Ubiquity

Ubiquity : Why Catastrophes Happen 2000

Beyond the labels “disaster” and “upheaval,” each of these events erupted from the soil of its own peculiar setting. Still, there is an intriguing similarity. In each case, it seems, the organization of the system—the web of international relations, the fabric of the forests or of the Earth’s crust, or the network of linked expectations and trading perspectives of investors—made it possible for a small shock to trigger a response out of all proportion to itself. It is as if these systems had been poised on some knife-edge of instability, merely waiting to be “set off.”

There is nothing new in the recognition that history follows tortuous paths, and that it has forever made a mockery of attempts to predict its course. My aim, however, is to convince you that we live in a special time, and that new ideas with a very unusual origin are beginning to make it possible to see why history is like it is; to see why it is and even must be punctuated by dramatic, unpredictable upheavals; and to see why all past efforts to perceive cycles, progressions, and understandable patterns of change in history have necessarily been doomed to failure.

A model of forest fires

Forest fires: How trying to surpress natural dynamics leads to even greater instability

…despite determined efforts to suppress naturally ignited fires, wildfires have in recent years become more numerous, severe, and difficult to control. From 1890 onward, the attitude of the U.S. Forest Service was one of “zero tolerance,” even for forest fires sparked by natural causes…

The trouble is that fires are an indispensable component of the natural dynamics that keep forests in that state, so by suppressing them, the Forest Service has instead driven the forests into an even more unstable state, a supercritical state, with a high density of burnable material everywhere.

TLDR

self-organized criticality: a that system naturally / robustly evolves towards the critical state without external tuning of parameters
Things that lead to power laws and the critical state:

• “historical physics” / frozen acidents (irreversible events; unique initial conditions that lead to unique paths)
• compounding / self-reinforcing / feedback loops (e.g. inertia)
• interconnectedness / interdependence

(extremely simple underlying geometric features, not complex details)

Properties of the critical state & patterns of change:

• power law scaling: the magnitude of events in relation to their frequency scales according to a power law $P(x)\propto x^{-\alpha }$.
• $⇝$ self-similarity, scale-invariance, fractal structure, pink noise:
  • patterns are similar at different scales
  • extreme events aren’t all that rare, compared to e.g. normal distribution “expect the unexpected”
  • there is no typical size / frequency of an event, no scale at which the behavior changes
  • the conditions that lead to small upheavals are no different to the ones for large upheavals
    • “catastrophic” events happen for no special / exceptional causes at all (no qualitative difference; e.g.)
    • unpredictability of upheavals/triggers: you would need near-perfect knwoledge of a system / the precise initial conditions
    • to understand why a single small event can trigger a massive upheaval (phase transition/revolution), you need to understand the global structure of the system
    • what drives revolutions is the buildup of internal stress (be it society, science, earthquakes, stock market crashes, evolution, …)
    • any system that does not adapt to changing conditions will accumulate stress, and eventually reach a tipping point
    • critical state universality: when looking at things in a critical state, details/context do not matter (the same properties hold; you can model the behavior with very simple abstracted models)
  • systems are categorized into universality classes based on dimensionality of the system, range of interaction, and the symmetry of the order parameter ¹
  • all systems of a given universality class exhibit the same critical exponents, regardless of the microscopic details of the system
  • even very elementary systems / toy models can exhibit the same complex/intricate behavior of much more complicated systems
    • hypersensitivity: small perturbations can have large effects
    • sporadic rhythms
    • things become more predictable on larger scales (averaging out small-scale unpredictability)
    • while avalanches reduce the stress, they also keep the system near the critical state

There are decades where nothing happens and there are weeks were decades happen - Lenin

Link to original

Complex systems at the edge of criticality are subject to unpredictable upheavals which follow a power law distribution with regards to their relation between frequency and intensity.

Such systems, like human history, are routinely and drastically altered by even the least significant of events.

Many of the most significant events in human history, such as WW1, the Kōbe earthquake, Wall Street crashed, … were not only unpredictable but also unforeseeable in their magnitude and consequences.

If the historian H. A. L. Fisher failed to see in history “a plot, a rhythm, a predetermined pattern,” then so too have geophysicists failed utterly, despite immense effort, to discern any simple pattern in the Earth’s seismic activity.

As with the First World War or the great quake in Kōbe, no one had predicted the crash. Immediately afterward, on the other hand, analysts produced all kinds of dubious explanations for why it had happened when it did.

Not everything is in a critical state. Tuning is necessary.

Obviously, the many things in equilibrium or chaos, like a cup of water or a hot gas, are not in a critical state.

So why does it work for rice but not sand? The answer, it seems, has to do with inertia. Sand grains are relatively heavy, and also slippery. Once they start sliding, they have a tendency to keep going, and to bring the whole pile down. By contrast, rice grains are relatively light, and more sticky. So when the rice begins sliding, it slides only until the pile has reached the very next barely stable configuration, and then the grains stop. In the sandpile game, Bak and his colleagues made their grains very sticky and gave them no inertia at all, so the grains were really much more like grains of rice.

Tuning to a critical state: Close to zero is easy.

For the sandpile game, it is only when grains are dropped much more slowly than the rate at which they topple that you find the critical state. In other words, the ratio of the rate of dropping to that of toppling has to be tuned to zero to achieve criticality.

→ The ratio of the rate of change of the system to the rate of change of the system’s response has to be tuned close to zero.
Tuning to zero is easier than tuning to any other number:
If you have a really small number, say $10^{-5}$, and you change it by 10 percent, or even multiply it by 2, 10 or 100, and you still have a very small number.

Freezing liquids: How the unity of opposites leads to change.

Toss a copper button into a pan of hot molten copper, and after a time there will be no button; it will have melted and its atoms will have dispersed into the liquid sea. After things settle down, the result is equilibrium.
In equilibrium, the notion of history has very little meaning.
The copper is now far from equilibrium, since the liquid “wants” to freeze into the solid form, but hasn’t managed it yet. Because of this imbalance, now there is such a thing as history, and the amount of solid copper will gradually increase with time. There is also something else—complexity.

Without contradictions, without opposites, without tendencies, without imbalances no motion, without motion no time.

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Sparse notes on examples given in the book:

Things that follow a power law distribution

• snowflake “arm”-sizes
• forest fire sizes
• earthquake magnitues
• measles-epidemic sizes
• pulsing rate of a pulsar
• solar flares
• traffic jams
• extinctions

Evolution

“For the species considered here,” Keitt and Stanley concluded, “there is no characteristic scale of fluctuation in population size….” In other words, what will happen next is unpredictable not only in its direction, up or down, but even in the rough scale of its magnitude. This is, of course, exactly the same kind of scale-invariance we have seen in the critical state.

sandpile model

The sandpile avalanches have the same properties as avalanches in the brain. → The Cortex and The Critical Point - Understanding The Power of Emergence

Snowflake: Self-reinforcing dynamics

The sticking of each particle changes the shape of the cluster and makes it more likely that other particles will stick near the same place. When they do, this makes it even more likely that still more particles will stick. The growth is highly unstable, and everyaccident leaves its indelible trace in the growing structure forevermore.

Earthquakes

Virtually all earthquakes still come unanounced.
Continuously moving mantle and solid crust → countervailing tendencies.
The inexorable movement cannot be stopped.
Enormous complexity in the earth’s crust (different types of rock, …).
The interaction of rocks in one place affects the neighbouring rocks.

The crust becomes riddled by fingers of instability of all possible lengths. So after the first bit of rock slips, somewhere, quite literally anything might happen. The earthquake may stop quickly. Or the initial movement may place enough stress on neighboring pieces of rock to cause further slipping. The ultimate size of an earthquake depends on one very tiny detail that perhaps lies forever beyond our scrutiny: the length of the particular finger of instability on which the first tiny slipping event takes place.

Opposing forces in a pulsar leading to a power law

Since the pure nuclear material making up a neutron star is so dense, the star’s surface lives under a terrific force of gravity. Indeed, gravity is trying to crush the star down to a smaller size. You might liken this force to that applied along a fault by the movement of continents. The material of the pulsar generally resists collapsing, just as the Earth’s crust resists slipping, but occasionally things give way. In such a “starquake,” the neutrons organize themselves into a somewhat smaller and denser ball, and just as an ice skater spins faster after pulling her arms in, so the star begins to spin a bit faster. If this idea is correct, then the power law for pulsar glitches simply reflects the Gutenberg-Richter law for earthquakes, as applied to the materials in a neutron star.

Extinctions – Food chain

In essence, the game fills out a food web randomly, allows a few species at the bottom to go extinct at any moment, and sends the effects of these extinctions rippling upward through the food web. The results of this trivial process are startling. The food chain naturally organizes itself into a critical state in which the extinction of just one inconspicuous species near the bottom can trigger anavalanche of further extinctions of any size. And most impressively, extinctions become precisely four times less likely each time the size is doubled, in excellent agreement with the real fossil record.

The ising model

a) chaos, uncorrelated spins
b) equilibrium; almost all spins aligned
c) critical state; power law distribution of cluster sizes; neighbouring spins correlated over long distances

Stock market

Not just the stock prices fluctuate according to a power law, but also the volatility itself (→ clustering; no efficient market).

Indivuals are not rational agents who always work out their “rational self-interests” and act on them, without being influenced by others.
… see the marketing industry.
Imagine the resources we could free if we rationalized the entire marketing industry, making its only job to offer information so that people could make better decisions.

Again these dynamics arise through correlated interactions between many individuals that cluster / move in avalanches.

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Notes on the philosophical side of the book towards the end + some own thoughts and connection.

agency / free will can coexist with regularity in the activity of a group (see desire paths).

The buildup of stress precedes revolutionary upheavals.

Hunger and nakedness and nightmare oppression lying heavy on twenty-five million hearts: this, not the wounded vanities or contradicted philosophies of philosophical advocates, rich shopkeepers, rural noblesse, was the prime mover in the French revolution; as the like will be in all such revolutions, in all countries

Intertia and conservatism in science

Michael Polanyi came to the conclusion that scientists are not actually so open-minded and rational as they might have you believe. Instead, he found that there must be at all times a predominant accepted scientific view of the nature of things….A strong presumption…must prevail…that any evidence which contradicts this view is invalid. Such evidence has to be disregarded, even if it cannot be accounted for, in the hope that it will turn out to be false or irrelevant.

Rather than always seeking evidence to test their ideas, they often ignore such evidence even when it hits them in the face.

Mental friction in the community of scientists → consciousness (or (living?) matter in general) is conservative / resistant to change.
On the one hand this inertia is natural (self-perserving; not discarding the entire body of scientific work over every crackpot’s theory – generally you want to only change what’s absolutely necessary), on the other hand, but paradoxically, you need change in order to preserve / progress.
In the space of ideas: Intellectual friction ←→ curiousity

→ The same parallels from history, revolutions, and all other complex systems / critical phenomena (interaction between individuals) apply to science itself.
Small scale revolutions and shifts in thinking etc. happen all. the. time, on a personal level, within teams, groups, etc.

See also The Structure of Scientific Revolutions.

… scientists should expect the unexpected. For the fabric of ideas is organized so that the tiniest chance discovery might at any moment and without warning activate a domino-like chain of effects leading to a terrific revolution. And foreseeing such revolutions is next to impossible, for the ultimate consequences of any new idea depend not so much on its own inherent profundity as on where it happens to fall within the network of all scientific ideas.
Everyone associates Einstein’s name with one of the greatest revolutions in scientific history. But the Einsteinian revolution started when Einstein began puzzling over a quirky feature of Maxwell’s equations, which describe light as an electromagnetic vibration. These simple equations, he found, would not permit him to imagine riding along with a light wave and studying it as if it were “standing still.” It was this minor conceptual paradox, almost a mere curiosity, that ultimately led to the revision of several hundred years of physics and the theory of relativity, and then, through myriad other pathways, to both nuclear energy and the atomic bomb.
…
The great scientist has skill in locating those ideas in the fabric that have the potential for setting off domino-like chains that will at least extend an appreciable way, and the ability and energy to make those repercussions explicit.

→ impactful ideas are stepping stones onto many more interesting ideas
→ following local gradients of interestingness → diverse exploration → serendipity
many ideas lead to nothing, but some ideas open up entirely new fields of inquiry
→ you don’t need to be the best in the world at any specific thing in order to achieve greatness, just the best at following your nose for the interesting (in fact if you set out to achieve any specific ambitiuous thing you’re less likely to achieve it … Why Greatness Cannot Be Planned)
→ Even if we were all equally smart, some people just by necessity are the ones who make the great discoveries, but they wouldn’t be made without the collective search process of all of us. “Genius is the summed production of the many, with the names of the few attached for easy recall.”
→ Just as there are no great causes behind earthquakes and great mass exinctions, great events in history do not require great men to bring them about.

The great man of the age is the one who can put into words the will of his age, tell his age what its will is, and accomplish it. What he does is the heart and the essence of his age; he actualizes his age. – Hegel

random quotes

It is in the nature of a hypothesis when once a man has conceived it, that it assimilates everything to itself, as proper nourishment, and from the first moment of your begetting it, it generally grows stronger by everything you see, hear or understand. - Laurence Sterne

There is no such thing as philosophy-free science; there is only science whose philosophical baggage is taken on board without examination. - Daniel Dennett

… ‘science’ is not a mystical force, existing external to society. Rather, it is a set of institutions, composed of living human beings, situated in a real material world, subject to – and shaped by – the same economic, social, and political forces as the rest of us. This includes all the pressures and prejudices that come with class society, which seep into science and affect the outlook of those operating within it.

Link to original

The art of being wise, is the art of konwing what to overlook.

Noticing patterns of similarity, knowing what to overlook and what to put into the same category.

If science is “the aggregate of all the recipes that are always successful,” and the rest is literature, then we must conclude that there is no science of earthquakes, since there are no successful recipes. When it comes to predicting earthquakes, there is only literature. A full century of research has apparently amounted to nothing.

Transclude of General-Relativity#^be6736

The idea of self-organized criticality shares this spirit, and herein lies its power. It is a one-size-fits-many explanation for the workings of things, irrespective of the myriad bewildering details of the molecules, trees, or what have you that make up those things.

To trace something unknown back to something known is alleviating, soothing, gratifying and gives moreover a feeling of power. Danger, disquiet, anxiety attend the unknown—the first instinct is to eliminate these distressing states. First principle: any explanation is better than none….The cause-creating drive is thus conditioned and excited by the feeling of fear…. - Friedrich Nietzsche

One of the chief services which mathematics has rendered the human race in the past century is to put “common sense” where it belongs: on the topmost shelf next to the dusty canister labeled “discarded nonsense.”

The historian is not really interested in the unique, but in what is general in the unique.

This reminds me of a clever bit of psychology (and clear thinking) employed by John Maddox, the former editor of Nature. Maddox had little sympathy for authors who wanted to title their paper “Evidence for…,” and always insisted that a paper’s title should describe the facts that the work really established, rather than what those facts might possibly be taken to imply. If authors objected, as they often did, Maddox offered to leave “Evidence for” in the title, so long as it was, for clarity, modified to “Inconclusive Evidence for.” I don’t believe there were any takers.

had intervened. This recourse to divine intervention to explain the unexpected illustrates the importance of contingency in history; the inability at early stages of the development to see all the connections between the events; the cataclysmic character of the happenings; the fact that great consequences can proceed out of little causes; the fears that men have in a world, the proceedings of which they do not understand; the feeling men have that history is a thing that happens to them rather than something that they are making; the feeling of dependence which they would doubtless have when they were unable to understand or master the operations of nature, the mystery of natural happenings…; all these things would lead men to feel in life that much depended on the gods….

References

book
quantity and quality
unity of opposites
negation of the negation
dialectical materialism

Footnotes

1. What transformations leave the disordered phase unchanged? E.g. flipping all spins in the ising model is physically equivalent (${\mathbb{Z}}_2$ symmetry; do nothing or invert), the order parameter is scalar. In other models, the order parameter could be a vector (e.g. magnetization direction), leading to different universality classes. ↩