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\newcommand{\autor}{Xabier Barandiaran}
\newcommand{\emailautor}{xabier@barandiaran.net}
\newcommand{\urlautor}{http://barandiaran.net}
\newcommand{\colectivo}{\textsf{Autonomía Situada}}
\newcommand{\urlcolectivo}{http://sindominio.net/autonomiasituada}
\newcommand{\emailcolectivo}{grey-walter@sindominio.net}
\newcommand{\titulo}{Complexity and evolutionary simulation models
in cognitive science}
\newcommand{\subtitulo}{Epistemology of synthetic bottom-up
simulation modelling}
\newcommand{\nomarch}{blending}
\newcommand{\titulocorto}{Complexity and evolutionary simulation
models}
\newcommand{\fecha}{26--06--03}
\newcommand{\anio}{2003}
\newcommand{\ultimaversion}{v.1.0}
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http://sindominio.net/\symbol{126}xabier/textos/}

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\author{
\textbf{\autor}\footnote{The ideas developed in this paper
have being originated in a paper working by Roberto Feltrero and
myself. Complete authorship of the present paper shall recognize
Roberto's contribution, specially on conceptual blending literature
and fruitfull discussion on the topics involved.} \\
\texttt{\emailautor}
\\ \texttt{\htmladdnormallink{\urlautor}{\urlautor}} \\ \\
%\texttt{xabier@sindominio.net} \\
%\texttt{http://sindominio.net/\symbol{126}xabier}\\
% -------------------------------
% UPV INGLES
%  PhD student on ``Philosophy, Science, Technology and Society'',\\
%  Departament of Logic and Philosophy of Science, \\
%  EHU-UPV University of the Basque Country, \\
%  Post Box 1249/20080 Donostia/San-Sebastian, Spain \\
% -------------------------------
% UPV CASTELLANO
%  Departamento de Lógica y Filosofía de la Ciencia, \\
%  EHU-UPV (Euskal Herriko Unibertsitatea, Universidad del País
%  Vasco), \\
%  Apartado de Correos 1249 / 20080 Donostia San Sebastian / Gipuzkoa
%  \\
% -------------------------------
% METABOLIK
%  Miembro de Metabolik BioHacklab \\
%  \texttt{metabolik@sindominio.net} \\
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%  Miembro de Autonomía Situada \\
%  \texttt{grey-walter@sindominio.net} \\
%  \texttt{http://autonomiasituada.org}
}

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\title{\titulo \\ \textit{\subtitulo}}

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{\footnotesize
\section*{Abstract}

In complex adaptive systems, where internal and external non-linear
interactions give rise to an emergent functionality, analytic
decomposition of component and isolated functional evaluation of them
is not a viable methodological practice. More recently, embodied
bottom-up synthetic methodological approaches have been proposed to
solve this problem. Evolutionary simulation modelling (specifically
evolutionary robotics) provides an explicit research methodology in
this direction. We argue and illustrate that the
scientific relevance of such methodology can be best understood in
terms of a double conceptual blending: i) a \emph{conceptual
blending} between structural and functional levels of description
embedded in the simulation; and ii) a \emph{methodological blending}
between empirical and theoretical work in scientific research.
Simulation models show their scientific value on: reconceptualization
of theoretical assumptions; hypothesis generation and proof of
concept. We conclude that simulation models are capable of extending
our cognitive and epistemological resources to (re)conceptualise
scientific domains and to establish causal relations between
different levels of description.


\section*{Keywords}
Scientific methodology, cognitive science, models, artificial life,
simulation of adaptive behaviour, emergence, epistemology,
explanation, conceptual blending, metaphors in science

} \normalsize

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\section*{Copyleft \textcopyleft}

\noindent
\textbf{\titulo .} \textit{\subtitulo .} \ultimaversion
\newline
\newline
\noindent
Copyright \copyright~\anio~\autor. \\
\noindent
Copyleft \textcopyleft~\anio~\autor:



% CREATIVE COMMONS ATTRIBUTION-NONCOMERCIAL-SHAREALIKE 1.0
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 The licensor permits others to copy, distribute,
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 This is not mean to be the full license but short guide of it.
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\noindent
\autor~(\anio) \titulo . \subtitulo . \ultimaversion . \textbf{url}:
\\ {\scriptsize{\texttt{\htmladdnormallink{
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\section{Structure and function: limits of traditional mechanistic
methodology in complex systems}


\subsection{Complexity and localisation}

The Cartesian method of divide and conqueer, the decomposition of a
system in components and their isolated analysis has long been the
mainstream methodological strategy of scientific enquiry on the
understanding of functional systems, i.e. mechanistic explanations.

In the field of cognitive science computational functionalism has
proceed by what \cite{bechtelandrichardson93} call a synthetic
top-down decompositional method, i.e. decomposing functional or task
related cognitive structures (perception, memory, reasoning,
action, etc.) dividing them into sub-components, and establishing a
set of computational relations among subsystems.

On the other hand neuroscientific research has
focused on neurophysiological decomposition of neural structures
and localisation of such functional cognitive components: an analytic
bottom-up approach.

We shall understand localisation (the main mechanistic explanatory
strategy) as a mapping between a physical structure (operationally
tractable set of variables, whether they are biochemical or
neurodynamic) and a functional structure (a set of computational
components). Advances on neurophysiology and computational
functionalism shall, in turn, end up providing us with such
mechanistic explanation if: a) we don't want to assume a metaphysical
dualism, and b) computational-functionalist interpretations of
cognitive behaviour are to be considered the `right' functional
interpretation among all the possible ones.

The problem arises when recent interest on complex systems has shown
that such methodology (decomposition and localisation) fails to
understand nonlinear systems \cite{langton91}. When the interactions
between components are non-linear the principle of aggregation or
localisation presupposed in traditional decompositional methods does
not hold. The system is more than the sum of its parts, the
superposition of isolated components does not give rise to the
essential properties of the whole system. It is the non-linear
interaction between components what  determines the properties of the
system creating a kind of \emph{structural complexity} where the
relation between function and structure cannot be established by the
traditional decompositional method; i.e. no mapping can be
established between functional components and structural
(neurophysiological) components.

% see harveyetal

In addition to this structural complexity we have an
\emph{interactive complexity} where the system interacts with its
environment in such a way that the overall functionality of the system
emerges from highly interactive loops. But things can go even worst
on complexity, as \cite{harveyetal97} put it: ``Interactions between
separate sub-systems are not limited to directly visible connecting
links between them, but also include interactions mediated \emph{via
the environment}'' (p.205).

As \cite{clark96, clark97} has pointed out the nature
of what he calls \emph{interactive emergence} seriously
compromises the classical computationalist definition of function by:
  \begin{itemize}
    \item The dissolution of functional structures
    in highly interactive loops between agent and
    environment.
    \item The dissolution of functional structures
    in distributed causal networks on the side
    of the agent's behavioural mechanism (neural
    networks).
  \end{itemize}

Thus in complex adaptive systems where internal and external
nonlinear interactions give rise to an emergent functionality
top-down functional or task decomposition and their structural
localisation is not a viable methodological practice. In
mathematical terms structural complexity is a consequence of the
impossibility of the analytic solution for the nonlinear differential
equations determining system behaviour and the high sensitivity of
the system to boundary conditions (when it exploit particular
features of the environment to achieve functionality) or the
opposite, the metaestability of the system under structural
perturbations, i.e. its self-regulating capacity.



\subsection{Complexity in cognitive science}

In the realm of cognitive science both aspects of emergent
functionality (the structural and interactive) gave rise to two
different radical modification of the orthodox
functionalist-computationalist
% citar fodor, putnam, block
research program \citep{fodor87, block96}. Concerning structural
emergence the PDP approach showed that cognitive processing was not
the output of sequential symbol manipulation procedures but the
outcome of highly distributed sub-symbolic  networks. The interactive
complexity has been highlighted by the more recent embodied and
situated approach to cognition \citep{brooks91a, brooks91b,
pfeiferandscheier99}.

What embodiment and situatedness illustrates
is that the way the specific adaptive function is achieved
involves a dynamic coupling between agent and environment
where no structure of the agent can be pointed to be
sufficient for the function to happen. We can contrast
this embodied and situated functionality, what Luc Steels
has called \emph{emergent functionality} \citep{steels91},
as opposed to \emph{hierarchical systems}. Hierarchical
systems are those where the system can be decomposed
into different components which perform isolated functions
by directly controlling the variables defining the function,
i.e. the structure of the mechanism and the function it
performs are codefined, localisation is possible. An example of a
hierarchical system is a motor engine where, for example, a valve
that controls the flow of oil to an engine performs it function by
directly manipulating the size of the gap through which the oil
flows.

\cite{bonabeauandtheraulaz95} show how
the manipulation of boundary conditions\footnote{
    According to \cite{bonabeauandtheraulaz95}
    \emph{boundary} conditions are those constraining lower-level
    processes to give rise to the ``proper'' emergent behavioural
    pattern. The internal local rules of a system (the neural
    network in an agent) are generally unspecific on their
    functionality. Extreme reductionism only considers internal
    explanations (logical/causal relationship defining
    functionality by means of their correspondence relation
    with the environmental variables defining the function) of
    the performance of a function.
  }
not defining
the function itself play a fundamental role in the performance
of emergent functions. Given an environment
$E=\{x_{1}, x_{2}, \ldots, x_{n}, \ldots, x_{m}\}$ and
the subset of environmental variables defining a function
$E_{n}= \{x_{1}, x_{2}, \ldots, x_{n}\}$ a function
is defined as $F(E_{n}) = dx_{1}/dt, \ldots, dx_{n}/dt$.
An structure $S$ performs the function F iff: $S(E)=F(E_{n})$.
What reductionists\footnote{Bonabeau and Theraulaz take for
reductionist those researches involved in the localisationist
program} presuppose is that $\{x_{n+1}, \ldots, x_{m}\}$ remains
constant, i.e. $\delta S / \delta x_{i} = 0 $ for $i= \{n+1, \ldots,
m\}$. In short: reductionists believe that the external variables of
those defining a function do not affect how a structure performs that
function. Embodiment and situatedness shows how agents exploit many
features of their body and environment (boundary conditions) to
perform functions which are not defined by those body/environment
features. In other words localisation (i.e. mapping between
structural and functional components) cannot succeed because the
system exploits interactive feed-back loops with environmental
features to satisfy functionality.

The way some adaptive systems exploit several environmental features
to perform functions and the highly interconnected and recursive
nature  of the causal network of their internal structure does not
allow for the traditional analytic methods to be successfully aplied.
Under this situation new methodologies has been proposed as suitable
tools to explore complex systems: what we will call \emph{synthetic
bottom-up simulation modelling}.

% Arbib and Seth could be cited.


\section{Synthetic bottom-up simulation modelling}

\subsection{The situated, synthetic bottom-up approach}

During the late 80s and early 90s a new methodological paradigm for
the study of complex adaptive systems came to being. Alife
\citep{langton91, bedau01} and situated robotics proposed a
bottom-up, situated and synthetic approach toward  the modelling of
complex systems. % citas ...

The approach is \emph{synthetic} because understanding of a systems
is expected to be achieved by building similar systems; i.e. by
synthesis rather than analysis. The approach is \emph{bottom-up}
because the functionality of the system is achieved as emergent from
structural local rules and local system environment interactions
rather than functional components and informational input-output
relations between them. Repeated and distributed
local interactions give rise to a global pattern of  system
behaviour, it is in this global pattern that functionality is found
and not in the local components of the system; i.e. there is no
mapping between structural components and functional components.
There is no explicit encoding of the global behaviour. Finally the
approach is \emph{situated}: systems are built in real or simulated
environments with direct sensory-motor links (i.e. input-output
relationships are not symbol based). This methodology is the core of
Alife techniques \citep{langton91, bonabeauandtheraulaz95, bedau01}
and embodied and situated robotics \citep{brooks91a, brooks91b,
pfeiferandscheier99}, among others. In order to understand the
scientific value of such methodology we shall focus on a well
established and successful specific methodology which is that of
evolutionary robotics \citep{harveyetal97, husbandsetal97,
nolfiandfloreano00} and Randall Beer's minimally cognitive behaviour
program \citep{beer01, slocumetal00}.


\subsection{Evolutionary Robotics and the minimally cognitive
behaviour program}

Since structural decomposition of a complex system fails to grasp the
essential local interactions that give rise to functional behaviour
synthesis looks  like a natural way to deal with such a problem, it
is on the synthesis that knowledge is achieved, on the manipulation of
parameters and local  rules while putting together the components of
the system. But the very  nature of complex systems makes its
synthesis a problematic issue, that's precisely the locus of
complexity and, unlike functionalist top-down synthesis, complex
systems are not manageable for human understanding\footnote{
``Recent research in the psychology of judgement indicates that humans
have great difficulty comprehending cases with more than a few
interacting variables. Humans \emph{cannot} use information involving
large numbers of components or complex interactions of components,
and even when the problem tasks are computationally tractable, human
beings \emph{do not} approach them in this way. Complex systems are
computationally as well as psychologically unmanageable for
humans'' \cite[p.27]{bechtelandrichardson93}, emphasis on the
original.}. As a solution to this problem artificial evolution has
been widely used to synthetize a functional system. A particular
case of this technique is given by evolutionary robotics and the
minimally cognitive behaviour program.

Evolutionary robotics and evolutionary simulation models have
successfully been applied to achieve a number of complex behaviours,
among them: plastic development \citep{floreanoandurzelai00,
floreanoandurzelai01}, robot team coordination and role allocation
\citep{quinnetal02}, communication \citep{quinn01}, shape recognition
\citep{cliffetal93} , pursuit and evasion \citep{cliffandmiller95},
acoustic coordination \citep{dipaolo00b}, learning
\citep{tucietal02}, adaptation to sensory inversion and other
sensorimotor disruptions \citep{dipaolo00}, active categorical
perception \citep{beer01}, short-term memory, self-nonself
discrimination, selective attention, attention switching,
anticipation of object movement \citep{beer96, gallagherandbeer99,
slocumetal00}, etc...

Evolutionary simulation model synthesis proceeds as follows:
\begin{enumerate}
\item Definition of a set of body, environment and neural structures
(unspecified on their parameter values).
\item Artificial evolution of parameters according to a given
fitness function.
\item Reproduction/simulation of system behaviour with numerical
methods.
\end{enumerate}


Body and environment can be real or simulated, in the last case
khepera like robots are usually simulated (i.e. circular two
dimensional robots with two wheels and different sensors) and the
resulting controll architecture exported to the real robot (not
without problems \citep{jakobietal95}). What is interesting for our
discussion is the structure of the neural controll architecture. The
basic structure of the neural network is generally a Continuous Time
Recurrent Neural Network CTRNN (which are in principle capable of the
dynamical behaviour of any other dynamical system with a finite
number of variables \citep{funakashiandnakamura93}). CTRNNs are
fully connected, recursive, dynamic (time and rate dependant),
controll architectures specified by the following state equation:

\begin{quote}
\begin{eqnarray}
  \tau_{i} \dot{y}_{i} = -y_{i} + \sum_{j=1}^n(w_{ij}z_{j}) +
  g_{i}\sum_{k=0}^{5} s_{ki}I_{k}~; \nonumber\\
  \textrm{where}~~~z_{j} = \frac{1}{1+exp(-(y_{j}+b_{j}))}
\end{eqnarray}

where $y$ is the state of each neuron, $\tau_{i}$ is the time
constant (decay constant for neural activity), $w_{ij}$ is the
connection weight between neuron $i$ and $j$, $z_{j}$ is the
activation of neuron $j$, $y_{j}$ is $j$'s state and $b_{j}$ a bias
term; $g_{i}$ is a gain applied to the overall sensory input to the
neuron, $s_{ki}$  is the input weight from sensor $k$ to neuron $i$
and $I_{k}$ is the input value of sensor $k$. States are initialized
at 0 or a random value and the CTRNN is integrated using forward
Euler method. All neurons are connected to each other and to
themselves.
\end{quote}


Over this basic architecture more complex mechanisms can be
implemented, such as gas-nets \citep{husbandsetal98} and synaptic
plasticity \citep{dipaolo00, floreanoandurzelai01}.

Controll parameters (plastic rules, time constants, number of
neurons, weight values, etc...) are left to evolutionary search as
well as some body-sensor parameters (motor transfer parameters,
position of sensors, etc. --depending on the particular case).  The
structure of the simulation is thus defined as a dynamical system and
is implemented in a simulation model where the state of the system is
numerically calculated for short time-steps.

After deciding the basic structure of the simulation a genetic
algorithm is used to evolve the parameters with the following
procedure:
\begin{enumerate}
\item All the parameters are encoded in a genotype
(taking random values constrained between pre-specified values).
\item A population of genotypes is randomly created.
\item A fitness function is defined to asses the fitness of the
produced behaviour given a set of parameter values (genotype).
Examples of fitness function are distance to a given object,
performance in a learning task, stability and robustness of walking
behaviour, etc.
\item All the genotypes in the population are evaluated
according to the fitness function in the body-environment simulation.
\item The best genotypes are selected for reproduction and a new
population (generation) of genotypes is created and randomly mutated.
\item Steeps 4 and 5 are repeated until a given fitness value is
achieved.
\end{enumerate}


In brief what we get is a simulation model were local interaction
rules (achieved determining parameter values through evolution),
recursively (through the numerical calculation of states) applied
give rise to a global system behaviour (specified by the evolutionary
fitness function). The question now is how does this modelling
technique contribute to scientific development once decomposition and
localisation are shown to be unapropiate methods?




\section{Methodological and conceptual blending}

The role of bottom-up synthetic simulation models (and more
specifically evolutionary robotic simulations) is, we will argue,
that of providing: a) a \emph{conceptual blending}
between lower level mechanisms and global behavioural patterns and b)
a \emph{methodological blending} between empirical and theoretical
domains. We take the notion of blending (and conceptual blending in
particular) from \cite{fauconnierandturner98} who analyse conceptual
blending as a major cognitive process in which projections from two
different conceptual spaces blend into a single conceptual space on
which new relations and structures are discovered, which feed-back to
the input spaces thus producing new knowledge.

% FALTA ELABORAR UN POCO MÁS

\subsection{Simulations as conceptual blenders}

The problem of functional decomposition explained above has been
skipped in traditional scientific practices by dividing natural
objects of study on different levels of description and finding
specific observables on each level and lawfull regularities among
those observables. This way neurophysiological and behavioural or
cognitive levels of observation become two separated scientific
domains. The problem arises when localisation of functional
(cognitive) components into structural components fails as a result
of the underlying complexity of the system.

In such cases we believe that simulation models act as computational
and exteriorized conceptual blenders, where two distinct conceptual
spaces, structural (neurodynamical) and behavioural (cognitive),
merge into the simulation, feeding back to both input domains.
Simulation models in evolutionary robotics are not neurobiological
models (in fact they are generally very poor in comparison with
computational neuroscientific models of neurons), nor they are purely
cognitive models (which are often build in purely functional or
representational terms) but conceptual blender between both
functional and neurobiological models.

At a first view it could be argued that the blended space being
artefactual doesn't satisfy Fauconnier and Turner's theory which
presupposes that the blended space is a mental space and that
cognitive operations on that mental space are the source of new
knowledge. Nontheless, carefully analysed, simulation models do in
fact satisfy most (if not all) of the characteristics of mental
blending spaces. The neurophysiological input space projects into the
blended through the abstraction of local rules from
neurophysiological models. The cognitive input space projects by
conceptualising the emergent behavioural pattern as non trivially
cognitive; i.e. the emergent global behaviour is considered a
cognitive behaviour. What remains opaque (until the experimenter
abstracts explanatory patterns) is the cross-pace mapping, because of
the dynamical complexity of the emergent phenomena. In
the case of evolutionary robotics artificial evolution is used to
\emph{create} the blended space, and numerical calculations to
\emph{run} the blended space which is not purely relational but
dynamical.

      \begin{figure}
      \begin{center}
      \includegraphics[width=1\textwidth]{epist}
      \caption{\footnotesize{\emph{Simulation models in scientific
                             processes}}}
      \label{epist}
      \end{center}
      \end{figure}

The main difference between mental and artifactual blended spaces is
not its position in relation to the skull (after all cognitive
capacities are well understood as being distributed and also
extracraneal \cite{clarkandchalmers98}) but the capacity of
computational simulation models to solve differential equations
numerically and implement massive and recursive computations to
\emph{produce} emergent simulation models; human manipulation,
transformation and experimentation with the computational model works
as well as it does with mental models.


\subsection{Simulations as methodological blenders}

After deciding \emph{what} evolutionary simulation models \emph{are}
the question now is to understand what is their \emph{scientific
value} if they aren't models of biological phenomena nor models of
cognitive functionality; if they don't even try to fit any
empirical data \citep{dipaoloetal00}.

We believe that simulation models are better understood as
methodological blenders (this time in a loose sense of
blending only metaphorically related to Fauconnier and Turner's work)
between purely empírical and purely theoretical domains (whether
this extreme positions exist or not, as such, is not an issue here).
Specially significant is the relation simulation models establish
between theoretical assumptions (adaptationism, representation,
innateness, etc.) and empirical models.

\cite{dipaoloetal00} argue that simulation models work as opaque
thought experiments halfway between empirical models (in virtue of
their capacity to produce non-trivial data through the
computational emergence of global patterns) and theoretical tools
(since they address abstract theoretical/conceptual issues
rather than specific empirical targets, unlike biorobotic models
\citep{webb01}). Following their argument we believe that simulation
models show a scientific value on: \begin{itemize}
\item \emph{reconceptualization of theoretical assumptions} by means
of the dissonances that come about in their implementation (as it has
been the case with emergent functionality and the discovery of the
significance of embodiment and situatedness in the production of
adaptive and cognitive behaviour);
\item \emph{hypothesis generation} by discovering intermediate
explanatory patterns (as internal homeostasis to explain readaptation
to sensorimotor disruptions \citep{dipaolo00}); and
\item \emph{proof of concept} by producing certain behavioural
patterns with or without certain lower level mechanisms (as it is
being the case on the representationalist-antirepresentationalist
debate in cognitive science).
\end{itemize}


\section{Conclusion}


The scientific value of computational simulation models can be
understood, from a higher perspective, as diminishing the constraints
acting upon scientific development, as defined by
\cite{bechtelandrichardson93}. In relation to \emph{psychological
constraints} it shall be clear by now that simulation models extend
human capacities providing a kind of externalized and computationally
powerfull conceptual space in silico. At the same time the way in
which human understanding is constrained on big search spaces is now
been solved by artificial evolution as a genuine tool to explore
search spaces \citep{mitchell96}. Thus there are, at least, two ways
in which human psychological capacities are enhanced with simulation
models (other than the classical memory capacity, computational
power, and speed): a) by conceiving dynamical objects composed of
highly interacting components, and b) by exploring search spaces with
artificial evolution. On the side of \emph{phenomenological
constraints} we believe that simulation models come to produce new
artificial phenomena which can be studied (and often are) in their
own right, and in a scientifically relevant way when considered as
artifactual phenomena blending distinct modelling (scientific)
spaces. It is possibly in relation to \emph{operational
constraints} where simulation models have being traditionally
considered to have a major contribution, on that simulation models
provide to the experimenter a complete control over variables, and
repeatability under different conditions. Finally \emph{physicall
constraints} are considered by \cite{bechtelandrichardson93} as
limiting the range of allowed component functions by the requirement
that they must be shown to depend systematically on physical
structures. Once again we believe that evolutionary simulation models
provide one of the most powerfull cognitive tools to explore the
systematic dependencies between lower level mechanistic (physical)
constraints and the produced emergent phenomena, acting themselves
(when no other complexity reduction is possible ---by extracting
intermediate explanatory patterns) as explanations of bottom-up
causation.


We conclude that simulation
models are capable of extending our cognitive and epistemological
resources to (re)conceptualise scientific domains and to establish
causal relations between different levels of description. Simulation
models become, blended with traditional empirical methodology,
crucial tools for the scientific research on complex systems and
cognitive science.



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