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Self-organised Criticality

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Presentation within the Supervenience Project series made to Melbourne Emergence Meetup Group August 2019 illustrating topic of Bak et al's 1987 paper which defined the topic.

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Self-organised Criticality

  1. 1. Self-organised Criticality Tony Smith Melbourne Emergence Meetup 8 August 2019
  2. 2. Placeholder for video slide at https://vimeo.com/353180022 Self-organised Criticality
  3. 3. Supervenience presentation 2 weeks earlier to Science, Technology and the Future on Life and Death as Systems Collapse included: Long histories and quick deaths Optimisation to threshold of criticality So a reason to review underlying complex systems theory that followed the 1987 paper by Per Bak, Chao Tang and Kurt Wiesenfeld “Self-organized criticality: an explanation of 1/f noise”. Long-wavelength perturbations cause a cascade of energy dissipation on all length scales, which is the main characteristic of turbulence. The (currently) “Self-organising, Adaptive” component of the Supervenience project has a uniquely chequered history. It follows some more general principles of Emergence and Complex Systems, getting into detail of many and varied processes which underly emergent complexity, as reflected in its original title: “Here Now Succession Process Traces Time Causation?” that didn’t fit well alongside more succinct component titles so we tried a couple of others which similarly disappointed: “Dynamic encodings in condensed matter” “Maintaining interesting isolates through cosmological timescales” Self-organised Criticality SUPERVENIENCEhow emergent minds and money seize power over matter
  4. 4. Too Funny for Words Abstractions, Category Errors, Epistemic Cuts Life on an Active Planet The Two-edged Sword Multiple Paths to Emergence Constraints and Degrees of Freedom Birds and Others Interweb to Facebook Better than Out of Control Information, Maps and Territories Urban Hydrology out of Sight Going Down with the Egg Basket Self-organising, Adaptive Codification and Communication Exploiting a Dissipating Gradient: creaming, trickle down Dystopian Utopias and Science Fiction Towards Healthy General Knowledge The Inside View: knowing when you're dreaming Verbal Blindness Accepting Cosmological Responsibility
  5. 5. We believe that the new concept of self-organized criticality can be taken much further and might be the underlying concept for temporal and spatial scaling in a wide class of dissipative systems with extended degrees of freedom. –Bac et al [1987] This presentation needs to be complemented by additional information on how natural and constructed systems evolve towards criticality, an exploration of benefits and costs of doing more of whatever seems to be operating well enough to keep each system holding together.
  6. 6. Bak et al’s 1987 paper was perfectly timed to catch the explosion of interest in complex systems that took off in the mid 1980s, its central concept soon being shown to be relevant to a long list of phenomena, starting with the classic sandpile which is slowly added to and maintains a critical slope through landslides that follow a power law distribution with many small and few larger. The short paper starts by discussing a conceptual “one-dimensional array of damped pendula (...) connected by torsion springs that are weak compared with the gravitational force” which settles to a “minimally stable” state rather than to the lowest possible state. It is disturbances to the minimally stable state which follow a power law as the range of impact is dependent on complexities that only show a pattern statistically. They then test this with a Von Neumann neighbourhood cellular automata rule (and a 3D analogue) which is designed to settle from an initially high “energy” random configuration into an equivalent minimally stable configuration, a rule that also appears analogous to the evolution of cosmological structure dominated by gravitational interaction of cold dark matter. It is in these CA models that the range in both time and space of the propagation of disturbances is demonstrated to have a power law distribution. Bak et al identify various other phenomena as candidates for similar analysis, including: river flow, luminosity of stars, fractal landscapes such as coast lines and mountains, and turbulence. Subsequently, self- organised criticality has been applied to understanding electromagnetic domain performance, earthquake magnitude and aftershock timing, financial indicators, wild fires, epidemics, landslides, and nerve signals (paraphrasing Wikipedia entry). “Criticality” here is defined by the proximity of an attractor state rather than a not directly related reference to phase transitions. This presentation sees an even broader range of phenomena edging ever closer to their threshold of criticality, both naturally and intentionally. It is particularly concerned with how approaching such critical thresholds empowers and constrains ecosystems and their inhabitants.
  7. 7. Tonight’s presentation looks at everyday behaviour through the lens of self-organised criticality, recognising that nothing occurs in isolation. Understanding the parts relies on recognising their environmental dependencies. We take this Big History tour in four major stages of increasing proximity to our present crises: • Universals • Animals • Civilisation • Modernity Within each, half a dozen topics are introduced, typically by a couple of images as examples of a much larger set of criticality to be briefly explored. Limpets at low tide Crayfish Bay 2016
  8. 8. Universals
  9. 9. Gravitational aggregation at cosmic scales produces rotating disks and cores through conservation of angular momentum
  10. 10. On big enough planets orbiting stars, atmospheric physics and chemistry drives condensation into clouds and storms
  11. 11. Impact cratering & internal tectonics feed surface processes
  12. 12. Stuart Kauffman [1995] proposed Autocatalytic Sets as a key step on the journey via an RNA world to Prokaryotes
  13. 13. Stromatolites formed by oxygenising cyanobacteria, ancient fossil from the Pilbara and current from nearby Shark Bay
  14. 14. Sunlight reflecting off Titan’s hydrocarbon lakes and off Wingecarribee Reservoir in NSW Southern Highlands
  15. 15. Animals
  16. 16. Development of animal zygotes is highly conserved but development of plants is more accessible to observation
  17. 17. Minimum set of requirements to function as mobile animal evidenced by sea snail art produced filtering food from sand
  18. 18. Us us us us and Them them them them And after all we’re only ordinary men (…) With with with with, without And who’ll deny that’s what the fighting’s all about —Wright and Waters, Pink Floyd from the album Dark Side of the Moon 1973 Life demands identifying one’s own kind and other kinds making the challenge to broaden inclusion to at least aves
  19. 19. All manner of nests and dens are created by animals to give the next generation a good start in life, including knowledge
  20. 20. Animals thrive on excess (re)production of other life forms which a few assist with the reproduction of in the process
  21. 21. Crested Terns and Silver Gulls happily share patch of sand
  22. 22. Civilisation
  23. 23. Wurundjeri cultural revival on the Merri highlights methods of preserving oral knowledge, complementing song lines
  24. 24. Awareness of Aboriginal agriculture too recent for pictures Imported domestication of other species, food processing
  25. 25. Human settlements were close to life sustaining resources until cities grew powerful enough to extract more widely
  26. 26. Language and opposable thumbs enabled division of labour and specialisation to reach new levels before settlements started to grow and provide support for more of the same
  27. 27. Long distance travel exploited seasonal variations, allowed trade, water flow provided energy, quarries useful minerals
  28. 28. Transition from autocracy to representative democracy and legal process gentrified everyday life, enabling many dreams
  29. 29. Modernity
  30. 30. Misinformation spread by writing, printing and the internet
  31. 31. Capital accumulation went from privilege to expectation Businesses avoid scrutiny via limited liability, externalities
  32. 32. After ownership changes glass bottles are still manufactured at old site of Australian Glass Manufacturers and its heritage celebrated. Coal seam exposed at beach shows fracking risk
  33. 33. Electricity generation and transmission underpins modernity enabling refrigeration to add dimensions to food processing
  34. 34. Academic scholarship built on the shoulders of giants Science found patterns in things measured in isolation
  35. 35. Expectation of a full life followed sanitation, medication and indiscriminate industrial killing of other life for convenience
  36. 36. Suggestions! Questions?