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Metaphors, analogies, thought mappings

Roald Hoffmann has a fine essay in the recent American Scientist on metaphors, which he describes at one point as "thought mappings." Hoffmann suggests that metaphors may be at times useful for (1) explaining technical results to a general audience and (2) achieving and understanding technical results.

In my work, the thought mapping "data graphics should operate at the same resolution as typography" (more generally: data graphics ~ words) was most helpful in creating and justifying sparklines. This mapping provided direct advice about the design of data graphics, and it also had a sustained quality since it carried through to ideas that sparklines could appear wherever words (and numbers) appear and that paragraphs of sparklines should be constructed. There is certainly something of an after-the-fact quality to some of this, and the mapping (data graphic ~ word) has its rhetorical as well as technical value in writing about sparklines.

Of course loose or strained metaphors notoriously produce loose thinking. "When a precise narrowly focused technical idea becomes metaphor and sprawls globally, its credibility must be earned afresh locally by means of specific evidence demonstrating the relevance and explanatory power of the idea in its new application. It is not enough for presenters to make ever-bolder puns, as meaning drifts into duplicity. Something has to be explained." (Beautiful Evidence, p. 151).

A good way for contributors to develop this thread would be to provide examples of specific metaphors that work in the sense that they have some explanatory power. Merely descriptive metaphors--such as the "tree of life" in evolution or the "hockey stick" in global warming time-series or, for that matter, "sparklines"--do not deepen substantive technical thought. Indeed descriptive metaphors may impede such thought. So let us look for some good explanatory metaphors. There needs to be some precision here lest all thought simply becomes defined as thought mappings.

-- Edward Tufte

Response to Metaphors, or thought mappings

A "hot wash-up" is a period of group reflection immediately after an event. Within the military, particularly in ground operations, one of the first things anyone wants to do after an exercise or operation is to wash up with some hot water, but everyone is also coming off the high of the event and so talking about it is natural. Fertile time period is then captured by extended the metaphor to any exercise or operation, whether the event took place in the subarctic atmosphere of a command-and-control center full of computers and radar or in the middle of a swamp.

The 18 April 2005 Fortune has an article "Get me a CEO from GE!" Among other things, it discusses the experience of a new CEO of Ikon, lured in from GE, who shared with the reporter that he'd learned to not talk about how things were done at GE. He went so far as to remove all GE memorabilia from his office. Similar advise is given to service members who are preparing to enter the civilian work force. This advise is somewhat odd, as many smaller companies who higher ex-military are very clear that they want their leadership and organizational methods. In the Navy, instead of quelching that urge to share lessons learned, while recognizing they can be off-putting in a sort of insular-camaraderie sort of way, people in conversations attempt to defuse the insular, group-oriented objections by acknowledging them, by starting their statement, regardless of the name of the command, "On USS Last Ship . . .". I'm not sure if that's a metaphor in and of itself, but I hope it helps to illustrate how the culture of an organization, let alone larger elements of culture, can infuse a person's thinking with all sorts metaphors we hardly think about until we suddenly find a new and useful extension for them. There is rich comedic material centered around old or recent veterans who can't seem to stop talking like they're in the military, but it is often the case they haven't heard anything better. Perhaps they have not yet perceived a need to reframe their thinking. Readers of this may want to reflect on some of those frames, those metaphors, they've learned in their experience.

George Lakoff has written extensively about metaphor. His best-known works are Metaphors We Live By and Women, Fire, and Dangerous Things.

-- Niels Olson (email)

Response to Metaphors, or thought mappings

"A hydrogen atom is only about a ten millionth of a millimeter in diameter, but the proton in the middle is a hundred thousand times smaller, and the electron whizzing around the outside is a thousand times smaller than THAT. The rest of the atom is empty."

Metaphors related to everyday things like cars or sports help get the point across. For example, if the proton of a hydrogen atom is the size of, say, a volleyball, then the electron is a spec of dust about 11 miles away.

-- Craig Pickering (email)

Width of Cassini division = width of United States.

-- ET

Response to Metaphors, or thought mappings

I've been teaching a class of 4th/5th grade students to create a blank map of a place as a class, then invent that place through their studies. They "discover" items on the map by turning up items in reading, looking at photos, listening to sounds, brainstorming, etc. When they've studied those items and written about them a bit they're drawn into the map. As the map grows denser their ability to explore it, and thus generate ideas from it, grows.

In a curious way, this is a way of reversing the metaphor of the mind map -- it's a mind map that really becomes a map.

I've been fascinated at how readily the students take to this kind of thinking. I've had to explain this approach to adult teachers many times and generally received confusion and skepticism in return. But when I showed it to the students not one of them needed an explanation. One said: "I can't wait to get started!" and there was lots of agreement.

I post this here because it is, in a sense, a large-scale metaphor for learning, although it's functional as well.

-- Andy James (email)

Response to Metaphors, or thought mappings

The mapping idea is intriguing. I have recently been thinking about the challenges of learning in medicine, how each professor emposses their schema on the material, because some framework is necessary. But the information is so vast that even schemas vary dramatically between professors. Certainly the most basic element of the schema, the human body, shares a certain physicality with geography.

One of the most common techniques memory champions use is a path. They memorize the order of deck of cards or the names associated with certain number of faces, or whatever, in sixty-seconds by placing one to a few of the associations on a path, often someplace they know well, perhaps the path they walked to school.

Joshua Foer. How to Win the World Memory Championship. Discover, 27:4, 2006.

Also, Joshua Foer's article in Slate, Forget Me Not. 16 March 2005.

Carl Malamud. Memory Palaces. Mappa.Mundi Magazine.

This is all somewhat contra to Lakhoff's position on metaphor, which is that they are derived from common experience, shared stories, and the like. I suspect the memory aid is as much a matter of physicality as shared story, but the element of story cannot be dismissed. Nor can the element of physicality.

-- Niels Olson (email)

Response to Metaphors, or thought mappings

I work with computers, and I'm always interested in how its metaphors define it. A handful of semi-conflicting insights:

"One of the most compelling snares is the use of the term metaphor to describe a correspondence between what the users see on the screen and how they should think about what they are manipulating ... There are clear connotations to the stage, theatrics, magic; all of which give much stronger hints as to the direction to be followed. For example, the screen as 'paper to be marked on' is a metaphor that suggests pencils, brushes, and typewriting....Should we transfer the paper metaphor so perfectly that the screen is as hard as paper to erase and change? Clearly not. If it is to be like magical paper, then it is the magical part that is all important..."
Alan Kay, User Interface: A Personal View
"There was a book, it was translated from the Danish, written about 1989. I forget the author but the name was, The User Illusion. This should ring a bell for everyone. The User Illusion is what Apple exploited to make the computer look different than it really is. To make it friendlier, easier to use. So the user has the illusion that he is dealing with the software when really he is dealing with the hardware. He viewed this as a good thing. Among many of his good comments this was a misunderstanding I think."
Chuck Moore, Dispelling the User Illusion
"Perhaps the chief insight from the Liddle piece is his emphasis on the importance of the user's conceptual model and his distinguishing it from a metaphor. The user's conceptual model is not a metaphor, but what Ted Nelson calls a 'virtuality.' It doesn't have to represent some real-life thing; it becomes its own reality. Gillian Crampton Smith and Philip Tabor push the idea further: the Platonic assumption that there is something behind the interface is not true, in the user's experience: 'As far as the user is concerned, WYGIWYS: What you get is what you see. The interface is the product.'"
Michael Swaine, Programming Paradigms

-- Jack Johnson (email)

Owen Gingerich ("The Inside Story of Pluto's Demotion," Sky & Telescope, November 2006, p.37) mentions this Saturnian metaphor:

"A celestial object is round when it is massive enough for its gravity to overpower the mechanical strength of its internal structure and pull it into a ball. Physicists refer to this state as hydrostatic equilibrium. In an astronomy textbook that I once adopted, Saturn was depicted floating in a bathtub, a vivid way to show that its average density is less than that of water. But one day a guest lecturer pointed out that it is physically impossible to build a bathtub big enough to hold Saturn--the tub's own gravity would collapse it into a ball of porcelain and steel. That's hydrostatic equilibrium! It applies to bodies with masses exceeding about 0.1% of Earth's mass and diameters about 800 kilometers (500 miles) or larger, and to icy ones about half that size."

This is an example of a collapsing metaphor and, as well, an unmetaphorically collapsing metaphor.

-- Edward Tufte

Another example of a metaphor under collapse.

"George Orwell was once arguing with a Communist sympathizer about the true nature of Stalin's Russia. Forced to concede that there might be some political repression, his opponent fell back on what was then a much-favoured cliché.

Communist sympathizer: Well, you can't make an omelette without breaking eggs.

Orwell: Where's the omelette?"

Source: John Gross, The New Oxford Book of Literary Anecdotes (Oxford, 2006), p. 287.

-- Edward Tufte

A Portrait of Bush as a Victim of His Own Certitude


Published: September 30, 2006

In Bob Woodward's highly anticipated new book, "State of Denial," President Bush emerges as a passive, impatient, sophomoric and intellectually incurious leader, presiding over a grossly dysfunctional war cabinet and given to an almost religious certainty that makes him disinclined to rethink or re-evaluate decisions he has made about the war. It's a portrait that stands in stark contrast to the laudatory one Mr. Woodward drew in "Bush at War," his 2002 book, which depicted the president -- in terms that the White House press office itself has purveyed -- as a judicious, resolute leader, blessed with the "vision thing" his father was accused of lacking and firmly in control of the ship of state. . . . .

Mr. Woodward reports that when he told Mr. Rumsfeld that the number of insurgent attacks was going up, the defense secretary replied that they're now "categorizing more things as attacks." Mr. Woodward quotes Mr. Rumsfeld as saying, "A random round can be an attack and all the way up to killing 50 people someplace. So you've got a whole fruit bowl of different things -- a banana and an apple and an orange."

Mr. Woodward adds: "I was speechless. Even with the loosest and most careless use of language and analogy, I did not understand how the secretary of defense would compare insurgent attacks to a `fruit bowl,' a metaphor that stripped them of all urgency and emotion. The official categories in the classified reports that Rumsfeld regularly received were the lethal I.E.D.'s, standoff attacks with mortars and close engagements such as ambushes."

New York Times

-- Edward Tufte

Response to Metaphors, or thought mappings

Isn't an "explanatory" metaphor an analogy? Or perhaps a parable? Maybe a fable?

I don't know who first said "analogy is always suspect in an argument," though I recall reading it in a Robert Heinlein novel. Using any of the above concepts for explanation risks highlighting the wrong aspect of the comparison to those who don't share a very high percentage of similar experiences.

We would all like pithy one-liners that result in epiphanies. But there is no substitute for experience and data, and metaphors/analogies/fables can only help us "see the elephant" if we have already touched many of its parts.

-- Gordon Fuller (email)

For more about the uses and misuses of metaphors, see Tihamer von Ghyczy's "The Fruitful Flaws of Strategy Metaphors" in the September 2003 edition of Harvard Business Review (reprint # R0309F). He distinguishes between "rhetorical" metaphors (use of the familiar) and "cognitive" metaphors (often relying on the unfamiliar). Ghyczy notes, "Indeed, linguists would rather uncharitably classify most rhetorical methaphors used in business ... as dead metaphors." Also, "[U]sing metaphors to generate new stategic perspectives begins to work only when the metaphors don't work, or at least don't seem to."

Joe McCaughey

-- Joe McCaughey (email)

Some "rhetorical" (use of the familiar) metaphors are so popular that they acquire the status of a 'figure of speech', and become a debating short-hand. For example, in creative engineering communities, the phrase "let's not re-invent the wheel!" represents a particular position, one that is well understood by all participants, regardless of the accuracy of the metaphor itself.

For such metaphors, it would be good to see counter-metaphors to avoid the original metaphor forcing an argument, fait accompli. For example: "many hands make light work" is countered by "too many cooks spoil the broth". I can think of plenty of examples in my software development career where the unarguable "let's not re-invent the wheel" metaphor has led to very poor decisions being made. While good metaphors have a high explanatory value, a bad metaphor in the wrong hands can be dangerous.

-- Malcolm Sparks (email)

Odd metaphor and odd flow diagrams at

Largely descriptive metaphors (such as the "internet is a bow tie" in the above, or the "hockey stick" in global warming time-series) don't contribute much to the substance at hand. Such metaphors are inevitably dequantified, turning data into vague, cute shapes.

-- Edward Tufte

Multifaceted metaphors

Useage of the term 'tree' in 'tree of life' may be a bad metaphor, yet it has been used to describe hierarchies so often that its definition has been extended beyond the physical object. It has become an idiom, and as such, good useage.

Metaphors are valuable when there are many parallels between the subject and the metaphorical object. If this metaphorical object is commonly well understood, then the metaphor is even better.

This also applies to extended metaphors (metaphors which are repeatedly referenced, perhaps as the subject of the essay). Sometimes, extended metaphors will make the most important of the parallels explicit. This may mean that the parallels are unobvious, likely indicating a bad metaphor.

With normal metaphors the reader is left to think about these parallels. This thinking reinforces the subject matter within the reader's brain, perhaps offering a memory tool for some. This is, of course, for the multifaceted metaphor.

A programming metaphor for the value of metaphors is found in the language Lua. In this language the primary data structure is a table linking keys to values. Lets say you have a new task which requires a table which is similar to a table used by a different task. Rather than recreating the new table from scratch, you copy the other table and modify it a little. With metaphors you are able to reuse your knowledge of something, with a little contextual modification.

The main source for my realization of the value of good metaphors was Paul Graham's essays ( Most of them are full of metaphors, though not all are good ones. There are definitely a few jems. Most of the essays are very long, and there are many - it would take too much effort to find the exemplary ones.

-- Michael Sloan (email)

From Robert Weintraub in Slate, about the OSU-Florida football game:

"The pregame buzzword was speed, and Florida definitely made the Buckeyes look like they were wearing anchor chains. More important than mere speed was scheme, and how Florida used all those burners. Meyer deploys a fleet of quick players to engage the defense, spread the field, and keep the other team off-balance and unsure of itself. As Fox analyst Charles Davis aptly put it, "cloudy minds equal slow feet." OSU looked slow because Florida's multiple formations and plethora of playmaking options made the defense have to react rather than attack."

-- Edward Tufte

As a responsible citizen I have engaged in a process of understanding where our global climate is going to. This is obviously no small feat but a necessary one if one wants to come to a good personal view on the whole situation.

One of the more stricking discussions is, as already mentioned above, the "hockey stick" discussion between, amongst others, Professor Edward Wegman (opponent) and profesor Michael Mann (proponent). The discussion is aimed if the global temperature trend ends in a "hockey stick" for the last 70~100 years or not.

See this link for the Wegman report:

And a link to one of Prof. Mann's articles:

In itself this whole discussion is already very interesting from a data processing and visualization point of view: how can a temperature trend be correctly predicted from many highly variating data sources? Additionally, most temperature data is inferred from other data like the width of tree rings and ice core air samples and many more.

On a more public level it is highly interesting to observe that many discussions seem to focus on the hockey stick effect only, ignoring most if not all relevant details from both proponents and opponents.

The whole global warming discussion appears (my view) to be divided into two groups (in favour and against) who are increasingly focusing on data that speaks in favour of their views. I have some difficulty finding an open discussion between proponents (climate is changing due to human carbonization) and opponents (climate is changing due to natural changes in carbon levels).

May I suggest that the global climate discussion would be deserving of a separate discussion on this website.

Paul van Oppen

-- Paul van Oppen (email)

George Orwell really has to be one of the masters, not only of the English language, but of correct use of metaphor. A full copy of his classic piece on Politics and the English Language is available on the website dedicated to his work:

Here is an excerpt, taken from a section immediately following his 'five specimens of the English language as it is now habitually written' (badly):

'Each of these passages has faults of its own, but, quite apart from avoidable ugliness, two qualities are common to all of them. The first is staleness of imagery; the other is lack of precision. The writer either has a meaning and cannot express it, or he inadvertently says something else, or he is almost indifferent as to whether his words mean anything or not. This mixture of vagueness and sheer incompetence is the most marked characteristic of modern English prose, and especially of any kind of political writing. As soon as certain topics are raised, the concrete melts into the abstract and no one seems able to think of turns of speech that are not hackneyed: prose consists less and less of words chosen for the sake of their meaning, and more and more of phrases tacked together like the sections of a prefabricated hen-house.'

And here are his guidelines for how to write well:

'In prose, the worst thing one can do with words is surrender to them. When you think of a concrete object, you think wordlessly, and then, if you want to describe the thing you have been visualising you probably hunt about until you find the exact words that seem to fit it. When you think of something abstract you are more inclined to use words from the start, and unless you make a conscious effort to prevent it, the existing dialect will come rushing in and do the job for you, at the expense of blurring or even changing your meaning. Probably it is better to put off using words as long as possible and get one's meaning as clear as one can through pictures and sensations... and one needs rules that one can rely on when instinct fails. I think the following rules will cover most cases:

1. Never use a metaphor, simile, or other figure of speech which you are used to seeing in print.

2. Never use a long word where a short one will do.

3. If it is possible to cut a word out, always cut it out.

4. Never use the passive where you can use the active.

5. Never use a foreign phrase, a scientific word, or a jargon word if you can think of an everyday English equivalent.

6. Break any of these rules sooner than say anything outright barbarous.'

_____ LF, April 2009

-- lisa (email)

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