Mark Buchanan
Ubiquity
The Science of History Why the World is Simpler than we Think
Weidenfels&Nicolson 2000


pg 9
Keywords: the organisation of networks (system) - 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 - instability – disaster – upheaval – The global ecosystem is occasionally visited by abrupt episodes of collapse - a profound similarity not between moving objects, but between the upheavals that affect our lives, and the ways in which the complicated networks in which they occur - economies, political systems, ecosystems and so on - are naturally organised - these events, and the workings of the systems in which they occur, may reflect the tenor of just a few simple and ubiquitous underlying processes.

Sand-pile game - Per Bak, Chao Tang, Kurt Weisenfeld - what is the typical size of an avalanche? How big, that is, should you expect the very next avalanche to be? The result? Well …there was no result, for there simply was no 'typical' avalanche - The hypersensitive state to which the computer sand pile organises itself is known as the critical state -

critical state - Could the special organisation of the critical state explain why the world at large seems so susceptible to unpredictable upheavals? - the peculiar and exceptionally unstable organisation of the critical state does indeed seem to be ubiquitous in our world – At the heart of our story, then, lies the discovery that networks of things of all kinds ‑ atoms, molecules, species, people, and even ideas ‑ have a marked tendency to organise themselves along similar lines. On the basis of this insight, scientists are finally beginning to fathom what lies behind tumultuous events of all sorts, and to see patterns at work where they have never seen them before.


Catastrophe theory - catastrophe theory, despite its provocative name, has very little to say about the workings of anything like the earth's crust, an economy, or an ecosystem. In these things, where thousands or millions of elements interact, what is important is the overall collective organisation and behaviour. To understand things of this sort, one needs a theory that applies generally to networks of interacting things.

Chaos theory - chaos by itself cannot explain why a butterfly can cause a thunderstorm. Chaos may indeed explain why a tiny cause can quickly make the future different in its details (the positions of many molecules) from what it might have been. But to explain why tiny causes can ultimately lead to great upheavals, we need something else. We may say that although chaos can explain simple unpredictability, it cannot explain upheavability.

complexity: networks of interacting things: For centuries, physicists have sought the fundamental laws of the universe in timeless and unchanging equations – equilibrium - the air in the atmosphere is very much out of equilibrium, since it is continually being stirred and agitated and energised by the influx of light from the sun, and here we have a clue to the origin of upheavals: it lies in the distinction between what happens in equilibrium, and what happens away from it. If things in equilibrium are fairly simple, things out of equilibrium can be decidedly complex

non­-equilibrium physics, or, to use the currently fashionable language, the physics of complex systems - the relationship between the critical state and complexity is really quite simple: the ubiquity of the critical state may well be considered the first really solid discovery of complexity theory

history: In coming to consider complex systems, physicists seem to have gained a new appreciation of a simple fact: in the immediate world around us, history is important - out of equilibrium, history does matter. One can only make sense of the infinitely detailed shape of a snowflake by following the history of its growth by slow freezing from the thin air. These are all problems in non‑equilibrium physics, the physics of complex systems, or, to coin a new term, historical physics. If the laws of physics are ultimately simple, why is the world so complex? Why don't ecosystems and economies reveal the same simplicity as Newton's laws? The answer, in a word, is history.

dynamics of history - For things out of equilibrium, one cannot proceed by solving timeless equations, and so physicists have turned to another approach ‑ replacing equations with games -

explore the basics of crystal growth – frozen accidents - If the laws of physics did not allow frozen accidents, the world would be in equilibrium, and everything would be like the gas in a balloon, resting forever in the same uniform and unchanging condition. But the laws of physics do allow events to have consequences that can become locked in place, and so alter the playing field on which the future unfolds. The laws of physics allow history to exist. The discovery of the ubiquity of the critical state, then, is not only the first solid discovery of complexity theory, but also the first deep discovery concerning the typical character of things historic.

pg 37
FRACTALS – NON-EQUILIBRIUM PHYSICS – IRREVERSIBILITY – POWER LAWS

Keywords: 'power law' – scale-invariance or self‑similarity - physics is naturally suited to producing fragments over a tremendous range of scales -

Determinism – the spirit of determinism implicit in Newton's ideas had fixed a debilitating stranglehold on the scientific imagination. To physicists grappling with the mysteries of the atomic world, New­tonian physics was mostly a hindrance, although ultimately a few sci­entists managed heroically to wrestle themselves free, and to create the new quantum theory. Along with the ideas of Niels Bohr, Werner Heisenberg and Paul Dirac, Schrödinger's creation liberated scientists once again, enabling them to see the world as if transformed. By the late 1920s, a world of confusing and inconsistent facts had again fallen naturally into place. More recently, a mathematician working for IBM kicked off a trans­formation of comparable scope - Benoit Mandelbrot - the study of fractals

pg 52

what causes fractals?

Keywords: fractals appear to arise most naturally in processes of growth or evolution – historical physics - non­equilibrium conditions - diffusion‑limited aggregation - definitive historical happening, irreversible in its consequences - In this non‑equilibrium setting, there is such a thing as history, and it is a very important thing indeed - generation of 'frozen accidents' as the essence of the evolutionary process - evolution is cumulative, and every frozen accident builds on the sequence of past frozen accidents to construct a tortuous path leading forward through time - That path is steeped in history, and its frozen accidents are the very embodiment of historical contingency - as soon as the rule for adding particles becomes irreversible, history appears on the scene, as does radical contingency - an historical, non‑equilibrium process that leads naturally to fractals and to scale invariance -



pg 68

Keywords: ubiquitous patterns of change and organisation - fractals and power laws are at work in all these settings, very possibly because the critical state underlies their dynamics - critical state – organisation – heat: the temperature of anything measures how much disorganised energy there is in it –

phase transition - critical point - At some intermediate temperature, the forces of order and chaos must fight to a stalemate. This is known as the critical point, and in iron, it occurs at 770 degrees Celsius - not only that the critical state and the rise of factions appear in every phase transition, but that the precise mathematical character of this state depends in almost no way on the details of the things involved - basic geometrical issue of how easy it is for an ordering influence at one point to bring similar order to another nearby. This is not physics, but geometry - critical state universality - 'universality classes' - Things that live in critical states tend to show similar kinds of organisation, and this organisation arises not from specific details of those systems and the elements that make them up, but from the far deeper skeleton of basic geometry and logic behind these details. The critical form wells up in things regardless of what they are. So when something is recognised to be in a critical state, its essential character can be understood even by ignoring most of the details -


pg 85

SELF-ORGANISED CRITICALITY

Keywords: Enrico Fermi: the first nuclear reactor 1942 - … nothing will reach the critical point all by itself. Tuning is crucial. – magnets 770degrees - sand‑pile game seemed to develop into the critical condition quite naturally - 'self‑organised criticality' - The pile grew, became steeper, and then the avalanches began. At first, they only involved a few grains. As the pile grew, so did the typical size of the avalanches. Ultimately, the pile entered the critical state and was susceptible to avalanches of all sizes, as had Fermi's pile when he tuned it properly. But Bak, Tang and Weisenfeld had not tweaked any knobs to bring it there. The critical organisation welled up on its own. Recognising a miracle when they saw one, they enshrined it with the name 'self‑organised criticality'. For the first time in history, physicists had an example of something in which the spectacular organisation of the critical state seemed to arise completely for free, with no tuning needed.


pg 113
Keywords:
the origin of life is not improbable, but inevitable - structure of an ecosystem - scale invariance seen in the critical state that arises when a substance is poised between two phases. – local interactions: a direct link to the science of phase transitions, noting that scale invariance at the critical point arises in these inanimate systems because each particle interacts directly with a few neighbouring particles and, as these neighbouring particles interact with their neighbours, interactions can 'propagate' long distances, resulting in power‑law distributions - If ecosystems live in a critical state, then large upheavals should be expected, and we should expect to find scale‑free distributions every­where - fast ecological dynamics: ecological chains of cause and effect. These involve populations of different species interacting with one another; and can lead to marked changes in the number of organisms in just a generation or two - Several scientists have come to suspect that the global ecosystem is tuned to a critical state not only in its ecological but also in its evo­lutionary workings, and that the extinction of just one species can sometimes trigger a system‑wide catastrophe –

Stuart Kauffman: radically new view of the origins of life on earth - autocatalytic set: the existence of such (feedback)-loops was absolutely certain if the number of kinds of molecules in the soup was large enough - a molecular mixture shows a natural phase transition from boring to fascinating behaviour as the number of kinds of molecules grows. This phase transition forms the basis of a completely new theory in which the origin of life is not improbable, but inevitable - as a result of the interaction between species, any evolutionary change in one can trigger evolutionary changes in another – the origin of life is not improbable, but inevitable.

co-evolution: looking instead at extremely oversimplified models, or games - because of universality, these games even turned out to give a spectacularly accurate picture of how real things work at the critical point between two phases. - An evolutionary change in a single species could trigger an avalanche of co‑evolution that could affect anything from a few species to almost every single species in the ecosystem. Indeed, in running their game for a long time, they found that the distribution of avalanches according to the number of species involved followed a power‑law form - tuned their ecosystem to the critical point -


pg 120

Keywords: basic skeleton of co‑evolution: the nature of evolution of fitness landscapes - The essence of co‑evolution is that species interact - an evolutionary change in a single species could trigger an avalanche of co‑evolution that could affect anything from a few species to almost every single species in the ecosystem - the distribution of avalanches according to the number of species involved followed a power‑law form

co‑evolution - the ordinary evolutionary workings of ecosystems should lead inevitably to dramatic upheavals having no identifiable cause whatsoever - these games suggest that the global ecosystem rests in a critical state, and they hint ‑ but only hint ‑ that the mass extinctions may simply be the rare but expected and natural result of ordinary evolution -


non‑equilibrium physics:

underline one of the broader themes of this book: …we have seen that many things do indeed seem to be organised into critical states. But there is far more in non‑equilibrium physics than a fixation on the notion of self‑organised criticality might suggest - power laws and fractals and the same wild sensitivity in which a quite ordinary, run-­of‑the‑mill shock can trigger an upheaval out of all proportion to itself. What is more, as with the critical state, this sensitivity comes about naturally under an extremely broad set of conditions. These are the ubiquitous properties that arise again and again in things driven away from equilibrium, and in things in which history matters - these are the things that are making a new kind of science possible ‑ a theoretical science tuned to the context of the historical sciences


pg 120

Keywords: basic skeleton of co‑evolution: the nature of evolution of fitness landscapes - The essence of co‑evolution is that species interact - an evolutionary change in a single species could trigger an avalanche of co‑evolution that could affect anything from a few species to almost every single species in the ecosystem - the distribution of avalanches according to the number of species involved followed a power‑law form

co‑evolution - the ordinary evolutionary workings of ecosystems should lead inevitably to dramatic upheavals having no identifiable cause whatsoever - these games suggest that the global ecosystem rests in a critical state, and they hint ‑ but only hint ‑ that the mass extinctions may simply be the rare but expected and natural result of ordinary evolution -


non‑equilibrium physics:

underline one of the broader themes of this book: …we have seen that many things do indeed seem to be organised into critical states. But there is far more in non‑equilibrium physics than a fixation on the notion of self‑organised criticality might suggest - power laws and fractals and the same wild sensitivity in which a quite ordinary, run-­of‑the‑mill shock can trigger an upheaval out of all proportion to itself. What is more, as with the critical state, this sensitivity comes about naturally under an extremely broad set of conditions. These are the ubiquitous properties that arise again and again in things driven away from equilibrium, and in things in which history matters - these are the things that are making a new kind of science possible ‑ a theoretical science tuned to the context of the historical sciences




HOME      BOE     SAL     TEXTE