Uncertainty, Emergence, and Statistics in Dendrochronology - Dendroclimatology - page 84

species. However, its occurrence over a broad range of taxa growing in extremely
diverse habitats worldwide indicates that crossdating is a property of tree growth
that frequently emerges from the radial growth increments of trees being subjected
to a highly variable set of microenvironmental conditions that contain within it a
secondary set of common external growth-limiting factors.
The principle of emergence in biological systems might be regarded as a funda-
mental flaw in the current state of biological theory, one that could be eliminated
if biologists knew how to develop exquisite mathematical models with high predic-
tive skill, like those produced by physicists using classical reductionist methods to
explain much of the physical world. However, the physical world is also filled with
emergent properties that can never be predicted from underlying theory, even in
principle. This fact was pointed out by the great evolutionary biologist Ernst Mayr,
in a May 1997 interview published in the magazine Natural History (Angier 1997 ) :
It's now so clear that every time you have a more complex system, new qualities appear
that you could not have predicted from the components. That's the principle of emergence.
I once gave a lecture in Copenhagen, and I said something I now realize to be wrong. I said
emergence is characteristic only of biology. That was in 1953, when emergence was very
suspect, nobody believed it. The famous physicist Niels Bohr got up to object, and I thought
he'd say emergence was metaphysical and supernatural and all sorts of things. Instead he
said, 'We have emergence all over the inanimate world,' and he gave the famous example of
water. If you know all the characteristics of hydrogen and all the characteristics of oxygen,
you still couldn't predict that the product would be liquid.
Mayr went on to say, 'So that's the end of reductionism' (Angier 1997 ) , a highly
provocative statement that is admittedly not readily accepted by many physicists
and biologists who are still committed to reductionism in science.
Among others, Hatcher and Tofts ( 2004 ) have countered Ernst Mayr's provoca-
tive statement in their recent paper Reductionism Isn't Functional . In it, the authors
propose a solution to the emergence-versus-reductionism problem based on a math-
ematical theorem in concurrency theory, a branch of theoretical computer science.
This theorem 'proves that all possible systems can be reasoned about in terms of
their subcomponents' based on methods of process algebra. Doing the modeling
this way replaces underlying functions with objects, 'i.e., every object in the system
is represented by an object in the model' (Hatcher and Tofts 2004 ) . This approach
accepts the validity of constitutive reductionism in biology, which states that 'sys-
tems are composed of systems or entities at a lower level and conform to the laws
governing the latter' (Hatcher and Tofts 2004 ) . If this statement is true, then object-
based methods of process algebra naturally lead to the conclusion that 'all systems
can be explained in terms of the sum (composition) of their parts' (Hatcher and Tofts
2004 ) . This conclusion thus formally rejects the fundamental premise of emergence,
i.e., the whole is greater than the sum of its parts, which allows for completely unex-
pected properties to emerge from the collective. Because constitutive reductionism
is based on 'objects' and not 'functions,' it differs from classical explanatory reduc-
tionism used in theoretical physics to deduce higher-order properties from more
fundamental processes. In this sense, constitutive reductionism is a weaker form of
reductionism, with little or no implied deductive ability.