First - his take-home message is that our reductionist
approaches (which include our complete scientific
training) render invisible the main organizational
aspect of life. His Relational Biology is an attempt to
make this organizational aspect (which he calls
complexity) visible and understandable. For many this
is like trying to describe visual perception to a person
who has been blind from birth.
Second - His conceptual proofs come from an obscure
branch of mathematics called category theory (of
which most of us are not acquainted). He even uses
the axioms of category theory in ways that seem alien
to most mathematicians. (Most mathematicians are
also reductionists)
Third - Unfortunately, as has been pointed out, LI contains
many typo's. There are many Greek symbols that are
accidentally switched and mixed up in his narrative
and diagrams. It is almost necessary to have a fairly
good idea of what he is trying to say before reading
his arguments to understand what he is saying. But I
have seen no conceptual errors in the book.
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Introduction to Complexity
by Jeff Prideaux
Abstract: Intuitively, we consider biological organisms to
possess organizational properties that are somewhat different
than man-made machines. Never-the-less, all of our
mechanistic models of biological sub-systems are simulatable
by man-made machines (computers). If this is always the
case, then it would suggest that biological organisms are
actually not fundamentally different than man-made machines
(which violates our intuition). This research-in-progress paper
explores the organizational properties of organisms and
machines and makes the conclusion that organisms possess
causal organizational properties that are fundamentally
different than man-made machines. This paper makes a
definition of complexity based on these differences.
Organisms will contain complex properties whereas machines
will not. A strategy of constructing a realization of a man-
made complex device will be suggested. If successful, then
any conceptual limitations of the experimental method could
be seen without the confounding complicatedness of natural
biological systems.
Introduction:
Complexity has become a much discussed topic (1,2)
from systems as diverse as protein folding, to eco-systems to
the stock market but unfortunately a precise definition of
complexity has been illusive. Complexity is routinely
associated with how complicated a system is (the number of
interacting parts and their interrelationships). This paper
takes the position that complicatedness and complexity are
really two different things. While some systems (example
biological) are both complicated and complex, it is possible to
arrive at a definition of complexity independent of
complicatedness.
For the discussion of the differences between
organisms and machines, it is necessary to identify
characteristics that all organisms share and also define
rigorously what is meant by a man-made-machine. This
paper will follow the same line of argument Robert Rosen
used in his book Life Itself (3). Machines would include such
man-made devices as cars, televisions, and computers.
Complex systems (organisms) would include, for example,
Prokaryotes and Eukaryotes. (Im leaving open the
possibility of non-biological organisms). All organisms share
the property that the functional molecules of their material
make-up (the proteins, fatty acids, etc.) are fabricated from
internal processes in the organism itself. One could say that
the functional hardware of the organism is continually
changing as new protein is translated and other molecules
synthesized.
Machines, on the other hand, have their functional
hardware designed from outside the machine itself (usually by
a human). Machines all have functional components that are
not defined from within.
It is helpful to go back to Aristotle for a consideration
of causality. Aristotle defined four causes that answer the
question "why" about systems: material, efficient, formal, and
final. The following describes the difference in explaining the
causality of a component of a man-made machine and a
component of a biological organism.
Material cause - The material substance of which the
component is constructed.
Man-made machine - All materials come from outside the
system.
Biological organism - Material may be from products of
other parts of the system.
Efficient cause - The labor or agent responsible for putting or
bringing the material aspects together.
Man-made machine - Put together by a human outside the
system.
Biological organism - Assembled by other components
inside the system.
Formal cause - The plan or internal organization responsible
for guiding or regulating the efficient
causation.
Man-made machine - The plan (or algorithm) developed
from outside the system.
Biological organism - The organization is intrinsic to the
system itself.
Final cause - The need for the sub-component.
Man-made machine - There must be a reason (from
outside) for the component to be
there.
Biological organism - The reason for the component is
from within the system.
In short, every component in a biological organism will have
an explanation due to efficient cause from within the
organism. This will not be the case for a man-made device
unless the person is considered part of the system.
The origins for the methods used in this paper were
developed by Rashevsky (4) and Rosen (5,6) back in the
1950's. Its a technique of studying biological systems called
relational biology. It is only through these techniques that
certain organizational relationships (such as the efficient
cause) become apparent.
Rosen (3), proposed relational diagrams (not shown)
in which every component, except the environmental input,
has an explanation due to efficient cause from within the
diagram. All that is explicitly included in Rosen's relational
diagrams are arrows representing material and efficient cause.
Formal and final cause are implicitly embedded in how the
arrows are connected.
In the language of enzymatic chemical reactions, the
material cause of some product molecule would be the
reactants. The efficient cause of the product molecule would
be the enzyme. To attach some biological meaning to these
concepts, consider the following three classes of functional
biological molecules: nucleic acid polymers, proteins,
individual amino and nucleic acids:
A closed efficient causal explanation of them would be the
following:
nucleic acid polymers
Material Cause = nucleic acids
Efficient Cause = DNA polymerase (a protein)
protein
Material Cause = amino acids
Efficient Cause = nucleic acid polymers
individual amino and nucleic acids
Material Cause = nutrient molecules
Efficient Cause = proteolytic enzymes (proteins)
Note that each of these classes of functional biological
molecules has an explanation (due to efficient cause) by one
of the other classes within the system.
Rosen (3) defines a complex system as a system in
which every functional component has an explanation due to
efficient causation from within the system. Systems where
not every component is explained by efficient causation will
be referred to as simple systems.
It is the premise of reductionism that all systems are
made up of separate parts and that through isolating and
understanding these parts, we can understand the whole. The
first aspect of reductionism is the identification of the
functional parts (while they are still part of the whole). This
is done through measurement and will be called the analytic
stage. The second aspect to reductionism is to conceptually
isolate these parts and then re-synthesize the whole by putting
these parts back together (the synthetic stage).
Reductionism thus claims that analytic = synthetic.
Step 1: identify the parts; step 2: figure out how the isolated
parts interact together. It is necessary in reductionism that
the parts can be isolated...that they can exist (have a
definition as for their functionality) independent of the whole
system. Otherwise, one could not form mechanistic models
of sub-systems of a larger system. If a stand-alone definition
(independent of the whole system) of a functional component
can be found, then a mechanistic model can be determined
that describes the functionality (input-output characteristics)
of that component. Thus, multiple mechanistic models can be
interconnected into larger and larger models until ultimately
one largest model can describe the complete system.
This is what we are doing in biology: identifying
separate mechanistic models and then concatenating them
into larger models. It may take millions of mechanistic
models (descriptions) to completely describe a biological
system (such as man) but reductionism (as a scientific
strategy) claims that it is at least theoretically possible to
form a complete description with a finite number of isolated
mechanistic models. Rosen (3) claims, though, that this is not
theoretically possible with reductionism and that we must
move beyond simple reductionist techniques to fully
understand biology. Reductionism fails as a paradigm for
complex systems. It only works for systems that aren't
complex.
Rosen goes through an argument (that helps to have
the accompanying relational diagrams) where it is shown that
a finite mechanistic description is not possible with a truly
complex system. An infinite regress forms if one uses only
isolated separable parts. This is a definition of a complex
system. It cannot be represented by a finite direct sum
(synthetic) model where all the components can be divided
into separate disjoint sets.
In a complex system there is not the restriction of
having analytic = synthetic. This means that some
components will not be able to be partitioned into disjoint
sets. The sets (components) would forever overlap. This
means that some parts making up one functional component
are also parts making up another functional component. The
two functional components, although they are performing
different functions, share some common physical material and
can not be completely separated (analytic doesn't equal
synthetic). This distinction also invalidates computer
simulation (which only pays attention to functionality and
ignores the material make-up) as a way of understanding
complex systems.
In Summary:
To fully understand a complex system, one must ask
two questions about every component of the system.
1. What were the reactants that formed the component? (the
material cause)
2. What was the enzyme that facilitated the above mentioned
reaction? (the efficient cause)
Note that there can be multiple reactants in a reaction
and there can be an enzyme complex with multiple subunits
that compose the enzyme. System functionality can exist at
many different hierarchical levels from single enzymes to
enzyme complexes to neuronal sub-circuits to eco-systems
and human societies.
Without a definition of complexity, it is possible to
manipulate complex relationships in two ways:
1 - Take a pre-existing complex system and manipulate
some of its parts to change its behavior. An example
would be transfecting some viral genome into a living
cell. New protein may end up being translated. This
is the type of thing we do in molecular biology.
2 - Form networks that consist of pre-existing complex
parts. For example the Internet has people (who are
complex) as some of its parts. This larger super-
organism (with people as parts) can express complex
behavior.
In both cases, we are working with complex pre-existing
entities of which we have no definition. Manipulation,
although useful, isnt understanding.
Rosen tries to define and understand complexity (or
life itself).
(1) Roger Lewin, Complexity, Life at the Edge of Chaos,
Collier Books, Macmillian Publishing Company, New
York, 1992.
(2) Mitchell M. Waldrop. Complexity: the emerging
science at the edge of order and chaos. Simon &
Schuster, New York, 1992.
(3) Robert Rosen, Life Itself: A comprehensive inquiry
into the nature, origin, and fabrication of life.
Columbia University Press, New York, 1991.
(4) Robert Rosen, "A relational theory of biological
systems", Bulletin of Mathematical Biophysics, 20,
245-60, 1958.
(5) Robert Rosen. "A relational theory of biological
systems II." Bulletin of Mathematical Biophysics,
21, 109-128, 1959.
(6) Nicholas Rashevsky , "Topology and Life." Bulletin
of Mathematical Biophysics, 16, 317-48, 1954.