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grokduel, n [grok deeply understand + duel]: a contest in which two or more parties vie to see who best understands (the position of) the other(s)

What do we really know about cognitive development? Robert S. Siegler of Carnegie Mellon University writes that "we know a great deal about differences in reasoning at different ages, but little about the change process itself." (1)

Cognitive developmentalists often have phrased their models in terms that suggest that children of a given age think about a task in a single way. Children of age N are said to have a particular mental structure, processing limit, strategy, or rule that gives rise to a certain type of behavior. Children of age N + m are said to have a different mental structure, processing limit, theory, strategy, or rule that gives rise to a different type of behavior.

Thus, argues Siegler, we liken children's development to ascending a flight of stairs. One stands entirely at a given level for some period; suddenly one makes a sharp vertical hop, and then one stands entirely on a higher level. No matter how many steps one imagines in the flight of stairs, however, this way of viewing the development of children's thinking "inhibits progress in understanding change." It produces data on the level of the treads but nothing about negotiating the risers. To get such data, one needs to focus on the process of change itself.

Microgenetic studies of training procedures offer the potential to study change, says Siegler, but unfortunately "most training studies have focused on which treatments are effective and the amount of change each engendered, rather than on how the change occurred."

To illustrate a better approach, Siegler uses the example of children learning the conservation of number, a vital step in mathematical learning, to wit, that the number of objects stays the same under various kinds of transformation. Jean Piaget, the influential Swiss psychologist, had shown that children of age 4 didn't understand number conservation. If, to take an example that the Mathsemantic Monitor has verified for himself, you first show a young child two rows with six objects (say, buttons) and then lengthen one row by putting more space between the buttons, the child will now say that the longer row has more buttons than the other. (2) By about age 6, children acquire a different understanding and say that the number of buttons stays the same.

These two beliefs, that the number changes and that it stays the same, form the basis of Siegler's investigation. He first looks at five different explanations children give of their thinking. I will describe these here as #1 - spacing doesn't change the number, #2 - lengthening changes the number, #3 - I counted them, #4 miscellaneous idiosyncratic explanations, and #5 - I don't know. Explanation #1 fits mature belief. The other four explanations occur earlier, with #2 predominating.

Siegler's example covers three groups of five-year-olds screened to determine that they did not yet understand number conservation, but stood, so to speak, at its threshold. They received (a) a session of pretest trials, used to elicit their explanations, and then (b) four training sessions, with three variations in feedback. One group heard only whether their answers qualified as right or wrong, a second group had to explain their answers, and a third group heard the experimenter's answer and had to try to explain it. This work yielded several findings:

1. Almost all the children in the pretest trials gave more than one of the five explanations.

2. In the pretest trials, explanation #1, the correct one, occurred in only 9% of the answers (not unexpectedly, given the child-selection criteria), yet 80% of the children cited it at least once.

3. Variations in the percentage of correct answers on the pretest did not help predict subsequent learning.

4. Instead, the "variability of reasoning ... predicted success." The greater the number of different explanations advanced by a child during the pretest, the more correct answers he or she gave during the training. The results rose considerably if the child had ever given more than one answer on a single pretest trial.

5. Some change toward understanding number conservation took place in each of the groups. "By far the greatest [also called "the most dramatic"] change occurred in the group of children asked to explain the experimenter's reasoning."

Others have surely made observations that fit with these findings. Open inquiry has had many champions. The method of Socrates, who lived twenty-four centuries ago, involves testing the implications of different sets of assumptions. Former ETC editor Neil Postman openly championed the inquiry method for teaching. (3) "In the logico-mathematical realm," wrote math-educator Constance Kamii, "children are bound to arrive at the truth autonomously if they debate long enough." (4) Yet nowhere has the Mathsemantic Monitor come across an essay that ties multiple explanations to learning more precisely than Siegler does. Siegler's data make the point that both a variety of explanations and an attempt to explain the reasoning of other persons (at least of more knowledgeable ones) provide statistically superior predictors of an individual's learning success.

These findings take me back, way back, to a time before the Mathsemantic Monitor appeared, to a time when I first discovered and practiced what I now call grokdueling. Before getting to that, however, let me digress on the first part of the word itself, on "grok."

I first ran across "grok" at the August 1985 International Conference on General Semantics held in La Jolla. It happened in an interesting session titled, Grokking: The Use of Symbols and Body Language in Inference-Making OR How Do I Know All This About You When We've Just Met, in which Ruth McCubbrey had all of us do some of the grokking implied by the second title. She told us that she'd picked up the term from Robert Heinlein's Stranger in a Strange Land. (5)

The verb "grok" (grokked, grokking) figures hugely in the book. It first appears, absent explanation (not unusual for science fiction), on page 22 in an odd sentence fragment, "Back even before the healing which had followed his first grokking of the fact that he was not as his nestling brothers ... back to the nest itself." It appears 29 more times in the next 100 pages, still with no explanation.

At page 136 a character remarks, "I'm not sure I know what 'grok' means," finally confirming that the lack of explanation reflects the author's intention. The term appears ever more often (reaching at least 483 times in all by my count) with its best explanation coming on pages 265-66, about halfway through the book. "Grok" originally, these pages tell us, had the literal meaning of "drink" (the Stranger of the title comes from a dry planet) but it acquired a richer meaning. "Grok," says a knowledgeable character, "means to understand so thoroughly that the observer becomes a part of the process being observed - to merge, to blend, to intermarry, to lose personal identity in group experience."

This description helps explain why the Stranger's actions fit so poorly into the worldly scene before he grokked people and the tragicomic human condition. He then remarks (p.387), "I grok that when apes learn to laugh, they'll be people."

Perhaps not, but anyway, as you can see, "grok" stands for a particularly powerful form of understanding. I found myself better able to grasp it by thinking of the French saying, Tout comprendre c'est tout pardonner [to understand all is to forgive all]. I don't necessarily subscribe to the sentiment, but the idea helped.

The term "grok" came my way long after I first resorted to what I now call "grokdueling." Somehow I'd become aware that I often understood the arguments of others better than they understood mine. From that I developed a strategy for dealing with friends who argued with me that usually worked out as follows. (6)

1. I'd suggest we each try to state the other's position to the other's satisfaction. I'd offer to go first or second, whichever my friend preferred. They always wanted me to go first. If at a party, say a class reunion, a few people would drift over to witness a new kind of spectacle.

2. I'd then state my friend's position in my own words with examples and feeling, trying to make a better case for it than I'd been given. (I found I could do this, because I'd listened earlier and tried to understand what my friend said.) A few more people would now join the onlookers.

3. My friend would beam with delight and agree that I understood his or her position, sometimes adding that we needn't continue inasmuch as I obviously agreed with the position. I'd say thank you but we had to continue because I hadn't agreed with the position, only tried to show that I understood it. The crowd continued to grow.

4. My friend would now start reluctantly to try to state my position but soon veer off into reasons against it. When he or she had finished, I'd point out that the statement didn't satisfy me because it consisted of arguments against rather than for my position. "Well," my friend would ask, "how can you expect me to give you a good argument for something I don't agree with?" The crowd would now begin to drift away.

The first few times this happened I said that the exercise, as we'd agreed at the outset, tested whether we really understood each other's position, because what sense did it make to argue about something before understanding it. My friends tried again to state my position, but stumbled, probably not having listened to my earlier points enough to understand them. The few people who hadn't already left now silently stole away and I found myself searching for a way to save face for my friend.

I had to give up social grokdueling for fear of running out of friends. It had too much power as a strategy for any but special occasions.

Nevertheless, I found times when the grokduel principle of showing an understanding of another's position came in very handy. I once had to explain to an early morning public session of the City Council of Kansas City why they should not back Trans World Airlines, then the largest employer and most politically important company in town, for an international airline route award in a proceeding then in progress before the Civil Aeronautics Board. I'd flown TWA very late the night before and because of tornadoes and luggage-handling ended up getting only two hours sleep. Turning my exhaustion to advantage, I argued that loyalty stood near the top of my list of virtues, that TWA had reason to expect Kansas City's loyalty, and that I'd tried every way I could to find a reasonable argument Kansas City could use to support TWA, but, sadly, had failed. By now my eyes began to mist up. (Of course I'd mentioned to nobody how little sleep I'd had.) I then passionately advanced each argument favoring TWA and sadly pointed out its fatal flaw, why it would hurt Kansas City's credibility and thereby reduce the city's power to help TWA in the future. When the City Manager called on TWA to speak, their representative said that TWA, the City Attorney, and the consultants (me) could handle it privately. We then met privately to hear TWA drop the matter.

The first time I used the term grokduel occurred immediately after the July 1988 International Conference on General Semantics held at Yale. The conference chairman, William Exton, Jr., and I had had a running disagreement on the role of goal-directed decision making in management. After my paper on the subject (it treated goal-directed decisions as only one of several varieties) (7) he made what I took as disparaging comments and allowed no questions. I recall that after that I made a nuisance of myself in other sessions Bill chaired, feeling he'd treated me unfairly.

My files contain a page in pencil that reads as follows:


Challenge Bill Extort to a GrokDuel

cc Ruth McCubbrey Russ Joyner Harry Maynard Stuart Mayper - SF Chap. Marjorie Zelner


Request publication of this challenge in the Map and ETC A way to use our disagreement to show GS in action Attachment re Grokduel (8)

At the time I wrote these notes I really wanted to grokduel Bill on our positions on goal-directed decision making. Given his showmanship, his sporting nature, our strong feelings about our positions, and our long history of mutual respect, I had a feeling that we could work it into an interesting spectacle. However, I also had my doubts about my motives and about how the grokduel might work out, so I took no action. Sadly, Bill died in an automobile crash that December.

This didn't constitute the first time nor the last that I felt general semanticists, of all people, failed to understand each other because they kept restating their own positions rather than attempting to grok each other. I remember a long-ago meeting of the Board of Directors of the International Society (attended by some of the most illustrious general semanticists) that failed in this way. After an hour's futile argument on a motion to ease chapter formation, the majority formally overrode a minority that said it agreed with the motion's aim but feared its wording would have an effect opposite to that intended. It took getting into the details of implementation the next day at the office for the motion's leading proponent, the Society's president, to discover that the minority had had it right.

To decide between two different readings of a text, or between any two ideas, would you rather trust someone who understood only one of them or someone who understood them both? The question almost answers itself. You'd rather trust someone who understood both. Why would anyone trust judgments based on one-sided understanding?

This simple answer suggests a better way to handle disputes about ideas. Don't stage debates, stage grokduels.

Grokdueling has simple rules.

1. Each party takes turns trying to state the other's position to the satisfaction of the other party.

2. A party who has not been satisfied must state at least one particular in which the statement fails.

3. The first party to make a satisfactory statement wins. If the second party then replies with a satisfactory statement, the second party also wins.

Grokdueling every question would waste too much time. But grokdueling selected impasses certainly seems like a useful tool to develop understanding and avoid mistakes.

To sum up with regard to trying to grok the positions of other people: (a) we have statistical evidence that it can help children learn math, (b) we have every reason to suspect that it can help more than just children learn more than just math, and (c) we have anecdotal evidence that it leads to more persuasive arguments. Therefore, it would seem to make sense for children to learn grokking in school and perhaps for adults to demonstrate their grokking capabilities in real grokduels before live audiences.

How about it? Grokdueling, anyone?


1. Robert S. Siegler, "Concepts and Methods for Studying Cognitive Change," in Change and Development, E. Amsel and K. A. Renninger, eds (Mahwah, NJ: Erlbaum, 1997).

2. For related examples, see Edward MacNeal, Mathsemantics: Making Numbers Talk Sense (New York: Viking, 1994) pp. 121-122.

3. Neil Postman and Charles Weingartner, Teaching as a Subversive Activity (New York: Dell, 1987), originally published in 1969.

4. Constance Kazuko Kamii, with Georgia DeClark, Young Children Reinvent Arithmetic: Implications of Piaget's Theory (New York: Teachers College Press, 1985), p.50.

5. Robert A. Heinlein, Stranger in a Strange Land, original version (New York: Ace, 1991), from which 70,000 words had been cut for the version published in 1961.

6. Such ideas developed in me quite naturally. My father welcomed reasoned argument and sometimes held mock court when we kids fought over something, at which time he would decide who had the most persuasive argument.

7. Edward MacNeal, "Management as a Specialized Approach to Decision Making." Unpublished talk.

8. The people, publications, and organization mentioned would have been important in getting word of the grokduel out to general semanticists. I had visions of holding the duel under the auspices of the San Francisco (SF) chapter. The "Attachment re GrokDuel" referred to a document unwritten in any form before now.

A persona of aviation-consultant, demalogician, etc., Edward MacNeal, a regular contributor to these pages.
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Title Annotation:coined phrase meaning a contest where two or more parties vie to see who best understands the position of the other
Author:MacNeal, Edward
Publication:ETC.: A Review of General Semantics
Date:Jun 22, 1999
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