In This Issue
Winter Issue of The Bridge on Complex Unifiable Systems
December 15, 2020 Volume 50 Issue 4
The articles in this issue are a first step toward exploring the notion of unifiability, not merely as an engineering ethos but also as a broader cultural responsibility.

Thinking Reflexively

Friday, December 18, 2020

Author: Richard N. Foster

The essence of the word reflexive is to act on one’s self. Reflexive systems act on themselves. For example, if one instinctively scratches one’s arm, this is a reflexive action.

Reflexive is closely related to a similar word, reflective. Looking at one’s reflection in a mirror may trigger reflective thought. In both cases, the concept involves acting on one’s self.

Reflexive acts can introduce unpredictability (it is not possible to forecast whether or when one is going to scratch one’s arm), instability, and uncertainty in a system’s future performance.

Reflexive systems are ubiquitous. They occur in almost all engineering fields—from the design of computers and artificial intelligence to electric power grid design, cancer therapy, astronomy, military action, economics, and transportation system design and operation.

But they are also complex to understand, difficult to model, and impossible to predict with accuracy. Accordingly, actions based on reflexive models can be misdirected, dangerous, and even treacherous.

Reflexivity through the Ages

The word reflexive was first used in 1615, according to Webster’s dictionary, but it was in people’s imagination well before that. For example, the ouroboros—a mythical serpent that lived (for a while) by devouring its own tail—first appeared in Egyptian tomb scenes in the 14th century BCE.

Epimenides, a (perhaps mythological) 6th BCE Cretan, has been reported to have said, “All Cretans are liars,” thus immersing the listener in an endless loop of dilemma. Shakespeare, Diderot, and Pirandello each used reflexivity as a literary device. In the 19th century Droste packaged its cocoa in a tin with a picture of a young woman holding a tin of Droste cocoa with a picture of a woman holding.... You get the picture.

More recently, the artist MC Escher (1898–1972) was famous for drawing pictures of hands drawing pictures of hands. Werner Heisenberg (1901–76), the founder of quantum mechanics, was the first to point out that there is a fundamental limit to the precision with which the values for certain pairs of physical variables can be predicted from initial conditions. Kurt Gödel (1906–78), the Princeton logician, believed reflexivity was ubiquitous. He proved that any system that was consistently described had not been completely described, and any system that had been completely described could not be internally consistent. Sixty years later financier George Soros reframed Heisenberg’s and Gödel’s messages for financial systems (Davis and Hands 2017).

There are nefarious uses of reflexivity. Double agents who spy against their own country are an example. Uncertainty about whether someone is a double agent provides a further example.

Lack of Predictability

The common feature of all reflexive systems is feedback between the “observer” and the “observed.” In financial equities trading, for example, predicting securities price behavior requires understanding not only the fundamentals of the securities but also the precise relationships between the securities and traders’ motivations in order to understand market behavior. Attempts to simplify the analysis run the risk of introducing errors into models.

As Soros pointed out (Davis and Hands 2017), the market is not precisely predictable in either the short or long term. Consider the VIX, the index of market volatility. If the market moves up or down with constant volatility the VIX will be constant. If, however, the volatility of prices of individual securities changes, then the VIX will change. The VIX is anything but constant or predictable.

The inability to predict reflexive system behavior creates substantial problems for decision makers in politics and finance as well as in physics. One needs to be skeptical of models that do appear to work, since the past will be an unreliable guide to the future. Heisenberg would have been comfortable in this environment.

Illustration: The 2008 Market Crash

The challenge for managers of reflexive systems comes when the systems are performing in a way that appears to be driven by cause and effect, but in fact is driven by hidden feedback. For example, in the middle of 2008, the financial markets were beginning to “jitter.” Half the market participants read the signs as a not unusual increase in daily variance. Others saw a quake coming and got out.

In July and August of 2008 all views were being reported hourly, as they always are in the capital markets. Volatility had increased significantly. Questions swirled: Was the increase in volatility “just noise” or a sign of an underlying instability—a coming quake—in the market? No one knew the answer, but everyone had a view.

Then it happened. On September 29, 2008, the market broke, and over the next 9 months it fell just over 50 percent. Half of America’s wealth—wealth that had taken decades to build—was destroyed. The market took 4 years to fully recover. In total the US economy lost 7 years of productive effort. It was a high cost to pay for failing to understand and manage recursive systems.

Reflexive Questions

As the speed and ubiquity of communication increase—with 24-hour news coverage, fake news (sometimes from state actors), and news about the news—reflexivity will play an increasingly important role. And, of course, now the dark web exists, with news that is hidden from the news.

The increasing ubiquity of reflexivity raises questions that must be answered:

  • Who gets to write history?
  • Who decides whether history as written should be rewritten?
  • Did the writer have hidden sponsors? We need to know as much about the writer as we do about the history.
  • What constitutes “well” or “poorly” written history?
  • When does it make sense to “revise” history?

These are all reflexive questions. In the reflexive future the challenge will be to be less wrong rather than precisely right.


Davis JB, Hands DW, eds. 2017. Reflexivity and Economics: George Soros’s Theory of Reflexivity and the Methodology of Economic Science. Oxon UK: Routledge.

About the Author:Richard Foster is an emeritus senior partner of McKinsey & Company.