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.

Drive for Teams

I recently re-read Daniel Pink’s book, “Drive: The Surprising Truth About What Motivates Us.” I read it when it was first published and I was still managing technical teams. Super brief summary: The central idea of the book is that people are mostly driven by intrinsic motivation based on three aspects:

  • Autonomy — The desire to be self directed.
  • Mastery — The urge to improve skills.
  • Purpose — The desire to engage with work that has meaning and purpose.

I find this holds true for individuals. However, when applied to teams optimizing for these three aspects can be problematic. If an individual on a team seeks to maximize autonomy, they are likely to come into conflict with the objectives of the team. For example, a software team that is tasked with developing a component that is expected to interact with several other components developed by other teams. If a single developer, in the interests of maximizing their individual autonomy, has decided to develop the component according to standards, design principles, and tools that are different from those of teammates and other teams (essentially, a local optimization,) then the result is likely to be sub-optimal overall.

Some individual autonomy must necessarily be sacrificed in the interests of effective collaboration. It’s possible, even desirable, that individual pursuits of mastery and purpose can be maintained. However, it may be necessary for an individual to focus on mundane tasks and the objectives of the team for periods of time. Finding ways to maintain a healthy balance between the intrinsic motivators and the purpose of the team is no small task and, when found, requires constant attention to maintain.

Perhaps it is possible to attach the team’s or organization’s purpose to the interests of the individual. Or sort for hiring people who have a personal purpose that is in-line with the organization’s purpose.

Image by M. Maggs from Pixabay