Operating in complex systems – and only in them – has, according to Taleb, a substantial limitation: it may lead to two extreme states, namely fragility or antifragility. Why? At the core of the functioning of anthropogenic complex systems consisting of independent elements that are in connection with each other, that mutually influence and adapt to the changing world using their behavioral lenses, there is variability and non-linearity additionally strengthened by negative and positive feedback loops. In such systems, efforts are not likely to be proportional to the results obtained as a result of pursuing such efforts. And average results will not correspond to average expenditure.

I will try to explain it on the example of car traffic. Philip Ball in his book Critical Mass shows how traffic on a motorway is an example of a complex system(53). Drivers in their cars are an element of this system. Each pair – a driver and a car – is characterized by individual parameters: level of driving skills, safe distance to the next car, reflexes, long-term concentration, willingness to perform additional activities (e.g. talking on the phone), the vehicle’s efficiency status or its technical advancement. If we look at the relation between the number of vehicles per kilometer of highway, that is the density, and its capacity, that is the number of vehicles passing through the control point in a unit of time, we will see, as Ball writes, that this function is not linear. The capacity of the motorway along with the increase in the density of cars first increases, but after exceeding a certain critical value falls sharply, until the movement comes to an eventual stop. This results in a traffic jam that cannot be discharged as long as the density of vehicles does not fall below the critical density (which happens most often automatically when rush hours pass).

Where does this effect come from? That is the way a complex system works! At some point, the density of cars on the highway exceeds the ability of a sufficient number of drivers to adapt and their mutual reactions do not phase out. A negative feedback loop is created – a tiniest, unexpected change in the movement of the neighboring car causes a reaction which in turn results in an even more substantial one, driving comfort begins to decrease, fear grows and vehicles speed drops. As a result, there is a harmonica-like traffic jam – without any visible obstacles, neckings or accidents. At some points, cars just stop for a moment.

Taleb describes in Antifragile the relation between the time of the day bringing an increase in the number of cars and the time of arrival to the airport in New York(54). With 90,000 cars in the road system the travel takes less than an hour; with 100,000 – not much more; with 110,000 cars such travel takes hours. The average number of cars in these three situations – 100,000 – translates into an acceptable travel time. But the road-car system is non-linear. The average travel time does not matter if the system is fragile due to deviations in the number of cars on the roads. The capacity of the road system is a function of the density of its components. And it is a concave function – therefore the road system is as a whole fragile in relation to the number of cars moving within it. And the concept of an average travel time, as a function of the average number of vehicles, completely loses its useful meaning.

Fragility, as Taleb writes, is an immanent feature of complex systems. Fragility is measurable, it can be detected, seen. Fragility is measured by detecting the effect of accelerating the accumulation of harmful effects of the tested system when changing the size of its parameters. In this way, in 2003, even before the outbreak of the mortgage crisis in the US in 2007, which spilled over the world a year later, Taleb and his colleagues analyzed the condition of Fannie Mae – the giant on the American real estate market. The increase in one of the economic variables of the modeled company translated into faster and faster losses, and its decline into lower profits. Taleb does not even say exactly what variable he meant because, in his opinion, fragility even against one variable in such a large scale, detected as a result of analyzes, suggested fragility towards all other parameters. The analysis had been ridiculed, but it did not take long to prove it right(55).

The United States – as a system of small-scale experimenters, namely companies acting on their own account, creative in the production of goods, concepts and ideas – are antifragile. The United States as a highly indebted empire become fragile

Taleb proposes introducing the concept of fragility instead of the notion of risk as the basic measure for assessing complex systems. The risk, in his opinion, is predictive(56) – we try to predict what will happen in the future and encounter the barrier of epistemological opacity. We do not know how anthropogenic complex systems will behave. The detailed analysis of past data, even if available and sufficiently precise, will not tell us anything about adaptive changes that have occurred between the system components in the meantime. Greenspan econometric models based on past and average parameters are helpless in the face of unpredictability and adaptive non-linearities from the assumption of complex systems. Fragility, on the other hand, is not predictive. Fragility is measured by simulating the system response to a parameter change to detect a nonlinear acceleration of the range of damage. At the same time, as Taleb points out, it is not even important whether you use the detailed, correct model of the assessed system – a company, a highway, a city, an energy system or a state budget – to assess the situation. The non-linear increase of damage is important! For example, the change in economic parameters in the situation of an indebted state budget – improvement of parameters (drop in unemployment, investment growth, etc.) which gives rise to income is the forest of hands to take advantage of good times, growing demand for additional expenses, usually resulting in marginal additional benefits. Deterioration in parameters with high indebtedness is a non-linear increase in tax revenue loss, a sharp, also non-linear increase in the costs of servicing the state debt, and consequently a long-term crisis or even a collapse of the state debtor.

Fragility as a concept that Taleb positions above the concept of risk has its opposite – antifragility. Fragility is concave in relation to the change of important parameters – it brings non-linearly increasing losses. Antifragility is convex – it brings a non-linear increase of gains. The United States – as a system of small-scale experimenters, namely companies acting on their own account, creative in the production of goods, concepts and ideas – are antifragile. The United States as a highly indebted empire, unable to apply the talents of all its citizens and exporting their jobs excessively abroad, increasing their debts, full of companies and corporations too big to fail, become fragile. As a global power – through the effect of scalability – they transfer the fragility further, to the interstate level, all over the world. And so, today fragility can knock on every door.

So, how to diagnose reality? By measuring the fragility and antifragility of complex systems. What to avoid – fragility. What to bet on – optionality, antifragility. How to deal with complexity? I suggest to look closer at this point at the theory of constraints.