Concave, Convex, and Nonlinear Fragility

Nassim Nicholas Taleb’s book, “Antifragile,” is a wealth of information. I’ve returned to it often since first reading it several years ago. My latest revisit has been to better understand his ideas about representing the nonlinear and asymmetric aspects of fragile/antifragile in terms of “concave” and “convex.” My first read of this left me a bit confused, but I got the gist of it and moved on. Taleb is a very smart guy so I need to understand this.

The first thing I needed to sort out on this revisit was Taleb’s use of language. The fragile/antifragile comparison is variously described in his book as:

  • Concave/Convex
  • Slumped solicitor/Humped solicitor
  • Curves inward/Curves outward
  • Frown/Smile
  • Negative convexity effects/Positive convexity effects
  • Pain more than gain/Gain more than pain
  • Doesn’t “like” volatility (presumable)/”Likes” volatility

Tracking his descriptions is made a little more challenging by reversals in reference when writing of both together (concave and convex then convex and concave) and mis-matches between the text and illustrations. For example:

Nonlinearity comes in two kinds: concave (curves inward), as in the case of the king and the stone, or its opposite, convex (curves outward). And of course, mixed, with concave and convex sections. (note the order: concave / convex) Figures 10 and 11 show the following simplifications of nonlinearity: the convex and the concave resemble a smile and a frown, respectively. (note the order: convex / concave)

Figure 10 shows:

So, “convex, curves outward” is illustrated as an upward curve and “concave, curves inward” is illustrated as a downward curve. Outward is upward and inward is downward. It reads like a yoga pose instruction or a play-by-play call for a game of a Twister.

After this presentation, Taleb simplifies the ideas:

I use the term “convexity effect” for both, in order to simplify the vocabulary, saying “positive convexity effects” and “negative convexity effects.”

This was helpful. The big gain is when Taleb gets to the math and graphs what he’s talking about. Maybe the presentation to this point is helpful to non-math thinkers, but for me it was more obfuscating than illuminating. My adaptation of the graphs presented by Taleb:

With this picture, it’s easier for me to understand the non-linear relationship between a variable’s volatility and fragility vs antifragility. The rest of the chapter is easier to understand with this picture of the relationships in mind.

Parkinson’s Law of Perfection

C. Northcote Parkinson is best known for, not surprisingly, Parkinson’s Law:

Work expands so as to fill the time available for its completion.

But there are many more gems in “Parkinson’s Law and Other Studies in Administration.” The value of re-reading classics is that what was missed on a prior read becomes apparent given the accumulation of a little more experience and the current context. On a re-read this past week, I discovered this:

It is now  known  that  a  perfection  of  planned  layout  is  achieved  only  by institutions  on  the   point  of  collapse.  This   apparently  paradoxical conclusion is based upon a wealth of archaeological and historical research, with the  more esoteric details of  which we need not concern  ourselves. In general  principle, however, the method pursued has been to  select and date the buildings  which  appear to have been perfectly  designed for  their purpose. A study and comparison of these has tended to prove that perfection of planning is a symptom of decay. During a  period of exciting discovery or progress there is  no time  to  plan the perfect headquarters.  The time for that comes  later, when all the important work has been done. Perfection, we know, is finality; and finality is death.

Several years back my focus for the better part of a year was on mapping out software design processes for a group of largely non-technical instructional designers. If managing software developers is akin to herding cats, finding a way to shepherd non-technical creative types such as instructional designers (particularly old school designers) can be likened to herding a flock of canaries – all over the place in three dimensions.

What made this effort successful was framing the design process as a set of guidelines that were easy to track and monitor. The design standards and common practices, for example, consisted of five bullet points. Building just enough fence to keep everyone in the same area while limiting free range behaviors to specific places was important. These were far from perfect, but they allowed for the dynamic vitality suggested by Parkinson. If the design standards and common practices document ever grew past something that could fit on one page, it would suggest the company was moving toward over specialization and providing services to a narrow slice of the potential client pie. In the rapidly changing world of adult education, this level of perfection would most certainly suggest decay and risk collapse as client needs change.

Image by EWAR from Pixabay

Best Practices or Common Practices

I’m using the phrase “best practices” less and less when working to establish good agile practices. In fact, I’ve stopped using it at all. The primary reason is that it implies there is a set of practices that apply to all circumstances. And in the case of “industry best practices,” they are externally established criteria – they are the best practices and all others have been fully vetted and found wanting. I have found that to be untrue. I’ve also found that people have a hard time letting go of things that are classified as “best.” When your practices are the “best,” there’s little incentive to change even when the evidence strongly suggests there are better alternatives. Moreover, peer pressure works against the introduction of innovative practices. Deviating from a “best” practice risks harsh judgment, retribution, and the dreaded “unprofessional” label.

If an organization is exploring a new area of business or bringing in-house a set of expertise that was previously outsourced, adopting “best” practices may be the smart way to go until some measure of stability has been established. But to keep the initial set of practices and change only as the external definition of “best” changes ends up dis-empowering the organization’s employees. It sends the message, “You aren’t smart enough to figure this out and improve on your own.” When denied the opportunity to excel and improve, employees that need that quality in their work will move on. Over time, the organization is left with just the sort of people who indeed are not inclined to improve – the type of individuals who need well defined job responsibilities and actively resist change of any sort. The friction builds until change and adaptation grind along at glacial speeds or stop altogether.

The inertia endemic to “best” practices often goes unnoticed. When one group reaches a level of success by implementing a particular practice, it is touted as one of the keys to its success. And so other groups or organizations adopt the practice. Since everyone wants success, these practices are faithfully implemented according to tradition and change little even as the world around them changes dramatically. Classic cargo cult thinking.

In his Harvard Business Review article “Which Best Practice Is Ruining Your Business?”, Freek Vermeulen observes that “when managers don’t see [a] practice as the root cause of their eroding competitive position, the practice persists — and may even spread further to other organizations in the same line of business.” Consequently, business leaders “never connect the problems of today with [a] practice launched years ago.” Common practices, on the other hand, suggest there is room for improvement. They are common because a collection of people have accepted them as generally valuable, not because they are presumed universally true or anointed as “best.” They are derived internally, not imposed externally. As a result, letting go of a “common” practice for a better practice is easier and carries less stigma. With enough adoption throughout the organization, the better practice often becomes the common practice. When we use practices that build upon the collected wisdom from an organization’s experiences we are more likely to take ownership of the process and adapt in ways that naturally lead to improvement.

There are long term benefits to framing prevailing practices as “common.” It reverses the “you are not smart enough” message and encourages practitioners to take more control and ownership in the quality of their practices. Cal Newport argues that “[g]iving people more control over what they do and how they do it increases their happiness, engagement, and sense of fulfillment.” This message is at the heart of Dan Pink’s book, “Drive,” in which he makes the case that more control leads to better grades, better sports performance, better productivity, and more happiness. Pink cites research from Cornell that followed over three hundred small businesses. Half of the businesses deliberately gave substantial control and autonomy to their employees. Over time, these businesses grew at four times the rate of their counterparts.

When you are considering the adoption or pursuit of any best practice, ask yourself, “best” according to whom? It may help avoid some unintended consequences down the line where someone else’s “best” practice yields the worst results for you, your team, or your organization.

Image by Clker-Free-Vector-Images from Pixabay


Newport, C. (2012). So Good They Can’t Ignore You. New York, NY: Grand Central Publishing.

Pink, D.H. (2009). Drive: The Surprising Truth About What Motivates Us. New York, NY: Riverhead

Vermeulen, F. (2012). Which Best Practice Is Ruining Your Business? Retrieved from