All 4 books by Edward Tufte now in
paperback editions, $100 for all 4
Visual Display of Quantitative Information
Beautiful EvidencePaper/printing = original clothbound books.
Only available through ET's Graphics Press:
catalog + shopping cart
All 4 clothbound books, autographed by the author $150
catalog + shopping cart
Edward Tufte e-books
Immediate download to any computer:
Visual and Statistical Thinking $2
The Cognitive Style of Powerpoint $2
Seeing Around + Feynman Diagrams $2
Data Analysis for Politics and Policy $2catalog + shopping cart
Edward Tufte one-day course,
Presenting Data and Information
Oakland, April 20
San Jose, April 21
Palo Alto, April 24
San Francisco, April 25, 26
Now and then the narrow bandwidth of lists presented on computer screens and bullet points on PowerPoint slides is said to be a virtue, a claim justified by loose reference to George Miller's classic 1956 paper "The Magical Number Seven, Plus or Minus Two." That essay reviews psychological experiments that discovered people had a hard time remembering more than about 7 unrelated pieces of really dull data all at once. These studies on memorizing nonsense then led some interface designers to conclude that only 7 items belong on a list or a slide, a conclusion which can be sustained only by not reading the paper. In fact Miller's paper neither states nor implies rules for the amount of information to be shown in a presentation (except possibly for slides that consist of nonsense syllables that the audience must memorize and repeat back to a psychologist). Indeed, the deep point of Miller's paper is to suggest strategies, such as placing information within a context, that extend the reach of memory beyond tiny clumps of data. George A. Miller, "The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information," Psychological Review, 63 (1956), 81-97 (here).
At Williams College in September 2000, I saw George Miller give a presentation that used an optimal number of bullet points on an optimal number of slides—zero. Just a nice straightforward talk with a long narrative structure. (George and I were there to pick up honorary degrees during the dedication of a new science building at Williams College. In addition, Donald Knuth's talk as well as my own deployed no bullet lists.)
"Williams College to Honor Eight Renowned Scientists," September 23, 2000.
-- Edward Tufte
Really stupid PowerPoint guidelines think 6 is magical
I frequently find rules with "six" as the magic number of bullets. But today I came across this expanded rule from the American College of Radiology. "Follow the 666 rule: Use no more than six words per bullet, six bullets per image, and six word slides in a row. Any more words per bullet, and you don't have a bullet. More than six bullets per slide are difficult to read. By the end of six text-filled slides you have been talking for about 10 minutes without a visual."
While the limit of six slides is a mercy, I expect that soon someone will demand that those six words be no longer than six letters.
-- David A. Nash (email)
Dick and Jane meet the magical 666 rule
The 6-line-only rule seems to come up in witless PP presentations on how to make witless PP presentations. Here is the full 666 rule in action, the Haiku Rule for presentations:
George Miller on the relevance of +/- seven
Here is a comment by the George Miller on the scope and relevance of his classic essay:
From: George Miller
To: Mark Halpern
Subject: Re: citation for your disclaimer
Many years ago landscape architects used my +/-7 paper as a basis to pass local laws restricting the number of items on a billboard. It was funded by the big motel chains; if you run a mom-and-pop motel you have to put a lot of information on your sign, but if you have a franchise everybody knows you have hot and cold running water, color televisions, free breakfasts, etc. The restriction on billboard content was driving the small motels out of business.
The same argument was used in the Lady Bird Johnson Act to prohibit billboards within X feet of highways, and the billboard industry (a strange group that deserves an essay of its own) was hurting. They hired a man to travel around from town to town trying to refute the claims that more than 7 items of information could cause accidents. The man's wife did not like her husband being constantly on the road, so she asked him about it. He told her that the root of his trouble was some damn Harvard professor who wrote a paper about 7 bits of information. She, being herself a psychologist, said that she did not think that that was what Professor Miller's paper said.
Armed with this insight, he looked me up and told me the whole story about my career, unknown to me, in the billboard industry. There was much more to it than I have outlined here, and I was shocked. So shocked that I wrote a long letter thing to set the record straight. The letter was published in the monthly journal of the billboard industry and that was the end of it. Unfortunately, I no longer have a copy of the letter an I don't recall the name of the journal (this was all back in the early 70s) so I cannot quote to you its contents. But the point was that 7 was a limit for the discrimination of unidimensional stimuli (pitches, loudness, brightness, etc.) and also a limit for immediate recall, neither of which has anything to do with a person's capacity to comprehend printed text.
If you want to quote the original article, it is on line and you can find a pointer to it at www.cogsci.princeton.edu/~wn. But if that is too time consuming—yes, you are right: nothing in my paper warrants asking Moses to discard any of the ten commandments.
-- Edward Tufte
Now it is 7 +/-2
In the participant's manual for a course titled "Developing Successful Proposals," created by Information Mapping, Inc., 1988, there is a statement on page 5-A-1 that "A manageable unit of information is defined by researchers as 7 +/- 2 units of information." This statement refers to the information mapping concept of "chunking" (not to be confused with how the term chunking is used in cognitive psychology). In information mapping, chunking refers to delivering information in bite-sized morsels.
-- Tom Snider-Lotz (email)
Morville and Rosenfeld, first edition
In considering breadth, you should be sensitive to the cognitive limits of the human mind. Particularly with ambiguous organization schemes, try to follow the seven- plus-or-minus-two rule. Web sites with more than ten options on the main menu can overwhelm users
Morville, Peter., and Rosenfeld, Louis. Information Architecture for the World Wide Web (Sebastopol: O'Reilly, 1998), 38.
-- Robert Simmon (email)
Some successful websites not consistent with magical numbers
For some web designs, it is hard to identify the "main menu".
For Arts & Letters Daily what must be the main menu has hundreds of items; for the New York Times again it is not clear what the main menu is (the 4 major news stories?); for Google News, the main menu might have 7 and the other candidate for the main menu might have 50 to 100. For this site, 11 in the nav bar. But does it matter how many links are in a particular box when there are dozens of other links adjacent?
For a telephone book, thousands of items. Would this 7 +/-2, or in the quote above 11, strategy apply to the design of a telephone book?
-- Edward Tufte
Jef Raskin gets Miller right
Another citation, what I believe is an appropriate use of Miller’s ideas:
Combining a sequence of actions into a gesture related to the psychological process is called chunking: the combining of separate items of cognition into a single mental unit, a process that allows us to deal with many items as though they were one.
Raskin, Jef. The Humane Interface p. 37 (Reading, MA: Addison-Wesley, 2000).
-- Robert Simmon (email)
Naive psychologizing about statistical displays
Here's another one, from Stephen M. Kosslyn, Elements of Graph Design (1994), a book confirming that psychology is for graphics like ornithology is for the birds.
Whether a statistical graphic can be "apprehended at a glance" is not a useful standard for graphics, at least if graphics are to be something other a than decorative logo. Every paragraph in a newspaper longer than 2 or 3 sentences flunks this standard.
Comparing one clunky graphic with pretend data ["widgets per captia (100s)"] with two clunky graphics with pretend data yields no intellectual or design leverage. Probably the best way to show these pretend data is in the form of a simple table of the type seen every data table in every sports section. Show 4 columns—nouns, 1980 performance, 1990 performance, and the difference between them. The nouns should probably be ordered by the difference between 1990 and 1980, just like wins/losses and games behind in baseball tables.
Here's a thought experiment: suppose a study showed that undergraduates taking Psych 101A remembered only one thing about psychology one week after the semester ended. Does that mean then that our data graphics should show only one element? If yes, this would invalidate 99% of all statistical graphics published, leaving behind only the really stupid graphics. If no, what is the relevance of evidence about memory—or is it apprehension at a glance—to the design of statistical graphics?
Why not make the graphic standard similar to the image standard? People see all the time the difference between 1 and 10 megapixel images for digital cameras. An image of a painting is sometimes several hundred megapixels. Such images often pass the instant apprehension test.
-- Edward Tufte
Response to The Magical Number Seven, Plus or Minus Two: Not relevant for design of text
Doesn't the Kosslyn example in the context of this discussion show that there are two separate questions here? One deals with the best or better organization of data for drawing inferences; it seems to me that the "don't" graph is far better for drawing inferences. But Kosslyn seems to be more interested in memory—whether someone confronting the "don't" graph would recall it accurately later, even a few seconds later. That's an empirical questions, but my guess is that it is perhaps easier to recall one or the other of the "do" graphs, but not both?
-- Mark Hineline (email)
"Don't Do" applies to both Kosslyn columns?
Perhaps an amusing interpretation of Kosslyn's page is that the words "don't do" form a single connected heading over the whole notion of shallow content.
When I first read ET's Envisioning Information, I highlighted and bookmarked this sentence on p. 35:
"Standards of excellence for information design are set by high quality maps, with diverse bountiful detail, several layers of close reading combined with an overview, and rigorous data from engineering surveys."
This is an excellent antidote to the common belief that visual content must be shallow, when in fact human visual cognition is vastly underutilized.
Then there is Ad Reinhardt's quote on p. 119 of Visual Explanations that is quite memorable: "As for a picture, if it isn't worth a thousand words, the hell with it."
-- Garry L. Booker (email)
Who controls information flow rates?
What I find interesting is that there is an assumption in the above references that we all live in an eternal powerpoint presentation or 30 second advertising spot where we have no control over the rate at which the information is being presented and that we have to remember what is being presented.
If you take the graph splitting suggestion given in Kosslyn above you are in fact forcing the use of short-term memory. What if in the two graphs example I want to compare Boston and New York? I have to remember where Boston lies on the first graph. Of course a professional powerpointer would put the graph on two slides to make the task truly difficult.
If I am looking at a web page, unless it is a Flash 'presentation,' I can take my time to work out what it all means. Web and print designers often assume that they have x seconds to grab my attention and that I don't have the time to comprehend what is being presented.
-- Andrew Nicholls (email)
Morville and Rosenfeld, second edition, +/-7 now infamous
In defense of "Information Architecture for the world wide web":
"Now, we're not going to tell you to follow the infamous seven plus-or-minus two rule. There is general consensus that the number of links you can safely include is constrained by users' abilities to visually scan the page rather than by their short-term memories."
Morville, Peter., and Rosenfeld, Louis. Information Architecture for the World Wide Web 2nd Edition (O'Reilly, 2002), Page 68
-- Chris McEvoy (email)
I recently had to devise an argument against the magical thinking discussed here, and found this research review by Sven Fuchs useful:
HCI 450 - Foundations of Usability
How magical is Miller's famous Seven for HCI issues?
-- LeMel (email)
Halpern's email leading to Miller's reply
Dear Mr Tufte,
You have posted a letter from George Miller to me in which he replies to one from me. I think his letter would be better understood if you had printed mine along with it; as it is, you have an answer without the question that prompted it. His reference to Moses, for example, will probably not be understood without a prior reading of my letter to him.
Yours, Mark Halpern
From: Mark Halpern
Sent: Thursday, July 30, 1998 12:04 PM
To: [George Miller, Princeton University]
Subject: citation for your disclaimer
Dear Professor Miller,
The director of the technical writing group which I serve as editor has issued an edict that lists and procedures in our printed and screen-displayed documentation should not exceed seven, or maybe nine at the most, items. This is of course a silly rule, whatever its origin, but I think that its source in this case is a fading memory of a third-hand report of a bad reading of your classic 1956 paper.
Of course you are in no way responsible for the misreadings of your paper, and the silly things done in its name, but I hope you can help my organization, at least, climb back out of the pit it has dug for itself, using your paper as its shovel. I have seen somewhere a quotation from you, or a paraphrase of your words, in which you deplore the strange conclusions that some have drawn from your paper, and express your dismay over all the half-baked rules that people have promulgated, citing it as their authority.
In my attempt to get our director to rescind his bad rule, I would like to be able to quote your very words against him; would you tell me where I might find such words? Or, if what you've said in the past is not on record, could I induce you to say now that nothing in your paper should be taken as warrant for asking Moses to discard at least one, and preferably three, of the Commandments?
With my thanks,
-- Mark Halpern (email)
Moses drops one slide
It's been a while since I first read this thread, but the updated iPhone entry from June 6 (what with the 3G iPhone allegedly due next week) caught my attention, and I wanted to re-read the Miller "Magic number 7" correspondence.
I had forgotten about the reference to Moses and dropping a commandment, but not completely - some part stuck in my mind. How so?
In my recent presentation training workshops I've been using sequences from award winning films to illustrate the importance of story-telling. Films such as "In the heat of the night", "Jaws", "Capricorn One", "Planet of the Apes" and so on. Each scene that I use has a "hook" to it, sometimes including a phrase that has entered colloquial speech, e.g., "You're gonna need a bigger boat" or "They call me Mister Tibbs!" etc.
But one film sequence I include is one of Mel Brooks' lesser known films, "History of the world. Part 1".
The scene I use, in order to demonstrate one of my main theses - don't stick slavishly to presentation laws (like the 666 one) for which there is no evidence - is one where Mel Brooks, playing Moses, returns with three tablets from Mt. Sinai, and tells the Hebrews who've been wandering in the desert that he has 15 commandments to share with them. Unfortunately, as he is about to saying "fifteen" he drops one of the tablets: "Oy... these ten, ten commandments".
It's my way of demonstrating that not all laws are set in stone, and some deserve to be broken!
-- Les Posen (email)
The Fifteen Commandments
YouTube has a clip of the scene Leo Posen mentions:
-- Dave Nash (email)
PP slides of Moses?
Returning to this thread today years after first reading it, I see the message from Mark Halpern expanding on the joke about Moses paring down his over-sized list.
I loved this pithy critique the first time I read it in your copy of Miller's letter to Halpern, and have used it on occasion to try to deflate nonsense. Once, though, I was stopped in my tracks by someone who pointed out that all of the commercial artists who have rendered Moses' return from the mountain show that God himself knew enough to spread his bullet points over a pair of stone tablets.
-- Stephen Ritcey (email)
But the 10 (or 15) commandments are sentences, not bullet grunts!
-- Edward Tufte
The instructions for presenters at this medical symposium repeat the seven-item myth.
Instructions were complete with atrocious graphic. But the instruction, "No more than 5 words across," is actually six words if we count the numeral 5 as a "word."
One wonders how many slides will be required to provide enough information for even a 10-minute presentation, given these suggestions, which, if followed would restrict a given bullet slide to 40 words.
-- Jim Dominic (email)
The Information - Seven plus or minus two
James Gleick has compiled a good history of information in his aptly titled recent book, The Information.
Pages 260 and 261 of the hardcover are of particular interest to this thread:
Gleick says, "Seven seemed to be the number of items that most people could hold in working memory at any only time: seven digits (the typical American telephone number at the time), seven words, or seven objects displayed by and experimental psychologist. The number also kept popping up, Miller claimed, in other sorts of experiments." (p 260)
There may be some interesting nuances to explore in the various readings of Miller.
-- Tchad (email)
The death of George Miller, as reported by the New York Times.
"George A. Miller, a Pioneer in Cognitive Psychology, Is Dead at 92"
by Paul Vitello
Psychological research was in a kind of rut in 1955 when George A. Miller, a professor at Harvard, delivered a paper titled "The Magical Number Seven, Plus or Minus Two," which helped set off an explosion of new thinking about thinking and opened a new field of research known as cognitive psychology.
The dominant form of psychological study at the time, behaviorism, had rejected Freud's theories of "the mind" as too intangible, untestable and vaguely mystical.
Its researchers instead studied behavior in laboratories, observing and recording test subjects' responses to carefully administered stimuli.
Mainly, they studied rats.
. . .
"George Miller, more than anyone else, deserves credit for the existence of the modern science of mind," the Harvard psychologist and author Steven Pinker said in an interview.
"He was certainly among the most influential experimental psychologists of the 20th century."
Dr. Miller borrowed a testing model from the emerging science of computer programming in the early 1950s to show that humans' short-term memory, when encountering the unfamiliar, could absorb roughly seven new things at a time.
When asked to repeat a random list of letters, words or numbers, he wrote, people got stuck "somewhere in the neighborhood of seven."
Some people could recall nine items on the list, some fewer than seven.
But regardless of the things being recalled—color-words, food-words, numbers with decimals, numbers without decimals, consonants, vowels—seven was the statistical average for short-term storage.
(Long-term memory, which followed another cognitive formula, was virtually unlimited.)
. . .
"Using 'cognitive' was an act of defiance," Dr. Miller wrote in 2006.
"For someone raised to respect reductionist science, 'cognitive psychology' made a definite statement. It meant that I was interested in the mind."
That new approach to psychological research came to be known as the cognitive revolution.
Dr. Miller's first and most enduring interest as a scientist was language.
His first book, "Language and Communication" (1951), is widely considered a foundational work in psycholinguistics, the study of how people learn, use and invent language.
He collaborated with the linguist Noam Chomsky in groundbreaking papers on the mathematics of language and the computational problems involved in interpreting syntax.
He conducted some of the first experiments on how people understand words and sentences, the basis of computer speech-recognition technology.
"Plans and the Structure of Behavior" (1960), written with Eugene Galanter and Karl H. Pribram, was an effort to synthesize artificial-intelligence research with psychological research on how humans initiate action—basically, a book about how to build a better robot.
Beginning in 1986, he oversaw the development of WordNet, an electronic reference databank intended to help computers understand human language.
Colleagues said he had a role in framing many of his era's most audacious thoughts about human and artificial thinking; typically, he then moved on to other projects.
"Like most great scientists, he became interested in some phenomenon or other and then simply jumped in to try to illuminate the problem," said Michael S. Gazzaniga, a leading researcher in cognitive neuroscience at the University of California, Santa Barbara.
Dr. Miller helped create the field of cognitive neuroscience in the late 1980s, he said.
"He was exceptionally generous."
. . .
The paper's["The Magic Number 7..."] ground-shifting implications made it one of the most frequently quoted texts in the canon of modern psychology (and by Dr. Miller's account, one of the most misquoted).
For better or worse, "The Magical Number Seven" came to haunt his scientific career, overshadowing his many other accomplishments.
It resonated more playfully in his golf game. "He made the one and only hole-in-one of his life at the age of 77, on the seventh green" at the Springdale Golf Club in Princeton, his daughter said.
"He made it with a seven iron. He loved that."
-- Les Posen (email)
The magic number 200 +/- 50
Perhaps more relevant to this forum than Miller's original is Dave McComb's short article The magic number 200 +/- 50.
Basically, offload the details to a big display (eg: 36″ x 44″ paper), and you can comprehend a whole lot more.
Quoting a few passages in particular (emphasis mine):
Somewhere around 200 items seems to be the optimum number of interrelated things we can deal with at one time, when dealing with complex systems such as computer software
the human mind coupled with external aids is capable of dealing with several hundred items simultaneously in its “near-term” memory
having a great deal of information in your field of view allows you to anchor some information in visible space while you confidently scan other areas of the design
In conclusion, we suspect that there is another level of human cognition aided by spatial diagrams where the mind is able to deal with hundreds of interrelated articles in nearly real-time
-- David Bruce (email)