I've tried to put the short definitions first for those who don't
have the time to read through the entire file. I also tried to
put definitions for self-organization last since one of my goals
in collecting these definitions was to understand precisely what
is meant by inserting the "self" in self-organization. Short
definitions for self-organization will thus be found later on,
about half-way through the file.
==================
Complexity: The study of the behavior of macroscopic collections
of simple units (e.g., atoms, molecules, bits, neurons) that are
endowed with the potential to evolve in time.
-- Coveney and Highfield (1995), p. 425
==================
<Complexity>
The degree of complexity in living organisms far exceeds that
of any other familiar physical system. The complexity is
hierarchical, ranging from the elaborate structure and activity
of macromolecules such as proteins and nucleic acid to the
exquisitely orchestrated complexity of animal behaviour. At
every level, and bridging between levels, is a bewildering
network of feedback mechanisms and controls.
<Organization>
Biological complexity is not merely complication. The complexity
is organized and harmonized so that the organism functions as an
integrated _whole_.
[...]
<Emergence>
Biological organisms most exemplify the dictum that 'the whole
is greater than the sum of its parts'. At each new level of
complexity in biology new and unexpected qualities appear,
qualities which apparently cannot be reduced to the properties
of the component parts.
-- Davies (1988), p. 94
=====================
Complex systems usually have a hierarchical structure, the
entities of one level being compounded into new entities at
the next higher level, as cells into tissues, tissues into
organs, and organs into functional systems. To be sure,
hierarchical organization is also found in the inanimate
world, such as between elementary particles, atoms, molecules,
crystals, and so on; but it is in living systems that hierarchical
structure is of special significance (Mayr, 1982, PP. 64-66).
-- Mayr (1985)
[This is what Mayr refers to as "highly organized"]
=========================
What, then, are complex systems? Complex systems are not
just complicated systems. A snowflake is complicated, but
the rules for generating it are simple. The structure of a
snowflake, moreover, persists unchanged, and crystalline,
from the first moment of its existence until it melts,
while complex systems change over time. It is true that a
turbulent river rushing through the narrow channel of a
rapids changes over time too, but it changes chaotically.
The kind of change characteristic of complex systems lies
somewhere between the pure order of crystalline snowflakes
and the disorder of chaotic or turbulent flow. So identified,
complex systems are systems that have a large number of
components that can interact simultaneously in a sufficiently
rich number of parallel ways so that the system shows
spontaneous self-organization and produces global, emergent
structures.
--Depew and Weber (1995), p. 437
=============================
So far I have been rather loose in my use of the words 'order',
'organization', 'complexity', etc. It is now necessary to
consider their meanings rather more precisely.
A clear meaning is attached to phrases such as 'a well-
ordered society' or 'an ordered list of names' . We have
in mind something in which all the component elements act
or are arranged in a cooperative, systematic way. In the
natural world, order is found in many different forms.
The very existence of laws of nature is a type of order
which manifests itself in the various regularities of
nature: the ticking of a clock, the geometrical precision
of the planets, the arrangement of spectral lines.
Order is often apparent in spatial patterns too. Striking
examples are the regular latticeworks of crystals and the
forms of living organisms. It is clear, however, that the
order implied by a crystal is very different from what we
have in mind in an organism. A crystal is ordered because
of its very simplicity, but an organism is ordered for
precisely the opposite reason - by virtue of its complexity.
In both cases the concept of order is a global one; the
orderliness refers to the system as a whole. Crystalline
order concerns the way that the atomic arrangement repeats
itself in a regular pattern throughout the material.
Biological order is recognized because the diverse component
parts of an organism cooperate to perform a coherent unitary
function.
[...]
Very often order is used interchangeably with organization,
but this can be misleading. It is natural to refer to a living
organism as organized, but this would not apply to a crystal,
though both are ordered. Organization is a quality that is most
distinctive when it refers to a process rather than a structure.
An amoeba is organized because its various components work
together as part of a common strategy, each component playing
a specialized and interlinking role with the others. A fossil
may retain something of the form of an organism, and is
undeniably ordered, but it does not share the organization of
its originator, because it is 'frozen'.
-- Davies (1988), pp.73-77.
======================
First of all, it is useful to distinguish between two forms
of complexity, which we will refer to as _Order_ and
_Organization_. The importance of such a distinction has
been particularly emphasized by Denbigh (1975), among others
(e.g., Wicken, (1987), May (1988)), but is certainly not
universally used (e.g, Nicolis, (1986); Kampis and Csanyi,
(1987)). Here we will loosely describe these concepts as follows.
*Order*
Concerns the spatial-temporal, or space-time 'structure' of
a model's (or PS's) dynamics, including stationary states; a
space/time sequential characterization of dynamics; possibly
arranged in 'degrees.'
*Organization*
Concerns the responsive, environmentally operative qualities
of a system's dynamics; the 'value', 'flexibility' , 'purpose',
'function', or 'adaptability' of various dynamic parts possibly
organized in hierarchical levels; possibly in commensurate
components.
The above complications of chaos and turbulence fall within
the 'Order' category. Indeed, the complications of most models
of inanimate systems have been judged under 'Order' tests.
Some exceptions to this involve aspects of bifurcations, or
dynamic stability under external perturbations, particularly
in the area of control systems (e.g., under stochastic actions),
but 'Order' tests appear to dominate the 'complexity studies'
of inanimate models. It should also be emphasized that many
systems which physicists and chemists call 'self-organizing',
such as phase transitions, superconductivity, superfluidity,
lasers, chemical oscillations, and Rayleigh-Benard convection
(e.g, Haken, (1983); Davies, (1989)) would fall in the above
category of 'self-Ordering'. This is, of course, only a semantic
problem, but it can cause confusion. Thus, the concepts under
'Organization', until very recently, have been largely the topics
of interest and development within the life-sciences, and more
recently, various cognitive and memory-model dynamics. These
scientists have been grappling with the most complicated systems,
and have developed the greatest understanding, if not yet many
quantitative measures of the terms in quotation marks under
'Organization' above.
-- Jackson (1991).
==============
Again, information depends on alternative. No information is
conveyed by a series of flips of a two-headed coin, however long,
that registers only heads. Similarly, if an inorganic crystal
has only one allowable lattice structure, its arrangement of
elements has no capacity to convey information. Each is an
example of "order" of "algorithmic compressibility" (Chaitin,
1975). In each case, the structure or sequence could be generated
by an algorithm much briefer than the number of elements or
interconnections involved. To have the _capacity_ to convey
information, a sequence or structure cannot be compressible in
this way. It must be generated from an alphabet, or from a set
of elements, whose affinities for interconnection are not
sufficient to determine that structure. Such systems are
_complex_. _Structural_ information is carved from complexity-
space rather than from entropy space. There is another context,
however, in which the term "information" is sometimes applied.
This involves thermodynamic state specifications.
-- Wicken (1988)
======================
So, we have pronounced this remarkable word _Self-organization_.
For contemporary science it is much more than a mere word: it
defines a new class of natural processes and systems with largely
nonclassical properties. These systems do not obey the classic
Curie principle and other maxims of a uniform determinism. They
are capable of "spontaneous" dissymmetrisation; negligibly small
causes may produce in these systems enormously large effects;
one "cause" can generate more than one effect; some strictly
localized "causes" may produce delocalized effects, and vice versa.
Generally, any kind of distinction into discrete "causes" and
"effects" looks inadequate for this class of systems. They should
be largely replaced by quite other notions, such as ,"stability"
and "instability" (it is only instability which permits the
"spontaneous" dissymmetrisation), parametric and dynamic influences,
and positive and/or negative feedback.
[...]
The interdisciplinary branch of science which deals with this kind
of system was outlined as a coherent body about two or three decades
ago and is usually defined as a theory of self-organization or
synergetics. Its creation is one of the most remarkable but as yet
underestimated (at least, by the representatives of the biological
"mass culture") scientific events of this century.
[...]
Those are some of the most primitive but, nevertheless, real
examples of self-organization going in a purely mechanical way.
In all of these cases, self-organization means the creation of
macroscopical patterns by the action of forces distributed in
a much more homogeneous way than the structures that arise.
Hence, this kind of transformation implies a spontaneous
breaking of symmetry.
[...]
Or, formulating the question more freely: is a developing
organism no more than a container for the genes which operate
as sole masters by their own rules and which change from time
to time the container's shape, or is it an integrated multileveled
system, each level possessing its own self-organizational
properties and being able to affect the other.
In my view (I hope, shared by many others), it is the second
possibility which corresponds to normal development, whereas
the first one may lead, in ultimate cases at least, only to
malformations (carcinogenesis). However, only a few attempts
have been made, until now, to investigate the higher level
effects upon molecular processes in living beings, including
gene expression. This will he an inspiring task for the coming
generation of investigators.
-- Beloussov (1993)
========================
Self-organization is to be understood as the spontaneous
emergence of coherence or structure without externally
applied coercion or control.
In a footnote:
Godfrey Vesey points out that in using language such as
'self-ordering' and 'self-organization', we are in part
returning to the Aristotelean view that teleology is internal
to matter. However, we definitely reject a teleology that
proposes organisms are shaped by adaptation to some external
purpose or function, whether it be natural selection or
some omnipotent creator that is postulated to account for it.
-- Ho and Saunders (1986)
===============
For what follows it will be useful to have a suitable
definition of self-organization at hand. We shall say
that a system is self-organizing if it acquires a spatial,
temporal or functional structure without specific interference
from the outside. By "specific" we mean that the structure or
functioning is not impressed on the system, but that the system
is acted on from the outside in a nonspecific fashion. For
instance, the fluid which forms hexagons is heated from below
in an entirely uniform fashion, and it acquires its specific
structure by self-organization.
-- Haken (1988), p.11.
===============
Technological systems become organized by commands from
outside, as human intentions lead to the building of
structures or machines. But many natural systems become
structured by their own internal processes: these are
the self-organizing systems, and the emergence of order
within them is a complex phenomenon that intrigues
scientists from many disciplines.
-- Yates (1994).
===============
Self-organisation can be defined as a process by which a
structure A transforms itself into a spatially more
complicated structure B without requiring any internal or
external blueprint homeomorphic to B. In somewhat more
precise terms, self-organising systems are those capable
of spontaneous symmetry-breaking (reduction in symmetry
order) without requiring an external influence. In
embryonic development there are many such transformations,
beginning with the first steps (the egg's capacity to
polarise and establish a plane of symmetry even in
isotropical conditions, for example in some kinds of
plane of symmetry even in isotropical conditions, for
example in some kinds of parthenogenesis) up to organogenesis
(metamerisation of mesoderm, formation of brain vesicles etc.
in the absence of homeomorphic prepatterns). It seems also
impossible to trace any homeomorphism between the structures
of embryonic inducers and the induced rudiments; the latter
structures are almost always more regular and complicated
than are the corresponding inducers.
-- Beloussov (1989), p. 121
======================
Self-organization: the mode of change of natural systems whereby
they become to varying degrees more complicated (or even complex)
and larger in size, scope, or throughput. To the degree that
it is predictable, it involves development; to the degree it is
not, it involves individuation. Importantly, some of the drive
to change must come from within the system itself, so this is
not a Newtonian idea. Since individuation is important, such
systems can acquire agency, and my own persuasion is to
emphasize that it is the gradual, asymptotic, acquisition of
determinability. Roughly measurable by ascendency.
--Salthe (1993), p. 323
=====================
[Self-Organization is] The spontaneous emergence of
nonequilibrium structural organization on a macroscopic
level due to collective interactions between a large number
of simple, usually microscopic, objects.
-- Coveney and Highfield (1995), p. 432
======================
The conspicuous complexity of many parts of the universe,
especially living organisms and their byproducts, was once
attributed to divine creativity, but is now generally thought
to reflect a capacity of matter, implicicit in known physical
laws, to "self-organize" under certain conditions. But before
this process can be understood at a fundamental level, we need
a correspondingly fundamental mathematical characterization of
"complexity", the quantity that increases when a self-organizing
system organizes itself. Informally, a complex object typically
contains structural features that could not plausibly have
arisen save as the outcome of a long evolution. This notion of
"logical depth" can be formalized with the help of the theory
of universal computers.
-- Bennett (1995)
======== REFERENCES =========================
Beloussov, L.V. (1989). "Dynamical Levels in Developing Systems,"
in <Dynamic Structures in Biology>, Editors B. Goodwin,
A. Sibatani and G. Webster, Edinburgh University Press,
Edinburgh, Great Britain.
Beloussov, L.V. (1993). "Generation of Morphological Patterns:
Mechanical Ways to Create Regular Structures in Embryonic
Development," in Thinking About Biology, Eds. W. D. Stein
and F. J. Varela, SFI Studies in the Sciences of Complexity,
Lect Note Vol. III, Addison-Wesley, Reading, MA., pp. 149-168.
Bennett, C.H. (1995). "Universal Computation and Physical
Dynamics," <Physica D> 86:268-273.
Coveney, P. and R. Highfield (1995). <Frontiers of Complexity>,
Fawcett Columbine, New York.
Davies, Paul (1988). <The Cosmic Blueprint>, Simon and Schuster.
Depew, David J. and Bruce H. Weber (1995). <Darwinism Evolving>,
MIT Press.
Haken, H. (1988). <Information and Self-Organization>,
Springer-Verlag.
M.W. Ho and P.T. Saunders, 1986,"Evolution: Natural Selection
or Self-Organization",<Disequilibrium and Self Organization>,
C.W. Kilmister, ed., D. Reidel, 1986, pp. 231-242.
Jackson, E. A. (1991). <Perspectives of Nonlinear Dynamics>,
Volume 2, Cambridge University Press, Cambridge.
Mayr, E. (1985). "How Biology Differs from the Physical Sciences",
<Evolution at a Crossroads: The New Biology and the New Philosophy
of Science>, Editors D.J. Depew and B.H. Weber, MIT Press,
Cambridge, MA, pp. 43-63.
Salthe, S.N. (1993). <Development and Evolution: Complexity
and Change in Biology>, MIT Press, Cambridge, MA.
Wicken, J.S. (1988). "Thermodynamics, Evolution, and Emergence:
Ingredients for a New Synthesis," in Entropy, Information,
and Evolution: New Perspectives on Physical and Biological
Evolution, Editors B.H. Weber, D.J. Depew and J.D. Smith,
MIT Press, Cambridge, MA, pp. 139-169.
Yates, F.E. (1994). "Order and Complexity in Dynamical Systems:
Homeodynamics as a Generalized Mechanics for Biology,"
<Mathematical and Computer Modelling>, 19(6-8):49-74.
========================
Brian Harper |
Associate Professor | "It is not certain that all is uncertain,
Applied Mechanics | to the glory of skepticism" -- Pascal
Ohio State University |
========================