Van Huyssteen J.W. (editor) Encyclopedia of Science and Religion

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CLOSED UNIVERSE

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Bruce, Donald, and Bruce, Ann, eds. Engineering Genesis:

The Ethics of Genetic Engineering in Non-Human

Species. London: Earthscan, 1998.

Cole-Turner, Ronald, ed. Human Cloning: Religious Re-

sponses. Louisville, Ky.: Westminster John Knox

Press, 1997.

Cole-Turner, Ronald, ed. Beyond Cloning: Religion and

the Remaking of Humanity. Harrisburg, Pa.: Trinity

Press International, 2001.

Hanson, Mark J., ed. Claiming Power over Life: Religion

and Biotechnology Policy. Washington, D.C.: George-

town University Press, 2001.

Kass, Leon R., and Wilson, James Q. The Ethics of Human

Cloning. Washington, D.C.: AEI Press, 1998.

McGee, Glenn, ed. The Human Cloning Debate. Berkeley,

Calif.: Berkeley Hills Books, 2000.

Nussbaum, M. C., and Sunstein, C. R., eds. Clones and

Clones: Facts and Fantasies About Human Cloning.

New York: Norton, 1998.

Pence, Gregory E. Who’s Afraid of Human Cloning? Lan-

ham, Md.: Rowman and Littlefield, 1998.

Pence, Gregory E., ed. Flesh of My Flesh: The Ethics of

Cloning Humans. Lanham, Md.: Rowman and Little-

field, 1998.

Ruse, Michael, and Sheppard, Aryne, eds. Cloning: Re-

sponsible Science or Technomadness? Amherst, N.Y.:

Prometheus, 2001.

RONALD COLE-TURNER

CLOSED UNIVERSE

Within standard Big Bang cosmology essentially

only three futures are available for the physical uni-

verse. The universe is either open, which means it

will continue to expand at an ever increasing rate;

or it is flat, which means it will only expand at a

rate just sufficient to avoid collapse; or it is closed,

which means the universe will expand to a maxi-

mum size and then collapse in upon itself. The total

mass-density of the universe determines which sce-

nario will be realized. At a critical mass-density, the

universe is flat. If the mass-density is higher than

the critical level, the universe is closed. Certain as-

tronomical measurements suggest that the universe

is very nearly flat, and yet estimates of mass-density

are far below the critical level. This has led scien-

tists to suspect that there is a great deal of matter as

yet undetected. Whether there is enough of this un-

seen dark matter to cause the recollapse of the uni-

verse is a still unresolved question.

See also BIG BANG THEORY; BIG CRUNCH THEORY;

OSMOLOGY, PHYSICAL ASPECTS

MARK WORTHING

COGNITIVE DEVELOPMENT

See EXPERIENCE, RELIGIOUS: COGNITIVE AND

NEUROPHYSIOLOGICAL ASPECTS; NEUROSCIENCES;

SYCHOLOGY

COGNITIVE FLUIDITY

The term cognitive fluidity refers to the capacity of

the modern human mind to combine different ways

of thinking with stores of knowledge to arrive at

original thoughts, which are often highly creative

and rely on metaphor and analogy. As such, cogni-

tive fluidity is a key element of the human imagi-

nation. The term has been principally used to con-

trast the mind of modern humans, especially those

after 50,000 B.P. (before present), with those of ar-

chaic humans such as Neanderthals and Homo

erectus. The latter appear to have had a mentality

that was domain-specific in nature—a series of

largely isolated cognitive domains for thinking

about the social, material, and natural worlds. With

the advent of modern humans the barriers between

these domains appear to have been largely re-

moved and hence cognition became more fluid.

See also EXPERIENCE, RELIGIOUS:COGNITIVE AND

NEUROPHYSIOLOGICAL ASPECTS; EVOLUTION,

UMAN

Bibliography

Mithen, Steven. The Prehistory of the Mind: The Cognitive

Origins of Art, Religion and Science. London: Thames

& Hudson, 1996.

STEVEN MITHEN

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COHERENTISM

Coherentism represents one of the most popular

alternatives to foundationalism as a theory of belief

justification. The easiest way to introduce the dif-

ference between them is to note their response to

the problem of epistemic regress. Proponents of

both sides agree that some beliefs are inferentially

derived from or justified by their relation to other

beliefs, which in turn are justified in relation to still

other beliefs, and so on. A looming skepticism

about the possibility of having any justified beliefs

threatens if this regress cannot be stopped. The

foundationalist halts the regress by identifying

foundational (basic) beliefs that are justified not in

relation to other beliefs, but by some other crite-

rion, such as self-evidence, incorrigibility, or being

evident to the senses. All other beliefs are founded

upon these basic beliefs. The coherentist rejects

this solution, arguing that the justification of every

belief is dependent on its inferential relation to

other beliefs and ultimately on its place in the

whole web of a person’s belief system. Founda-

tionalists use the images of a linear chain or a pyra-

mid to depict the structure of belief justification,

while coherentists prefer the images of a web of

belief or a raft with interlocking planks of diver-

gent size and color.

It is important to understand the scope of any

particular proposal for coherentism. If a compre-

hensive metaphysical theory of truth is the goal,

coherentism may be linked to a radical idealist

embracing of antirealism. Such a pure coherentism

asserts that a belief is true if, and only if, it is a

member of a consistent set of beliefs. In this ex-

treme form, coherentism is open to several objec-

tions. For example, it appears to involve a vi-

ciously circular argument, in which beliefs

mutually justify each other. It also allows for the

possibility that two internally consistent sets of be-

liefs could both be true even if they contain con-

tradictory beliefs between them. Finally, the radical

coherentist position can lead to one despairing of

ever justifying any belief, for how can one evalu-

ate the inner logical consistency of every belief and

its complex relation to the whole web of beliefs?

For these and other reasons, most contempo-

rary coherence theories focus not on the meta-

physical issue of truth but on the epistemological

concern with knowledge and justification. Moder-

ate forms of coherentism do not deny that sense

experience plays a role in the formation of beliefs;

they deny that this role is foundational. Beliefs

must be justified in the context of the whole. For

example, Nicholas Rescher’s version of coheren-

tism fits into his broader call for a “pragmatic ide-

alism” that accounts for the role of experience and

practice in the formation and justification of be-

liefs. Niels Henrik Gregersen has shown how a

“contextual coherence” theory may provide a com-

mon framework of rationality for theology, sci-

ence, and other modes of human inquiry. Those

participants in the religion-science dialogue who

prefer some form of critical realism over naïve re-

alism or antirealism typically affirm coherence as a

criterion of truth, but not as the definition of truth.

See also CRITICAL REALISM; EPISTEMOLOGY;

XPLANATION; FOUNDATIONALISM; REALISM;

RUTH, THEORIES OF

Bibliography

Gregersen, Niels Henrik. “A Contextual Coherence Theory

for the Science-Theology Dialogue.” In Rethinking

Theology and Science: Six Models for the Current Dia-

logue, eds. Niels Henrik Gregersen and J. Wentzel

van Huyssteen. Grand Rapids, Mich.: Eerdmans, 1998.

Haack, Susan. Evidence and Inquiry: Towards Reconstruc-

tion in Epistemology. Oxford: Blackwell, 1993.

Pappas, George, and Swain, Marshall, eds. Essays on

Knowledge and Justification. Ithaca, N.Y.: Cornell

University Press, 1978.

Rescher, Nicholas. A System of Pragmatic Idealism, Vol. 1.

Princeton, N. J.: Princeton University Press, 1992.

F. LERON SHULTS

COMMON ANCESTOR

See EVOLUTION, BIOLOGICAL; EVOLUTION, HUMAN

COMPETITION

An important component of the neo-Darwinian the-

ory of evolution, competition describes the theory

that there is a struggle among organisms both of the

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same species (intraspecific) and between species

(interspecific) for food, space, reproduction, and

other requirements for existence. Through natural

selection organisms develop adaptations to over-

come or resist their own destruction in competition

with the counter-adaptations developed by other

organisms. These adaptations include physiologi-

cal, chemical, and psychological traits. For exam-

ple, organisms may evolve to become larger, more

poisonous, or more aggressive. Such adaptations

are not developed on the short timescale of indi-

vidual lifetime but on the long evolutionary

timescale of the species.

See also ADAPTATION; AGGRESSION; EVOLUTION;

EO-DARWINISM

ARN O. GYLDENHOLM

COMPLEMENTARITY

In his 1948/1949 Gifford lectures the Danish

physicist Niels Bohr (1885–1962) suggested that

theologians make more use of the Complementar-

ity Principle. Articles in Zygon: Journal of Religion

and Science from 1966 and elsewhere advocate

and also oppose such use in regard to both theol-

ogy and the relation of science and religion

(Reich, 1994).

Bohr had introduced complementarity in 1927:

“The very nature of the quantum theory thus forces

us to regard the space-time co-ordination and the

claim of causality, the union of which characterizes

the classical theories, as complementary but exclu-

sive features of the description” (Bohr, p. 115).

Thus, complementarity here means to keep dis-

tinct what has traditionally been merged. In con-

trast, the complementarity of the particle-like and

the wave-like behavior of light brings together

“contradictory” models that traditionally are re-

garded as excluding each other.

A definition of complementarity that is appli-

cable to both physics and theology reads as fol-

lows: Complementarity refers to the possibility that

the same entity/phenomenon manifests itself in

distinct, categorically different ways. All the differ-

ing manifestations need to be described and ex-

plained, and be part of an overarching theory of

the entity/phenomenon, but not all occur in the

same spatial, temporal, or situational context, re-

spectively. Unfortunately, the meaning of the terms

complementarity and complementary changes in

everyday use (e.g., we are not opposed to or com-

peting with each other but are complementary), as

well as in communication theory (in contrast to

symmetrical communication between same-level

partners, complementary communication takes

place between a superior and an inferior position),

and in psychotherapy (in a complementary relation

between client and psychotherapist the client’s

wishes regarding mutual love or hate and domi-

nance or subjection are met; in an anti-comple-

mentary position none are met).

Given such a difficulty, why nevertheless

search for complementarity in regard to science

and religion? Because it opens up a logical possi-

bility not covered by the traditional relationships

(conflict, independence, dialogue, and integration)

as defined by classical logic (Reich, 1996). That

logic is binary: If the choice is between A and B,

and A is correct, then B must necessarily be wrong.

Genuine complementarity involves a trivalent

logic, articulated by Hugo Bedau and Paul Oppen-

heimer in 1961 (compatible, incompatible, and

noncompatible), which allows for a context-de-

pendence of the respective explanatory powers.

For instance, whereas both science and religion

can contribute to the understanding and the signif-

icance of the origin and the evolution of the uni-

verse, science contributes more to an explanation

of what actually happened, and religion to what it

means for human living.

Complementarity as defined above involves

ontology, epistemology, logic, and methodology.

Ontologically, a meta-relation ( entanglement as

described in quantum physics by Werner Heisen-

berg’s principle of indeterminacy) is posited be-

tween the class of contents/meanings pertaining to

science and the class of contents/meanings per-

taining to religion. For example, a person to whom

God entrusts a mission (religion) also receives the

capacity (science) to carry it through. The episte-

mology calls for ascertaining that the statements

concerning science and religion are co-exten-

sional, that is, they refer to the same entity/phe-

nomenon. The logic has already been indicated.

And finally, the methodological issue implies that

science and religion/theology each use their own

methods. From such a perspective one is led to

conclude that complementarity cannot be looked

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for in science and religion tout court, but (if at all)

in selected issues (Reich, 2002).

See also PHYSICS, QUANTUM; SCIENCE AND RELIGION,

ODELS AND RELATIONS

Bibliography

Bedau, Hugo, and Oppenheim, Paul. “Complementarity in

Quantum Mechanics.” Synthese 13 (1961): 201–232.

Bohr, Niels. Collected Works, ed. E. Rüdinger. Vol. 6: The

Foundation of Quantum Physics I (1926–1932), ed.

J. Kalckar. Amsterdam: North Holland Publishing

Company, 1985.

Reich, K. Helmut. “The Relation between Science and

Theology: A Response to Critics of Complementarity.”

In: Studies in Science and Theology, eds. George V.

Coyne and Karl Schmitz-Moormann. Vol. 2: Origins,

Time, and Complexity. Geneva, Switzerland: Labor et

Fides, 1994.

Reich, K. Helmut “A Logic-Based Typology of Science and

Theology.” Journal of Interdisciplinary Studies 8, nos.

1–2 (1996): 149–167.

Reich, K. Helmut. Developing the Horizons of the Mind.

Relational and Contextual Reasoning and the Resolu-

tion of Cognitive Conflict. Cambridge, UK: Cambridge

University Press, 2002.

K. HELMUT REICH

COMPLEXITY

Whereas cosmology explores the boundaries of

the very large, and quantum theory the nature of

the very small, complexity theory aims to under-

stand the emergence and development of orders at

every level, including the medium size world. To

the riddles of the macroscopic and the microscopic

are added the puzzles of complex pattern forma-

tion in semistable dynamical systems known from

everyday life.

Semistable systems are usually nonlinear, so

small inputs may trigger dramatic changes. Exam-

ples are volcanos and tornados, embryologic and

ecological evolution, traffic systems, and stock

markets. These are not new areas of research, but

the computerization of science since the 1970s has

made possible new formalistic approaches to the

study of dynamical systems. The question is

hereby not so much “What are the constituents of

nature (quarks, protons, electrons, etc.)?” but rather

“How does nature work?”

Complexity theory, however, is not the name

of a single theory comparable to, say, Albert Ein-

stein’s Theory of Relativity. There hardly exists one

overarching “law of complexity” waiting to be dis-

covered. Rather, complexity research is an um-

brella term for a wide variety of studies on pattern

formation, some more general, some arising under

specific organizational conditions. The field builds

on thermodynamics, information theory, cybernet-

ics, evolutionary biology, economics, systems the-

ory, and other disciplines. Since complexity re-

search consistently crosses the boundaries

between the inorganic and the organic, the natural

and the cultural, it is likely to influence the sci-

ence-religion dialogue significantly.

Algorithmic complexity

There is no consensus on a general definition of

complexity. The complex is usually defined in con-

trast to the simple, but the distinction between sim-

ple and complex is a relative one. What is simple

in one frame of reference may be complex in an-

other. Walking downstairs, for example, is simple

from the perspective of a healthy person, but phys-

iologically it is highly complex. On the other hand,

chaos theory shows that complex phenomena can

be described by simple nonlinear equations.

An exact measure of algorithmic complexity

has been available since the 1960s. In the Kol-

mogorov-Chaitin model, the complexity of a digital

code consisting of 0s and 1s is measured by the

length of the computer program needed to de-

scribe it. Even a long series of digits (e.g.,

01010101010101010101 . . . ) can be compressed

into a compact description: “write 01 x times.” By

contrast, a complex code is a series without a dis-

cernable pattern; in the worst case, the series

would simply need to be repeated by the com-

puter program (e.g., 1001110010011000011 . . . ).

Such systems are by definition random. However,

one can never know with certainty whether a se-

ries that one sees as random could be further com-

pressed. This is an information-theoretical version

of Gödel’s incompleteness theorem discovered by

Gregory Chaitin.

Similarly, C. H. Bennett suggested a measure

for a structure’s degree of complexity by referring

to its logical depth, defined as the time needed

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(measured by the number of computational steps)

for the shortest possible program to generate that

structure. Both Chaitin and Bennett presuppose

Claude Shannon’s mathematical concept of infor-

mation: The more disordered a message is, the

higher is its informational content. While Chaitin’s

basic definition has the advantage of being ex-

tremely economic, Bennett’s definition is capable

of measuring the discrete operational steps in-

volved in problem solutions. However, none of

these formal definitions of complexity can distin-

guish organized complexity from pure random-

ness. The main interest of complexity studies,

though, is to understand the self-organized com-

plexity that arises in the creative zones between

pure order and pure randomness.

Real-world complexity

To catch the idea of organized complexity, it may

be useful to distinguish between descriptive,

causal, and ontological aspects of complexity of

natural and social systems. Systems that require dif-

ferent sorts of analyses have been called descrip-

tively complex (Wimsatt, 1976). Fruit flies, for ex-

ample, require a variety of descriptions, such as

physical descriptions of their thermal conductivity,

biochemical descriptions of their constitution, mor-

phological descriptions of their anatomical organs,

functional descriptions, and so on. This idea of de-

scriptive complexity lends support to an explana-

tory pluralism, which emphasizes the need for dif-

ferent types of explanation at different levels.

Systems, however, can also be pathway com-

plex while simple in structure if their causal effects

are highly sensitive to environmental conditions. A

hormone is a natural-kind entity with an easily

specifiable molecular composition, but since the ef-

fects of the hormone depend on a variety of bodily

constellations (which cannot be finitely deter-

mined), the causal trajectory of the hormone is com-

plex. Systems theory and organicist proposals in bi-

ology have focused on this aspect of complexity.

The most difficult thing to define is ontological

complexity. An element-based definition of com-

plexity defines complexity by its large number of

variegated elements (Bak, 1997, p. 5). This defini-

tion centers on the fact that many large-scale sys-

tems (mountains, geological plates, etc.) do not

allow for an analytical approach of their micro-

physical states. A relation-based definition of com-

plexity will rather focus on the multiple couplings

of a system in relation to its environments (Luh-

mann, 1995, p. 23–28). The human brain with its

high number of flexible neurons exemplifies that

more possibilities of couplings exist than can be ac-

tualized in a life history. Since the capacity for com-

plex interactions with the environment is usually in-

creased by operational subsystems, organizational

features can be added to the definition of com-

plexity. An organization-based definition of com-

plexity thus emphasizes the hierarchical structure

of interacting levels. Analogously, a performance-

based definition focuses on the capacity for self-or-

ganizing activity. Systems are thus ontologically

complex if they (1) consist of many variegated ele-

ments (in terms of sizes and types), (2) have a high

capacity for relating to themselves and their envi-

ronments, (3) are highly organized in subsystems,

multilevel structures, and internal programs, and (4)

can perform self-organized activities by flexible

couplings to the environment. On this scheme it is

possible to evaluate different aspects of complexity.

A volcano will be more complex than an amoeba

on (1) elements and perhaps on (2) relations, but

far less complex on the score of (3) hierarchical

order and (4) self-organizing activity.

On this scheme, the complex can also be dis-

tinguished from the merely complicated (Cilliers,

1998). Even “primitive” natural entities such as

genes may be ontologically more complex than so-

phisticated artificial systems such as airplanes. A

Boeing 747 jet consists of highly specified ele-

ments, related to one another in predescribed

ways, and there exists a clear recipe for how to as-

semble the elements into a unified system, which

again has a predesigned purpose: being able to

take off, fly, and land safely. The Boeing is a highly

complicated machine but not terribly complex. In

this sense, the complex is more than the simple

but also more than the complicated.

Noncomputational complexity

Complexity studies fall into two main families of

research, one more conceptual (organicism, emer-

gentism, and systems theory) and another more

formalistic (information theory, cybernetics, and

computational complexity). Both types of research

continue to interact in understanding complex

phenomena. While a conceptual preunderstanding

of complex phenomena guides the construction of

computational models, these will afterwards have

to be tested on real-world situations.

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Complexity studies did not start with comput-

ers. The idea that the whole is more than the sum

of the parts goes back to Plato’s notion of divine

providence (Laws 903 B-C), and in Critique of

Judgment (1790) Immanuel Kant describes a natu-

ralized version of the same idea of self-adjustment:

“parts bind themselves mutually into the unity of a

whole in such a way that they are mutually cause

and effect of one another”(B 292).

Embryologists from Karl Ernst von Baer and

Hans Spemann up to C. H. Waddington embraced

organicism as the middle course between vitalism

and reductionism. In organicism a materialist on-

tology (“there exists nothing but matter”) was com-

bined with the observation that new properties are

causally effective within higher-order wholes. Mol-

ecules are not semipermeable, but cell membranes

are, and without this capacity organisms cannot

survive. In the 1920s writers such as C. Lloyd Mor-

gan, C. D. Broad, and Samuel Alexander devel-

oped organicism from an empirical research pro-

gram into a metaphysical program of emergent

evolutionism. The point here was that in the

course of evolution higher-order levels are formed

in which new properties emerge. Whereas the so-

lidity of a table is a mere “resultant” of solid state

physics, the evolution of life is ripe with “emer-

gent” properties (for example, metabolism) that

require new forms of description and eventually

will have real causal feedback effects on the phys-

ical system (the atmosphere) that nourished life in

the first place.

After World War II the general systems theory

combined organicistic intuitions with cybernetics.

Ludwig von Bertalanffy replaced the traditional

whole/part difference by the difference between

systems and environments. Systems are constitu-

tionally open for environmental inputs and are

bound to develop beyond equilibrium under se-

lective pressures. Thereby systems theory estab-

lished itself as a theory combining thermodynam-

ics and evolutionary theory. Systems are structures

of dynamic relations, not frozen objects.

In the 1960s Heinz von Foerster and others in-

troduced the theory of self-referential systems ac-

cording to which all systems relate to their envi-

ronments by relating to their own internal codes or

programs. Brains don’t respond to cats in the

world, but only to the internal firings of its neurons

within the brain. “Click, click is the vocabulary of

neural language” (von Foerster). In this perspec-

tive, closure is the precondition of openness, not

its preclusion. In this vein, biologists Francisco J.

Varela and Humberto Maturana developed a con-

structionist research program of autopoietic (self-

productive) systems. The sociologist Niklas Luh-

mann has further emphasized how systems

proceed by self-differentiation and can no longer

be analyzed by reference to global physical fea-

tures of the world-as-a-whole. In this perspective,

each system needs to reduce, by its own internal

operations, the complexities produced by other

systems. Different systems (for example, biological,

social, psychic) operate with different codes (en-

ergy, communication, consciousness), and even

though they coevolve they cannot communicate

with one another on neutral ground. The fleeting

experience of consciousness, for example, remains

coupled to physiological processes and to social

communication, yet has its own irreducible life.

Computational complexity

Computational complexity presupposes the idea of

algorithmic compression and embodies the spirit

of cybernetics. The dictum of Norbert Wiener that

“Cybernetics is nothing if it is not mathematical”

(1990, p. 88) could also be said of computational

complexity.

The field of cybernetics was developed after

World War II by John von Neumann, Ross Ashby,

Norbert Wiener, and others. Central to cybernetics

is the concept of automata, defined as machines

open for information input but leading to an out-

put modified by an internal program. In cybernetic

learning machines, the output functions are rein-

troduced into the input function, so that the inter-

nal program can be tested via trial and error

processes. However, the measure for success or

failure is still fixed by preset criteria.

The cybernetic automata were the direct pre-

cursors of cellular automata, used in the artificial

life models designed by John Conway and Chris

Langton in the 1970s. Cellular automata use indi-

vidual based modeling: “Organisms” are placed in

cubic cells in a two-dimensional grid, and their “ac-

tions” (die or divide) are specified by the number

of living cells in their immediate neighborhood. In

this way, the positive feedback of breeding can be

modeled as well as the negative feedback of com-

petition. The result is self-reproducing loops gen-

erated by very simple rules.

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With the establishment of the Santa Fe Institute

in New Mexico in 1984 a multidisciplinary center

for computational complexity was formed. Physi-

cist Murray Gell-Mann, computer scientist John

Holland, and others introduced the idea of com-

plex adaptive systems. As opposed to simple adap-

tation (as in a thermostat), there are no preset

goals for complex adaptive systems. Like cellular

automata, complex adaptive systems are individu-

ally modeled systems, but complex adaptive sys-

tems also involve “cognition.” Complex adaptive

systems are able to identify perceived regularities

and to compress regular inputs into various

schemata. Unlike cybernetic learning machines,

there may be several different schemata competing

simultaneously, thus simulating cognitive selection

processes. In this manner self-adaptation coevolves

with adaptation beyond a preset design. Whereas

Gell-Mann uses complex adaptive systems as a

general concept, Holland uses the term only about

interacting individual agents. Complex adaptive

systems agents thus proceed by a limited set of in-

teraction rules, governed by simple stimulus-re-

sponse mechanisms such as (1) tags (e.g., if some-

thing big, then flee; if something small, then

approach), (2) internal models (or schemata), and

(3) rules for connecting building blocks to one an-

other (e.g., eyes and mouth to facial recognition).

The result of these local mechanisms, however, is

the emergence of global properties such as non-

linearity, flow, diversity, and recognition.

Insofar as complex patterns are generated by

simple mechanisms, computational complexity can

be seen as a reductionist research paradigm; in con-

tradistinction to physical reductionism, however,

the reduction is to interaction rules, not to physical

entities. But insofar as higher-level systems can be

shown to exert a “downwards” feedback influence

on lower-level interaction-rules, computational

complexity may also count as an antireductionist

research program. The issues of reductionism ver-

sus antireductionism, bottom-up versus top-down

causality, are still debated within the computational

complexity community. But anyway, it is informa-

tion and not physics that matters.

Computational complexity and real-world

complexity

The spirit of computational complexity is not to

collect empirical evidence and “reflect” reality, but

to “generate” reality and explore virtual worlds of

possibility. Computational complexity is nonethe-

less empirically motivated and aims to understand

real-world complexity by computer modeling. The

aspiration is to uncover deep mathematical struc-

tures common to virtual worlds and real-world dy-

namical systems.

The mathematical chaos theory is an example

of a computer-generated science that has suc-

ceeded in explaining many dynamical patterns in

nature. Yet the relation between chaos theory and

computational complexity is disputed. While

chaotic systems (in the technical sense) are ex-

tremely sensitive to the initial conditions, complex

systems are more robust (that is, they can start

from different conditions and still end up in almost

the same states). Accordingly, chaos theory can

predict the immediate next states but not long-term

developments, whereas complex systems can reli-

ably describe long-term prospects but cannot pre-

dict the immediate following steps. Moreover,

chaos systems do not display the kind of evolu-

tionary ascent and learning characteristic of com-

plex adaptive systems, but oscillate or bifurcate

endlessly. It therefore seems fair to say that chaos

theory is only a small pane in the much larger win-

dow of complexity studies. Chaos, in the colloquial

sense of disorder, is everywhere in complex sys-

tems (and so are fractals and strange attractors),

but the equations of chaos in the technical sense

(the specific Lyapunov-exponent, etc.) cannot ex-

plain self-organized complexity.

There are also connections between thermo-

dynamics and complexity theory. Beginning in the

1960s, the chemist Ilya Prigogine studied the so-

called dissipative structures that arise sponta-

neously in systems dissipated by energy. While

classical thermodynamics described isolated sys-

tems where nonhomogeneities tend to even out

over time, Prigogine studied nonequilibrium

processes of “order out of chaos” (chaos in the

nontechnical sense). Famous examples are the

convection patterns of Bénards cells formed spon-

taneously under heating or the beautiful chemical

clocks of the Belousov-Zhabotinski reaction. While

Ludwig Boltzmann’s law of entropy from 1865 still

holds for the universe as a whole, the formation of

local orders is produced by nonequilibrium ther-

modynamics. The averaging laws of statistical me-

chanics are not contradicted, but they simply do

not explain the specific trajectories that develop

beyond thermodynamical equilibrium.

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In the wake of Prigogine, a new search for the

thermodynamical basis of evolution began

(Wicken, 1987). The bifurcation diagrams of Pri-

gogine showed amazing similarities to evolutionary

trees. Reaching back to the seminal work of D’Arcy

Wentworth Thompson in On Growth and Form

(1916), many began to think that the interplay of

selection and mutation is not self-sufficient for ex-

plaining the evolutionary tendency towards com-

plexification. Evolution may be driven by gene se-

lection and prebiotic laws of physical economy.

Since the 1970s, theoretical biologist Stuart

Kauffmann has constructed computational models

of self-organizing principles at many levels. Moti-

vated by the almost ubiquitous tendency of chem-

ical systems to produce autocatalytic systems,

Kauffman theorizes that life may have emerged

quite suddenly through phase transitions where

chemical reactions function as catalysts for one an-

other far below the threshold of the RNA-DNA cy-

clus. Kauffman uses a similar model for simulating

the empirical findings of Francois Jacob and

Jacques Monod, who showed that genes switch on

and off depending on the network in which they

are situated. In the simplest model of Boolean net-

works, each “gene” is coupled randomly to two

other genes with only two possible states, on or off

(states that are determined by the states of the two

other genes). Running this small system with only

three genes and two activities recurrently (and later

with much larger networks), Kauffman was able to

show that the number of state cycles (attractors) in-

crease with the number of genes. Moreover, their

relation is constant so that the number of state cy-

cles is roughly the square root of the number of

genes, and Kauffman points out in The Origins of

Order (1993) that in real-world species one finds

roughly the same relation between the number of

genes and the number of cell types in a given

species. Thus, agents in coupled systems seem to

tune themselves to the optimal number of cou-

plings with other agents. In addition, when inves-

tigating fitness landscapes of interacting species at

the ecological level, Kauffman finds the principle

of “order for free.” Evolutionary innovations tend

to happen “at the edge of chaos,” between the

strategy of evolutionarily stable orders and the

strategy of the constant evolutionary arms race. In

Investigations (2000), Kauffman pursues a search

for laws by which the biosphere is coconstructed

by “autonomous agents” who are able run up

against the stream of entropy. Kauffman hereby

acknowledges the impossibility of prestating fi-

nitely what will come to be within the vast config-

uration space of the biosphere.

The theory of self-organized criticality formu-

lated by Per Bak and his colleagues starts in empir-

ically confirmed regularities (such as the Gutenberg-

Richter law of earthquakes). Many systems show

slow variation over long periods, rare catastrophic

activities over short time, and some critical phases in

between. The building up of sand piles shows these

phase transitions, but so do earthquakes, extinction

rates, and light from quasars. Bak’s point is that self-

organized criticality systems are self-organizing,

since they (1) are robust and do not depend on spe-

cific initial conditions, (2) emerge spontaneously

over time (with no external designer), and (3) are

governed by the same mathematical principles in

stationary, critical, and catastrophic states. Bak has

made both real-world experiments and simplified

computer-models of self-organized criticality sys-

tems, but he believes that self-organized criticality is

only a first approximation of stronger explanations

of nature’s tendency to build up balances between

order and disorder.

Relevance for the science-religion discussion.

While organicist programs of noncomputational

complexity have played a major role in the sci-

ence-religion dialogue since the seminal works of

Ian Barbour, Arthur Peacocke, and others, the rel-

evance of computational complexity for theology

largely remains to be explored. The following is-

sues are therefore to be taken more as pointers

than as conclusions:

(1) The sciences of complexity study pattern for-

mations in the midst of the world rather than

in a hidden world beyond imagination. The

features of organized complexity resonate

with the experiences of being-part-of-a-

whole, experiences that since Friedrich

Schleiermacher’s On Religion (1799) have

been taken to be essential to religious intu-

ition.

(2) While presupposing a robust naturalism,

complexity theory suggests that “informa-

tion” is as seminal to nature as are the sub-

stance and energy aspects of matter. Com-

plexity theory may thus give further impetus

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to the dematerialization of the scientific idea

of matter in the wake of relativity theory.

(3) By focusing on relations and interactions

rather than on particular objects, complexity

theory supports a shift in worldview from a

mechanical clockwork view of the world to

an emergentist view of the world as an inter-

connected network, where flows of informa-

tion take precedence over localized entities.

Complexity theory also offers a road for un-

derstanding the evolution of coevolution. By

balancing the principle of individual selec-

tion by principles of self-organization, the

focus on individual genes is supplemented

by the importance of interconnected living

organisms, a view closer to ethical and reli-

gious sentiments than the inherited view of

the omnipotence of selection.

(4) Even though natural evils (from earthquakes

to selection) remain a challenge to religions

that presuppose a loving almighty God, the

costs of evolutionary creativity are now

being placed in a wider framework of evolu-

tion. If the same underlying dynamics of self-

organized criticality produce both stability,

criticality, and catastrophes, and the con-

structive aspects of nature cannot exist with-

out the destructive aspects, a theodicy of nat-

ural evils may be facilitated.

(5) The idea of complex adaptive systems gives

biological learning and human culture (in-

cluding science, ethics, and religion) a piv-

otal role in the understanding of what nature

is, and what makes human and animal life

grow and flourish. In addition, since com-

plexity theory consistently crosses the

boundaries between physics, biology, and

the cultural sciences, theologians and human

scientists may be prompted to rethink

human culture (including religion) in terms

of the creative interactions between the inor-

ganic, the organic, and the cultural.

(6) From an external scientific perspective, com-

putational complexity may be used to ex-

plain a variety of religious phenomena that

arise at the critical interface between adapta-

tion and self-adaptation, such as the interac-

tion between religious groups, individual

conversion experiences, and so on. The first

computer models in this area have already

been completed.

(7) From an internal religious perspective, com-

plexity theory offers religious thought a new

set of thought models and metaphors, which

(when adopted) can stimulate the heuristics

of theology when complex phenomena are

redescribed from the perspective of religious

symbolics. Self-organization, coupled net-

works, and adaptation by self-adaption

are candidates for such religious self-

interpretation. The principles of complexity

are in particular consonant with the idea that

a divine Logos is creatively at work in the

pattern formations of nature and drives na-

ture towards further complexification.

(8) The computational complexity idea of self-

organization is a challenge to the Enlighten-

ment idea of a divine designer of all natural

processes. Self-organization is also a chal-

lenge to the creationist Intelligent Design

movement, which gives priority to the idea

of “original creation” and tends to perceive

novelties as perversions of pre-established

designs. However, self-organizational

processes never happen from scratch, but al-

ways presuppose a framework of laws and

natural tendencies that could well be said to

be “designed” by God. While a design of

specific evolutionary outcomes is obsolete in

light of self-organized complexity, the coor-

dination of laws leading towards self-organi-

zation and coevolution may be explained by

a divine metadesign.

(9) Since emergence takes place in the merging

of coupled systems, theology may escape the

alternative between an interventionist God,

who acts by breaking natural laws, and a

God who only sustains the laws of nature

uniformly over time. In higher-organized sys-

tems, new informational pathways are con-

tinuously tried out in adventurelike proc-

esses. If the local interaction rules and the

overall probability patterns are constantly

changed over time, the actual pathways of

large-scale coupled systems are not reducible

to the general laws of physics. Special divine

interaction with the evolving world can thus

no longer be said to “break laws” in an in-

terventionist manner, since there are no fixed

laws to break in coupled systems.

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(10) The seminal idea of self-organization may

help overcome the idea that God and nature

are contraries, so that God is powerless, if

nature is powerful, and vice versa. A more

adequate view may be to understand God as

the creator who continuously hands over cre-

ativity to nature so that natural processes are

the signs of a divine self-divestment into the

very heart of nature’s creativity. On this view,

God is at work “in, with, and under” natural

and social processes, and self-organization

takes place within a world already created

and continuously gifted by God.

See also AUTOMATA, CELLULAR; AUTOPOIESIS; CHAOS

THEORY; CYBERNETICS; EMERGENCE; INFORMATION

THEORY; INTELLIGENT DESIGN; SYSTEMS THEORY;

HERMODYNAMICS, SECOND LAW OF

Bibliography

Ball, Philip. The Self-Made Tapestry: Pattern Formation in

Nature. Oxford: Oxford University Press, 1999.

Bak, Per. How Nature Works: The Science of Self-Organized

Criticality. Oxford: Oxford University Press, 1997.

Bennett, C. H. “Logical Depth and Physical Complexity.”

The Universal Turing Machine. A Half-Century Sur-

vey, ed. Rolf Herken. Oxford: Oxford University

Press, 1987.

Chaitin, Gregory. Algorithmic Information Theory. Cam-

bridge: Cambridge University Press, 1975.

Cilliers, Paul. Complexity and Postmodernism: Under-

standing Complex Systems. London: Routledge, 1998.

Clayton, Philip. God and Contemporary Science. Grand

Rapids, Mich.: Eerdmans, 1997.

Cowan, George A.; Pines, David; and Meltzer, David, eds.

Complexity: Metaphors, Models, and Reality. Cam-

bridge, Mass.: Perseus Books, 1994.

Emmeche, Claus. The Garden in the Machine: The Emerg-

ing Science of Artificial Life. Princeton, N.J.: Princeton

University Press, 1994.

Gell-Mann, Murray. The Quark and the Jaguar: Adven-

tures in the Simple and the Complex. New York: W.

H. Freeman, 1994.

Gilbert, Scott F., and Sarkar, Sahotra. “Embracing Com-

plexity: Organicism for the 21st Century.” Develop-

mental Dynamics 219 (2000): 1–9.

Gregersen, Niels Henrik. “The Idea of Creation and the

Theory of Autopoetic Processes.” Zygon 33, no. 3

(1998): 333–367.

Gregersen, Niels Henrik, ed. From Complexity to Life: On

the Emergence of Life and Meaning. New York: Ox-

ford University Press, 2002.

Holland, John. Hidden Order: How Adaptation Builds

Complexity. Reading, Mass.: Addison-Wesley, 1995.

Holland, John. Emergence: From Chaos to Order. Oxford:

Oxford University Press, 1998.

Kauffman, Stuart. The Origins of Order: Self-Organization

and Selection in Evolution. New York: Oxford Uni-

versity Press, 1993.

Kauffman, Stuart. At Home in the Universe: The Search for

Laws of Self-Organization and Complexity. New

York: Oxford University Press, 1995.

Kauffman, Stuart. Investigations. New York: Oxford Uni-

versity Press, 2000.

Luhmann, Niklas. Social Systems, trans. John Bednarz Jr.

with Dirk Baecker. Stanford, Calif.: Stanford Univer-

sity Press, 1995.

Maturana, Humberto R., and Varela, Fransisco. The Tree of

Knowledge: The Biological Roots of Human Under-

standing, rev. edition. Boston: Shambala, 1992.

Peacocke, Arthur. Theology for a Scientific Age: Being and

Becoming—Natural, Divine and Human, enlarged

edition. London: SCM Press, 1993.

Rasch, William, and Wolfe, Cary, eds. Observing Complex-

ity: Systems Theory and Postmodernity. Minneapolis,

Minn.: University of Minnesota Press, 2000.

Russell, Robert John; Murphy, Nancey; and Peacocke,

Arthur A., eds. Chaos and Complexity: Scientific Per-

pectives on Divine Action. Berkeley, Calif.: Center for

Theology and the Natural Sciences; Notre Dame,

Ind.: Notre Dame University Press, 1995.

Russell, Robert John; Murphy, Nancey; Meyering, Theo;

and Arbib, Michael A., eds. Neuroscience and the

Human Person: Scientific Perpectives on Divine Ac-

tion. Berkeley, Calif: Center for Theology and the

Natural Sciences; Notre Dame, Ind.: Notre Dame Uni-

versity Press, 1999.

Schmidt, Siegfried J., ed. Der Diskurs des radikalen Kon-

struktivismus. Frankfurt am Main, Germany:

Suhrkamp, 1988.

Solé, Richard, and Goodwin, Brian. Signs of Life: How

Complexity Pervades Biology. New York: Basic

Books, 2000.

Stengers, Isabelle. La vie et l’artifice: Visage de l’émer-

gence. Paris: La Découverte, 1997.

Thompson, D’Arcy Wentworth. On Growth and Form

(1916). New York: Dover, 1992.

LetterC.qxd 3/18/03 1:05 PM Page 157