A Metarevolutionary Manifesto: Serialized (Part 15 of 50)

[This is Part 15 of a series of posts which serialize my book, A Metarevolutionary Manifesto. Read Part 14 here.]

 d. Fractality

Fractality - in general

They say the “B.” in “Benoit B. Mandelbrot” stands for “Benoit B. Mandelbrot”. As the “Father of Fractals”, his name itself hints at one of their key features: self-similarity. In “The Fractal Geometry of Nature” he identifies naturally occurring fractal patterns in plants, coastlines, galaxies, human bodies (as in the branching patterns of veins), and even in some man-made structures like the Eiffel Tower. 

Benoit Mandelbrot: “The tower that Gustave Eiffel built in Paris deliberately incorporates the idea of a fractal curve full of branch points. In a first approximation, the Eiffel Tower is made of four A-shaped structures. Legend has it that Eiffel chose A to express Amour for his work… However, the A’s and the tower are not made up of solid beams, but of colossal trusses. A truss is a rigid assemblage of interconnected submembers, which one cannot deform without deforming at least one submember. Trusses can be made enormously lighter than cylindrical beams of identical strength. And Eiffel knew that trusses whose ‘members’ are themselves subtrusses are even lighter. The fact that the key to strength lies in branch points, popularized by Buckminster Fuller, was already known to the sophisticated designers of Gothic cathedrals.”

Like the feedback loops and nonlinear patterns explored previously, fractals are a pervasive and yet often-ignored feature of our world. What might seem strange or unexplainable without fractal geometry becomes quite clear when we incorporate it into our worldview. 

Benoit Mandelbrot: “It will be argued that many so-called ‘anomalies’ coalesce in one major phenomenon that deserves to be investigated on its own.”

Fractals, we will see, convey important principles for complex systems in general. Among its teachings, we find that systems have self-similarity (the whole system is partially reflected in each holon), turbulent behaviors, and non-Gaussian probability curves. So fractal geometry is a way to study and interact with complex systems, and be better equipped to weather the storm of the above behaviors. To take a perfect example, let’s discuss financial markets, which illustrate all of these fractal traits at once.

Markets, as almost anyone could tell you, are turbulent—but this commonplace term has a special and precise meaning in our present context. A metacrisis is turbulent, and it is important for metarevolutionaries to understand exactly what this means.

Benoit Mandelbrot: “The study of turbulence is one of the oldest, hardest, and most frustrating chapters of physics… Should the term ‘turbulence’ denote all unsmooth flows, including much of meteorology and oceanography? Or is it better to reserve it for a narrow class, and, if so, for which one?… The theory [of fractals] expounded in this book allows a return of geometry into the study of turbulence, and shows that many other fields of science are very analogous geometrically and can be handled by related techniques.”

Financial markets are a microcosm of all the features of complexity we’ve been exploring. And Mandelbrot spent much time scrutinizing the old view of markets, including the Gaussian or “Normal” distribution of price movements—a probability distribution which is frequently known as “the” bell curve even though it is just “a” bell curve. 

Variables such as people’s heights tend to fit this type of “normal” distribution. A majority of people, about 68%, are in the middle of the curve—their height is within one “standard deviation” from the average. Within two and three standard deviations, respectively, fall 95.4% and 99.7% of the population’s heights. This distribution describes many things, but despite our mightiest efforts, it is not a perfect fit when it comes to financial markets.

Benoit Mandelbrot: “Many scholars resort to the Gaussian probability distribution in their disquisitions, without feeling that this choice has to be justified. Either it is the only distribution they know intimately and trust, or they believe it accounts for the distribution of every random quantity in Nature, from conscripts’ heights to astronomers’ errors of measurement.”

The “tails” of the Gaussian bell curve are tiny—short tails. Thus, it is fitting for something like human heights. As Mandelbrot tells us, the Gaussian distribution conveys that it is nearly impossible to have an adult human who is a fraction of an inch tall or 3039 feet tall—many, many deviations from the average. The “tail events” are indeed exceedingly rare and quickly taper off into near-impossibility. But in complex systems such as financial markets, that is not the case. The Gaussian bell curve says that market crashes of a certain scale are so unlikely that they should not be expected even in a billion years of trading. The fact that a single century has had multiple crashes of this magnitude shows clearly the inadequacy of the Gaussian distribution for many aspects of complex systems.

The so-called “normal” bell curve is a miscalculation of volatility, of risk, when applied to markets and many complex systems of all types. The fractal view, on the other hand, helps to expose the weakness of the mechanistic-reductionist approach (and its related assumptions) as applied to financial complexity. Although Mandelbrot does not explicitly use terms like “synergy” or “emergence”, he describes the combination of stock traders, banks, institutional investors, and exogenous factors like weather events into something that is not just a simple combination of its parts. Thus, traditional tools of financial analysis are insufficient. Analysis, by definition, looks to explain a thing by examining parts of a whole. Complex systems, like financial markets, can be better understood through the relationships and interactions of their holons or subsystems, which altogether generate synergetic and emergent properties. This led Mandelbrot to further distance himself from other financial analysts on the matter of market efficiency.

Benoit Mandelbrot: “The hypothesis holds that in an ideal market, all relevant information is already priced into a security today. One illustrative possibility is that yesterday’s change does not influence today’s, nor today’s, tomorrow’s; each price change is ‘independent’ from the last… According to the theory, a fund manager can build an ‘efficient’ portfolio to target a specific return, with a desired level of risk.”

Mandelbrot’s work rejects this, and uses the insights of fractals to create a more accurate picture of financial markets. He gives the example of widely-used stock-trading strategies, and how their acceptance as analytical tools create feedback loops. If a certain “chart pattern” is accepted as a signal to buy a stock, then its appearance will cause people to place trades. The price changes, but not because it efficiently accounted for the best-available information. Rather, human behavior influences the price, and the resulting price affects our behavior, which affects the price again. As Rowson said about chess, systems may be merely “complicated” when viewed in isolation, but a chess game in progress is a complex system involving the game and the people playing it. The same is true of stock markets and the way that human psychology enters the price equation.

Finally, markets (and other complex systems) operate according to a clock of their own—in this case, “trading time”. Market volatility is much like the passing of a week in our lives where it seems like a decade’s worth of change has occurred. 

Fractality - in a metacrisis

Fractality as a general feature of complex system conveys how holons reflect a holarchy, and vice versa. Or, in other words, the “parts” and the “whole” are alike. The reason for their prevalence is in fact their relative simplicity—as in, they also demonstrate how great complexity is built from a few basic units and simple rules for their dynamic interaction.

Benoit B. Mandelbrot: “Fractal shapes of great complexity can be obtained merely by repeating a simple geometric transformation, and small changes in parameters of that transformation provoke global changes. This suggests that a small amount of genetic information can give rise to complex shapes and that small genetic changes can lead to a substantial change in shape.”

Fractals can also help us understand risk and reward as we interact with and within complexity. Our habitual misunderstanding of risk is a crisis of its own within our metacrisis, and it threatens to derail all of our other metarevolutionary efforts. A proper relationship with risk, where we understand it and accept it and use it to our advantage, will lead us to a better world.

We should think of crises as having a certain “magnitude” in their effects, and at once remember that an event of a very high magnitude (like a 9.5 on the Richter scale for earthquakes) may be more likely than we think. As in, at any given time, a metacrisis is a distribution of distributions, itself representing a collection of possible and actual states which the whole system may occupy, and continually evolving as a metadistribution or multifractal. 

Fractality - in a metarevolution:

One direction we might take in light of this information is to use a Markov-switching multifractal model of risk, as suggested by two of Mandelbrot’s students. In this way, fractals can help us accurately measure our risk-level at any moment, and thereby find a harmonious middle between recklessness and trepidation. To foreshadow what this change would mean for the world as a whole, recall how the Gaussian distribution is a miscalculation of actual risk, and therefore leads us into a precarious comfort made of illusory safety. That is a situation in which we face the potential catastrophic collapse of multiple systems at once, possibly including entire societies or ecosystems. A fractal model of risk, on the other hand, shows us the long tails of system volatility. With a proper “risk profile”, we will have guidance in our relationship with risk, and therefore be able to maximize reward (pursue the perfection of value) without overextending ourselves.

In a deeper sense, fractals enter into the metarevolutionary ethos as further proof that everything is at least a little like everything else. The universe is composed of nested, self-similar holons, and even the theoretically “smallest” holon contains a mirror-like reflection of an ungraspable infinity.

e. Fragility & antifragility

Fragility & antifragility - in general

We have said that complexity has much to do with interconnection—holons coming together into an integrated, more complex holon (or holarchy) which is difficult to disentangle. Once formed, the complex system takes on traits and behaviors which are emergent properties—features which would disappear if the system broke apart. Stability, then, is the measure of how easily a system may break. And this measure falls within a spectrum of fragile to antifragile. People and dogs and societies and markets and ecosystems are all complex systems and thus contain this property.

Nassim Nicholas Taleb: “Some things benefit from shocks; they thrive and grow when exposed to volatility, randomness, disorder, and stressors and love adventure, risk, and uncertainty. Yet, in spite of the ubiquity of the phenomenon, there is no word for the exact opposite of fragile. Let us call it antifragile. Antifragility is beyond resilience or robustness. The resilient resists shocks and stays the same; the antifragile gets better. This property is behind everything that has changed with time: evolution, culture, ideas, revolutions, political systems, technological innovation.”

Taleb, who coined “antifragile”, describes three main categories of system stability—fragile, robust/resilient, and antifragile—with a mythological example. Damocles, representing fragility, has a sword hanging over his head. It is suspended by a strand of hair, which gets weaker from the weight of the sword. It’s a matter of time before the sword falls upon the man in its path. The phoenix, a bird with resilience, is continually reborn from its own ashes—getting no weaker or stronger from stress. And finally, the Hydra regrows two heads each time you cut one off. As Taleb puts it, this antifragile creature “gains from disorder”.

Martin Monperrus: “In Taleb’s view, a key point of antifragility is that an antifragile system becomes better and stronger under continuous attacks and errors. The immune system, for instance, has this property: it requires constant pressure from microbes to stay reactive… A system is antifragile if it thrives and improves when facing errors. Taleb has a broad definition of ‘error’: it can be volatility (e.g. for financial systems), attacks and shocks (e.g. for immune systems), death (e.g. for human systems), etc.”

As with our discussion of fractal turbulence, we must consider how fragility and antifragility can affect a metacrisis or metarevolution.

Fragility & antifragility - in a metacrisis

Antifragility, as a measurable waypoint of systemic health, is part of the all-important relationship between holons at different scales of nested holarchies. Viewing the whole system together, properties like fragility come about as a result of a complex interaction of people, institutions, and their environment. Yet we do not look to the whole system for all of our insights. A fragile or antifragile system depends on every “layer”, as it were, just as in our metacrisis we can’t totally isolate any individual crisis from the others. The stability of a larger system depends, to some degree, on the stability of the smaller systems which compose it. In that sense, stability is an instance of synergy (as a quantitative phenomenon): Subsystems are more fragile or antifragile, and the larger system in which they are integrated may be either more or less fragile than a simple sum of subsystem fragility. 

Further, it is clear that it is not enough to address our meaning crisis—we must address any such crisis in relation to every other one within our metacrisis. Metarevolutionaries seek coherence. If we are on the road which leads to the recovery of meaning, we must simultaneously attend to the many features and behaviors of complex systems, such as its stability, or else we risk the wheels coming off the proverbial vehicle before we reach that destination. In the second half, we will have to find ways to move our systems in the direction of antifragility as part of the same metarevolutionary process which resolves our meaning crisis.

Before we move on, let’s explore a few examples of systemic fragility in order to understand how stability relates to our complex system of crises. In speaking of people within a society, each member can be relatively fragile or antifragile to any number of risks. Yet, the antifragility of the whole system is not just an additive measure (or “heap”) of these individual risk-profiles, but rather has its own unique measure of fragility based on the complex interactions between every one of these holons. 

Ervin Laszlo: “In the biosphere of the Earth, organic systems interact with one another, mutually eliciting creative responses. The progressive transformation of organic species pushes the front of evolution forward, exploring various forms and possibilities, each tending to be more complex than the foregoing. Some are successful, others fail. Even minor factors, such as a drop of a few degrees in the average annual temperature, can produce major effects, as modifications snowball and get magnified in the process. The demise of the dinosaurs, after the longest undisputed reign of any species on earth, bears testimony on this point.”

The systems we've built rely heavily on each other, so a failure in one area tends to cascade through the rest. 

John Casti: “The systems that underwrite our lifestyle are completely intertwined: the Internet depends on the electrical power grid, which in turn relies on energy supply from oil, coal, and nuclear fission, which likewise rests on manufacturing technologies that themselves require electricity.”

This is a feature called “strong links”—which might sound like a good thing, but actually contributes to fragility. “Weak links” on the other hand, is a feature we will explore in the second half of this book as a design principle of antifragility. As in, we live in a universe of interconnected systems, and we aspire to shape societies in which, should some system suffer a catastrophic failure, its links to other systems will “break”—isolating the event rather than allowing it to propagate through a chain of strong links.

Our discussion of fractals has already illuminated the next feature of fragility, which is risk-mismanagement. This will lead us to consider the “value-at-risk” of our actions and systems—in other words, how to relate to risk in a way which maximizes reward.

A final contributing factor is whether we hide from risk, or bravely confront it. Fragility results from the habit of denying the existence of risk; antifragility results from the habit of active failure (or the “fail fast” principle). We will return to this subject later and discuss chaos engineering.

Fragility & antifragility - in a metarevolution

The metarevolutionary mode is one that is oriented towards developing the antifragility of holons, accurately modeling risk as to maximize reward, collectively generating predictions which help us navigate the future, and transcending catastrophic and existential risks whenever possible.

When we move the discussion from crisis to action in the second half of this book, it will become clear why antifragility is a crucial aspect of the metarevolutionary trajectory. Our success or failure, indeed our very survival, depends on the measure of fragility or antifragility which is present in every center of action, whether that is a person, a city, or a planet.