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Autocatalytic Feedback Loops
Amplify Microscopic Random
Events to Systemic Complex
Changes
Sorin Solomon
Racah Institute of Physics
Hebrew University, Jerusalem
[email protected]
For a long while it was customary in many disciplines to formalize a collective of many
similar objects in terms of a "mean field" / "representative agent" characterized by the average
of their individual properties and behaviour. In reality such collectives may possess completely
new properties and behaviour then their components. They often constitute the elementary
objects of a higher level of organization. The "representative agent" / "mean field" / continuum
/ linear way of thinking missed the very rare events that are responsible for dramatic systemic
transitions: the emergence of life from chemistry, conscience from life, society from conscious
individuals, etc. Ignoring this connection between the elementary objects of one science and
the collective phenomena underlying them (relegated to another science) prevented scientists
from achieving many syntheses and insights and kept the classical sciences as isolated subcultures.
1 Introduction
In his “more is different” paradigm [1] Phil Anderson proposes that“the
behaviour of large and complex aggregates of elementary particles, [...], is not to be
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understood in terms of a simple extrapolation of the properties of a few particles.
Instead, at each level of complexity, entirely new properties appear”.
Within this complexity paradigm, the singular, extreme, very rare events and
interactions become crucial.
Is there a way to make sense of such a world in which the average doesn't mean
anything?
Can we predict or control anything in a world in which the exception rules?
The present talk I will substantiate that the answer may be: “autocatalytic
feedback loops”.
In order to understand the stability and the crises of the macroscopic systems,
one has to identify and characterise the autocatalytic loops that act between their
microscopic components and between their various scales. The autocatalytic loops
are the filter that sorts out the individual events that may trigger a systemic
catastrophe from the ones destined to drown in the noise of local, short lived
perturbations. This implies that the vast majority of phenomena that make it to the
macroscopic / systemic level do present, and are fuelled by, some kind of
autocatalytic positive feedback loop. This fact was noticed in the past in many
occasions but in the absence of specific mechanisms that could explain it, it was often
dismissed as incompatible with the ethos and ideology of scientific thinking.
Such proposals that postulated that the biosphere or the society possess such
intrinsic autocatalytic properties met mixed reaction from the scientific community:
Gaia hypothesis [8], The Crude Law of Social Relations [4], Memes [3], selffulfilling prophecy [10], Oedipus effect [12], reflexivity [14]
The ubiquity of such rules in so many fields (markets, economies, social
organization, life, ecology, conscience, creativity) suggests an equally generic
paradigm: in order to understand the emergence of global behaviors in macroscopic
systems, one has to find among the myriads of interactions and rules that govern their
microscopic components, the ones that have the capability to generate autocatalytic
feedback loops. It is only a behavior associated with such a positive feedback
autocatalytic loop that has the chance to be amplified to the macroscopic scale and to
govern the system global dynamics.
One is led to the conclusion that the generic criterion that separate phenomena
doomed to remain local and buried in the noise from the ones destined to take over
the system is positive feedback in its many disguises and forms. In order to
understand, predict and steer systemic changes one has to discover, identify and
characterize the particular feedback loops that sustain and amplify them.
These autocatalytic processes are responsible for many of the sudden changes
that threaten the climate, the environment ecology, the social order, or the economic
stability around the world. The introduction of external elements that trigger in the
system new autocatalytic loops may highly and rapidly destabilize the previous state
of the system.
I will review a series of heterogeneous interacting agent models where it has
been found, using analytical, simulation and empirical methods, that indeed such
positive feedback loops lead to the emergence of adaptive collective objects that
change completely the global system dynamics [2, 5, 7, 9, 11, 13, 15, 16].
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The challenge is now to overcome the language and social barriers between the
disciplinary domains and connect the physics and mathematics methods, ideas and
techniques to the cognitive, social, ecological and biological domains that so badly
need them. Moreover one has to make the results, conclusions and tools known to the
general public and the decision makers in order to help them prepare and react to
otherwise unexpected crises and opportunities.
Bibliography
[1] Anderson P. W. (1972) More Is Different, Science, Vol. 177 (4047).
[2] Cantono S. and Solomon S. (2010) When the collective acts on its components:
economic crisis autocatalytic percolation, New J. Phys. 12, 075038,
http://iopscience.iop.org/1367-2630/12/7/075038
[3] Dawkins R. (1986) The Blind Watchmaker, W. W. Norton & Company, Inc.
New York , pp. 148–161.
[4] Deutsch, M. (1973). The resolution of conflict: Constructive and destructive
processes, Yale University Press.
[5] Dover Y., Moulet S., Solomon S. and Yaari G. (2009) Do all economies grow
equally fast?, The journal Risk and Decision Analysis, Vol. 1/3, special issue
Black Swans, Rare and Persistent Events, Dependence and Default Models and
the Modelling of Uncommon Risks.
[6] Levy M., Levy H. and Solomon S. (1994) A microscopic model of the stock
market; Cycles, booms and crashes, Economics Letters, 45, 103-111.
[7] Levy M., Levy H. and Solomon S. (2000) Microscopic Simulation of Financial
Markets: from investor behaviour to market phenomena, Academic Press.
[8] Lovelock, J. (1979). Gaia: A New Look at Life on Earth, Oxford University
Press.
[9] Malcai O., Biham O. and Solomon S. (1999) Power-law distributions and Levystable intermittent fluctuations in stochastic systems of many autocatalytic
elements, Physical Review E, 60, 1299-1305.
[10] Merton R. K.(1968). Social Theory and Social Structure. Free Press, New York.
[11] Nowak A., Deutsch M., Bartkowski W. and Solomon S. (2010) From Crude
Law to Civil Relations: The Dynamics and Potential Resolution of Intractable
Conflict, Peace and Conflict, Journal of Peace Psychology, 2, 189 – 209.
[12] Popper K. (1976). Unended Quest: An Intellectual Autobiography, Open Court,
LaSalle, Illinois.
[13] Shnerb M. N., Louzoun Y., Bettelheim E. and Solomon S. (2000) The
importance of being discrete: Life always wins on the surface, Proc. Natl. Acad.
Sci. USA, Vol. 97(19), 10322-10324.
[14] Soros, G (1987) The Alchemy of Finance, Wiley.
[15] Yaari G., Solomon S., Rakocy K. and Nowak A. (2008) Microscopic Study
Reveals the Singular Origins of Growth, European physics journal B, Vol.
62(4), 505-513.
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[16] Yaari G., Stauffer d. and Solomon S. (2009) Intermittency and Localization, in
Encyclopedia of Complexity and Systems Science, edited by R Meyers, Springer,
4920-4930.