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Business Management: Chaos Theory in Financial and Managerial Accounting White Paper
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Chaos Theory in Accounting

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By James A. Brimson

 A butterfly flapping its wings in Alaska can cause a tornado in Texas. So suggests the butterfly effect that is the centerpiece of Chaos Theory. Chaos Theory deals with dynamic natural systems that are termed chaotic when a very small variation in its initial conditions, after a very short time, can produces vast differences in the final outcome. Thus, a seemly insignificant event can cause a chain of events that over time creates unpredictable outcomes. Heaven forbid a seagull flaps its wing as one scientist observed.

Uncertainty rules in today's chaotic world.  Managers of financial and managerial accounting need only look at the front page of any newspaper to grasp the impact of our turbulent times where significant forces can alter the status quo overnight. Our chaotic world has even greater import for government accountants since it is driven by emotions and politics. Agencies are often called upon to make momentous choices with little time to weigh all the potential consequences. Soon unintended consequences await us. There simply are no guarantees. How we deal with an uncertain world separates the good from the mediocre agencies?

Those of you reading this article whom are accountants or use accounting information must be pleading Say it is not so, Joe (or Jim). Fortunately, it does not have to be so! Following the Chaos Theory train of thought, any analytical methodology that provides greater understanding of how to reduce uncertainty will improve the probability of better resource allocation and ultimately create more value. The time of the dominance of historical analysis in management practice must come to an end. Historical analysis has failed to provide the early warning indicators needed to dampen crises. It is time for government agencies to usher in the era of processes analytics and reporting.

 This article addresses why process reporting is superior to historical reporting. The reasoning is based on two primary tenants: (1) the irrelevance of historical analysis and (2) process analysis reduces uncertainty.

 The irrelevance of historical analysis

The White Queen says to Alice in Lewis Carroll in Through the Looking-Glass:
"It's a poor sort of memory that only works backwards".

 Historical analysis is inferior to process analysis. Today's accounting analysis and financial reporting model is founded on historical data the "historical cost convention". This requires transactions to be recorded at the price ruling at the time, and for assets to be valued at their original cost. It then follows that the historical costs should be reported periodically monthly, quarterly and yearly. Financial reporting gurus develop a set of rules, FASAB, that govern how an government agency results are reported to external parties.

 Historical financial data is, in addition, used for internal management decision making. Enter management accounting whose analytical tools include forecasting techniques measures the past to extrapolate to the future budget variance analysis to understand actual versus planned spending and so on. Management accounting sheds the restrictive FASAB bonds and allows an agency to look at cost in the most relevant manner to support its decision making process. In a practical sense, this enables an agency to use a variety of algorithms to restructure historical data in a variety of formats to answer questions such as: Why current results are as reported? What are the likely future results? What actions are necessary to improve future results? All the above questions are logical and pertinent but is historical analysis to the best analytical tool to answer these questions?  

 It is reasoned that the past portends the future. Many people point to how frequently historical analysis is widely used today as a justification of its relevance. It is true that historical analysis does provide a degree of forward looking ability when a process is stable and the destabilizing factors are very few in numbers. However, historical analysis is unreliable when a process is complex, in disequilibrium, and there are a multitude of destabilizing factors is in play. Historical analysis simply is not robust enough to a reliable forward looking tool.

 There are a multitude of reasons why historical analysis is flawed. Chief among the reasons include the following:

 The past is unchangeable and the full extent of its impact is embedded in a process initial state. At any point in time, the initial conditions fully encapsulate the total impact of past events. The past cannot be changed!! Nevertheless, the past dictates the initial conditions from which a process begins its transformation cycle.

 If you could freeze time and observe your agency work activities, you would see a mix of good and poor performance. The factors that cause diverse levels of process outcomes vary with each work activity. The factors you observe at any point in time are a manifestation of past force that shaped the current work activities. The forces that shaped the past result are hidden from you today. At most only memories remain. Also hidden is the multitude of possibilities that could have been but were not. A small change of forces could have resulted in a very different today according to Chaos Theory.

 We try to observe the results of past forces through the lens of historical analysis. Yet everything we need to know about the past is embedded in the here and now. We simply need process analytics to unlock the needed knowledge.

 The past is a function of conditions that existed in the past. To go back in time and extract selected data points (results) without an understanding of the forces that shaped the results is overly simplistic. Historical analysis assumes a consistency of past forces.

 For a moment, reflect on your own life. How did you become a government accountant? What if an influential person in your early life had persuaded you to become a medical doctor, how different would your life be today? Historical analysis is a relevant tool only if the world in which your agency works is linear and your work processes in equilibrium. However life is not linear, it adapts to an infinite and complex number of things both in the past and future.

 It is of equal importance what has not happened. Sherlock Holmes observed in the story Silver Blaze by Sir Arthur Conan Doyle, To the curious incident of the dog in the night-time." Watson replied "The dog did nothing in the night-time." "That was the curious incident," remarked Sherlock Holmes. Conditions that have not been manifested in the past cannot be reflected in historical data. The new conditions might have a significant impact of future performance.

 Historical analysis requires selected data. Historical analysis requires the analyst to sift through past data and select the most relevant data based on the historical analysis models assumptions. Any data sifting will skew the results. It is hoped that any such skewing will be minimal. However, the skew will always exist.

 Historical analysis can be distorted to reflect the analysts bias. It is human nature on the part of the analyst to present results that reflect their bias. Contradictory data is inconvenient. Often the data analysis is selective and, in the most blatant cases, can exclude important but contradictory data. Joseph Freeman once said that Everyone falsifies history even if it is only his own personal history. Sometimes the falsification is deliberate, sometimes unconscious; put always the past is altered to suit the needs of the present. The best we can say of any account is not that it is the real truth at last, but that this is how the story appears now.

 Historical analysis is indirect. Historical analysis looks at the shadow of what was to project what might be. Historical analysis is backward looking and thus indirect. An indirect measure is less sensitive to a changing environment than direct measures since forces that might have been insignificant in the past can dramatically alter future results. An indirect measure is always inferior to a direct measure.

 In conclusion, historical analysis will always be flawed. To try and understand the significance of past events will always be problematic only a process can make history. Why? A process and its interaction with its environment determine the transformation from one state to the next leading to an outcome.

Process analysis reduces uncertainty

Process analysis views a government agency as a collection of manmade processes. A manmade process, in contrast to a natural process, is largely under the control of an agency. A government agency configures how it functions, the resources needed, the products and services delivered and the targeted outcomes. The needed resources are acquired via a yearly budgeting process.

 Processes are forward looking and by nature can reduce uncertainty due to the ability of an agency to exercise control over a process. A process evaluates the initial starting condition, monitors the current environmental forces, and applies the process transformation logic to project a likely outcome. Processes do not look back to the past; processes embrace the here and now as a guide to the future.

Time and demand for services is the key that unlocks an agencies work processes. Work processes (transformation) can only occur in the here and now. Work processes are constantly being initiated to meet the needs of the agency customers and internal/external stakeholders. An agency finds itself forever in the midst of a vortex of work processes that are simultaneously in action. Each process is influenced by an ever changing environment that impacts its performance results.

 Consider an airport immigration process. Each immigration processing instance is different from all others. The applicant is different, the handwriting is different, some part of the completed form might have missing or incorrect information, the mental state of the immigration agent will differ, and the operating conditions of the computer will differ, and so on. It is hoped that these changed conditions are minor. But, in any case, each instance of the same immigration process will vary.

 It is this change in initial conditions that makes each individual instance of a process unique. The unique initial conditions can, in turn, lead to a completely different behavior of any complex process. In some instances, a suspected terrorist may be overlooked by the immigration process while the same process may identify another suspected terrorist. The initial process conditions are critical to success!

 The importance of initial conditions brings us to Chaos Theory. The first tenant of Chaos Theory is that initial process conditions matter. It is at this point that Chaos Theory and Process Theory are in alignment. However, Process Theory goes beyond Chaos Theory to introduce the concept of embedded history in a process initial state. The gist of the observation is that any past forces that have influenced the initial state has already occurred since the past is unchangeable.

The expanded concept of initial conditions is the basis of the irrelevance of historical analysis. Any use of historical data in an analysis tool introduces an unnecessary bias as discussed earlier in this article. The use of historical data assumes that the selected data can come close to creating the initial conditions. Any error in the explanation (calculation) or data selected (including data excluded) will invalidate the analysis as does disequilibrium and complexity. The question is: why introduce a bias when there is none needed? A direct analysis of the initial conditions avoids a historical bias.

Furthermore, scientific literature links Chaos Theory to Fractals. A fractal is a geometric shape that is self similar. This means that the geometric shape can be split into parts, each of which is repeated at ever smaller scales to produce what resembles an irregular shape yet are merely smaller versions of the same shape. The importance of fractals is the patterns they leave behind by a dynamically changing system (process). Their inherent property is that no matter how close or far away one gets the basic pattern is always the same. Fractals are the basis for understanding the simplicity behind the complexity of everyday life. Fractals are also used to explain Chaos Theory one could start with simple systems, in time complex outcomes emerge. The resulting structures are always on the edge of sudden and radical change.

 Fractals are of critical importance to accountants. Fractals provide patterns and order to an otherwise chaotic world. Being self similar is critical to an ordered world. For instance, immigration is not concerned with poor purchasing practices. Immigration is focused on screening people entering the United States to ensure they are legally eligible to enter the United States. Self similarity bounds each process outcome thus reducing its complexity. Constraining complexity is critical any process success and would be impossible without self similarity.

 Fractals also leave patterns. A pattern implies that an underlying order prevails. Accounting would be irrelevant without patterns. Consider that the initial starting conditions are unique for each process (Chaos Theory) and yet the outcomes leave a pattern (Fractals), then what brings a degree of order? It is the process transformation logic and process control.

 Process transformation logic (Process Theory) is the set of rules that consumes resources and technology to convert an initial state of an input into an output that mimics an outcome. By linking Process Theory with Chaos Theory and Fractals an understanding of the business environment emerges as illustrated in Figure 1:

Figure 1: Process Cycle Phases

  • A process cycle is initiated by an agency to provide a product or service to its citizen constituents or to support agency operations.
  • An initial state of conditions exists at the beginning of the process cycle that makes each instance slightly different from other instances. The initial state has embedded all historical forces that have influenced the initial state.
  • The external environment in which the process operates is an important force that impacts its initial conditions. The external environment is unique to each process instance.
  • Process transformation logic converts and input (process startup), consuming resources and technology, through a set of logical rules.
  • The transformation process is manifested in a series of intermediary transformation states.
  • A process output emerges at the conclusion of the transformation process.
  • Each process output seeks to emulate a process outcome.
  • The transformation process cycle must be adapted to ensure the process output achieves the targeted outcome and remains in equilibrium with its external environment
  • The transformation process cycle begins anew when triggered.
  • Process Theory brings control and adaptation to Chaos Theory. Process Theory shares self similarity with fractals. Most important to accountants, processes do not have to be subject to an infinite number of possible intermediary transformation states. An agency can control and adapt its processes through an understanding of transformation logic and its dependence on the initial state and environmental forces.


    Government agencies need a wider implementation of process reporting. Process reporting and analytics are in their infancy in government accounting. "Performance-Based Management" AGA CPAG Research Series, Report No. 20, March 2009 ( research paper is an excellent starting point for understanding the relevance of process reporting to government agencies.


    The key to Process Theory is to develop a direct process knowledge rather than relying on backward looking historical analytics. The processes at your agency are going to behave in accordance with Chaos Theory, Fractals and Process Theory. There is nothing anyone can do to eliminate these factors. These theories describe the natural forces that govern process behavior. However, these forces can be held at bay. By continuing to use obsolete analytics that do not mirror the natural world, accountants will hinder their efforts to provide actionable information to their agency.

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