Why Gliders Don't Exist:
Anti-Reductionism and Emergence
Joe Faith
School of Cognitive and Computing Sciences
University of Sussex, Brighton, UK.
[email protected]
Abstract
ALife has always been centrally concerned with the
nature and origins of emergent phenomena and their
anti-reductionist implications for our understanding
of complex systems. I argue that the traditional
approach to understanding emergent phenomena in
physical systems is still fundamentally reductionist,
and outline an anti-reductionist alternative.
Keywords: philosophy; philosophy of articial life;
anti-reductionism; emergence
Contemporary debate about emergence can only be
understood as part of the much older debate about
reductionism. Indeed much of the importance of, and
interest in, the question of emergence in Articial Life
is because of the light that it can shed on this much
wider issue.
The central point of this paper is that the usual arguments against reductionism are too weak, that they
concede a crucial part of the reductionist case, and
that a more radical approach is required. When we
apply these arguments to the question of emergence
we nd that the usual models of emergent phenomena
are awed, and that an alternative is needed.
Pragmatic Anti-Reductionism
The central claim of reductionism is that if all phenomena are on every occasion physically realised, then
the laws governing those phenomena are determined
by, and derivable from, the laws governing their constituent parts. Does a materialist have any alternative
but to accept this priority of lower level entities over
those they comprise?
The usual alternative to reductionism is some form
of pragmatic anti-reductionism which argues that although reductionism may be correct in principle, it
can rarely be used in practise: it is simply not feasible
to collect all the data, and perform the calculations
necessary, for all but the most trivial of systems. In
other words, that the properties of the whole may be
determined by those of the parts, but it is (usually)
impossible for us to derive them.
Basic pragmatic anti-reductionism can be strengthened in various ways. We can borrow from chaos theory and argue that aggregate properties of the system
may be sensitive to some properties of a part, such
as the infamous sensitivity of weather systems to a
buttery's wing. If this is the case then an accurate
derivation of a higher level description would require
that the properties of the parts are known with unbounded accuracy, and there are various reasons, such
as the Uncertainty Principle, why this is not possible.
A pragmatic anti-reductionist can also argue that
just knowing the properties of the parts is not enough
to derive higher level properties; we also have to know
the composition of the higher level entities that we
are interested in, i.e. a set of bridging laws. Thus although the set of valid higher level descriptions may be
determined by the lower level properties, they cannot
be discovered or derived without additional knowledge.
Thus we nd that there is not a single case in the history of science in which a higher level scientic law or
description has been derived from laws governing its
constituent parts; rather such phenomena are discovered by investigation at the appropriate level and only
subsequently related to lower level properties.
The problem with pragmatic anti-reductionism is
that it implies that as soon as we can discover some systematic relationship between phenomena at higher and
lower levels of organisation, then the status of the former is threatened. They become potentially reducible,
or reducible in principle. Pragmatic anti-reductionism
fails to rebut the central reductionist claim that higher
properties are determined by, even whilst they may not
be derivable from, the lower. Is there an alternative
anti-reductionism that can?
Principled Anti-Reductionism
Let us consider the particular example of the gas laws.
This is a locus classicus of emergent behaviour and
exemplies many of the properties found in the more
complex models used in ALife. Understanding the relationship between the bulk gas laws and the collisions
of individual particles was a triumph of reductionism,
so hopefully by questioning this example I can cast
doubt on reductionism as a whole.
The reductionist picture of how gases behave is that
a property such as pressure is an intrinsic property of
the gas as a whole that rises with temperature and produces a force exerted on the container wall. This latter
property is supervenient upon the set of molecular momenta, each of which is a prior property, intrinsic to
each molecule, and determining the course of its collisions. The pressure is then equal to, and determined
by, the mean of the set of momenta of molecules in a
given volume.
The pragmatic anti-reductionist would argue that
we cannot measure the momentum of every single
molecule in practise. However they would (probably)
concede that the derivations on which statistical thermodynamics are based are theoretically sound. Therefore the pragmatic anti-reductionist must agree with
reductionist that the properties of the whole gas are
not only determined by, but also derivable from, those
of the molecular parts in this case. Therefore the gas
laws are a case in which the reductionist and pragmatic
anti-reductionist agree.
However there are two key dierences between the
reductionist idealisation and how things work in real
life.
The rst is that in real life gas molecules do not behave like atomistic billiard balls, but are complex structured entities. Van der Waals forces between adjacent
electron clouds mean that the molecular collisions are
not perfectly elastic, but instead are slightly `lossy',
with the exact behaviour being dependent on the particular physical characteristics of the molecules, and
on the velocity and direction of the collision. Indeed,
as the temperature drops, the molecules can stop rebounding at all and instead form weak bonds as the gas
condenses or even crystallises. The gas laws are an approximation, describing `ideal' gases whose molecules
collide perfectly elastically under all conditions. In
short, the pressure of a real gas is not equal to its
mean molecular momentum.
The second problem is that, in real life, volumes of
gas are not in static, isolated, thermal equilibrium. As
Feynman puts it,
we shall nd that we can derive all kinds of things
| marvelous things | from the kinetic theory,
and it is most interesting that we can apparently
get so much from so little. . .. How do we get so
much out? The answer is that we have been per-
petually making a certain important assumption,
which is that if a system is in thermal equilibrium
at some temperature, it will also be in thermal
equilibrium with anything else at the same temperature. (Feynman 1963, p40-1)
So what happens if the system is not in equilibrium?1
The easiest way to nd out is to compress it. As soon
as we do this the measured pressure will rise. As we
continue to push we do work in compressing the gas,
and this energy diuses through the gas and raises
the mean molecular momentum per unit volume. The
properties of the parts are therefore causally dependent
on those of the wholes. The constituent molecules have
the momentum that they do because of the pressure on
the whole. The dependency only appears to run the
other way when the system is static.
The purpose in these examples is not nit pick, or to
criticise the classical reductionist understanding of the
gas laws per se, but to make explicit the assumptions
that it depends on. In particular it is only accurate to
say that properties of parts determine those of wholes
when the entire system is in a narrow range of thermal
equilibria. Outside of these specic cases it is equally
true to say that the properties of parts are determined
by those of the whole, in contrast to both reductionism
and pragmatic anti-reductionism. Therefore the `upward' dependency on which reductionism depends is
an artefact of how we choose to model a system, not a
property of the system itself.
Reductionism
(including
pragmatic anti-reductionism) is often seen as a necessary
implication of physicalism (Melnyk 1995). After all, if
every object is instantiated in a set of lower-level parts,
then it seems obvious and necessary that the properties of those parts will determine those of the whole.
But this statement of physicalism neglects that every
object is also situated in an overall context, and that
it will only have the properties it does because of that
context. The causal dependence between parts and
wholes goes down, as well as up.
Emergence
Following Nagel (Nagel 1961) the relationship between
levels of organisation in nature has increasingly been
described in terms of emergence, and more recently
the sciences of complexity and articial life have made
emergent phenomena their special area of concern.
Within ALife, emergent phenomena have usually been
understood in terms of what Casti and others have
1
The study of non-equilibirum systems has been largely
neglected, with the notable exception of Prigogine (Prigogine 1962).
called complex adaptive systems, indeed Langton has
described such systems as the \distilled essence of articial life"(Langton 1988). Such systems start with
a collection of well-dened objects each with intrinsic
individual properties and governed by laws. These interact, producing an overall behaviour which is then
described as emergent since it is not explicitly dened
in any of the rules governing any part, but rather is the
novel product of the interaction of them all. A typical
example is the higher level behaviours of gliders and
blinkers in Conway's Game of Life. A great deal of energy is then spent trying to dene precisely what sort
of higher order entities should count as emergent and
which as reducible, usually by trying to pin down the
intuitive notions of \explicit" or \novel".
Understood this way, emergent phenomena t a
category-theoretic commutativity diagram:
X (t)
B
6
F- X (t + 1)
6
B
f x(t + 1)
in which the states of the lower and upper levels are
described by x(t) and X (t) respectively, the trajectory
of the lower level is described by the state equation
x(t + 1) = f (x(t)), the upper by X (t + 1) = F (X (t)),
and the synchronic bridging law describing the composition of the higher entities in terms of the lower by
X (t) = B (x(t)). In some cases, such as Life, the lower
state equation is exact, quantitative and deterministic, whereas the higher level rules, such as \eaters tend
to destroy blinkers", are statistical and qualitative. In
other cases, such as the model of an ideal gas used to
derive the gas laws, the higher will also be exact.
The commutativity of the diagram is ensured by the
fact that F is determined by B and f , since it is that
mapping that satises FB = Bf | though F will only
be formally derivable if B is invertible. In other words,
if there are a set of laws governing the behaviour of the
objects at the lower level then, given the composition of
an aggregate, the behaviour of that aggregate is determined. Therefore higher-level behaviours produced in
this way can never count as truly emergent, but rather
are determined by the properties of the atomistic objects. Many aspects of the higher behaviour may not
be analytically derivable from those of the parts, and
must be discovered through empirical computer experiments; but this is just a failure of our analysis and does
not mean that they are not determined by the lower
x(t)
properties. Such higher level behaviours are emergent
in only an epistemic sense; only for a pragmatist, such
as Dennett, will they also be ontologically emergent
(Dennett 1991).
I do not wish to make this a terminological dispute:
if we wish to describe phenomena such as gliders as
emergent, then so be it. However, in this case we can
no longer associate emergent with non-reducible, and
if we want to be anti-reductionist about physical phenomena, then we have to nd a dierent way of understanding them than emergence as it is traditionally
used. Also note that this is not a criticism of the study
of systems such as Life per se; after all they are a fascinating class of formal system, and can give us clues
about the origins of much natural pattern and order.
The problem comes when they are used as the sole intuition pump and model for understanding emergence,
reductionism, and the relationship between levels of
organisation in natural systems. But what is the alternative?
Consider this example. Every cell in an organism
carries exactly the same genome as every other. However in, say, a mammal, there will be around 300 different types of cells | blood cells, hair cells, liver cells,
and so on | depending on which genes are expressed.
When a new cell is produced, why does it become one
type of cell rather than another? There are two sorts of
answer. The rst points to the particular biochemical
mechanisms in the new cell's environment that caused
particular genes to switch on. The second identies
the cause at a higher level: a cell becomes a liver cell
because it is born in a liver, and so on. Both of these
stories are correct. There is no conict between them
and which one we choose to tell depends on what aspects of development we want to understand. The latter explains how the body maintains a stable overall
structure despite individual cell death. The former explains how this is achieved in a particular case. The
lower level story is not `more right' than the higher, and
nor is the higher assymetrically dependent on the latter. The reductionist intuition is to say that given the
range of biomolecular mechanisms, then the eects of
the liver context are xed. But this misses the fact that
if it were not for the presence of the entire liver, then
those mechanisms would not be produced in the rst
place. Indeed it was precisely the problem of restoring
the totipotency of dierentiated cells | and so neutralising the eect of the context upon them | that
made the cloning of adult mammals seemingly impossible. Even now that it has been done with a particular
group of cells taken from the udder of a sheep we still
have very little idea of how the process works, how to
make it reliable, or whether the technique will gener-
alise to cells taken from other contexts.
In the case of Life, the rules governing the fate of
a cell are written in lower level terms such as \a cell
will not survive into the next generation if it has no
neighbours". In practise the fate of a particular cell
will be instrumentally dependent on its context, but
this dependence is derived from the more fundamental
dependence expressed in formal atomistic terms. In
other words, the fate of a particular cell will be dependent on its position within a glider or blinker, but
only because the future state of a cell is a function of
the number of neighbours that it has, and gliders and
blinkers are made from dierent arrangements of cells.
The future of a cell is not aected by its position within
a glider qua glider.
In general the reductionist approach is to start with
a set of deterministic laws governing the atoms of the
system expressed as functions of atomistic properties.
We can then derive | if not formally then at least
empirically | qualitative, statistical, rules governing
higher level objects expressed only in terms of higher
level properties. However, if we accept that these latter rules are real, then we should also accept that distal
rules that describe the fate of cells in terms of the properties that they are part of, are also real. For example
\a cell that is part of a blinker will tend to go into the
reverse state in the next generation", \a cell that is
part of an aggregate that is attacked by an eater will
soon die" (or \cells born in livers become liver cells").
These downward rules, which attribute the cause of
the fate of the part to the properties of the whole, may
be qualitative and non-deterministic, but no more so
than the derived higher level rules that we all wish to
defend; and they should be accorded the same status.
In the case of physical systems we are not presented
with a set of laws, but with a set of empirical regularities: the job of the scientist is then to nd accurate
ways to describe and account for those regularities in
descriptive laws. If we want to describe a physical system in such a way that preserves the non-reducible and
non-eliminable nature of its emergent phenomena we
should therefore include three sorts of laws: atomistic
laws that describe the interactions of parts; `bridging'
laws that describe the composition of higher order entities in terms of their parts; and `downwards' laws
that describe how properties of those entities act as
contexts to aect their parts.
We also need to be careful how we individuate the
parts, as this too can be dependent on the context.
In Life, for example, `a cell' usually refers to a value
ascribed to a xed coordinate position; `the fate of a
cell' then refers to what happens at that position in
the future. However we could also refer to a cell by
reference to the higher order object that it is part of.
For example, we could refer to `the cell' at the nose of
a glider even as it traverses the grid, occupying a series
of positions. If we individuate the parts of the system
in this way | a way which is irreducibly dependent
on prior individuation of higher level objects | then a
whole new type of order is revealled. The xed coordinate positions only seem like the `real' cells compared
with the `virtual' mobile ones because of the way the
formal system is dened. In nature there are no such
given formal rules.
Conclusion
The starting-point of reductionism is that wholes are
dependent on parts, but not vice versa. This assumption is also carried over into traditional models of emergent phenomena, such as the Game of Life. Pragmatic
anti-reductionism agrees with this starting point but
denies some of the implications that a reductionist
draws, such that there are higher properties and behaviours of a system that cannot be analytically derived from those of the parts.
A more principled anti-reductionism holds that
properties are held by objects in, and because of, their
context; which implies that the dependence relation
between levels of organisation is symmetrical. According to this reductionism is not just wrong in practise,
but wrong in principle.
New assumptions about the relationship between
levels of organisation in nature require new models to
describe them. Therefore if we want to understand
emergent phenomena in nature, then we will need models in which ontological symmetry between levels is
built into their formal denition.
Acknowledgement
Thanks to members of the E-Intentionality discussion
group at the University of Sussex for comments on an earlier draft of this paper.
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