The matrix revisited

Journal of Business Strategy

ISSN: 0275-6668

Article publication date: 1 August 2004


Marren, P. (2004), "The matrix revisited", Journal of Business Strategy, Vol. 25 No. 4.



Emerald Group Publishing Limited

Copyright © 2004, Emerald Group Publishing Limited

The matrix revisited

Patrick Marrenstrategic consultant with the Futures Strategy Group. Clients he has worked for have included the US Coast Guard, NASA, the FAA, the Panama Canal Commission, various aspects of the US military, and numerous Fortune 500 companies. He lives in Crystal Lake, IL (

This column is not about the movie and its sequels, but about the matrix as a key element of strategic planning. Too many matrices used in planning unconsciously purport to "cover the waterfront", and serious plans are made on this assumption. The sad fact is that no humanly-constructed matrix outside the theoretical world of mathematics can possibly hope to capture the variety of reality.

In Plan of Attack, Bob Woodward's best-selling account of the Bush administration's planning for and conduct of the Iraq war, there is an interesting turning point recorded on 28 December, 2001.

It came during a presentation by General Tommy Franks, head of Central Command, to President Bush and members of his war cabinet, on the latest plan for an invasion of Iraq. Such plans are kept "on the shelf" for contingencies in all major areas of the world. Bush had requested an update of the Iraq contingency plan from Donald Rumsfeld, Secretary of Defense, the previous month. Rumsfeld had pushed Franks, then in the midst of conducting the war in Afghanistan, to have his staff redo the Iraq plan from the ground up, examining all the assumptions that went into it.

Franks' initial response is not printable in this magazine. But he soon got on board and worked closely with Rumsfeld through several "iterations" of a new battle plan for Iraq. The real turning point of this work, however, took place at the meeting on Bush's Crawford ranch on 28 December, a scant month after the subject had been mooted to Rumsfeld by Bush. The attendees were Franks and his operations director, General Gene Renuart; Bush; and, via secure video conference, National Security Advisor Condoleezza Rice, Vice President Dick Cheney, Secretary of State Colin Powell, CIA Director George Tenet, and Rumsfeld.

Now, many people have already jumped all over the contents of this book, using it to either defend or excoriate the Bush administration. Like most other people not living in caves since 1970, I have my opinions on these events. But since every conceivable shade of opinion on this subject has been expressed ad nauseam through every conceivable medium, and since these expressions seem to have changed practically no minds at all, and, most of all, because this is a business magazine and not a soapbox in Bughouse Square, I would like to use the Woodward book to examine a business issue, not a political one.

Franks' very well received 26-page presentation altered the US approach to an Iraq invasion fundamentally. Previously, the plan on the shelf had dictated a "Gulf War plus" approach: essentially replicating the successful 1991 Gulf War plan and augmenting it a bit in order to accomplish the expanded objective of "regime change": getting Saddam Hussein out of power. The initial plan had foreseen the use of some 400,000 troops and a seven-month buildup. Rumsfeld had demanded a more flexible, less visible plan, one that could be put into operation far more quickly if the President deemed action to be necessary.

The fulcrum of Franks' presentation was a comparison of the "lines of operation", or methods of attack (or other action), available to the United States, against the "slices" of the Iraqi regime's capabilities – the targets. The "lines of operation" included things as disparate as cruise missiles and ground forces, psychological operations, information dissemination, diplomacy, and humanitarian assistance. The "slices" included the Hussein family, Republican Guards, WMD infrastructure, commercial and economic infrastructure, and the civilian population.

Arraying the "lines of operations" against the "slices", Franks and his staff created a matrix. Where a tool was thought usable against a target, Woodward reports, "little graphic signs of explosions or starbursts indicated where particular 'lines of operations' could be effectively employed against 'slices' of regime vulnerability". President Bush, interviewed about the presentation two years later, "recalled 'the little starbursts' on the matrix but not much of the detail".

The presentation was a great success. The Iraq plan continued to be refined for a year or more, right up until the attack in March 2003. But the basic outlines of the approach were contained in this initial presentation on 28 December, 2001. And much of the power of the presentation derived from its use of a matrix to illustrate a complicated analysis in a restricted space. Dwelling on this slide far longer than the others, the attendees became convinced that their former approach had been needlessly crude and large-scale and unsubtle, and that a more precisely targeted, elegant approach was warranted – and possible.

A matrix is a mechanism that confronts one set of phenomena with another set of phenomena (or with itself – one of the first "matrices" I ran into was the mileage chart on a state map, which arrayed a list of all the major towns in Illinois against themselves to give the mileage between them). Strategy consulting is rife with the use of matrices. I myself have previously mockingly defined "matrix" as "a frequently-employed management consulting tool used when actual thought would be either too painful or too expensive".

But, like most really funny statements, this is unfair and inaccurate – to an extent. Matrices are an inevitable element of management, planning – and, it might be said, of human thought itself. Anything that can be digitized – a music CD, a database, the birthdays of your friends and relatives, the latest eleven-dimensional model of subatomic physical reality, a map of Akron, the Michael Porter Five Forces Model, a calendar, a budget, an order of battle, employee files, the human genome – must at some level be understood as a matrix of different identifiable attributes. To say otherwise is to abandon all intellectual rigor.

That is not to say that all matrices are equal, or equally well-constructed or well-used. Myriad are the different ways in which matrices can be misused – consciously or unconsciously. An examination of some of the errors matricizers ("matricians"? "matrixians"? "matri-archs"?) fall into may not only be amusing, but also instructive.

There are, as stated above, different types of matrices. One type, one I might describe as the Aristotelian, is a matrix that attempts to divide the entire world into separate parts. Aristotle used to say things like, "All dogs are divided into two types: those with floppy ears, and those without floppy ears". That is a one-by-two matrix. His successors try to expand this concept into a larger number of dimensions: "Americans can be subdivided by the following categories: Miracle Whip eaters versus Hellmann's eaters on one axis, and Ford versus Chevy buyers on the other".

This illustrates the first error that tends to bedevil matricizers: that of the excluded middle. This matrix divides the US into four groups: Hellmann's-Ford buyers, Hellmann's-Chevy buyers, Miracle Whip-Ford buyers, and Miracle Whip-Chevy buyers. But this is not an accurate way of dividing up the US because there are plenty of Americans who eat peanut butter and drive a Toyota. The matrix, while purporting to be universal, is not.

This would not be a problem, except that many matrices used in planning unconsciously purport to "cover the waterfront", and serious plans are made on this assumption. The sad fact is that no humanly-constructed matrix outside the theoretical world of mathematics can possibly hope to capture the variety of reality, because some dogs have no ears at all, while others have one ear that is floppy and one that is not.

I cannot resist sharing with you my all-time favorite example of an attempt to divide an unmanageable set of phenomena into mutually exclusive, collectively exhaustive sets. It is from a manuscript unearthed by the poet and scholar Jorge Luis Borges. In it, a Chinese author states the following: "Animals are divided into: (a) belonging to the emperor; (b) embalmed; (c) tame; (d) sucking pigs; (e) sirens; (f) fabulous; (g) stray dogs; (h) included in the present classification; (i) frenzied; (j) innumerable; (k) drawn with a very fine camel-hair brush; (l) et cetera; (m) having just broken the water pitcher; (n) that from a long way off look like flies".

General Franks' matrix is not quite so obviously flawed, nor does it openly claim to be all-inclusive. But it's possible that the attendees may have assumed that his array of "lines of operations" versus "slices of Iraqi regime" contained the entire universe of actions and targets. I do not necessarily say that this is the case, but this type of error is extremely common in planning – the necessarily approximate but ingenious schematic that is so compelling that viewers begin to substitute it in their minds for the vast, unmanageable reality that lurks outside, evolving, mutating, and refusing to conform to human categories. It would only be human of the attendees to forget that there might be other "slices" to consider, both inside and outside of Iraq; it would also only be human for them to begin to assume that the only "lines of operations" available to them were those under General Franks' command, i.e. military ones.

I doubt very much that General Franks' matrix caused all thinking about other alternative ways of framing the problem to be shut down, particularly when his boss, Donald Rumsfeld, prides himself on the grounding in philosophy he got at Princeton (and as an all-American wrestler). But there is another element of this vignette that exemplifies a use of matrices that can lead to error in the wrong hands.

A matrix may also be seen to be an analog to a mathematical function. One of the most basic mathematical functions is the multiplication table we all learned in grammar school. Across the top are numbers; along the left margin are numbers. Each cell in the matrix is filled in with the multiplicative product of the corresponding numbers at the far left and top of the matrix. In the case of the multiplication table, the answer to "what goes into each cell?" is straightforward. The function to be applied to the two variables (let's call them "x" and "y") is simple: xy.

But things are rarely so cut and dried in the world of planning matrices. Let's take General Franks' matrix again. He has arrayed "lines of operations" on the "x" axis, and "slices of the Iraqi regime" on the "y" axis. So far, so good.

But now the question arises: what is the function to be applied to the two "variables"? What, for example, should appear in the cell corresponding to "influence operations"::"the civilian population"?

Certainly it is not their multiplicative product, since these "variables" are not numbers. What should the cell contain in this case, then?

It might be filled in with text, such as "psychological operations designed to cause favorable public reaction to US forces as they enter Iraqi cities". It might also have simply been filled in with an "x" mark denoting something along the lines of "this line of operations is relevant to this slice of the Iraqi regime".

General Franks did not enter text into his seven-by-nine matrix, for which he ought to be applauded by PowerPoint experts and decried by under-employed optometrists. But neither did he simply put in an "x". He seems to have used the logic detailed above: "this line of operations is relevant to this slice of the Iraqi regime". But instead of an "x" or a check mark, he entered the "little graphic signs of explosions or starbursts" that President Bush recalled two years later, long after "much of the detail" had faded from his mind.

Now, explosions might be appropriate symbols for the combination, say, of "operational fires"::"Republican Guard divisions". But their significance for the intersection between the Iraqi public and "influence operations" is a little hazier. Critics of the administration would undoubtedly leap on this example as illustrating a tendency on their part to leap to violence as the first option.

As a veteran of many over-rushed PowerPoint presentations to audiences of high-level decision-makers, public and private, I would be more inclined to attribute the explosions to the appetite for graphically appealing simplification (not to say over-simplification) that such audiences seem to eat up. The one point of criticism I would insist on, however, is that a certain amount of vagueness obviously was allowed to creep into the Franks matrix when the decision was made to include the explosions. The amount of strategic insight that was actually conveyed by the Franks matrix was far less than might have been assumed by the people who attended.

Whatever level and type of effectiveness and predictability might have been conveyed by an "explosion" in the "operational fires"::"Republican Guards" slot, it could not possibly have had the same meaning as an "explosion" in the "influence operations"::"Iraqi public" slot. Thus the Franks graphic may have smoothed over any number of very thorny distinctions, upon the clearing up of which the success of the entire enterprise may have depended.

If I myself had not witnessed and, indeed, created matrices that contained very similar or identical flaws, I might be harsher on General Franks. Whenever humans create matrices, and thus try to categorize reality, they inevitably oversimplify; when they have to present their oversimplification to the boss by, say, 3:30, the temptation to further sacrifice rigor for drama is nearly impossible to resist. Granted, the stakes of oversimplification on a set of slides detailing the latest ERP project are slightly less daunting than those of oversimplifying the ease with which a country might be conquered.

But the process can be very similar.

NOT the same. Just, similar.