In Book V, the author tried to explain the concept of convexity/concavity, basic mathematical concepts, and their manifestation in different aspects of our life.

Chapter 18, On the difference between a large stone and a  thousand pebbles

For the fragile, the cumulative effect of small shocks is smaller than the single effect of an equivalent single large shock. For the antifragile, shocks bring more benefits (equivalently, less harm) as their intensity increases (up to a point).

Travel time is fragile to the volatility of the number of cars on the highway; it does not depend so much on their average number. Every additional car increases travel time more than the previous one. For instance, European airports and railroads are stretched, seeming overly efficient. They operate at close to maximal capacity, with minimal redundancies and idle capacity, hence acceptable costs; but a small increase in congestion, say 5 percent more planes in the sky owing to a tiny backlog, can give rise to chaos in airports and cause scenes of unhappy travelers.

We can see applications of the point across economic domains: central banks can print money; they print and print with no effect (and claim the “safety” of such a measure), then, “unexpectedly,” the printing causes a jump in inflation. Many economic results are completely canceled by convexity effects—and the happy news is that we know why. Alas, the tools (and culture) of policymakers are based on the overly linear, ignoring these hidden effects. They call it “approximation.” When you hear of a “second-order” effect, it means convexity is causing the failure of approximation to represent the real story.

It turns out that the effect of variability in food sources and the nonlinearity in the physiological response is central to biological systems. Consuming no protein at all on Monday and catching up on Wednesday seemingly causes a different—better—physiological response, possibly because the deprivation, as a stressor, activates some pathways that facilitate the subsequent absorption of the nutrients (or something similar). And, until a few recent (and disconnected) empirical studies, this convexity effect has been totally missed by science—though not by religions, ancestral heuristics, and traditions.

SMALL MAY BE UGLY, IT IS CERTAINLY LESS FRAGILE

Large animals, such as elephants, boa constrictors, mammoths, and other animals of size tend to become rapidly extinct. Aside from the squeeze when resources are tight, there are mechanical considerations. Large animals are more fragile to shocks than small ones—again, stone and pebbles. Jared Diamond, always ahead of others, figured out such vulnerability in a paper called “Why Cats Have Nine Lives.” If you throw a cat or a mouse from an elevation of several times their height, they will typically manage to survive. Elephants, by comparison, break limbs very easily.

How to Be Squeezed

Squeezes are exacerbated by size. When one is large, one becomes vulnerable to some errors, particularly horrendous squeezes. The squeezes become nonlinearly costlier as size increases. Another example of the costs of a squeeze: Imagine how people exit a movie theater. Someone shouts “fire,” and you have a dozen persons squashed to death. So we have a fragility of the theater. to size, stemming from the fact that every additional person exiting brings more and more trauma (such disproportional harm is a negative convexity effect). A thousand people exiting (or trying to exit) in one minute is not the same as the same number exiting in half an hour. Someone unfamiliar with the business who naively optimizes the size of the place (Heathrow airport, for example) might miss the idea that smooth functioning at regular times is different from the rough functioning at times of stress.

Comment: cascading effect because the behavior of one person affects many others often making all others want to do the same thing. In the economic realm, the stock market bubble, real estate market bubble all follow a similar pattern; perhaps political zeal as well: when people seem to lose their own mind in a crowd and behave vastly differently if they are by themselves. 

This also explains the irreversibility of time, in a way, if you consider the passage of time as an increase in disorder. Let us now apply this concept to projects. Just as when you add uncertainty to a flight, the planes tend to land later, not earlier (and these laws of physics are so universal that they even work in Russia), when you add uncertainty to projects, they tend to cost more and take longer to complete. This applies to many, in fact almost all, projects.

Comment: Airlines schedule buffer time in their flights. If a plane arrives at a destination ahead of time, oftentimes there will be no free runway for it to decent if the airport has no excess capacity. As a result, flights rarely arrive early but often arrive late.

But the puzzle was that such underestimation did not seem to exist in the past century or so, though we were dealing with the very same humans, endowed with the same biases. Many large-scale projects a century and a half ago were completed on time; many of the tall buildings and monuments we see today are not just more elegant than modernistic structures but were completed within, and often ahead of, schedule. These include not just the Empire State Building (still standing in New York), but the London Crystal Palace, erected for the Great Exhibition of 1851, the hallmark of the Victorian reign, based on the inventive ideas of a gardener. The Palace, which housed the exhibition, went from concept to grand opening in just nine months. The building took the form of a massive glass house, 1,848 feet long by 454 feet wide; it was constructed from cast iron frame components and glass made almost exclusively in Birmingham and Smethwick. The obvious is usually missed here: the Crystal Palace project did not use computers, and the parts were built not far from the source, with a small number of businesses involved in the supply chain. Further, there were no business schools at the time to teach something called “project management” and increase overconfidence. There were no consulting firms. The agency problem(which we defined as the divergence between the interest of the agent and that of his client) was not significant. In other words, it was a much more linear economy—less complex—than today. And we have more nonlinearities—asymmetries, convexities—in today’s world.

Comment: Globalization lengthens supply chains. Thus, every link can potentially cause a delay.  Agency problem also exists in between every two links. As a whole, globalization indeed added uncertainty and complexity to the world although the average cost may be reduced due to comparative advantages. Business school professors have coined a word for this phenomenon— the bullwhip effect. The bullwhip effect takes a step forward—–the further away a link is from the source of uncertainty (such as customer demand), the more variable the link’s ordering /production quantities, inventory levels. Furthermore, prediction errors can be amplified as it moves from downstream to upstream along a supply chain.

In lieu of the above “good old days”, 19 century is at the cusp of industrialization before fast across-ocean ships or the invention of aircraft, supply chains were much shorter, probably regional. As a result, much fewer things went wrong; even if they went wrong; remedies were probably easier to identify.

Black Swan effects are necessarily increasing, as a result of complexity, interdependence between parts, globalization, and the beastly thing called “efficiency” that makes people now sail too close to the wind. Add to that consultants and business schools. One problem somewhere can halt the entire project—so the projects tend to get as weak as the weakest link in their chain (an acute negative convexity effect). The world is getting less and less predictable, and we rely more and more on technologies that have errors and interactions that are harder to estimate, let alone predict.

Comment: Caleb someone has the tendency to overcriticize academia. Practitioners are often occupied with local interests; without a sense of detachment, it is hard to identify the bullwhip effect that spans the whole supply chain. Only academicians or consultants who are not vested in a particular link of supply chains are in a position to have a holistic view of the entirety of a supply chain and diagnose the causes of the bullwhip effect.

No psychologist who has discussed the “planning fallacy” has realized that, at the core, it is not essentially a psychological problem, not an issue with human errors; it is inherent to the nonlinear structure of the projects. Just as time cannot be negative, a three-month project cannot be completed in zero or negative time. So, on a timeline going left to right, errors add to the right end, not the left end of it. If uncertainty were linear we would observe some projects completed extremely early (just as we would arrive sometimes very early, sometimes very late). But this is not the case.

Pollution and Harm to the Planet

We can generate a simple ecological policy. We know that fossil fuels are harmful in a nonlinear way. The harm is necessarily concave (if a little bit of it is devoid of harm, a lot can cause climatic disturbances). While on epistemological grounds, because of opacity, we do not need to believe in anthropogenic climate change (caused by humans) in order to be ecologically conservative, we can put these convexity effects to use in producing a risk management rule for pollution. Simply, just as with size, split your sources of pollution among many natural sources. The harm from polluting with ten different sources is smaller than the equivalent pollution from a single source

Let’s look at nature-like ancestral mechanisms for regulating the concentration effects. We, contemporary humans, go to the stores to purchase the same items, say tuna, coffee or tea, rice, mozzarella, Cabernet wine, olive oil, and other items that appear to us as not easily substitutable. Because of sticky contemporary habits, cultural contagion, and the rigidity of factories, we are led to the excessive use of specific products. This concentration is harmful. Extreme consumption of, say, tuna, can hurt other animals, mess with the ecosystem, and lead species to extinction. And not only does the harm scale nonlinearly, but the shortages lead to disproportional rises in prices.

Ancestral humans did it differently. Jennifer Dunne, a complexity researcher who studies hunter-gatherers, examined evidence about the behavior of the Aleuts, a North American native tribe, for which we have ample data, covering five millennia. They exhibit a remarkable lack of concentration in their predatorial behavior, with a strategy of prey switching. They were not as sticky and rigid as us in their habits. Whenever they got low on a resource, they switched to another one, as if to preserve the ecosystem. So they understood convexity effects—or, rather, their habits did.

Note that globalization has had the effect of making contagions planetary—as if the entire world became a huge room with narrow exits and people rushing to the same doors, with accelerated harm. Just as about every child reads Harry Potter and joins (for now) Facebook, people when they get rich are starting to engage in the same activities and buy the same items. They drink Cabernet wine, hope to visit Venice and Florence, dream of buying a second home in the South of France, etc. Tourist locations are becoming unbearable: just go to Venice next July.

Comments: globalization has the effect of homogenizing planetary. the ways of living across different regions of civilized societies tend to converge. Jeans and t-shirt, Nike shoes, coca-cola, Mcdonald’s, Burger King, Starbucks coffees, movies we watch seemingly permeate all corners of the world. Semi-annual travel for holidays, family cars, two kids, modern housing all become universal symbols of a standard middle-class life. Hollywood even enables two people from the north pole or the south pole to have common things to talk about–movies, tv-series, and movies stars.   Youtube and Facebook demystify certain ways of living; the world seemly becomes a huge open book. whatever you want to learn, it is only a few clicks away. Computer mouse is  modern-day magic wand.

The Nonlinearity of Wealth We can certainly attribute the fragilizing effect of contemporary globalization to complexity, and how connectivity and cultural contagions make gyrations in economic variables much more severe— the classic switch to Extremistan. But there is another effect: wealth. Wealth means more, and because of nonlinear scaling, more is different. We are prone to make more severe errors because we are simply wealthier. Just as projects of one hundred million dollars are more unpredictable and more likely to incur overruns than five-million-dollar ones, simply by being richer, the world is troubled with additional unpredictability and fragility. This comes with growth—at a country level, this Highly Dreamed-of GDP Growth. Even at an individual level, wealth means more headaches; we may need to work harder at mitigating the complications arising from wealth than we do at acquiring it.

Chapter 19. The Philosopher’s Stone and Its Inverse.

Financial leverage for a company has the same effect: you need to borrow more and more to get the same effect. Just as in a Ponzi scheme. The same with operational leverage on the part of a fragile company. Should sales increase 10 percent, then profits would increase less than they would decrease should sales drop 10 percent.

In the case of the grandmother’s health response to temperature: (a) there is nonlinearity (the response is not a straight line, not “linear”), (b) it curves inward, too much so, and, finally, (c) the more nonlinear the response, the less relevant the average, and the more relevant the stability around such average.