrams with arrows “showing” causality can be taken as hypotheses, as statements of fact, or as theory. No standardized rule tells us how to read arrows. Compare this with (to take just one example) an equal sign in arithmetic or algebra. An equal sign is univocal. Arrows are multivocal.

Dr. Tufte’s work is an important first step in devising more rigorous rules for the languague games that are diagrams, but there are many, many steps to go.

• Maximilian Schich says:

Every Arrow in Barr’s diagram is based on a simplification, as are the nodes. Two horizontal single headed arrows between two nodes would infer, that the two nodes influence each other, because the non-headed end of each arrow points to the cause of influence.

In most cases we have no evidence for such a direct influence. We are able to see a corellation, but the cause for the corellation is still hidden. This is true not only for isms but also for single pieces of art, for e.g. drawings after a known object.

Another issue: should we use double-headed or non-headed arrows for such a relation.

• Steve Sprague says:

Dr. Tufte’s points are well taken regarding the limitations of Alfred Barr’s chart of Cubism and Abstract Art. Rather than address the myriad errors, misdirections and conceits on the Barr graph (forgive me), I offer these related musings.

Most of the criticisms in Dr. Tufte’s commentary relate to ideas known in the ’30s, so perhaps the chart wasn’t meant to be an exhaustive diagram. Maybe its intent was more akin to advertising. The Museum of Modern Art was still a fledgling institutions in 1936, its directors anxious of establishing the museum as the preeminent repository of not only modern art objects but of their meaning and history. As a commanding visual presentation in the mode of science, the chart conveys by its scientific look an exhaustive, even hermetic, and hence unchallengeable layout of the history of modern art; the course of modern art takes on the aura of inevitable technological advance (note that “Machine Esthetic” is very nearly in the center of the chart). By using the same image throughout the graphic media related to the exhibition, the chart became something of a logo whose meaning was clear: this is the only place you need come to for Modern Art.

Dr. Tufte provided a three star thread on rhetorical ploys in presentations. This chart is a good example of one not discussed there: donning the cloak (lab coat?) of unchallengeable authority.

The very look of the chart presages Richard Feynman’s diagrams, with objects/movements acting upon other objects/movements at various stages of time. They share a common visual language: key elements indicated by text descriptions (Barr enclosed supposed external influences in boxes), connections between elements and the course of influence indicated by lines (albeit arrowless in Feynman, and Barr without those nifty wavy lines), an indication of the direction of time. Hopefully I’ve not misunderstood this concept, but I believe I’m correct in remembering that quantum theory (and thus Feynman diagrams) allows for objects (virtual particles? anti-particles?) to move backward in time and Feynman’s method may provide insight into a way of diagramming non-lineal or reciprocating causal events in art and other disciplines.

One of our fellow correspondents, Martin Ternouth, discussed the potential pitfalls of crafting visually sophisticated yet content thin presentations (I have to apologize for losing the thread).

There are a number of threads on Mark Lombardi’s drawings of corporate and political intrigue: including analytical design / sculpture.

There’s also an article in the November 2003 Art in America. Certainly, Lombardi’s drawings of the 1990s address similar design concerns in a more cartographic and thorough manner, yet I find it interesting that Lombardi has something of the same problem that Barr did: where to start and how to finish.

Charles and Ray Eames have come up in several contexts on Ask E.T. and they have a place here too. Here’s a set of network diagrams Charles made (taken from “The Work of Charles and Ray Eames,” Abrams 1997); both place the key figures at the center of the arrays. The first, a preparatory sketch for their 1969 “What Is Design” exhibition, is captioned “Diagram by Charles Eames showing the connection of the Eames Office to important clients, patrons and colleagues.”

The second, ca. 1971, bears this caption: “Diagram by Charles Eames entitled ‘Friends and Acquaintances’ for the Bicentennial exhibition ‘The World of Franklin and Jefferson’.”

These obviously show only connections (as do the Barr and Lombardi diagrams), with scant emphasis given to strength of the connection or the waxing and waning of the relationships over time (the Eames Connections diagram does set up a planetary system of links that indicate some strenght of relationship). But these diagrams may provide a different way of looking at the course of modern art. The Barr chart makes bare the predilections and prejudices of its preparer: that advances in art are generated primarily by prior movements. This belies the active searching out of influences by artists. Perhaps a more interesting chart would go the other way: lines heading out from various artists to what they were looking at, including their own prior work, similar to the Eames diagrams. This could include a double-headed arrow or opposing arrows between Matisse and Picasso, for instance, or a circular arrow arcing from Picasso back to himself. David Smith, in whose work can be found a broad set of external influences, also wrote “My sculpture and especially my drawings relate to my past works, the 3 or 4 works in progress and to the visionary projection of what the next sculptures are to be.” (1953, in “David Smith by David Smith,” Holt Rinehart and Winston, 1968) Artists study no work with greater intensity than they do their own.

Barr, Feynman and Lombardi all use the same line weight, although Barr and Lombardi make use of both black and red in text and connecting lines. With Barr and Feynman, this may be as a result of limitations coming from the print shop; clearly it’s an aesthetic decision with Lombardi. Perhaps differing line weights, differing colors or color densities could indicate the import of any influence or connection.

There may also be elements of influence that remain unavailable to diagrammatic description. Late in his life, Georges Braque commented on the height of the Cubist years, ” … Picasso and I said things to one another that will never be said again … that no one will ever be able to understand …” (1978, in “Picasso and Braque: Pioneering Cubism, MOMA 1989) What must that have been like, and how do you diagram that?

• Edward Tufte says:

The inherent evidential and presentional problem in linking a network of nouns by arrows or lines is that while the nouns are specific, narrow, complex, the arrows are non-specific, generic, ambiguous, and mean differently in nearly every use. That is, the level of analysis greatly differs for nouns compared to the links. The nouns are relatively crisp, detailed; the links soft, simple, dichotomous (either there is an arrow or there is not).

To understand the content here, the nature of the link is the key issue: what was the dynamic character of the relationship, say, among Picasso, Braque, and Matisse?

Lines and arrows are, in effect, verbs showing how one noun is related to another. Yet the verb is just a arrow, always an arrow. In the art chart, the arrows mean all sorts of things: caused, saw, taught, visited, saw in a gallery, was a friend of, was thought by Barr to be linked, traded paintings with, was imitated by, answered paintings by, and so on.

The Barr art chart is an important and powerful drawing. It does illustrate, however, the necessity of presenting some evidence about the character of the relationships somewhere else in the essay–because the arrows don’t say much at all.

Exactly same issues arise from the absence of arrows between certain nouns as well.

One practical design consequence is that each arrow might be accompanied by one or two verbs describing the character of the relationship between the pair of nouns.

• Dave Nash says:

Would Barr’s chart be improved by adding miniature archetypes of each school? While not a substitute for a walk through the gallery, the small multiples can show why Barr finds a link and what was adopted: color, line, shape, subject, space, etc.

Are all of Barr’s arrow verbs positive? Surely some influences must be: rejected, mocked, loathed, escaped.

• Steve Sprague says:

Dave Nash’s last comment is on the money. Barr’s solid lines do imply a wholesale direct/positive/defining connection, if not stylistic influence, while the absence of a line (as Dr. Tufte points out) suggests none at all. But it ain’t, as George and Ira told us, necessarily so.

That’s one of the problems with connecting artists solely by style or movement. The (sometimes contradictory) thinking and practices of individual artists are what count and these change with time and prove nearly impossible to pigeonhole. In this light (and as Dr. Tufte suggests), the connecting lines on Barr’s chart could use some annotation. One example with rejection in mind: the link from Cubism to Dadaism surely refers at least to Duchamp and Picabia, both of whom came under the sway of Cubism early in their careers and then rejected it. In fact, a part of Dada rhetoric (especially from Duchamp) came to include a renunciation of all art and artists involved with the merely “optical,” including Cubism and the Cubists (Picasso, Braque, the whole lot).

Would you characterize that as a positive influence? Depends, I suppose, on how you define positive, and which side of the influence you’re looking from. Jackson Pollock once said that his time in the studio of Thomas Hart Benton was important to him mainly as something to react against. (He later came to feel that he was better off having studied with such a strong, if oppositional, personality; an aesthetic character building experience, if you will.) However, Benton clearly had a profound impact on Pollock’s art and you can see the abstract ghosts of Benton’s looping figuration in Pollock’s mature work. Was that a rejection or a fundamental influence? Or some sort of hybrid? And you certainly wouldn’t want to ascribe that sort of relationship to any of the other New York School artists.

These complex subjects are debated at length in classrooms and studios, coffee shops and bars, and multitudinous books and articles are written about them. Maybe the connecting lines should be underwritten with source citations for further contemplation.

• Edward Tufte says:

See the interesting (and understandable) discussion of Feynman diagrams at the American Scientist here.

Note the labels on the linking lines and the lack of node boxes and circles.

• Niels Olson says:

In the chemistry building of the University of Maryland I ran across a similar diagram, the Mallinckrodt Outline of the History of Chemistry, copyright 1961. Prepared by Herbert S. Klickstein, based on the 1927 outline by Norris W. Rakestraw. It was far more dense and detailed than this. I regret I haven’t had need to go by the poster again with a camera, and I haven’t found a digital rendition on-line.

ExPASy has two wonderful diagrams of biological pathways. The home page has links to both. Each cell links to a detail, and each name in the detail links to specific enzyme information. They are available in paper copy, although the enzyme data isn’t in the wall-sized poster. The diagram was originally designed by Dr. Gerhard Michal in 1965 as a wall poster, but (unusually) it adapts well to this web presentation format. The diagram requires careful study; while the overall structure is visible at a distance, one must zoom in to see individual links. Copies of the poster are now produced in collaboration with Roche and can be ordered for free.

• Maximilian Schich says:

There is a new book dealing chiefly with Barr’s Chart(s):

Astrit Schmidt-Burkhardt:
Stammbaume der Kunst. Zur Genealogie der Avantgarde.Berlin, Akademie Verlag 2005, ca. 500 pages

In English the same author has published the article “Shaping modernism: Alfred Barr’s genealogy of art“in Word & Image 16,4 (October-December 2000) p. 387-400.

• Ken Burnside says:

In my line of work (designing games) I have to give referees a mind set and tool set for describing relationships between antagonist characters, their motivations, and the motivations of the characters played by other players.

I use causal diagrams, based somewhat off of Tufte, and a few books on writing romance novels(!).

There are three basic ties that matter for writing fiction, and for running roleplaying games: Ties of blood, ties of sexual tension, and ties of obligation. These all form bonds between characters that can be used to coerce them into acting.

So I give the following advice:

“Start with a blank sheet of paper—the bigger the better. 11×17 is ideal. In the center of the paper, write the name of your chief antagonist. Under that character’s name, write down what they want, and if different, what they think they want, preferably in two different colors of ink, or one in block printing, the other in cursive.

Next, write down the names, wants and believed wants of people related to your antagonist. “Related” in this context means one of the following relationships: Ties of blood and kinship, ties of sex or sexual tension, and ties of obligation and duty.

Now, write down the names and the motivations of all the player characters who will be playing in this scenario.

Draw thick black lines between the names of characters that are related to each other by blood.

Draw medium weight black lines between characters that are related by sex or sexual tension.

Draw lightweight black lines between the names of characters related by duty and obligation.

If there’s a power disparity, have an arrowhead on the end of the line of the person at the lower end of the power continuum. If the power level is roughly equal, use a circle to indicate this. If you haven’t decided on the power level, don’t adorn the ends of the line—do that during the game.

This is the “sinew” layer of your conflict and relationship map. The next layer up are the nerves.

Take two highlighters (we recommend blue and pink, but any two colors will work), and draw arrows between characters – a blue arrow means that the character the arrow originates from likes the character the arrow points to. A pink arrow means the target is disliked by the originating character. If the tenor of the relationship is mutual, draw two arrows, going in opposite directions. If you need to, you can specify a particularly intense relationship with a thicker highlighter line, but we recommend against it.

This map is an easily grasped graphic of all the relationships that give velocity to your story. In particular, note that we’ve minimized the words put on the map to motivations and wants; this is deliberate. You may not even know, until the game is running, why there’s a pink line indicating dislike between two characters…and something will pop into your head when you’re setting up the scene. Jot a quick note down for future reference, and run with it—this is giving you a frame work for improvisational storytelling, and should be fluid, rather than rigid.

Because this is a graphical display of narration, any scene that doesn’t alter a relationship on the map, or alter the perception of any relationship on the map, is unimportant and should be minimized or skipped. Similarly, when assigning motivations (the only words on the maps), you’re assigning motivations that will be interesting for your players, not motivations that are interesting to the characters in question.

• Matt R says:

Here is a very nice causal diagram linking people who attended a wedding by one of (the most?) memorable story that linked them. The text provides concrete reasons why the people are linked and also a directionality inherent in the direction of the text. It shows a number of ET’s design principles at work, one of which is passion for the content—this clearly took a lot of time (finding the definitive story that could be shared and hints at relationships, humour and life history) and shows a high regard for the guests at the wedding. Featured here on Visual Complexity.

I was recently shown a Fishbone Diagram, which I am told was
invented in 1943 in Tokyo by Professor Kaoru Ishikawa.

• Niels Olson says:

This is about an hour Google tech talk on server-side security in which Neil Daswani has some very good work-a-day diagrams of the code that goes between web browsers, servers, and attackers, which he uses to very effectively illustrate how websites can be hijacked for the purpose of aiding and abetting in theft of private information and money. He explains the very common attack mechanisms of SQL injection and cross-site scripting, but the reason for the post here is really the diagrams. That he uses PowerPoint is unfortunate, but these diagrams, in and of themselves, were probably born on a chalkboard somewhere. They are remarkably similar to Feynman diagrams. Can any computer science folks tell us, are these standard forms or something novel?

For example:

• Mark says:

Yes, they are very common in Computer Science, you will typically see them in description of protocols, or any sequenced set of operations. You might see them coded up in tools for UML, as they are part of basic behavioral modeling, in this case they are called interactional diagrams or sequence diagrams, but they definitely pre-date UML.

• Niels Olson says:

The New York Times has an interesting visualization of what people were text messaging during the Super Bowl.

• Niels Olson says:

Compare Barr’s chart, which opens this thread, to this chart, illustrating the connections between NP-complete problems:

• Cory Bernat says:

Nina Katchadourian is another artist who takes advantage of how “it is easy to draw a linking line or an arrow of implied causality.”

Her Genealogy of the Supermarket arranges advertising icons into a humorous but insightful family tree. By not attempting any “credible causal inferences,” her clever chart asks more questions than it answers.

To help me make this argument, I quoted ET in an essay about this artwork, appearing in Gastronomica 8, no.4 (November 08): 7-9.

“By employing the irrefutable logic of a genealogy chart (double lines denote a marriage or partnership; single lines, biological offspring; and dotted lines, adopted offspring), Katchadourian adds an air of authority to her family tree and, thus, another layer of absurdity. Through the clarity of her display, Katchadourian reveals how advertising icons operate: they have been designed to appeal to our emotions, not our intellects. As the shrewd data design analyst Edward Tufte has written, successful displays of visual information are governed by principles of reasoning, by means of which ‘clear and precise seeing become one with clear and precise thinking.’ Herein lies the tension in Katchadourian’s work. Advertising icons are not designed to withstand the rigors of clear and precise seeing or thinking…

“The seventy-eight icons in Katchadourian’s family tree provide sufficient characters to form separate ethnic enclaves of Hispanic, Asian, African-American, Jewish, and Italian icons. There is even a half-human, half-vegetable section, in which the Jolly Green Giant has fathered the Corn Maiden, who represents Argo Corn Starch. Katchadourian’s pairings make us smile, but they also raise important questions. Is the Native Indian icon found on Land O’Lakes butter the Corn Maiden’s mother because Native peoples are more connected to the earth? Or because they were treated for a long time as less than human, making the half-vegetable reference more pointed? Whether the icon is viewed as related to a product, to a people, or to advertising history, Katchadourian’s pairings encourage speculation, along with multiple interpretations and, at times, misinterpretations…

“…Even without a depiction of the earlier, kerchief-wearing “mammy” version of Aunt Jemima, Katchadourian’s family tree investigates the use of ethnic stereotypes to sell products; when the icons are removed from the packaging and placed in this ahistorical chart, it becomes obvious how loaded they are as images. Is the marriage of the smiling Quaker of Quaker Oats fame to Aunt Jemima a reference to the business-trivia fact that his parent company purchased hers? Is it, perhaps, a commentary on marriage as ownership? Or on slave-holding whites? Or, as one historian friend has suggested, perhaps the interracial union is a reference to the Quakers as early abolitionists?”

Images are from the artist’s website:

• John Leferovich says:

Here is a rather interesting art history flow chart:

Source here.

Quoted from the website:

Witness the Italian Renaissance as a Mark Lombardi conspiracy. Above is the 1930 Uffizi Gallery chart mentioned in a earlier post. The Uffizi chart demonstrates that the nonlinear nature of art history is not such a new insight after all. Solid, arrow-directed lines mark “a direct relation between master and scholar,” and dashed, undirected lines indicate “artistic influence or connection between masters.” The colors key schools approximately west to east (Siena to Venice), and time moves from top to bottom (before 1300 to after 1550), with each artist’s vertical position precisely determined by the date of his death. With its commitment to letting the information speak for itself (and be a glorious mess), it anticipates the philosophy of visualization maven Edward Tufte…

• Santiago Ortiz says:

And there’s a bull

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