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Number 139, May 1998

SimplifiedComplexity:*Thinking in the White Spaces
by Gerry Gingrich

Conclusions- Change, not stability, is the constant    in today’s world. Massive amounts of information flow around our global system in    milliseconds, breaking down the borders of nation states and shifting the balance of power    among old and new players. Widely separated and disparate places around our globe    communicate across electronic networks in real time, reducing the effects of distance and    time.  
- Closer to home, America maintains its    position as the leading edge player in the information society, adapting to the global    information ebb and flow more quickly than any other nation on earth. We rethink our    national security strategy more and more frequently, and the number and variety of    relevant factors increase daily. Our public and private organizations continue to re-size,    restructure, and reengineer. And our citizens enter new educational programs, lose and    change jobs, and explore new models of management and leadership. As Carl Builder warns,    it is a time for humility, not hubris. 
- Military thinkers, politicians,    scientists, and corporate executives are all looking for ways to understand the dynamics    of global change and to prepare for the 21st century. Many are looking to the new science    of complexity for answers. The science of complexity, however, does not yield answers, at    least not in the sense that we have typically sought to describe our world and predict its    events since the beginning of the Scientific Revolution. What it does yield is a new way    of thinking about the world. 
**Old or New: Simple or Complex**
For the last 300 years, Western sciencehas progressed through the discovery and accumulation of "laws," each judged andmeasured against the aesthetic of simplicity. Laws that are simple are better than thosethat are complex. In contrast, the new way of thinking is ruled by an aesthetic ofcomplexity. Empowered by the computer and the powerful manipulations it makes possible,this new thinking focuses on complex phenomena. Indeed, the new way of thinking assumesthat many worldly phenomena are complex, not simple, and that *ipso facto*, thescientific description of these phenomena must also be complex.

As a framework for illustrating thedifferences between the old and new ways of thinking, consider regression analysis, apopular technique used by both the hard and soft sciences to model worldly phenomena.Regression analysis develops mathematical models to describe the functional relationshipbetween a phenomenon, *y*, and a set of variables, *x1, x2, . . . , xn*. Old thinking, the traditionalparadigm of Western science, argues in favor of simplicity. So the fewer the *x*’sin the regression model, the better. Thus we have typically built our regression models ofpolitical and economic phenomena by starting with a very small number of variables andadding new ones *only* if they are statistically important. For example a traditionalpolitical scientist might use the two variables of military strength and economic healthto build the first iteration of a hypothetical model describing the possibility of anoutbreak of a major regional conflict (MRC) such as the Persian Gulf War. Additionalvariables might be useful for a full understanding of the nature of MRCs, but unless thepolitical scientist can prove that they’re statistically important, they’ll beexcluded from the model.

New thinking, or the complexity paradigm,would build its first iteration of a regression model by including *all* thevariables relevant to describing and understanding the complex MRC phenomena. So anontraditional political scientist might create the first iteration of a MRC model byincluding the variables of military effectiveness, political leadership, andcivil-military balance in addition to the variables of military strength and economichealth. Each of the five variables would remain in the final model as long as it was notproven to be statistically insignificant.

In short, old thinking is exclusive andnew thinking is inclusive. But more importantly, old and new thinking can result indramatically different final models. A well-known quirk of regression analysis is that theprocess of model building itself, for example the order in which variables are enteredinto the equation, affects the form of the final model. Thus a final model built with thecomplexity paradigm can be both qualitatively and quantitatively distinct from a finalmodel built with the traditional scientific paradigm. In this way, new thinking leadsintrepid explorers into the "white spaces"—areas of thought and discoverynot covered by old thinking and the traditional academic disciplines.

It’s important to note that noteveryone is interested in the new science of complexity. Indeed historians sometimes pointout that, for them, there is "nothing new" in the new science of complexity andthe new thinking. Historians and other humanities scholars have been constructing complexunderstandings of reality for as long as people have been interested in learning about theworld around them. The humanities have their intellectual roots in the philosophers andthinkers of two and three thousand years ago, long before the Scientific Revolutionoccurred.

In contrast most hard sciences weredeveloped after the 17th century and closely follow the traditional Western scientificparadigm with its emphasis on simple laws and simple representations of worldly phenomena.And the majority of the soft sciences, such as political science and economics, have"aped" the hard sciences and followed the same paradigm. There are a fewexceptions, but they tend to be infrequent, unrecognized, or ignored. In his brilliantdescription of scientific progress in the Western world, *The Structure of ScientificRevolutions,*Thomas Kuhn explains why methods and "ways of knowing" that arenot compatible with the dominant paradigm are perceived as anomalous. Beware to scholarswho ignore the aesthetic of simplicity!
**Old or New: Linear or Nonlinear**
The aesthetic of simplicity drives anothercharacteristic of the traditional Western paradigm, that is, the ubiquity of linearthinking. But what exactly *is* linear thinking? Again the modeling technique ofregression analysis provides a useful intellectual framework for illustrating thedifferences between old and new thinking. This time consider linear regression, the mostfrequently used form of regression analysis. Linear regression models describe thefunctional relationship between a phenomenon, *y,* and a set of variables, *x1, x2, . . . , xn* usingthe equation of a line. In general linear regression models take the form: *y = b + a1x1 + a2x2+ . . . + anxn, where *a1,a2, . . . , an* and *b* are constants.All *x*’s are raised to the first power and all *x*’s are combinedwith all other *x*’s additively.
When all the variables in a linearequation are raised to the first power, the equation exhibits "proportionality":increases in an *x*-value result in proportional increases in the phenomenon. Forexample, given the equation, *y = 3 + 10x1 + 4x2,a one unit increase in the variable *x1leads to a 10 unitincrease in *y*. The next one unit increase in *x1alsoleads to a ten unit increase in *y,* as does each additional one unit increase in *x1*. Similarly, each one unit increase in the variable *x2* leads to a four unit increase in the phenomenon under study.
Proportionality is a comfortable thing. Itlets us know that when we change one side of a linear equation, the other side changes ata constant rate. In other words, changes to the inputs of a system lead to constantchanges in the output of that system. Such a relationship between inputs and outputs issimple, easily understood, and predictable. For example, proportionality exists when eachfive percent increase in the DoD budget translates into a one percent increase in militaryreadiness, or when each one percent increase in the Federal Funds rate results in aone-half percent decrease in inflation. For our hypothetical major regional conflict (MRC)example, a decline in either variable—military strength or economic health—leadsto a constant and thus predictable increase in the possibility of an MRC.

Because proportionality is simple and easyto understand, we rely on it heavily in our traditional thinking. In fact, it’sdifficult to think in any other way. Just contrast the simplicity and predictability ofproportional relationships with the complexity and unpredictability of nonproportionalrelationships. The universe of nonproportional relationships is so varied and so largethat the human mind can not even imagine all the possible alternatives. And mostnonproportional relationships, by definition, exist in the white spaces. And thinking inthe white spaces is ambiguous and uncertain, sometimes netting us nothing more than thefrustrating awareness that we simply do not understand. Easier to stick to the traditionalparadigm of proportional relationships!

Proportionality is not the onlycharacteristic of linear thinking, however. The second requirement of a linear model isthat all *x*’s are combined with all other *x*’s additively. Thecharacteristic of "additivity," like that of proportionality, renders ourthinking simple, easy, and comfortable. When variables are additive, models can bedecomposed; that is, variables can be separated from one another, studied individually,and added back together to obtain the complete picture. Decomposition implies that thedescribed phenomenon *y* is equal to the sum of all the individual variables, or thatthe whole is equal to the sum of its parts. Thus there is no problem so difficult that itcan’t be solved by breaking it into smaller and smaller pieces that can then beanalyzed individually to obtain results that are, in turn, added back together to obtainthe final solution.

Consider our major regional conflict (MRC)example again. The traditional political scientist breaks the problem into two separatepieces—the variable of military strength and the variable of economic health—andstudies each one in isolation. When sufficient understanding of both variables is reached,they are translated to a common measuring stick and then added together to achieve adescription of MRC outbreaks. Thus with additivity and decomposition, old thinking assumesaway any relationship between the variables of military strength and economic health, andso continues to "keep it simple."

In contrast, the new thinking paradigm ofcomplexity assumes that military strength and economic health are *not* independent,that there are interdependencies between the variables. Military strength and economichealth cannot be decomposed and studied in isolation. Rather they are integrally relatedas part of a larger system in which the whole is something significantly different fromthe simple sum of its parts; the variables and their interdependencies must be studiedtogether as one system. So new thinking leads to a more sophisticated understanding of theMRC phenomenon. And again it probably occurs in the white spaces untravelled bytraditional linear thinkers.
**Old or New: Universal or Specific**
In addition to simplicity, traditionalWestern science has progressed by judging and measuring its laws and models againstanother aesthetic of beauty and perfection, that of universality. All other things beingequal, laws that explain more of the universe are better than those that explain less.Laws are universal when they explain or describe all of the varied events of a certaintype under all conditions. The aesthetic of universality drives the search for the Theoryof Everything (TOE) and its current incarnation, superstring theory. The simpler are ourscientific laws, the more likely they are to be universal, and thus the aesthetics ofsimplicity and universality reinforce one another.

The complexity paradigm again encouragesthat which the traditional Western paradigm does not. New thinking does not search foruniversal laws but rather encourages "specificity"—the identification ofall variables and parameters necessary to fully describe a *particular event*. If anevent is important enough to be studied, then it’s important enough to be specifiedin detail—only then can it be understood. The aesthetics of complexity andspecificity reinforce one another just as the aesthetics of simplicity and universalitydo: the more complex is a law, the more likely it is to be specific.

Revisiting our hypothetical model of majorregional conflicts one last time, recall that the aesthetic of complexity suggested amodel with five, not two variables, as well as interdependencies between the variables.Now, the aesthetic of specificity suggests the use of additional variables if we are tofully understand and describe the MRC phenomenon. For example, MRCs occur within thecontext of a global environment so additional variables might specify global conditionssuch as economic trading communities, international information flows, and non-statecoalitions. And we might include variables that capture the temporal context of the MRCphenomenon; certainly the possibility of an MRC differs at different points in time.

Thus new thinking, or the complexityparadigm, can create a model and an understanding of major regional conflicts that couldnot be developed by our traditional scientific paradigm and its simple, linear, universalmodels. Driven by the aesthetics of complexity and specificity, new thinking developsmodels that strengthen our understanding with increased numbers of variables; that builddepth and sophistication with interdependent variables; that describe open systems subjectto global conditions; and that capture political and economic phenomena as products of theera in which they occur. Operating in the white spaces, new thinking challenges us todefend our 300 year old thinking patterns: Are simplicity, linearity, and universality theonly way to think about the world?
**Recommendations**- Finding "the truth" in a    dynamic world of global change may involve thinking in a new way. The complexity paradigm    may provide that new way for some national security problems. For example, phenomena such    as the outbreak of major regional conflicts (MRCs) are highly complex. To achieve a full    understanding of MRCs and other national security phenomena, we may need to build complex    models with many, interdependent variables instead of simple models with a few,    independent variables. 
- Our models and understanding of national    security must increasingly encompass events in the larger global environment such as    non-state coalitions and international trading communities. 
- Our models of national security    phenomena need to shift away from the Industrial Age assumptions of predictability and    linearity to the Information Age assumptions of uncertainty and nonlinearity. 

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In this way, new thinking leads intrepid explorers intothe “white spaces”—areas of thought and discovery not covered by oldthinking and the traditional academic disciplines

Dr. Gerry Gingrich teaches at theInformation Resources Managment College, National Defense University, Fort McNair,Washington, DC 20319-6000; (202) 685-2103; [email protected].

The Strategic Forum provides summaries of work by members and guests of the Institutefor National Strategic Studies and the National Defense University faculty. These includereports of original research, synopses of seminars and conferences,the results ofunclassified war games, and digests of remarks by distinguished speakers.

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