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Links, Causal Arrows, Networks

Here are some ideas on linking lines and causal arrows a draft of some material from my Beautiful Evidence.

The chapter suggests methods for showing linking lines and causal arrows, and also demonstrates ideas for assessing the credibility of various links. That is, the links themselves are taken as explanatory evidence. Note the typographic design of the organization chart which replaces the conventional design of bureaucrats-in-boxes.

Four previous threads have discussed technical details of a few parts of the chapter:   Barr Art Chart    Feynman Diagrams
Cladograms    Lombardi

I'd be grateful for helpful comments.


-- Edward Tufte


A fascinating discussion on how we typically represent cause in very simplistic terms, like vague unlabeled arrows. Such a tactic is true for any representation of information. We are bound to compress and abstract only the most important information, and cast it in convenient terms. Whenever we make a statement in any language (graphical, spoken, gestural) we must make a judgement about what to leave out. The fact that most of us do this all the time, effortlessly, and to good effect, is some kind miracle (try programing a computer to do it).

On boxed text: ET rightly criticizes the boxed bureaucrat in the organization chart: an example of casting information in convenient terms, visually protecting, emphasizing and obscuring identity all at the same time. The SARS graphic on p. 14 uses two boxes: one to emphasize "Guangdong", the other to group together the list of countries with outbreaks. The Barr art chart also uses boxes: in four cases (red) to decorate the influences coming from outside the realm of the chart, and in one case to distinguish the output MODERN ARCHITECTURE, again identifying it as outside the realm of the graphic. But why does it remain black? Shouldn't it be red like the other boxes? Maybe Barr is almost admitting MODERN ARCHTECTURE into the realm of abstract art, even though the name doesn't end in "ism". I this case the box would be information-carrying.

Some of the graphics I found hard to read on the online preview (the Reinhardt send-up and the Lombardi conspiracy theory).

The questions about the cladogram seemed good, but I would like to have seen a more detailed discussion of them. How exactly are the non-quantitative features (hairy/smooth etc.) translated into the tree diagram? No doubt creationists would latch onto the doubts and ambiguities in cladograms, and use them to cast doubt on evolution itself. The answer to their charges would make interesting reading.

On ET's remark about marketing and science: the two domains are often linked. Scientific theories compete in the marketplace of ideas, and are often couched in marketable terms. I work in a government science department in which senior managers often make the statement "perception is reality".

Much space is given to the Galileo graphic to make the point that links should be annotated. Is there a fuller discussion in the book? I feel a bit cheated to have a elaborate exemplar put before me, and yet have no idea what it's about. Can it at least be redrawn with English typography rather than Galileo's beautiful but (to me) uninformative script?

Edward: thanks for making this chapter available. I enjoyed reading it, and will now look at arrows much more questioningly.

-- Drew Knight (email)

Problem with Barr art chart?

Dynamite chapter. Do I see a poster coming from the Galileo diagram?

The statement, "FAUVISM has 6 entrances and a single exit - but what an exit, ABSTRACT EXPRESSIONISM," brings my only real criticism, humbly offered. In the chart, Barr offers the term "ABSTRACT" in parentheses and in type smaller than EXPRESSIONISM; the reference is clearly to Kandinsky and his circle and this lineage is continued roughly to (ABSTRACT) DADAISM (meaning, among others, Arp), then (ABSTRACT) SURREALISM (perhaps Miro, or Moore) onto NON-GEOMETRICAL ABSTRACT ART (which could be a whole lot of people, including maybe Arp again or even the earliest sculptures of David Smith), with an apparent dead-end link to the Bauhaus.

With Abstract Expressionism in all caps, no parens., and somewhat glibly introduced by "but what an exit", you seem to make reference to the New York School of the '40s and '50s and add, I think, an implication that Barr meant Fauvism was the direct precursor of the big-A big-E Abstract Expressionism of Pollock, de Kooning and gang, a notion he could not have imagined in 1936. To be sure, most of that group was arriving in New York in the mid 1930s (and certainly could have seen this show), but their mature work was at least another 10 or 12 years away.

The term Abstract Expressionism was, and often still is, used to identify the early style of Kandinsky (and others) and to differentiate it from the work of both realist expressionists and other early abstract artists. With all the other complaints we can make about this chart, we can at least treat this term even-handedly and give Barr a measure credit for its then common usage.

-- Steve Sprague (email)

ET happy visit to Feynman's Feynman diagram van

In California last week, I gave a talk at Caltech for the Skeptics society. They asked what I expected for an honorarium; I replied the opportunity to take photographs of Richard Feynman's van, painted with Feynman diagrams. My good host, Michael Shermer, knew where the van was stored in Los Angeles.

Inside the van, there were some posters used in a display of the van. Here is the text:

"Richard Feynman bought this 1975 Dodge Tradesman Maxivan and had it outfitted in Long Beach according to the cultural trends of the time with a mustard-yellow and avocado-green interior and a customized mural exterior.Although the van outfitter took some artistic liberty with the diagrams (changing the angles at which the straight-line electrons and the wavy-line photons are shown, in order to fit them onto the panels). They are for the most part, correct.Feynman also obtained personalized license plates. Because a maximum of six letters was allowed at that time, Feynman settled for QANTUM. (Other possible combinations, such as QED and QUARK had already been taken.) During the summers of the late 1970's, when son Carl was a teenager and daughter Michelle was around 10, the Feynman family took several trips in the vehicle often camping out in remote, random spots in the wilderness of the American West. Although Feynman occasionally used the van to commute from his home in Altadena to Caltech (note the weathered Caltech sticker on the driver's side corner of the front windshield), the van was usually driven by his wife, Gweneth.Richard Feynman invented his diagrams as roadmaps for calculating how things happen in the world of QED, quantum electrodynamics. There are three basic actions:

1) a photon (depicted by a wavy line "for no good reason" according to Feynman) goes from place to place;

2) an electron (depicted by a straight line, or a curved, non-wavy line) goes from place to place; and

3) an electron emits or absorbs a photon at a "junction."

Actions 1) and 2) have sets of equations associated with them, while Action 3) is associated with a mysterious number sometimes called "the charge."

Feynman diagrams can help a physicist avoid getting lost in the intricate calculations that result in probabilities of a particular event happening. When such possibilities are taken into account when calculating, the theory of QED more closely matches actual observations. Simple phenomena, such as electrons and photons going from place to place, can happen in several different ways; some of them quite strange. For example, a photon traveling between two electrons could disintegrate into a positron and an electron which annihilate each other to form a new photon which disintegrates into a new positron and a new electron which annihilate each other to form yet another photon."

Here are photographs of the van and of ET with the keeper of the van, Larry Schmidt, a used book dealer with an excellent collection of scientific books for sale. Museums do not appear to be interested in the van (it is a very large van, a Maxivan) although probably the side and back panels will be part of a collection someday. No doubt Sotheby's or Christie's would be delighted to auction it off. Photographs by Michael Shermer at http://skeptic.com/

-- Edward Tufte

Feynman van visit

e, sub-s, asymptotically approaches infinity, where e (set in italic) = the maximum possible envy carried by a given body and s = Steve.

-- Steve Sprague (email)

Link diagrams

1) The History of Programming Languages

2) Genopro's Genogram language. See also the tutorials.

-- Ricardo Stuven (email)

Biochemical pathways

Beautifully complex network diagram - biochemical pathways This is easily the most complex network graphic I have ever seem - a clickable map showing the structure and linkages of hundreds of biochemical pathways involving thousands of chemical compounds. The subject matter defies simplification, and the strategy of embracing the complexity and putting everything on one sheet seems to have worked. Helped by judicious use of spot color and appropriate typography. http://www.expasy.ch/cgi-bin/show_thumbnails.pl

It appears that the diagram was originally designed as a wall poster, unfortunately out of print, but (unusually) it adapts well to this web presentation format.

-- Brian Davies

The magnificent Biochemical Pathways Wall Chart referenced by Brian Davies is still available, for free:


-- Alex Merz (email)

Number spiral

This number spiral has been around for a while. I saw it again when a colleague sent it to me the other day: I thought I would share it.


-- Tchad (email)

Patent diagrams: Is everything wrong?

Patents employ a relatively unstylized diagramming technique that is relied upon by very demanding professionals: laywers and engineers. See www.uspto.gov for millions of examples. Features are monochrome black content on white page, single font, usually all capitalized, and line drawings only. A requirement is that all objects in a patent diagram must be numbered and explained in the text. I find this visual style to be effective in communicating concepts in a concise, unambiguous manner. Noting that patent diagrams are often derived from phluffy PowerPoint charts, the process of converting to USPTO standards produces rigourous documentation. Having said all that, engineers and scientists are very often expected, if not required, to use their day-to-day diagrams to convince their funders or managers to support their work. This is to appeal to the emotional side of mostly extroverted leaders, and is in stark contrast to the often introverted nature of many engineers and scientists. Since it lacks emotional elements, the patent diagram style is likely to be ineffective at sparking the interest of funders and managers. Unless there are exciting numerical data to accompany the diagrams, such as sales forcasts, the diagrams will likely be glossed over. So, the engineer is tacitly expected to adopt a more embellished approach to diagrams, although usually with no formal training in visual arts. It seems that lawyers have the cool analytical style to match the temperament of many engineers and scientists. As for an appropriate engineering diagram style, I appreciate your pointers and techniques very much. I also feel very aggravated at the lack of dicipline in technical report writing and consumption in the PowerPoint wastelands. I author word documents whenever possible. Cheers,

-- John Watkins (email)

Manuel Lima's wonderful collection of network and linking diagrams

Here's a beautiful, intriguing, and smart collection of 260 network and linking diagrams brought together by Manuel Lima. Nearly all the examples attempt to get a handle on, or at least layout, immense multidimensional data sets.

Few of the examples have a scale of measurement (except for those with an object of known size in the scene, such as a country). The general cognitive style generally tends toward amazing visualizations and data-mining, rather than quantitative description, explanation, evidence-making, or causal analysis. This has been the history of scientific visualization (see Visual Explanations, chapter 1 on this point). One useful question to ask of each image is: What did I learn from this, in addition to seeing an elegant architecture?

The examples also make clear that the computer screen, since it is direct rather than reflected light, is wonderful for anti-aliased images; and since it is pixelated, not so good for typography, which is clunky compared to fine scale of the images.

It is interesting to compare the examples in the above draft chapter with the 260 network diagrams

My current favorites: 145 blue brain project, 166 critical paths and trajectories in networks, 235 North American subways, and 248 micro fashion network

The site is a must to check out, and to stay at for a long time to see the many design possibilities for big multivariate data sets.


-- Edward Tufte

Surgery planning diagrams

Here is a challenge that medical folks and many others might find stimulating. I am interpreting a surgery planning diagram for a wide audience (I am visual editor for a broadsheet newspaper). The diagram, supplied to us voluntarily by a major teaching hospital, depicts a day in the life of two adjacent operating rooms where knee and hip reconstructions are performed. The hospital is clearly trying to maximize its resources. We see in the diagram how just two surgeons can conduct eight procedures in a workday by flitting back and forth between ORs, teaming up for some tasks and going solo for others. I find it fascinating and we are preparing a feature article to accompany it (dealing also with wider resource issues in British Columbia's public health system). The diagram here

is rather nicely put together, obviously by someone who understands the process intimately and has a strong visual sensibility. I am also in possession of a much more detailed table showing the day's progression for the full 10-person OR staff complement, in 5-minute increments. This graphic appears to be based on that table. We are taking some pictures too that will show some of the procedures. However, I do not think that the graphic in its present form is as clear and evocative as it could be, particularly for my type of audience. Maybe some things could be thrown out and others emphasized more strongly? I welcome your questions and feedback.

-- Stewart Muir (email)

I for one am happy that surgeons (and hospitals) treat their scheduling with such care. Any discussion of timing, delays and emergencies would drive us into gantt charts and project management ... but that, as they say, is another thread.

The diagram itself is an interesting exercise in redundancy, repetition and overkill: we are presented eight times with the six steps of an operation, each time with a number of arrows, supposedly depicting movement to and from each operating room.

I had a hard time visualising the main points of the diagram, which seem to me to be :

  1. closely timed cadences in each rooms
  2. continuous work by both surgeons
  3. Cut to Stitch is ALWAYS performed by two surgeons
  4. Anesthesists always check with their surgeon before induction (wich is probably the "fail safe" mechanism used to keep both rooms in lockstep)
I actually only got it once I gave each surgeon a color, and filled in the timelines for each operating room with the color of the surgeon(s) present (I haven't a clue how to add images to my text, or I would have uploaded a crude example).

On this very simple framework, (which adresses points 2 & 3), you can add various time references (to adress point 1 and give a sense of the sequence of events in one operation), and finally, at the relevant points, show the anesthesists checking in.

In short : loose the many colors, emphasize where the surgeons are and the timing of events.

Finally, I find it interesting that you say that you are planning a feature article to accompany the diagram. Is it just a turn of phrase, or is this image really the origin of your story?

Hoping these comments are helpful...


-- Paul Atlan (email)

Quick thoughts:

Interesting that the text says that it depicts two operating rooms but the headings say "Surgeon A" and "Surgeon B"... We really should have two operating rooms and the surgeons bounding back and forth as time goes on, right?

Then it is really a grid of operating room against time. In each room at each time the response is "who" and "what" --- as such, put that information at that intersection. So, I imagine each operating room column split into three subcolumns: one for "what" (a description of what is happening; probably text but perhaps gently colored to show the action), one for surgeon A, and one for surgeon B. If the surgeon is there at that time, then there is some kind of mark there (an "X" or a scapel or a word describing his or her particular action or something). Thus, when A and B are working together, they have marks next to each other. You could even just have two vertical lines within each room, one for A and one for B. We could tell by the brokenness how often they come and go, how often they work together, how frequently they are in neither one room nor the other, and so forth.

Thus, at any point in time we should be able to tell what is happening and who is there doing it and who is or isn't helping. Subtle annotations describing interesting aspects of what is going on could be placed around the outside.

Oh, and put the timescale, perhaps demarcated hourly, subtlely in the background behind the operating rooms; don't just give us the time points at the boundary lines.

Of course, all the usual considerations apply: focus on the data, get rid of worthless ink, facilitate comparisons of interest, etc...

Then again, all of these design thoughts I have center on what *I* would like to get out of the data; what would your viewers want to see?


-- rafe donahue (email)

To Stewart Muir's request, here's another thread with some process flow diagrams: Visualizing song structure to maximize studio productivity

-- Niels Olson (email)

Adware advertising diagrams

An interesting diagram of links in this report on adware advertising by the Center for Democracy and Technology (see page 4):


-- Edward Tufte


Returning to links and networks, I would be interested in your thoughts on Henry Small and Eugene Garfield's 'Scientography', which is an attempt to create maps of the geography of scientific ideas and discoveries through citation metrics.

The original article: http://www.garfield.library.upenn.edu/essays/v9p324y1986.pdf

Some interesting examples: http://vw.indiana.edu/places&spaces/nypl/readings/Borner2003visknow.pdf

In this case, the credibility of the links cannot be questioned. Citations can be verified and counted, and they can only go in one direction.

-- Neil Mussett (email)

Biochemical pathways

ET suggests, in response to a letter about the depiction of biochemical pathways, that I contribute to the forum. Accordingly, I enclose some examples for a single pathway, called the pentose phosphate pathway, with a few comments.

The following example is from a widely used web site with biological information (biocyc.org, from the Stanford Research Institute), showing the reactants by name, the arrows connecting them representing the individual enzymes for interconverting the reactants.

The next example shows the version obtained by clicking the "more detail" button in example 1, the reactants now being given as chemical structures, together with the three letter gene mnemonic, classification number, and name (e.g., RPE1,, Ribulose-phosphate epimerase). The example appears over several screens (p.2 is shown, p.1 does not print), some structures are unaccountably compressed, and in many other examples at this site vast areas of the screen are empty. The same two pictures are somewhat improved at another web site, Sacharomyces Geneome Database (www.yeastgenome.org, also at Stanford), probably through individual curation. It should be remarked that both web sites are marvelous and astonishing founts of information, barely imaginable a decade ago.

The third example refers to the extraordinary chart of much of the metabolism referred to by Brian Davies in his Nov. 9, 2005 letter to the forum. The chart, now on line and no longer available on paper, was produced over several decades and three editions by the major European supplier of biochemicals, the Boehringer-Mannheim Corp. Interestingly, an expanded paper version with the same editor, Gerhard Michal, was published as a hard bound book, Biochemical Pathways: An Atlas of Biochemistry and Molecular Biology (Wiley, New York and Spektrum, Heidelberg, 1998). As Michal says in the Preface, "over the years [he] developed a preference for the graphic presentation of scientific facts" - and it shows!

This is the lower half of p. 40 (the pages are ca. 8" x 11 1/2"), five colors are used, there is an immense amount of information and the whole aspect is most pleasing. A magnifying glass helps.

The fourth example is the same pathway as shown in an excellent advanced textbook, David White's The Physiology and Biochemistry of Prokaryotes (Second ed., Oxford Univ. Press, 2000), p.192. This one is just all right, the names of the compounds are too small, and the names of the enzymes are only given in the legend - which is inconvenient. The artwork does not do justice to the text. As surely has been often mentioned, it appears that fancy graphics (good or not) appear only in wide circulation textbooks but not monographs or advanced textbooks like this one.

Finally, to illustrate how good graphics is not just a matter of color, the last two examples are for the same pathway from W.W. Umbreit's Metabolic Maps (Burgess Publishing Co., Minneapolis 1960). The cartoon of the overall pathway, here:

is followed by nine additional full pages;

with details of parts of the pathway, including some indication of reaction mechanism, given in none of the other examples above. I suppose there is an axiom in graphics that the less information the clearer they can be? Contrasing Umbreit and Michal's books, there is 40 years more of information in the latter (which is much more than just pathways). Still, for the basic pathways and reaction mechanisms, Umbreit's text is an enviable model. Who could get away with such use of space nowadays? (I should ruefully admit that in spite of being a professional in this field I was unaware of either Umbreit's or Michal's book until recently. The latter I chanced on in the local medical textbook shop, and the former by scanning the book stacks at our library - the very stacks soon to be halved in favor of more digital library, with the books going to "The Depository.")

In the present case, how to depict biochemical pathways arose in thinking about artwork for a new textbook. The issues are obvious: what is a desirable format and how to accomplish it. On the latter, unfortunately, the answer is no more complicated than the banal one, that it will be an immense amount of work getting the chemistry right and applying the appropriate drawing program. This is a substantial challenge for a book with a couple of hundred figures, and not one lending itself to an easy fix.

-- Dan Fraenkel (email)

Another example of the pentose phosphate pathway is on page 552 of the fourth edition of Lehninger's Biochemistry. It is my favorite, though even this required some mark-up, because, 1) in the medical student's persistent quest to organize information, any symmetry is highly desirable, and 2) it tells at least part of the story: we're turning 5-carbon sugars into 6-carbon sugars.Figure 14-22 from Lehninger's Biochemistry, 4th Ed.

I also adore the watercolors in Lehninger, though I haven't yet determined who does them. Similarly, I think a fair amount of the appeal in Umbreit's work is the hand drawing. Yesterday my wife asked me for "the best pen you've got." Why? "Because I hate filling out these forms. I need something pleasurable in it." Perhaps the drawing program you should use is India ink and some thick, acid-free 100% cotton rag on a drawing board.

-- Niels Olson (email)

Retro flowchart

-- Edward Tufte

Causal diagrams for distributed systems

Distributed systems make use of causal diagrams. This link is to one of the two researchers who extended Lamport's original concept of logical clocks. Although the diagrams are simple, they are invaluable for comprehension. http://www.vs.inf.ethz.ch/publ/papers/logtime.pdf

-- SJG (email)

Originally developed when sensor signals were transmitted using pneumatics, SAMA (Scientific Apparatus Manufacturers Association) diagrams helped engineers make sense of an industrial plant full of pipe, tubing, bellows, relays, etc. http://www.measure.org/PDF/FunctionalDiagramming1.pdf#search=%22sama%20diagrams%22 This concept evolved into todays diagramming standards for control systems (function block programming, see http://en.wikipedia.org/wiki/IEC_61131-3)

-- SJG (email)

Unfortunate diagrams

Odd flow diagrams at



-- Edward Tufte

See the discussion of flow diagrams at Junk Charts:


and follow through to Graphical Equity 2 and 3.

-- Edward Tufte

Wall chart of biochemical pathways

The Biochemical Pathways Wall Chart previously available from Boehringer seems still to be available from Roche. It is still listed near the bottom of this page:


-- Alexey J. Merz (email)

I have a better formulation of my requirement: is there a graphics program (flexible, relatively easy to use, not costing a fortune) that will accept quantitative information? My need is not for representation of say biochemical pathways, but for a way to represent all the steps of a fermentation of a batch of wine, and the change in composition from grape juice to young wine. So, the things we want to represent over a span of two weeks might be 1)temperature 2) yeast addition and type 3) extraction method, timing and duration (e.g. the "pumping over" of fermenting juice over the skins 4) a plot of the concentation of one constituent(or more) as it rises in the fermenting wine vs. a starting value measured in the grapes. (These are constituents are quantifiable.)

-- David Graves (email)

David, if you've already got MS Excel on your hard drive, as so many people do, you might be interested in Zach Gemigniani's recent blog post, "A Breakup Letter", addressed to Powerpoint. E.T. has elsewhere suggested that MS Word is an acceptable alternative to Powerpoint for its combination of text and picture tools, while here, Zach suggests Excel, for its ability to handle drawing objects (via Autoshapes) and numbers in a single screen.

The key to making the spreadsheet visually acceptable is turning off the grid. After that, you can put all the arrows, links (called "connectors" by Autoshapes), and boxes you like, as well as filling them with quantities that are dynamic, updateable, and able to calculate based on other quantities on the page.

-- Derek Cotter (email)

Social network map of Enron email dataset

Chris Potts, "Swearing and social networks," at the always interesting Language Log:


-- Edward Tufte

Here's another version of the biochemical pathways chart, apparently drawing inspiration from the London subway map. Note the zoom feature.

-- Niels Olson (email)

Martin Krzywinski, of the Genome Sciences Center in Vancouver, has published a new rigorous way to visualize large networks, putting nodes on polar-arranged axes and connecting them with arcing edges:
Applications of the linear layout for network visualization.

-- Niels Olson (email)

I found the following example in the book "Case Problems in Finance", 10th edition 1992 by William E. Fruhan Jr., W. Carl Kester, Scott P. Mason, Thomas R. Piper and Richard S. Ruback.

It is an interesting graph representing an extremely complex financing package for an investment opportunity in ore mining in Indonesia back in 1967.

The financing setup involved three governments (USA, Germany and Japan) guaranteeing USD100m of loans provided by 12 US banks and insurance companies, one German bank and 13 Japanese smelting and trading companies. Southport Minerals, Inc., the investment company, provided the USD20m shortage of funding in equity.

The financing package involved a contractual agreement to sell two thirds of the ore output to Japanese companies and the remaining one-third to German companies.

Inspired by the ideas in Dr. ET's "Beautiful Evidence", I made the following changes to the original graph:

1.Changed the thickness of the arrows and links to reflect the relative size of the loan guarantees, loan amounts and quantity of ore purchased.

2.Differentiated between guarantees and, money and product flows by using dashed lines for the former and continuous lines for the latter.

3.Annotated the links and arrows with information such as guarantee amount and type, loan amounts, interest rates, loan terms and split in ore production.

4.Reordered the guarantors and fund providers based on the seniority of the debt and its amount by decreasing order.

Best regards,

Hicham Bou Habib

-- Hicham Bou Habib (email)

Threads relevant to analytic design:

Seeing Around: New ET essay published