REDUCTIONISM AND
COMPLEXITY:CONTINUUM OR
DICHOTOMY?
DON MIKULECKY
PROFESSOR EMERITUS OF PHYSIOLOGY AND
SENIOR FELLOW IN THE CENTER FOR THE STUDY
OF BIOLOGICAL COMPLEXITY-VCU
http://www.people.vcu.edu/~mikuleck/
ONE OF THE MAIN FUNCTIONS OF
REDUCTIONISM IN SOCIETY
 IF THE SYSTEM IS CORRUPT THEN HOW
CAN A PERSON WHO WANTS NOT TO
PARTICIPATE IN CORRUPTION BE A
PARTICIPANT?
 HE MUST REDUCE THE SYSTEM TO
UNRELATED ENDEAVORS SO THAT HE
CAN ESCAPE RECOGNIZING HIS
PARTICIPATION IN THE CORRUPT WHOLE
COMPLEXITY
 REQUIRES A CIRCLE OF IDEAS AND METHODS
THAT DEPART RADICALLY FROM THOSE TAKEN
AS AXIOMATIC FOR THE PAST 300 YEARS
 OUR CURRENT SYSTEMS THEORY, INCLUDING
ALL THAT IS TAKEN FROM PHYSICS OR
PHYSICAL SCIENCE, DEALS EXCLUSIVELY WITH
SIMPLE SYSTEMS OR MECHANISMS
 COMPLEX AND SIMPLE SYSTEMS ARE DISJOINT
CATEGORIES
COMPLEXITY VS COMPLICATION
 Von NEUMAN THOUGHT THAT A CRITICAL LEVEL OF
“SYSTEM SIZE” WOULD “TRIGGER” THE ONSET OF
“COMPLEXITY” (REALLY COMPLICATION)
 COMPLEXITY IS MORE A FUNCTION OF SYSTEM
QUALITIES RATHER THAN SIZE
 COMPLEXITY RESULTS FROM BIFURCATIONS -NOT IN THE
DYNAMICS, BUT IN THE DESCRIPTION!
 THUS COMPLEX SYSTEMS REQUIRE THAT THEY BE
ENCODED INTO MORE THAN ONE FORMAL SYSTEM IN
ORDER TO BE MORE COMPLETELY UNDERSTOOD
IN ORDER TO SEE FURTHER
THAN BEFORE IT IS OFTEN
NECESSARY TO STAND ON THE
SHOULDERS OF GIANTS!
SOME OF MY GIANTS:
 AHARON KATZIR-KATCHALSKY (died in
terrorist massacre in Lod Airport 1972)
 LEONARDO PEUSNER (alive and well in
Argentina)
 ROBERT ROSEN (died December 29, 1998)
SOME REFERENCES
 FOR A BIBLIOGRAPHY OF ROSEN’S
WORK: http://views.vcu.edu/complex/
 Pusner, Leonardo: Two books on network
thermodynamics
 My book: Application of network
thermodynamics to problems in biomedical
engineering, NYU Press, 1993

Recent work:
 New review:The Circle That Never Ends: Can
Complexity Be Made Simple? In Complexity
in Chemistry, Biology, and Ecology
Bonchev, Danail D.; Rouvray, Dennis (Eds.)
2005
 New Book: Into the Cool: Energy Flow,
Thermodynamics and Life by: Eric D.
Schneider and Dorion Sagan, University of
Chicago Press, 2005
THE MODELING RELATION: THE
ESSENCE OF SCIENCE
 ALLOWS US TO ASSIGN MEANING TO THE




WORLD AROUND US
STANDS FOR OUR THINKING PROCESS
CAUSALITY IN THE NATURAL SYSTEM IS DEALT
WITH THROUGH IMPLICATION IN A FORMAL
SYSTEM
THERE IS AN ENCODING OF THE NATURAL
SYSTEM INTO THE FORMAL SYSTEM AND A
DECODING BACK
WHEN IT ALL HANGS TOGETHER WE HAVE A
MODEL
THE MODELING RELATION: A MODEL OF HOW WE MAKE
MODELS, A SCIENCE OF FRAMING
NATURAL
SYSTEM
ENCODING
CAUSAL
EVENT
MANIPULATION
DECODING
NATURAL
SYSTEM
FORMAL
SYSTEM
FORMAL
SYSTEM
WE HAVE A USEFUL MODEL
WHEN
ARE SATISFACTORY WAYS OF “UNDERSTANDING”
THE CHANGE IN THE WORLD “OUT THERE”
THE MODELING RELATION: A MODEL
OF HOW WE MAKE MODELS
NATURAL
SYSTEM
ENCODING
CAUSAL
EVENT
IMPLICATION
DECODING
NATURAL
SYSTEM
FORMAL
SYSTEM
FORMAL
SYSTEM
MORE ON THE MODELING RELATION
 THE FORMAL SYSTEM DOES NOT INCLUDE INFORMATION
ABOUT ENCODING AND/OR DECODING
 THEREFORE MODELING WILL ALWAYS BE AN ART
 ONLY IN THE NEWTONIAN PARADIGM DOES THE FORMAL
SYSTEM BECOME THE NATURAL SYSTEM (ENCODING
AND DECODING ARE AUTOMATIC) AND ALL THAT IS LEFT
TO DO IS TO MEASURE THINGS
WHY IS “OBJECTIVITY” A MYTH? (OR: WHY IS SCIENCE A
BELIEF STRUCTURE)
 THE FORMAL SYSTEM DOES NOT AND
CAN NOT TELL US HOW TO ENCODE AND
DECODE. (MODELING IS AN ART!)
 THE FORMAL SYSTEM DOES NOT AND
CAN NOT TELL US WHEN THE MODEL
WORKS, THAT IS A JUDGEMENT CALL
EVEN IF OTHER FORMALISMS ARE
ENLISTED TO HELP (FOR EXAMPLE:
STATISTICS)
 MODELS EXIST IN A CONTEXT: A FRAME
WHY WHAT “TRADITIONAL SCIENCE” DID TO THE MODELING
RELATION MADE THE PRESENT SITUATION INEVITABLE:
 WE ARE TOO AFRAID OF
“BELIEFS” (SCEPTICISM IS “IN”)
 WE DEVELOPED THE MYTH OF
“OBJECTIVITY”
WHAT IS “FRAMING THE
QUESTION”?
 Based on the work of George Lakoff
 Cognitive Linguistics
 Frames are the mental structures that shape
the way we see the world
 Facts, data, models, etc. only have meaning
in a context
 Leads us to a scientific application of framing:
Rosen’s theory of complexity
Framing the question
 Don’t think of an elephant
 Impossibility of avoiding the frame
 In science the dominant frame is
reductionism and the associated mechanical
thinking
 The dominant modern manifestations include
molecular biology and nonlinear dynamics
WHY ARE THERE SO MANY
DEFINITIONS OF COMPLEXITY?
 SCIENTISTS FOCUS ON THE FORMAL
DESCRIPTION RATHER THAN THE REAL
WORLD
 THE REAL WORLD IS COMPLEX
 FORMAL SYSTEMS COME IN VARYING
SHADES AND DEGREES OF
COMPLICATION
Reductionism has framed complexity
theory
 Rather than change methods we have the changed names
for what we do
 The consequences are significant
 It is impossible for you to believe what is being taught in
this lecture and to then simply add it to your repertoire
 The reason is that in order to see the world in a new way
you have to step out of the traditional frame and into a new
one. Once done, you can never go back. The ability to
reframe a question is the basis for change and broadening
of ideas.
WHAT “TRADITIONAL SCIENCE” DID TO FRAME THE
MODELING RELATION
FORMAL
SYSTEM
NATURAL
MANIPULATION
SYSTEM
CAUSAL
EVENT
FORMAL
SYSTEM
NATURAL
SYSTEM
WHAT “TRADITIONAL SCIENCE” DID TO FRAME THE
MODELING RELATION
FORMAL
NATURAL
SYSTEM
SYSTEM
MANIPULATION
FORMAL
NATURAL
SYSTEM
SYSTEM
WHY WHAT “TRADITIONAL SCIENCE” DID TO THE MODELING
RELATION MADE THE PRESENT SITUATION INEVITABLE:
 WE MORE OR LESS FORGOT THAT
THERE WAS AN ENCODING AND
DECODING
WHY WHAT “TRADITIONAL SCIENCE” DID TO THE MODELING
RELATION MADE THE PRESENT SITUATION INEVITABLE: IT
FRAMED THE QUESTIN
 THE “REAL WORLD” REQUIRES
MORE THAN ONE “FORMAL
SYSTEM” TO MODEL IT (THERE IS
NO “UNIVERSAL MODEL”)
Syntax vs Semantics
 The map is not the territory
 An equation is just an equation without
interpretation
 This means we use formalisms in a context
 This context dependence also exists in nature
 This is one reason why there can never be a
largest model
Context dependence necessarily
introduces circularity
 A process happens in a context
 The process usually changes that context
 If the context changes the process usually
changes as a result.
 Living systems are replete with examples
of this
SELF-REFERENCE, CIRCULARITY AND
THE GENOME
REPLICATION
TRANSCRIPTION
HOMEOSTASIS
CAN WE GET RID OF SELF-REFERENCE, THAT
IS, CIRCULARITY?
 IT HAS BEEN TRIED
 IT FAILED
 THE ALTERNATIVE IS TO “GO AROUND”
IT – THAT IS TO IGNORE CASES WHERE
IT POPS UP
 WHAT IF IT IS VERY COMMON?
WHAT IS COMPLEXITY?
 TOO MANY DEFINITIONS, SOME CONFLICTING
 OFTEN INTERCHANGED WITH “COMPLICATED”
 HAS A REAL MEANING BUT AFTER THE
QUESTION IS REFRAMED
 THAT MEANING ITSELF IS COMPLEX(THIS IS
SELF-REFERENTIAL: HOW CAN WE DEFINE
“COMPLEX” USING “COMPLEX”?)
ROSEN’S CONCEPT FOR
COMPLEXITY: A NEW FRAME
Complexity is the property of a real world system
that is manifest in the inability of any one
formalism being adequate to capture all its
properties. It requires that we find distinctly
different ways of interacting with systems.
Distinctly different in
the sense that when we make successful models,
the formal systems needed to describe each
distinct aspect are NOT
derivable from each other
The Mexican sierra [fish] has "XVII-15-IX" spines
in the dorsal fin. These can easily be counted ...
We could, if we wished, describe the sierra thus:
"D. XVII-15-IX; A. II-15-IX," but we could see the
fish alive and swimming, feel it plunge against
the lines, drag it threshing over the rail, and
even finally eat it. And there is no reason why
either approach should be inaccurate.
Spine-count description need not
suffer because another approach is also used.
Perhaps, out of the two approaches we thought
there might emerge a picture more complete and
even more accurate that either alone could
produce.
-- John Steinbeck, novelist,
with Edward Ricketts, marine biologist (1941)
COMPLEX SYSTEMS VS SIMPLE
MECHANISMS
 COMPLEX
 SIMPLE
 NO LARGEST MODEL
 LARGEST MODEL
 WHOLE MORE THAN SUM
 WHOLE IS SUM OF PARTS






OF PARTS
CAUSAL RELATIONS RICH
AND INTERTWINED
GENERIC
ANALYTIC  SYNTHETIC
NON-FRAGMENTABLE
NON-COMPUTABLE
REAL WORLD
 CAUSAL RELATIONS





DISTINCT
N0N-GENERIC
ANALYTIC = SYNTHETIC
FRAGMENTABLE
COMPUTABLE
FORMAL SYSTEM
An Example of Reframing the question to get an answer : The work of Robert
Rosen
 What is life?
 Why is an organism different from a
machine?
ROBERT ROSEN: THE WELL POSED QUESTION AND ITS
ANSWER-WHY ARE ORGANISMS DIFFERENT FROM
MACHINES?
 Rosen used relational ideas to apply category theory




to living systems
These were called “Metabolism/Repair” systems oo
M-R systems
Causal mappings were diagramed a syntax involving
category theory mappings and the semantics were
used along with this to apply the causal interpretaion
The result was a clear demonstration that the
machine and the organism are disjoint in this context
An organism is closed to efficient cause while a
machine is not
AMONG OTHER CONCLUSION THAT CAN BE DRAWN FROM
THIS ELEGANT STUDY IS ONE THAT MIGHT SEEM
SURPRISING
 Since machines are causally impoverished, they




lead to an infinite regress of causes.
Descartes led us to use the machine metaphor for
organisms
In so doing he made a concept of God necessary
Today, “Intelligent Design” is based on this
erroneous Cartesian metaphor: The Machine
Metaphor
Real orgainisms are closed causually and escape
this fallacy
WHAT IS SCIENCE?
 HAS MANY DEFINTIONS
 SOME OF THESE ARE IN CONFLICT
 SCIENCE IS A BELIEF STRUCTURE
 SCIENCE OF METHOD VS SCIENCE OF
CONTENT
WHAT ARE SOME OF THE THINGS THAT MAKE “COMPLEXITY
THEORY” NECESSARY? (WHAT HAS “TRADITIONAL SCIENCE”
FAILED TO EXPLAIN?)
 WHY IS THE WHOLE MORE THAN THE
SOME OF THE PARTS?
 SELF-REFERENCE AND CIRCULARITY
 THE LIFE/ORGANISM PROBLEM
 THE MIND/BODY PROBLEM
CIRCULARITY (SELF-REFERENCE) CAUSES
PROBLEMS FOR LOGIC AND SCIENCE
 I AM A CORINTHIAN
 ALL CORINTHIANS ARE LIARS
 OR
 “THE STATEMENT ON THE OTHER SIDE
IS FALSE”-ON BOTH SIDES
WHERE DO CELLS COME
FROM?
 DNA?
 GENES?
 PROTEINS?
 OTHER CELLS?
 SPONTANEOUS GENERATION?
THE CELL THEORY
 CELLS COME FROM OTHER CELLS
WHY WHAT “TRADITIONAL SCIENCE” DID TO THE QUESTION
MADE THE PRESENT SITUATION INEVITABLE:
 THE MACHINE METAPHOR TELLS US
TO ASK “HOW?”
 REAL WORLD COMPLEXITY TELLS
US TO ASK “WHY?”
THE FOUR BECAUSES: WHY A
HOUSE?
 MATERIAL: THE STUFF IT’S MADE OF
 EFFICIENT: IT NEEDED A BUILDER
 FORMAL: THERE WAS A BLUEPRINT
 FINAL: IT HAS A PURPOSE
WHY IS THE WHOLE MORE THAN THE SOME OF THE PARTS?
 BECAUSE REDUCING A REAL SYSTEM
TO ATOMS AND MOLECULES LOOSES
IMPORTANT THINGS THAT MAKE THE
SYSTEM WHAT IT IS
 BECAUSE THERE IS MORE TO REALITY
THAN JUST ATOMS AND MOLECULES
(ORGANIZATION, PROCESS, QUALITIES,
ETC.)
SELF-REFERENCE AND CIRCULARITY
 THE “LAWS” OF NATURE THAT
TRADITIONAL SCIENCE TEACHES ARE
ARTIFACTS OF A LIMITED MODEL
 THE REAL “RULES OF THE GAME” ARE
CONTEXT DEPENDENT AND EVER
CHANGING- THEY MAKE THE CONTEXT
AND THE CONTEXT MAKES THEM (SELFREFERENCE)
EXAMPLE: THE LIFE/ORGANISM PROBLEM
 LIFE IS CONSISTENT WITH THE LAWS OF
PHYSICS
 PHYSICS DOES NOT PREDICT LIFE
 LIVING CELLS COME FROM OTHER
LIVING CELLS
 AN ORGANISM MUST INVOLVE CLOSED
LOOPS OF CAUSALITY
 LIFE DOES INVOLVE PURPOSE: See Into
the cool
Complexity is inescapable even in
reductionism
 Thermodynamics is an example of how
attempts to remove complexity from
reductionist thought can not succeed
 The nature of thermodynamic reasoning had
resisted this tendency very well and we will
look at why this is so
SOME CONSEQUENCES
 REDUCTIONISM DID SERIOUS DAMAGE
TO THERMODYNAMICS
 THERMODYNAMICS IS MORE IN
HARMONY WITH TOPOLOGICAL
MATHEMATICS THAN IT IS WITH
ANALYTICAL MATHEMATICS
 THUS TOPOLOGY AND NOT MOLECULAR
STATISTICS IS THE FUNDAMENTAL TOOL
EXAMPLES:
 CAROTHEODRY’S PROOF OF THE
SECOND LAW OF THERMODYNAMICS
 THE PROOF OF TELLEGEN’S THEOREM
AND THE QUASI-POWER THEOREM
 THE PROOF OF “ONSAGER’S”
RECIPROCITY THEOREM
THE NATURE OF THERMODYNAMIC REASONING
 THERMODYNAMICS IS ABOUT THOSE
PROPERTIES OF SYSTEMS WHICH ARE
TRUE INDEPENDENT OF MECHANISM
 THEREFORE WE CAN NOT LEARN TO
DISTINGUISH MECHANISMS BY
THERMODYNAMIC REASONING
NETWORKS IN NATURE
 NATURE EDITORIAL: VOL 234, DECEMBER 17,
1971, pp380-381
 “KATCHALSKY AND HIS COLLEAGUES SHOW,
WITH EXAMPLES FROM MEMBRANE SYSTEMS,
HOW THE TECHNIQUES DEVELOPED IN
ENGINEERING SYSTEMS MIGHT BE APPLIED TO
THE EXTREMELY HIGHLY CONNECTED AND
INHOMOGENEOUS PATTERNS OF FORCES AND
FLUXES WHICH ARE CHARACTERISTIC OF CELL
BIOLOGY”
THERMODYNAMICS OF OPEN
SYSTEMS
 THE NATURE OF THERMODYNAMIC
REASONING
 HOW CAN LIFE FIGHT ENTROPY?
 WHAT ARE THERMODYNAMIC
NETWORKS?
DISSIPATION AND THE SECOND LAW
OF THERMODYNAMICS
 ENTROPY MUST INCREASE IN A REAL
PROCESS
 IN A CLOSED SYSTEM THIS MEANS IT
WILL ALWAYS GO TO EQUILIBRIUM
 LIVING SYSTEMS ARE CLEARLY “SELF ORGANIZING SYSTEMS”
 HOW DO THEY REMAIN CONSISTENT
WITH THIS LAW?
HOW CAN LIFE FIGHT
ENTROPY?
 DISSIPATION AND THE SECOND LAW OF
THERMODYNAMICS
 PHENOMENOLOGICAL DESCRIPTION OF
A SYTEM
 COUPLED PROCESSES
 STATIONARY STATES AWAY FROM
EQUILIBRIUM
PHENOMENOLOGICAL
DESCRIPTION OF A SYTEM
 WE CHOSE TO LOOK AT FLOWS
“THROUGH” A STRUCTURE AND
DIFFERENCES “ACROSS” THAT
STRUCTURE (DRIVING FORCES)
 EXAMPLES ARE DIFFUSION, BULK FLOW,
CURRENT FLOW
A GENERALISATION FOR ALL
LINEAR FLOW PROCESSES
FLOW = CONDUCTANCE x FORCE
FORCE = RESISTANCE x FLOW
CONDUCTANCE = 1/RESISTANCE
COUPLED PROCESSES
 KEDEM AND KATCHALSKY, LATE 1950’S
 J1 = L11 X1 + L12 X2
 J2 = L21 X1 + L22 X2
STATIONARY STATES AWAY FROM EQUILIBRIUM
AND THE SECOND LAW OF THERMODYNAMICS
 T Ds/dt = J1 X1 +J2 X2 > 0
 EITHER TERM CAN BE NEGATIVE IF THE
OTHER IS POSITIVE AND OF GREATER
MAGNITUDE
 THUS COUPLING BETWEEN SYSTEMS
ALLOWS THE GROWTH AND
DEVELOPMENT OF SYSTEMS AS LONG
AS THEY ARE OPEN!
STATIONARY STATES AWAY
FROM EQUILIBRIUM
 LIKE A CIRCUIT
 REQUIRE A CONSTANT SOURCE OF
ENERGY
 SEEM TO BE TIME INDEPENDENT
 HAS A FLOW GOING THROUGH IT
 SYSTEM WILL GO TO EQUILIBRIUM IF
ISLOATED
HOMEOSTASIS IS LIKE A STEADY
STATE AWAY FROM EQUILIBRIUM
INLET VALVE
OUTLET
VALVE
ORIFICE CONNECTING TANKS
PUMP
RESERVOIR
IT HAS A CIRCUIT ANALOG
J
x
L
THE RESTING CELL
 High potassium
 Low Sodium
 Na/K ATPase pump
 Resting potential about 90 - 120
mV
 Osmotically balanced (constant
volume)
WHAT ARE THERMODYNAMIC
NETWORKS?
 ELECTRICAL NETWORKS ARE
THERMODYNAMIC
 MOST DYNAMIC PHYSIOLOGICAL
PROCESSES ARE ANALOGS OF
ELECTRICAL PROCESSES
 COUPLED PROCESSES HAVE A NATURAL
REPRESENTATION AS MULTI-PORT
NETWORKS
ELECTRICAL NETWORKS ARE
THERMODYNAMIC
 RESISTANCE IS ENERGY DISSIPATION
(TURNING “GOOD” ENERGY TO HEAT
IRREVERSIBLY - LIKE FRICTION)
 CAPACITANCE IS ENERGY WHICH IS
STORED WITHOUT DISSIPATION
 INDUCTANCE IS ANOTHER FORM OF
STORAGE
A SUMMARY OF ALL LINEAR
FLOW PROCESSES
PROCESS
FLOW
J
DIFFUSION
n /t
BULK FLOW Q
FORCE
CONSTANT
C=C1-C2
P
p=p1-p2
LP
V=V1-V2
G
v/t
CURRENT
I
MOST DYNAMIC PHYSIOLOGICAL PROCESSES
ARE ANALOGS OF ELECTRICAL PROCESSES
L
J
x
C
COUPLED PROCESSES HAVE A NATURAL REPRESENTATION AS
MULTI-PORT NETWORKS
J2
L
J1
x2
x1
C2
C1
An Epithelial Membrane in
Cartoon Form:
A Network Model of Coupled Salt and
Volume Flow Through an Epithelium
REACTION KINETICS AND
THERMODYNAMIC NETWORKS
 START WITH KINETIC DESRIPTION OF
DYNAMICS
 ENCODE AS A NETWORK
 TWO POSSIBLE KINDS OF ENCODINGS
AND THE REFERENCE STATE
EXAMPLE: ATP SYNTHESIS IN
MITOCHONDRIA
EH+ <--------> [EH+]
H+
[H+]
E <-------------> [E]
S
P
E
MEMBRANE
EXAMPLE: ATP SYNTHESIS IN
MITOCHONDRIA-NETWORK I
IN THE REFERENCE STATE IT
IS SIMPLY NETWORK II
L22-L12
L11-L12
J2
J1
x1
L22
x2
THE SAME KINETIC SYSTEM HAS AT LEAST TWO
NETWORK REPRESENTATIONS, BOTH VALID
 ONE CAPTURES THE UNCONSTRAINED
BEHAVIOR OF THE SYSTEM AND IS
GENERALLY NON-LINEAR
 THE OTHER IS ONLY VALID WHEN THE
SYSTEM IS CONSTRAINED (IN A
REFERENCE STATE) AND IS THE USUAL
THERMODYNAMIC DESRIPTION OF A
COUPLED SYSTEM
SOME PUBLISHED NETWORK MODELS OF
PHYSIOLOGICAL SYSTEMS
 SR (BRIGGS,FEHER)
 KIDNEY
 GLOMERULUS (OKEN)
(FIDELMAN,WATTLING
TON)
 FOLATE METABOLISM
(GOLDMAN, WHITE)
 ATP SYNTHETASE
(CAPLAN,
PIETROBON, AZZONE)
 ADIPOCYTE
GLUCOSE
TRANSPORT AND
METABOLISM (MAY)
 FROG SKIN MODEL
(HUF)
 TOAD BLADDER
(MINZ)
CONCLUSIONS
 THE REAL WORLD IS COMPLEX
 THE WORLD OF “SIMPLE MECHANISMS” IS A
SURROGATE WORLD CREATED BY
TRADITIONAL SCIENCE
 WE ARE AT A CROSSROADS: A NEW
WORLDVIEW IS NEEDED
 THERE WILL ALWAYS BE RISK ASSOCIATED
WITH ATTEMPTS TO PROGRESS
 YOUR CRYSTAL BALL MAY BE AS GOOD AS
MINE OR BETTER
POST SCRIPT
 WE LIVE IN A WORLD DOMINATED BY COMPUTERS
 MOST COMPLEXIFIERS BELIEVE THAT COMPLEXITY IS
SOMETHING WE CAN DEAL WITH ON THE COMPUTER
 THIS NOTION OF COMPLEXITY FOCUSES ON THE
MECHANICAL ASPECTS OF THE REAL WORLD
 WHAT MAKES THE REAL WORLD COMPLEX IS ITS NONCOMPUTABILITY