Complex Adaptive Systems: A Primer

Several years ago, a friend and mentor recommended The Origin of Wealth by Eric Beinhocker, a book that looks at the economy as a complex adaptive system in which physical and social technologies are constantly evolving. This view of economics, according to Beinhocker, calls into question every fundamental assumption of classical economics and has profound implications for the ways in which we engage instrumentally with the economic environment.

I was astonished by the work and the concepts it presented, and I've been wrestling with complex adaptive systems as a minor obsession ever since, with a particular focus on the implications for my own fields of military operations research and force structure analysis (a subject on which I'll have more to say another day).

In this intellectual wrestling match, I found myself in need of a working definition of these systems, and because of the applications I was pondering I needed that definition to work from the bottom up. In other words, I needed a list of the desiderata that characterize what a complex adaptive system is and does (to provide a heuristic for classifying such a system). In the end, I arrived at the following:

A complex adaptive system is any system comprised of diverse, interdependent, adaptive elements interacting nonlinearly and exhibiting systemic behaviors including emergence, coevolution, and path dependence across multiple scales.

As a standalone definition, this has served me fairly well in pulling together the various descriptive and behavioral elements of complex adaptive systems as they've been articulated by those far more expert than I (e.g., Brian Arthur, Yaneer Bar-Yam, Eric Beinhocker, John Holland, Melanie Mitchell, Scott Page, and too many more to name). What it doesn't do, however, is lay out in detail what each of these seven characteristics mean for how we understand and engage complex systems. More depth is really needed. Then enters opportunity ...

In writing a thesis (now a short book on the subject of complex systems as a lens for understanding (material) military force structure published by Air University Press and available for free download here), I've put together a short and (I hope) useful primer on complex adaptive systems. In the interest of adding a verse to the powerful complexity play, that primer is available as a standalone document here ... Complex Adaptive Systems: A Primer.

The Challenge of Integrated Space Analysis

I've spent the past three years working to overcome these challenges.  Here is my summary in an article just published in MORS Phalanx last month.

The Challenge of Integrated Space Analysis

Ruminations on Path Dependence and Archimedes

A few days ago, I collided at a dead run with one of the hazards--one might go so far as to call it one of the nightmares--of working in the business of analysis. Having conducted a thorough assessment of a problem, applying every tool available and appropriate, carefully weighing every assumption, considering every possible solution, and expending significant manpower, a methodological course of action emerged that incontrovertibly increases both effectiveness and efficiency in the process under investigation. The results were presented to the customer, and the answer came back: "Thanks for the great effort. We love the solution you've given us. It's brilliant! We're going to stick with our current process."

I've been in this business for nearly half my life, and I shouldn't be surprised by this outcome. In this instance, though, I was floored. Then, after a few hours of frustrated muttering, I had an epiphany (or calmed down enough to recognize the dynamics in play). There was a reason for the outcome, and understanding the reason both soothed my frayed analytic psyche and helped me to understand the way ahead. That reason? A favorite concept from economics: path dependence.

So, what is path dependence? The simplest possible expression of the concept is the statement that history matters, but this doesn't do the idea justice. In path dependence, history matters in particular mathematical ways and with particular mathematical and practical consequences. Essentially, though, it boils down to the notion (contrary to classical economics) that positive feedback mechanisms create multiple stable equilibria in dynamic social, technological, and economic systems. (Scott Page describes multiple forms of path dependence in a wonderful essay on the subject, but the naive notion given here is sufficient for most purposes.)  Accidental perturbation (or human decision) at critical junctures may nudge a system's trajectory toward an outcome that is unforeseen and sub-optimal (as many, most, or all of the stable equilibria may be). If one is in a tautological mood, one might then say that these stable equilibria are difficult to escape, but the point is that positive social, technological, and fiscal returns incentize stability.

Examples of path dependent behaviors are everywhere, if we take the time to think about it. Arbitrary coherence--the idea that an arbitrary initial price affects the long-term price irrespective of intrinsic value--is a classic path dependence phenomenon. A favorite military example is low-observable technology in the Air Force's force structure. A little stealth incentivizes improvements in adversary radar that encourages more stealth, and positive feedback takes over. This is a gross oversimplification of the many social factors in play, and it leaves out a number of positive feedback mechanisms, but it illustrates the idea. (I should also note that the situation that smacked me in the face with 'thank you for your interest in national defense' had nothing to do with this example or with questions of force structure.)

So, why am I comforted by this idea? There are two reasons.

First, it helps to know that adherence to the status quo is in some sense and in some cases independent of whether the status quo is the best position available. This realization provides a partial response to the question, "What did we do wrong?" (The other parts of that response involve a close examination of the analysis to make sure we hadn't missed something critical.) We are where we are for reasons of history, and the equilibrium is stable for any number of systemic reasons. We can be both right and rejected.

Second, it gives me hope and encourages me to continue laying the intellectual groundwork for the position. Path dependence and positive returns depend on context, but a fundamental characteristic of complex adaptive (social and technological) systems is that the context is always in motion. There may come a time when the status quo is no longer attractive. There may come a time when the costs of achieving escape velocity are within reach. There may come an opportunity, and if the work is done in anticipation of that opportunity we'll be in a position to exploit it. In the end, much of the great analysis we do is anticipatory. That is, if we wait for the question to be asked (or the opportunity to prevent itself), the analysis to support the decision will almost certainly be too late. Anticipatory analysis creates the lever, and we simply wait for a fulcrum to present itself.

No matter how brilliant an idea may be, no matter how solid the recommendation, it won't always change the world. And the reasons it won't are not always rational or in our control. But that's not a reason to not do the work. In some ways, good work is its own reward (for me). More importantly, doing the work is how we change the context and prepare for the opportunity to move the world.

Social Media for Military Analysts

In response to a recent post noting a lack of social networking presence in the Air Force's analytic community I was asked a slightly surprising question. On reflection this should not have been surprising if I were taking more time to examine my own assumptions and for introspection, but here it is:

What is the value of social networking to analysts ... and the rest of us? 

It occurs to me that there is more than a little wisdom in the question. It has become an assumption and article of faith (at least for some) that social networking is a value-added activity. But unexamined assumptions are something to fear, so here we are.

I've spent some time and glucose turning over my own assumptions, and I've come up with a few interrelated ideas for why social networking technologies can not only add value to the analytic enterprise but may even be essential to the continued success of our community.

Thomas More
Wikimedia Commons

To begin, and to make sure we're all on the same argumentative page, what do we mean by social networking? The dictionary, that most reliable of sources (and a favorite), defines social networking as "the development of social and professional contacts; the sharing of information and services among people with a common interest." Like a lot of definitions, this doesn't necessarily clear things up, not least because under this definition prolific and brilliant correspondents such as Thomas More and Desiderius Erasmus were a social network, and while this is true it also isn't the focus of the contemporary conversation. These legacy networks all still exist, but there are new technologies that facilitate the creation of new (or if not entirely new then at least new in scale) networks. So, what we're talking about here are the new, technologically-enabled forms of social networks and social media. ("Social media" isn't much better as a terminology, since the same objections apply. More and Erasmus interacted in a social network via the available social media of letters.)

Desiderius Erasmus
Wikimedia Commons

Without trying to create a precise definition of the technologies and forums involved, I include in the model outlets such as Twitter, Facebook, blogs (like this one), communities of practice (consider the Military Writers Guild as a fine new example), and other online publications with relatively low cost of entry (e.g., The Strategy Bridge, War Council, The Constant Strategist, The Complex Systems Channel, etc.). The line blurs with more traditional forms based in an online medium (look to ForeignPolicy.com and War on the Rocks as examples), and gets really fuzzy from a social network perspective when we start talking about traditional media with an online presence (e.g., the Air & Space Power Journal, the MOR Journal, etc.). These are all very much in the mix, but it's really the first category that's of most interest here.

One thing you may notice about this list is a general absence of robust exploitation of the digital social media by the Air Force's analytic enterprise. But these efforts take ... effort ... and one wouldn't expect a wholesale plunge into the available medium if there weren't tangible benefits that outweigh the costs, opportunity and otherwise, and I suppose this is the fundamental motivation for this post. Here are four broad reasons for social networking in our community that resonate with me.

Lifelong Learning

There are effective models for distance learning, but in general the value of an educational experience is multiplied by active, daily engagement with those around you (professors and fellow students). This engagement enhances the pedagogical experience in any number of ways. 

For any given concept we are almost certain to hear alternative views and questions we never thought to ask, increasing our understanding of it. These alternatives can be found without that engagement (e.g., by actively seeking and reading competing visions of a given topic), but the costs associated with this sort of study are high and the human  proclivities for delightful cognitive biases present a non-trivial barrier. When each member of the group is exploring the possibilities in their own way and informed by their own background, we distribute the effort in and increase the likelihood of finding constructive gems. 

Gerhard von Scharnhorst
Wikimedia Commons

In addition, I happen to think that writing our ideas down and putting them out in the world forces us to consider our positions more carefully even than conversational academic interaction. As Scharnhorst said, "The preparation of a short essay is often more instructive for the author than the reading of a thick book" because a requirement to present and discuss an issue drives a deeper study. Thus, we are enjoined to read, think, and write, a common theme in this space (here and here, for example). This achieves the noted first order pedagogical outcomes and also yields second order benefits (e.g., improved communication skills). We further experience the tertiary benefit of permanence, since ideas captured and promulgated in writing are not lost. Conversation in the classroom is ephemeral, but discourse in social media is accessible, searchable, and cross-linkable. (Big data, anyone?) This last alone is powerful enough to motivate alternatives to learning and interaction driven exclusively by conversation. 

Finally, the inevitable divergence of intellectual ideas, with equally serious, well-intended, and well-informed students arriving at divergent conclusions, teaches us something important about contingency and uncertainty. In a perfect world, this also inculcates a certain amount of intellectual humility. 

All of these may be available to an individual among their local peers, but they may also be difficult to access ... and well-formed social networks in a digital medium can fill the resulting gap. We can also exploit the revolution in massive online open courses (the Santa Fe Institute has some fantastic things going on in complexity studies, for example). These are easy to access and bring in the flavor of social networks, but why would we leave another low-cost rock un-turned?

Carefully-constructed social networks are one way of replicating the values of brick-and-mortar education and augmenting the available alternatives in an environment that does not permit face-to-face engagement in the context of life-long rather than episodic learning. And we earn many second-order benefits in the process. With blogs we get comfortable with and better at writing. With Twitter we learn the value of a bottom line and elevator speeches. And so on ...

Access to Expertise

The second idea that occurs to me is one I've mentioned elsewhere in this space: expertise. Effective analysis encompasses a myriad of disciplines (military history, military theory, sociology, psychology, international relations, economics, mathematics, statistics, religion, regional history, anthropology, computer science, military technology and capabilities, etc.), and analogies from each of these can inform our understanding of the others in the context the decisions we inform. This is deeply ingrained in our humanity, but it is also in the nature of humanity to make mistakes, and we do so with alarming frequency and occasionally unpleasant consequences. The likelihood of mistakes is amplified when the export of these metaphors is overseen by dilettantes since amateurs by definition lack the tools in either the source or destination context to evaluate the utility of those metaphors. So, expertise is important. On the other hand, it is difficult for any one individual, or even any one organization, to include deep expertise in the diverse areas that encompass effective analysis ... and we are left with a conundrum.

As an antidote, social networking offers access to the extended mind, the notion that the environment plays an active role in cognitive processes. Social networking facilitates the creation of an environment in which experts can interact and access the expertise of others, and our own ideas are shaped and improved by the process. In a sense, anyone who has worked on a headquarters staff has seen this concept made concrete. A staff is essentially an extended mind for the commander, improving his or her memory, facilitating multi-tasking, and enabling decisions across a broader array of activities than would be possible for the commander alone. Social networks simply extend this idea to digital interaction.

Adam Smith
Wikimedia Commons

The emphasis placed on expertise here does not mean we should each be narrowly or perfectly stove-piped in our education and experience, storing all expertise in each field of interest in distinct socially-networked nodes. There are efficiencies to be gained from this kind of specialization "and the division of labour is in this, as in all other cases, advantageous to all the different persons employed in the various occupations into which it is subdivided," but we each need enough breadth to inform the creation of potentially useful metaphors, applying our individual fields to other fields and to common problems. We need enough commonality and sufficient linguistic overlap to communicate our ideas to each other. Interestingly, this is also something social networking can facilitate, though it comes with a corollary danger in that we may choose our socially-networked associations unwisely or narrowly and create digital echo chambers for ourselves.

This notion of collaborative expertise makes me consider my own profession. I come from an Air Force community culturally dominated by Operations Research, a discipline "employing techniques from other mathematical sciences, such as mathematical modeling, statistical analysis, and mathematical optimization" to arrive "at optimal or near-optimal solutions to complex decision-making problems." This is a relatively young and inherently cross disciplinary field (with all the depth-and-breadth-balance problems that entails) that grew out of efforts by scientists, mathematicians, computer scientists, etc., to solve operational problems in World War II. These folks were experts (in some cases luminaries) in their respective fields, and together they were able to do incredible things that might have been impossible for any subset to accomplish on their own. Social networking is one way to access and connect that kind of expertise.

Expertise is obviously available through scholarly journals and other professional reading (and we should be reading them). But that places the onus of expertise back on us. It is also something we can access in forums like the annual Military Operations Research Society Symposium, but the cost of entry in a forum like this one is surprisingly high and in times of budget constraint (now?) this is at least problematic.

Networks and Requisite Variety

The third idea is related to Ross Ashby's law of requisite variety (from cybernetics/control theory). Basically the ability of a system to influence outcomes in the environment is contingent on the number of possible disturbances in the environment and the number of responses available to the system. More responses available reduces the variability of outcomes. This is very much related to John Boyd's so-called OODA "loop" (nothing more than a cybernetic feedback process).

The OODA "Loop"
Adapted from Frans B. Osinga
Science,Strategy, and War

To survive in an environment, a system must be able to orient to disturbances in the environment (i.e., understand its causes and effects) and have as many responses available as there are potential disturbances. What happens when a system doesn't have the wherewithal? It can die out, it can change, or it can organize into a higher-order system with greater complexity and more available responses. A cell may not be able to defend against a contagion, so some cells organize as organisms (e.g., people). Organisms may not be able survive in the environment alone. So organisms organize as families, tribes, and nations. Another way of saying this is that an system must be as complex as its environment.

(The language I'm using here is a little sloppy, and I don't mean to imply that there is consciousness in the cells and that they choose to organize. There are energy efficiencies and synergistic outcomes from organization that make these states structural basins of attraction and the outcomes emerge. They are not designed, as such, in either a bottom up or top down way. A more agency-oriented argument can be made when talking about collections of rational organisms--i.e., us.)

Social networking is one factor creating an environment in which new and more disturbances are possible. But networks create social structures with increasing complexity and associated with this complexity we can achieve greater potential for appropriate orientation and add potential responses, giving us more capability to influence and respond to the environment. (I hesitate to use the word "control" in this context for fear the semantics of that word are too loaded.)

There is an interesting aspect of this network concept. We have to be careful about the networks we create. Connecting everyone to everyone else is a recipe for entropy and white noise. Some of the necessary controls tend to happen in an emergent way. But some of it will generally come from conscious choices by those involved as well.

Lt Gen Glenn A. Kent
Courtesy of USAF

In any case, it is clear that the world is changing under us, and changing rapidly. As it does so, the tools of analysis must change as well. Glenn Kent is and should be a hero to our profession, but the world he faced was different, and optimizing against an analytically stable and monolithic adversary is no longer an option. It is our professional obligation to help our senior leaders understand the interactions of the dynamic environment and evolving force structure in the context of adversaries large and small, shifting alliances, changing footprints and geopolitical realities, new opportnities and threats in the domains of space and cyberspace, and more. These are nontrivial problems with the future in the balance and muddling through in isolation is not an option.

Because I Must
There is a final reason for pursuing the possibilities of social media and social networking in our community that touches on the personal. Rainer Maria Rilke's advice to a young poet is resonant for me.

"Search for the cause, find the impetus that bids you write. Put it to this test: Does it stretch out its roots in the deepest place of your heart? Can you avow that you would die if you were forbidden to write? Above all, in the most silent hour of your night, ask yourself this: Must I write? Dig deep into yourself for a true answer. And if it should ring its assent, if you can confidently meet this serious question with a simple, ‘I must,’ then build your life upon it.”

Not everyone may feel the same, but I feel I have a voice. I have things to say about things that matter ... and so do you. Social media gives us an opportunity to give those things voice, to touch the lives and minds of others, and to have our lives and minds touched in return. Social media, if you use it with deliberate intent, enables your humanity.

So What?
I've asked before, and I'll ask again. I see forums all about dedicated to collaboration in national security endeavors. If there is value in these endeavors, then where are the options for the analytic community?

Analysis and the Innovation Imperative

The defense community is recently (and not-so-recently) awash in calls for innovation to ensure that we are militarily postured to meet future challenges and possess the agility necessary to turn toward those challenges we did not anticipate.

For example, we have the Pentagon's Third Offset Strategy and Air University's call for "Airmen to offer innovative solutions to address problems facing the Air Force in a time of increasingly daunting global and fiscal challenges." We also see what B. J. Armstrong describes as a small movement

... growing across the defense community which realizes that the challenges of the new century are going to require innovative and creative solutions. Parts of this movement, inspired from the junior ranks of our services, look to embrace the ideals of innovation and entrepreneurship from the business world. These dedicated women and men recognize that the budget, manpower, and resource challenges in a post-war drawdown mean that new ways of doing things will be required.

The Red Queen and Alice

The ways in which this small (but growing) movement manifests are legion, including formal organizations such as the Defense Entrepreneurs Forum and  CIMSEC, online venues for the exchange of ideas (The Strategy Bridge, War Council, The Constant Strategist, etc.), and the growth of peer-mentoring communities of practice (whether on the model of Scharnhorst's Militarische Gesellschaft or something less formal). I am a huge fan of these efforts, and I think the powers-that-be should support them in any way they can. They will, I believe, be a critical part of creating innovation going forward.

Why should the powers-that-be support such an effort, though, especially in the face of limited resources? In times of plenty, we have the resources but lack the imperatives for innovation. In times of need, we lack the resources but the necessity is much more clear. This is the conundrum.

That innovation (or at least the ability to innovate) is necessary in the abstract seems self-evident (and if not self-evident then compelling arguments can be made for its necessity). The world changes around us. There are adversaries, potential adversaries, allies, and potential allies all about us who all seek to increase their own relative advantage, and every change they make (whether they intend it or we like it) affects the calculus of our own continuing advantage. We are all trapped in a Red Queen Race, and survival depends upon our capacity to find new solutions to new problems, more efficient solutions to old problems, and the creation of new problems for our competitors.

But innovation for the sake of innovation is a mistake. The folks at the Havok Journal make a fine argument that not all "outside the container" thinking is worthwhile. Paraphrasing egregiously, they claim that the container was built by someone for some reason, sometimes the container is just fine, and those looking to operate outside its confines often "don’t really understand the fundamentals of [their] profession and don’t want to take the time to learn." (The full article is well worth reading, and I highly recommend it. My self-serving paraphrasing does not do it justice.)

Art, Science, and Engineering

There is a real and important tension here, described in the fields of expert systems and evolution as a trade-off between exploration and exploitation. If a particular strategy works, it makes sense to exploit that strategy. But we should also explore the strategic environment for approaches that work better and for changes in that environment that might compromise the approaches we've exploited so successfully. A nice metaphor for this tension has been described elsewhere in this space as the interaction between art, science, and engineering. (I won't lie. The parallel with Clausewitz's wonderful trinity and the chaotic dynamics of the three-body problem add an undeniable attraction to the model.)  The balance between these is the difference between evolutionary success and failure.

So, why post this thought in a forum all about analysis? I thought you'd never ask.

We (analysts, mathematicians, statisticians, modelers, computer scientists, etc.) are a part of this environment, too. Our worldviews and tools must be no less adaptable than those of the doctrine writers, planners, and strategists of the world. More important (and a little frightening) is the possibility of reified and static analytic ideas becoming framing concepts for the rest of the strategic world.

Optimality is a favorite and appropriate example. For what do we optimize force structure? A world and a worldview. What is the consequence if either situation fails to meet our assumptions? Something less than optimal. How do we minimize the probability that failures of optimality (or analysis in general) are catastrophic? Welcome to the problem of framing analysis in a way that supports the decision needs of leadership in a way that meets the needs of today, tomorrow, and the future. And welcome to the need for innovation in our own community.

So, what does this all mean? How are art, science, engineering, innovation, expertise, exploration, and exploitation to be managed? Not surprisingly, I have some thoughts on the matter:

1. Expertise matters. The problems we face as military analysts are trivial in neither their costs not their consequences. If military operations research is to synthesize inputs and techniques from diverse disciplines (math, statistics, economics, computer science, etc.) expertise in those disciplines is important. Destruction and creation can produce positive results by accident, but will produce innovation far more reliably if the agents involved really understand the underlying philosophical and technical principles.
2. Diversity is more than important. Without diversity of experience and expertise, it is difficult to find and exploit the skis, handlebars, outboard motors, and tank treads in our experience to create effective snowmobiles. This is an interesting concept for military operations research. Ours is an academic discipline that is inherently interdisciplinary, but an interdisciplinary field will always struggle with sufficient isolated expertise to facilitate effective interdisciplinary exploration.
3. Tolerance for individual failure is critical. Evolution and innovation are bottom-up processes, and there must be room for both exploration and exploitation. In an ecosystem, failure is fatal, but that is a system relying on chance to create the necessary genetic and phenotypic variations that facilitate adaptation to changing environments at a population level. The loss of individuals is not important, since the adaptation is neither social nor volitional. On the other hand, analytic innovation is a volitional act by rational social agents, and intellectual variation leading to dead ends cannot lead to deadly individual ends (unless the objective is abject conformity). This is the primary purpose of a community/institution in the context of organizational innovation. It exists to exploit the known, incentivize exploration, and protect the explorers from censure. We need to be free to disagree, argue, and explore.

For our community these observations result in some imperatives for action. Simply put, a structure that prizes expertise and diversity in that expertise (not expertise in that diversity) while facilitating exploration of new ideas and analytic approaches is what we should seek. 

Commission for Military
Reorganization at Konigsberg, 1807

This blog notwithstanding, I'm left wondering why there aren't analytic equivalents of CIMSEC, The Strategy Bridge, War Council, The Constant Strategist, the Militarische Gesellschaft, etc. I'm left wondering why so many of our analysts attend the same school (singular) to receive the same graduate education. I'm left wondering if we will find a way to be relevant in the face of a future that looks decidedly unlike the world in which our "discipline" emerged.

The Right Answer?

It is strange how serendipity occasionally intervenes to link multiple lines of thinking and the conversations that go along with them and thinking on a subject crystallizes. In June 2014, Harvard Business Review published an article titled "Why Smart People Struggle With Strategy." The piece begins thus:

Strategy is often seen as something really smart people do — those head-of-the-class folks with top-notch academic credentials. But just because these are the folks attracted to strategy doesn't mean they will naturally excel at it. The problem with smart people is that they are used to seeking and finding the right answer; unfortunately, in strategy there is no single right answer to find. Strategy requires making choices about an uncertain future. It is not possible, no matter how much of the ocean you boil, to discover the one right answer. There isn't one. In fact, even after the fact, there is no way to determine that one’s strategy choice was “right,” because there is no way to judge the relative quality of any path against all the paths not actually chosen. There are no double-blind experiments in strategy.

When this crossed my digital desk this week, I was reminded of a slew of recent articles on the Service Academies (here, here, and here) and a great discussion that ensued on The Constant Strategist over the questions raised in the first of the linked articles. Here, two questions matter: What was the crux of the original issue and where have I landed in the overarching questions?

The initial online debate in this exploration centered on the curriculum most appropriate to the education of military officers. What should be the emphasis in a liberal education intended to develop them deliberately? There are two--one might call them adversarial--camps in this debate centered on the relative importance of the sciences and the humanities. I have always found myself standing athwart the apparent chasm between these two positions. As a military analyst with too many graduate degrees in math, I have enormous sympathy for the technical side of this debate (perhaps selfishly, since another position would invalidate much of my education and professional life). But I began my life as a student of English Literature and I spent a formative interlude as a graduate student in military history and strategy, and I know the technocrat's approach to conflict and strategic planning is problematic. But since it is hard to ask that everyone know everything, what is the right answer?

In the end, I think appropriate diversity is the answer, at every unit of analysis from the individual to the population. The trick is to ensure both expertise in the population (i.e., someone somewhere has spent a life studying the topics of interest) and familiarity in individuals (i.e., we have all studied enough of the other that we can speak a common language and seek useful metaphors). That means we should encourage and incentivize both expertise and exposure in a variety of disciplines--math, statistics, physics, chemistry, engineering, history, anthropology, theology, literature, etc. But there's a catch.

In our world of military operations research analysts so well trained in seeking optimality the idea of external familiarity really matters, and this is why I'm writing. There is a distressing and problematic bias in the technical fields toward the existence of a "correct" answer, not unlike the assertion in the Harvard Business Review piece. It's how we're trained. In our education, there exists a provably true answer (at least within the constraints of our axiomatic systems) to most of the textbook questions we answer as we learn our trade. This is, in fact, part of the reason for my own shift once upon a time between literature and math as a chosen field of study. Certainty has a certain comfort and led to fewer arguments between student and teacher.

I do NOT want to encourage anyone to not study the sciences, operations research, or (my own love) mathematics. And I do NOT want to encourage avoidance of the the less technical disciplines. Rather, what I want to encourage is an appreciation of contingency in the application of the technical disciplines and a rigor in the application of the non-technical disciplines, especially the context of militarily relevant questions.

Why? Fundamentally because our models and computational tools are by definition rife with assumptions. What if one or more of those assumptions are wrong? What if we forget some minor idea that turns out to be critical? What if our axioms don't work? (I'm looking at you, Economics.) What if optimality itself is a chimera?

For us, reading history of various kinds and actively considering the question of how our forebears (analytic and otherwise) erred is perhaps a useful remedy. The problem is not that one is smart or not. The problem is how and what one studies and with what intent.

The proverb says, "Iron sharpeneth iron." A suggested circular addendum to this wisdom is that the humanities temper the steel of the sciences while the sciences sharpen the analytic edge of the humanities.

Seeking Truth

The last few posts I've penned for this forum (here and here) have danced around the edges--and occasionally jumped up and down on--the notion that we humans are flawed, cognitively compromised, and subject to some intrinsic constraints on our ability to see, understand, communicate, and act on the truth. Though this is not a new soapbox, I hadn't realized that this notion had taken over my writing and become as strident as it had. Then a good friend asked a simple question, and I found myself wrestling with the consequences of the human cognitive silliness on which I've been recently focused and what it means for truth in general and, perfectly apropos of this forum, truth in our analytic profession.

So, what poser did my wise friend propose? He offered three alternative positions based on the existence of truth and our ability to know it:

1. There is a truth and we can grow to understand it.
2. There is a truth and we cannot understand it.
3. There is no truth for us to understand.

(Technically, I suppose there is a fourth possibility--that there is no truth and we can grow to understand it--but this isn't a particularly useful alternative to consider. As a mathematician and pedant by training and inclination, though, it is difficult to not at least acknowledge this.) 

The question is then where I fall on this list of possibilities. It's an important question, if for no other reason than where we sit is where we stand, and it becomes difficult to hypocritical to conscientiously pursue an analytic profession if we believe either two or three is the case. Strangely, though, I found this a harder question to answer than perhaps I should have, but here is where I landed:

At least with respect to the human physical and social universes with which we contend, there is an objective truth that is in some sense knowable and we, finite and flawed as we are, can discover these truths via observation, experimentation, and analysis.

In retrospect, my position on this question should have been obvious. I've been making statements that human cognition is biased and flawed, averring that this is a truth, and I believe it to be one. We can observe any number of truths in the way humans and the universe we occupy behave. I find, on refection, though that there is a limit to this idea. Specifically, we can probably never know with precision the underlying mechanisms that produce the truths we observe. We may know that cognitive biases exist and we may be able to describe their tendencies, but (speaking charitably) we are unlikely to ever have an incontrovertible cause-and-effect model to allow us to interact with and influence these tendencies in a push-button way.

So, the trouble I have with truth is that we apply truth value to the explanatory models we create. Since these models are artificial creations and not the systems themselves they must, by definition, fail to represent the system perfectly. Newtonian theories of gravity based on mass give way to relativistic theories of gravity based on energy. In some ways one is better than the other, but neither is true in a deep sense. Our models are never true in the larger sense. They may constitute the best available model. They may be "true enough" or " right in all the ways that matter." But both of these conditions are mutable and context-dependent. In a sense, I find myself intellectually drawn to the notion that truth in the contexts that matter to us professionally is an inductive question and not a deductive one.

In the end, I'm actually encouraged by this reflection, though the conclusion that models are and must be inherently flawed results in some serious consternation for this mathematician (soothed only by the clarity with which mathematicians state and evaluate our axiomatic models). I understand better what I'm seeking. I understand better the limitations involved. And, at the risk of beating a dead horse, I am more convinced of the need to put our ideas out in the world. This reflection might never have taken place if not for Admiral Stavridis and his injunction to read, think, and write.