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Computing Nature – A Network of Networks of
Concurrent Information Processes
Gordana Dodig Crnkovic 1 and Raffaela Giovagnoli 2
1 Department of Computer Science and Networks, Mälardalen University, Sweden
email: gordana.dodig-crnkovic@mdh.se
2 Faculty of Philosophy. Lateran University, Rome (Italy)
email: raffa.giovagnoli@tiscali.it
1 Introduction
The articles in the volume COMPUTING NATURE, forthcoming in Springer
SAPERE book series http://www.springer.com/series/10087 present a selection of
works from the Symposium on Natural/Unconventional Computing at AISB/IACAP
(British Society for the Study of Artificial Intelligence and the Simulation of Behav-
iour and The International Association for Computing and Philosophy) World Con-
gress 2012, held at the University of Birmingham, celebrating Turing centenary.
This book is about nature considered as the totality of physical existence, the uni-
verse. By physical we mean all phenomena - objects and processes - that are possible
to detect either directly by our senses or via instruments. Historically, there have been
many ways of describing the universe (cosmic egg, cosmic tree, theistic universe,
mechanistic universe) while a particularly prominent contemporary approach is com-
putational universe.
One of the most important pioneers of computing, Turing, described by Hodges as
natural philosopher, can be identified as a forerunner and founder of the notion of
computing nature and natural computing through his morphological computing and
”unorganized” (neural-network type) machines. Dodig-Crnkovic and Basti in this
volume address Turing’s role as pioneer of natural computation.
Present day computers are distinctly different from the early stand-alone calculat-
ing machines designed to mechanize computation of mathematical functions. Com-
puters today are networked and largely used for world-wide communication and vari-
ety of information processing and knowledge management. They are cognitive tools
of extended mind used in social interactions and ever increasing repositories of in-
formation. Moreover, computers play an important role in the control of physical
processes and thus connect directly to the physical world, especially in automation,
traffic control and robotics. Apart from classical engineering and hard-scientific do-
mains, computing has in recent decades pervaded new fields such as biology and
social sciences, humanities and arts – all previously considered as typical soft, non-
mechanical and unautomatable domains.
Computational processes running in networks of networks (such as the internet)
can be modeled as distributed, reactive, agent-based and concurrent computation. The
main criterion of success of this computation is not its termination, but its behavior -
response to changes, its speed, generality and flexibility, adaptability, and tolerance to
noise, error, faults, and damage. Internet, as well as operating systems and database
management systems are designed to operate indefinitely and termination for them
indicates an error. We will return to the topic of concurrent computing and its rela-
tionship with Turing machine model in more detail later on.
One of the aims of this book is to show the state of the art of developments in the
field of natural/unconventional computation which can be seen as generalization and
enrichment of the repertoire of classical computation models (all of them considered
to be equivalent to the Turing machine model). As a generalization of the traditional
algorithmic Turing Machine model of computation, (in which the computer was an
isolated box provided with a suitable algorithm and an input, left alone to compute
until the algorithm terminated), natural computation models interaction i.e. communi-
cation of computing processes with each other and with the environment during the
computation.
Hewitt [1] characterizes the Turing machine model as an internal (individual)
framework and the Actor model of concurrent computation as an external (sociologi-
cal) model of computing. This tension between (isolated) individual one and (interact-
ing) social many resonates with two articles from this volume: Cottam et al. who dis-
tinguish ”conceptual umbrella of entity and its ecosystem” and Schroeder’s view that
“Information can be defined in terms of the categorical opposition of one and many,
leading to two manifestations of information, selective and structural. These manifes-
tations of information are dual in the sense that one always is associated with the oth-
er.” Here information is directly related with computation defined as information
processing. [2]
The frequent objection against the computational view of the universe, elaborated
by Zenil in this volume, is that ”it is hard to see how any physical system would not
be computational.” The next frequently asked question is: if the universe computes,
what is its input and output of its computation? This presupposes that a computing
system must have input from the outside and that it must deliver some output to the
outside world. But actor system [1] for example needs no input. Within
pancomputationalist framework, the whole universe computes its own next state from
its current state [3]. As all of physics is based on quantum mechanical layers of in-
formation processing, one may say that zero-point (vacuum) oscillations can be seen
as one of the constant inputs for the computational network of the universe. What
causes different processes in the universe is the interaction between its parts or ex-
change of information. The universe is a result of evolution from the moment of big-
bang or some other primordial state, through the complexification of the relationships
between its actors by computation as a process of changes of its informational struc-
ture. Physical forces are established through particle exchanges (message exchanges)
which necessarily connect particles into a web of physical interactions which are
manifestation of natural laws. The whole of the universe is in the state of permanent
flow, far from steady state, which results in forming increasingly complex structures,
[4]. So much about the input-output question.
As to the objection that not all of the universe can be computational, it is essential
to keep in mind the complex layered architecture of the computing nature, as not all
of computation is the same – computation is proceeding on many scales, on many
levels of hierarchical organization. Moreover, in tandem with computation, universe
is described by information, representing its structures. Given that computation fol-
lows physical laws, or represents/implements physical laws, generative model of the
universe can be devised such that some initial network of informational processes
develops in time into increasingly complex (fractal, according to Kurakin) infor-
mation structures.
The parallel could be drawn between natural computationalism and atomic theory
of matter which implies that all of matter is made of atoms (and void). We may also
say that all of physics (structures and processes) can be derived from elementary par-
ticles (and void that is an ocean of virtual particles which for short time, obeying Hei-
senberg uncertainty relations, pop into existence and quickly thereafter disappear).
This does not make the world a soup of elementary particles where no differences can
be made, and nothing new can emerge. Those basic elements can be imagined as neo-
dymium ball magnets from which countless structures can be constructed (in space
and time through interactions).
Unified theories are common and valued in physics and other sciences, and natural
computationalism is such a unified framework. It is therefore not unexpected that
physicists are found among the leading advocates of the new unified theory of infor-
mational and computational universe – from Wheeler, via Feynman, to our contempo-
raries such as Fredkin, Lloyd, Wolfram, Goyal and Chiribella. For the articles of latter
two physicists on the topic of informational universe, see the special issue of the jour-
nal Information titled Information and Energy/Matter [5] and the special issue of the
journal Entropy titled Selected Papers from Symposium on Natural/ Unconventional
Computing and its Philosophical Significance [6].
Conceptualizing the physical world as a network of information networks evolving
through processes of natural computation helps us to make more compact and coher-
ent models of nature, connecting non-living and living worlds. It presents a suitable
basis for incorporating current developments in understanding of biological, cognitive
and social systems as generated by complexification of physicochemical processes
through self-organization of molecules into dynamic adaptive complex systems by
morphogenesis, adaptation and learning—all of which are understood as computation
(information processing).
2 Re-Conceptualizing of Nature as Hierarchically Organized
Computational Network of Networks Architecture
2.1 Natural Hierarchy
“If computation is understood as a physical process, if nature computes with
physical bodies as objects (informational structures) and physical laws govern
process of computation, then the computation necessarily appears on many differ-
ent levels of organization. Natural sciences provide such a layered view of nature.
One sort of computation process is found on the quantum-mechanical level of el-
ementary particles, atoms and molecules; yet another on the level of classical
physical objects. In the sphere of biology, different processes (computations = in-
formation processing) are going on in biological cells, tissues, organs, organisms,
and eco-systems. Social interactions are governed by still another kind of commu-
nicative/interactive process. If we compare this to physics where specific “force
carriers” are exchanged between elementary particles, here the carriers can be
complex chunks of information such as molecules or sentences and the nodes
(agents) might be organisms or groups—that shows the width of a difference.”
Dodig Crnkovic [2]
Searching for a framework for natural computation and looking at nature from vari-
ety of perspectives and levels of organization, Cottam et al. in this book address the
general question of hierarchy in nature and point to Salthe who ” restricts the term
hierarchy to two forms: the scale (or compositional) hierarchy and the specification
(or subsumption) hierarchy. However, we find that a third form – the representation or
model hierarchy – is most suitable for describing the properties of Natural systems.”
Special emphasis is on birational ecosystemic principles: “Nature seen through sci-
ences brings all of Science under a generalized umbrella of entity and its ecosystem,
and then characterizes different types of entity by their relationships with their rele-
vant ecosystems.” (emphasis added)
In spite of suggested tree-structure with representation on top, followed by model
hierarchy with subsequent compositional and subsumption hierarchy, the authors
point out that “even here the movement between two extremes can be observed –
from the bottom up and from the top down. Parts defining the whole, which once
established, affect its parts. As a case in point, they provide an example of a (Natural)
model hierarchy for a tree represented at different scales: ”{a tree described in terms
of atoms}, {a tree described in terms of molecules}, {a tree described in terms of
cells}… up to {a tree described in terms of branches}, {a tree as itself – a tree}”. Here
inter-scale interfacing and consequently digital-analog interfaces are discussed and it
is emphasized that naturally-hierarchical multi-scale organisms function differently
from a digital computer. The article concludes with the hope that this birational
ecosystemic hierarchical framework will be capable of defining computation which is
closer to processes that we find in nature.
2.2 Cognitive Level of Information Processing
In a hierarchy of organizational levels in nature the most complex level of infor-
mation processing is cognitive level and it subsumes all lower levels that successively
emerge from their antecedent lower levels. Lindley in this volume addresses the prob-
lems encountered in the development of engineered autonomous and intelligent sys-
tems caused by exclusively linguistic models of intelligence. The alternative proposed
is “taking inspiration more directly from biological nervous systems”. This approach
is argued to be able to go “far beyond twentieth century models of artificial neural
networks (ANNs), which greatly oversimplified brain and neural functions”. This
implies study of computation as information processing in neural and glial systems in
order to implement “asynchronous, analog and self-* architectures that digital com-
puters can only simulate.” (emphasis added)
Continuing on the level of neural systems, Phillips’s paper addresses the important
topic of coordination of concurrent probabilistic inference. Adaptively organized
complexity of life builds on information processing and in cognitive agents with neu-
ral systems also on inference. The paper discusses the theory of Coherent Infomax in
relation to the Theory of free energy reduction of probabilistic inference. Coherent
Infomax show how neural systems combine local reliability with context-sensitivity
and here we recognize the leitmotif of individual and social, agent and its eco-system
from several other papers.
Bull et al. in this volume address Turing’s unorganized machines as models of neu-
ral systems - a form of discrete dynamical system. Turing in his 1948 paper [7] made
an essential insight about the connection of social aspects of learning and intelligence.
From the contemporary perspective of natural computing we see networks as infor-
mation processing mechanisms and their role in intelligence is fundamental. Suggest-
ing that natural evolution may provide inspiration for search mechanisms to design
machines, Bull et al investigate Turing’s dynamical representation for networks of
vesicles, membrane-bound compartments filled with Belousov-Zhabotinsky chemical
mixture, used as liquid information processing system. Communication between vesi-
cles was implemented as chemical signals - excitations propagating between vesicles,
which was seen as imitation or cultural information communication, that may provide
“a useful representation scheme for unconventional computing substrates”.
Even Arriola-Rios et al. contribute to this book with a high level of abstraction, in-
terdisciplinary perspective, this time on object representation in animals and robots
from segregate information about objects. This work makes contribution to better
understanding of the details of information processing on cognitive level. As infor-
mation in a cognizing agent forms internal representations, which depend on the way
of agent’s use of information, it could be compressed and thus re-used “for deriving
interpretations, causal relationships, functions or affordances”. Particular analysis is
devoted reasoning about deformable objects.
3 The Unreasonable Effectiveness of Mathematics in the
Natural Sciences (Except for Biology). Mathematicians Bias
and Computing Beyond the Turing Limit
Mathematician’s contribution to the development of the idea of computing nature
is central. Turing as an early proponent of natural computing put forward a machine
model that is still in use. How far can we hope to go with Turing machine model of
computation?
In the context of computing nature, living systems are of extraordinary importance
as up to now science haven’t been able to model and simulate the behavior of even
the simplest living organisms. “The unreasonable effectiveness of mathematics” ob-
served in physics (Wigner) is missing for complex phenomena like biology that today
lack mathematical effectiveness (Gelfand), see [8].
Not many people today would claim that human cognition (information processing
going on in our body, including thinking) can be adequately modeled as a result of
computation of one Turing machine, however complex function it might compute. In
the next attempt, one may imagine a complex architecture of Turing machines run-
ning in parallel as communicating sequential processes (CSPs) exchanging infor-
mation. We know today that such a system of Turing machines cannot produce the
most general kind of computation, as truly asynchronous concurrent information pro-
cessing going on in our brains.
However, one may object that IBM’s super-computer Watson, the winner in man
vs. machine "Jeopardy!" challenge, runs on contemporary (super)computer which is
claimed to be implementations of Turing machine. Yet, Watson is connected to the
Internet. And Internet is not a Turing machine equivalent. It is not even a network of
Turing Machines. Information processing going on throughout the entire Internet
includes signaling and communication based on complex asynchronous physical pro-
cesses that cannot be sequentionalized. (Hewitt, Sloman) As an illustration see
Barabási et al. article [9] on parasitic computing that implements computation on the
communication infrastructure of the internet, thus using communication for computa-
tion.
Zenil in this volume examines the question: “What does it mean to claim that a
physical or natural system computes?” He proposes a behavioural characterisation of
computing in terms of a measure of programmability, which reflects a system’s ability
to react to external stimuli. To that end Zenil investigates classical foundations for
unconventional computation.
Hernandez-Espinosa and Hernandez-Quiroz, starting from the old
computationalism defined as the claim that the human mind can be modeled by Tu-
ring Machines, analyze Wolfram’s Principle of Computational Equivalence – the
claim that “any natural (and even human) phenomenon can be explained as the inter-
action of very simple rules.”
The next step would be to replace present basic simple rules of cellular automata
with more elaborate ones. Instead of synchronous update of the the whole system;
they can be made asynchronous networks of agents, placed in layered architectures on
different scales etc. The basic idea of generative science is to generate apparently
unanticipated and infinite behaviour based on deterministic and finite rules and pa-
rameters reproducing or resembling the behavior of natural and social phenomena. As
an illustration see Epstein, [10].
If we want to generalize the idea of computation to be able to encompass more
complex operations than mechanical execution of an algorithm, simulating not only a
person executing strictly mechanical procedure, but the one constructing new theory,
we must go back to underlying mathematics.
Burgin and Dodig-Crnkovic, in present volume analyze methodological and philo-
sophical implications of algorithmic aspects of unconventional/natural computation
that extends the closed classical universe of computation of the Turing machine type.
The new model constitute an open world of algorithmic constellations, allowing in-
creased flexibility and expressive power, supporting constructivism and creativity in
mathematical modeling and enabling richer understanding of computation, see [11].
3.1 Hypercomputation - Beyond the Turing Limit
Hypercomputation is the research field that formulated the first ideas about the
possibility of computing beyond Turing machine model limits. The term
hypercomputation was introduced by Copeland and Proudfoot [12]. The expression
"super-Turing computation" was coined by Siegelman and usually implies that the
model is supposed to be physically realizable, while hypercomputation frequently
relies on thought experiments. Present volume offers two contributions that sort under
hypercomputation, written by Franchette and Douglas.
Franchette studies the possibility of a physical device that hypercomputes by build-
ing an oracle hypermachine, “namely a device which is to be able to use some extern
information from nature to go beyond Turing machines limits.” The author addresses
an analysis of the verification problem for oracle hypermachines.
Douglas in his contribution presents a critical analysis of Siegelmann Networks.
3.2 Physical Computation “In Materio” - Beyond the Turing Limit
Several authors at the Symposium on Natural/Unconventional Computing at
AISB/IACAP World Congress 2012 (Stepney, Cooper, Goyal, Basti, Dodig-
Crnkovic) emphasized the importance of physical computing, or as Stepney [13]
termed it, “computation in materio”.
Barry Cooper: What Makes A Computation Unconventional? (coming paper)
Cooper in his article Turing's Titanic Machine? [14] diagnoses the limitations of
the Turing machine model and identifies the ways of overcoming those limitations:
− Embodiment invalidating the `machine as data' and universality paradigm.
− The organic linking of mechanics and emergent outcomes delivering a clear-
er model of supervenience of mentality on brain functionality, and a recon-
ciliation of different levels of effectivity.
− A reaffirmation of the importance of experiment and evolving hardware, for
both AI and extended computing generally.
− The validating of a route to creation of new information through interaction
and emergence.
Related article by the same author elucidates the role of physical computation vs
universal symbol manipulation: The Mathematician's Bias and the Return to Embod-
ied Computation from the book A Computable Universe: Understanding and Explor-
ing Nature As Computation. [15]
The theme of embodied computation is addressed in this volume by Hernandez-
Quiroz and Padilla who examine actual physical realizability of mathematical con-
structions of abstract entities - a controversial issue and important in the debate about
limits of Turing model. The authors study a simple special of “physical realizability
of the enumeration of rational numbers by Cantor's diagonalization by means of an
Ising system”.
3.3 Higher Order Computability - Beyond the Turing Limit
One of the main steps towards the new paradigm of natural/unconventional compu-
ting is to make visible host of myths surrounding the old paradigm and helping it to
survive. One of those myths is that our modern computers with all their programming
languages are diverse implementations of Turing machines. However, as Kanneganti
and Cartwright already argued twenty years ago:
“Classic recursion theory asserts that all conventional programming languages
are equally expressive because they can define all partial recursive functions over
the natural numbers. This statement is misleading because programming lan-
guages support and enforce a more abstract view of data than bit strings. In partic-
ular, most real programming languages support some form of higher-order data
such as potentially infinite streams (input and output), lazy trees, and functions.”
Kanneganti and Cartwright [16]
Kleene was a pioneer of higher order computability as he “opened the frontiers of
computability on higher type objects in a series of papers first on constructive ordinals
and hierarchies of number-theoretical predicates and later on computability in higher
types. “The form of the changing surface of the stream appears to constrain the
movements of the molecules of water, while at the same time being traceable back to
those same movements.” Soare [17]
Cooper [18] underlines the importance of higher-order computational structures as
characteristic of human thinking. This can be connected to higher-order functional
programming, which means, among others, programming with functions whose input
and/or output may consist of other functions.
“Kreisel [21] was one of the first to separate cooperative phenomena (not
known to have Turing computable behaviour), from classical systems and pro-
posed [22] (p˙143, Note 2) a collision problem related to the 3-body problem as a
possible source of incomputability, suggesting that this might result in “an analog
computation of a non-recursive function (by repeating collision experiments suffi-
ciently often)”. This was before the huge growth in the attention given to chaos
theory, with its multitude of different examples of the generation of informational
complexity via very simple rules, accompanied by the emergence of new regulari-
ties (see for example the two classic papers of Robert Shaw [33], [32]). We now
have a much better understanding of the relationship between emergence and cha-
os, but this still does not provide the basis for a practically computable relation-
ship.“ Cooper [18] (emphasis added)
4 Concurrent Computing and Turing Machine Model
4.1 Bi-Directional Model Development of Natural Computation
Turing machine model (originally named “Logical calculating machine”) was de-
veloped by Turing in order to describe a human (at that time called ”computer”) exe-
cuting an algorithm:
“It is possible to produce the effect of a computing machine by writing down a
set of rules of procedure and asking a man to carry them out. Such a combination
of a man with written instructions will be called a ‘Paper Machine’. A man pro-
vided with paper, pencil, and rubber, and subject to strict discipline, is in effect a
universal machine.” Turing [7]
The underlying logic of Turing’s “logical calculating machine” is fully consistent
standard logic. Turing machine is assumed always to be in a well defined state. [1]
In contemporary computing machinery, however, we face both states that are not
well defined (in the process of transition) and states that contain inconsistency:
“Consider a computer which stores a large amount of information. While the
computer stores the information, it is also used to operate on it, and, crucially, to
infer from it. Now it is quite common for the computer to contain inconsistent in-
formation, because of mistakes by the data entry operators or because of multiple
sourcing. This is certainly a problem for database operations with theorem-
provers, and so has drawn much attention from computer scientists. Techniques
for removing inconsistent information have been investigated. Yet all have limited
applicability, and, in any case, are not guaranteed to produce consistency. (There
is no algorithm for logical falsehood.) Hence, even if steps are taken to get rid of
contradictions when they are found, an underlying paraconsistent logic is desirable
if hidden contradictions are not to generate spurious answers to queries.” Priest
and Tanaka [19]
Open, interactive and asynchronous systems have special requirements on logic.
Goldin and Wegner [20], and Hewitt [1] argue e.g. that computational logic must be
able to model interactive computation, and that classical logic must be robust towards
inconsistencies i.e. must be paraconsistent due to the incompleteness of interaction.
As Sloman [21] points out, concurrent and synchronized machines are equivalent
to sequential machines, but some concurrent machines are asynchronous, and thus not
equivalent to Turing machines. If a machine is composed of asynchronous concur-
rently running subsystems, and their relative frequencies vary randomly, then such a
machine cannot be adequately modeled by Turing machine, see also [3].
Turing machines are discrete but can in principle approximate machines with con-
tinuous changes, yet cannot implement them exactly. Continuous systems with non-
linear feedback loops may be chaotic and impossible to approximate discretely, even
over short time scales, see [22] and [1]. Clearly Turing machine model of computa-
tion is an abstraction and idealization. In general, instead of idealized, symbol-
manipulating models, more and more physics-inspired modeling is taking place.
Theoretical model of concurrent (interactive) computing corresponding to Turing
machine model of algorithmic computing is under development. (Abramsky, Hewitt,
Wegner) From the experience with present day networked concurrent computation it
becomes obvious that Turing machine model can be seen as a special case of a more
general computation. During the process of learning from nature how to compute, we
both develop computing and at the same time improve understanding of natural phe-
nomena.
“In particular, the quantum informatic endeavor is not just a matter of feeding
physical theory into the general field of natural computation, but also one of using
high-level methods developed in Computer Science to improve on the quantum
physical formalism itself, and the understanding thereof. We highlight a seemingly
contradictory phenomenon: passing to an abstract, categorical quantum informat-
ics formalism leads directly to a simple and elegant graphical formulation of quan-
tum theory itself, which for example makes the design of some important quantum
informatic protocols completely transparent. It turns out that essentially all of the
quantum informatic machinery can be recovered from this graphical calculus. But
in turn, this graphical formalism provides a bridge between methods of logic and
computer science, and some of the most exciting developments in the mathematics
of the past two decades“ Abramsky and Coecke [23]
The similar two-way process of learning is visible in biocomputing, see Rozenberg
and Kari [24]. As we already mentioned “the unreasonable effectiveness of mathe-
matics in the natural sciences” does not (yet) apply to biology, as modeling of biolog-
ical systems attempted up to now was too crude. Living systems are essentially open
and in constant communication with the environment. New computational models
must be interactive, concurrent, and asynchronous in order to be applicable to biolog-
ical and social phenomena and to approach richness of their information processing
repertoire.
Present account of models of computation highlights several topics of importance
for the development of new understanding of computing and its role: natural compu-
tation and the relationship between the model and physical implementation, interac-
tivity as fundamental for computational modeling of concurrent information pro-
cessing systems such as living organisms and their networks, and new developments
in logic needed to support this generalized framework. Computing understood as
information processing is closely related to natural sciences; it helps us recognize
connections between sciences, and provides a unified approach for modeling and
simulating of both living and non-living systems. [3]
4.2 Concurrency vs. Symbolic Computation of Function Values
In his article: What is computation? Concurrency versus Turing's Model, Hewitt
[1] makes the following very apt analysis of the relationship between Turing ma-
chines and concurrent computing processes:
“Concurrency is of crucial importance to the science and engineering of com-
putation in part because of the rise of the Internet and many-core architectures.
However, concurrency extends computation beyond the conceptual framework of
Church, Gandy [1980], Gödel, Herbrand, Kleene [1987], Post, Rosser, Sieg
[2008], Turing, etc. because there are effective computations that cannot be per-
formed by Turing Machines. In the Actor model [Hewitt, Bishop and Steiger 1973;
Hewitt 2010], computation is conceived as distributed in space where computa-
tional devices communicate asynchronously and the entire computation is not in
any well-defined state. (An Actor can have information about other Actors that it
has received in a message about what it was like when the message was sent.) Tu-
ring's Model is a special case of the Actor Model.” Hewitt [1] (emphasis added)
According to natural computationalism/pancomputationalism [3] every physical
system is computational, but there are many different sorts of computations going on
in nature seen as a network of agents/actors exchanging ”messages”. The simplest
agents communicate with simplest messages such as elementary particles (with 12
kinds of matter and 12 anti-matter particles) exchanging 12 kinds of force-
communicating particles. An example from physics is Yukawa’s theory of strong
nuclear force understood as exchange of mesons, which explained the interaction
between nucleons. Complex agents like humans communicate through languages
which use very complex messages for communication. Natural computational systems
as networks of agents exchanging messages are in general asynchronous concurrent
systems. Conceptually, agent-based models and Actor model are closely related, and
as mentioned, even the understanding of interactions (forces) between elementary
particles as exchanges of elementary particles fits in this framework.
4.3 Physical Computing - New Computationalism.
Embodied Networks and Symbolic Representation
It is often argued that computationalism is the opposite of connectionism and that
connectionist networks and dynamic systems do not compute. However, if we define
computation in a more general sense of natural computation, instead of high level
symbol manipulation of Turing machine, it is obvious that connectionist networks and
dynamical systems do compute. That is also the claim made by Scheutz in the Epi-
logue of the book Computationalism: New Directions [25], where he notices that:
“Today it seems clear, for example, that classical notions of computation alone
cannot serve as foundations for a viable theory of the mind, especially in light of
the real-world, realtime, embedded, embodied, situated, and interactive nature of
minds, although they may well be adequate for a limited subset of mental process-
es (e.g., processes that participate in solving mathematical problems). Reserva-
tions about the classical conception of computation, however, do not automatically
transfer and apply to real-world computing systems. This fact is often ignored by
opponents of computationalism, who construe the underlying notion of computa-
tion as that of Turing-machine computation.” Scheutz [25] p. 176
Classical computationalism was the view that classical theory of computation (Tu-
ring-machine-based, universal, disembodied) might be enough to explain cognitive
phenomena. New computationalism (natural computationalism) emphasizes that em-
bodiment is essential and thus physical computation - natural computationalism.
The view of Scheutz is supported by O'Brien [26] who refers to Horgan and
Tienson [27] arguing that “cognitive processes, are not governed by exceptionless,
representation-level rules; they are instead the work of defeasible cognitive tendencies
subserved by the non-linear dynamics of the brains neural networks.”
Dynamical characterization of the brain is consistent with the analog interpretation
of connectionism. But dynamical systems theory is often not considered to be a com-
putational framework. O'Brien [26] notices that “In this sense, dynamical systems
theory dissolves the distinction between intelligent and unintelligent behaviour, and
hence is quite incapable, without supplementation, of explaining cognition. In order
for dynamical engines to be capable of driving intelligent behaviour they must do
some computational work: they must learn to behave as if they were semantic en-
gines.”
O’Brien and Opie [28] thus search for an answer to the question how connectionist
networks compute, and come with the following problem characterization:
”Connectionism was first considered as the opposed to the classical computa-
tional theory of mind. Yet, it is still considered by many that a satisfactory account
of how connectionist networks compute is lacking. In recent years networks were
much in focus and agent models as well so the number of those who cannot imag-
ine computational networks has rapidly decreased. Doubt about computational na-
ture of connectionism frequently takes the following two forms.
1. “(W)hile connectionists typically interpret the states and activity of connec-
tionist networks in representational terms, closer scrutiny reveals that these puta-
tive representations fail to do any explanatory work, and since there is ‘‘no com-
putation without representation’’ (Pylyshyn 1984, p. 62), the connectionist frame-
work is better interpreted non-computationally.
2. Moreover it is argued that “the connectionist networks are better character-
ized as dynamical systems rather than computational devices.”
In the above denial of connectionist models computational nature the following
confusions are evident.
1. Even though it is correct that there is “no computation without representation”,
representation in this context can be any step in the process of information transfor-
mation from the physical world (object) to the cognitive state where an agent “recog-
nizes” the object represented. It can be the dynamical state induced in the agents’
brain as a consequence of perception of an object.
2. Dynamical systems compute as well and their computation in general is natural
computation. One of the central questions in this context is the distinction between
symbolic and non-symbolic computing. Trenholme [29] describes the relationship of
analog vs. symbolic simulation:
“Symbolic simulation is thus a two-stage affair: first the mapping of inference
structure of the theory onto hardware states which defines symbolic computation;
second, the mapping of inference structure of the theory onto hardware states
which (under appropriate conditions) qualifies the processing as a symbolic simu-
lation. Analog simulation, in contrast, is defined by a single mapping from causal
relations among elements of the simulation to causal relations among elements of
the simulated phenomenon.” Trenholme [29] p.119.
Both symbolic and sub-symbolic (analog) simulations depend on caus-
al/analog/physical and symbolic type of computation on some level but in the case of
symbolic computation it is the symbolic level where information processing is ob-
served. Similarly, even though in the analog model symbolic representation exists at
some high level of abstraction, it is the physical agency and its causal structure that
define computation (simulation).
Basti in this volume suggests how to “integrate in one only formalism the physical
(“natural”) realm, with the logical-mathematical (“computation”) one, as well as their
relationships. That is, the passage from the realm of the causal necessity (“natural”)
of the physical processes, to the realm of the logical necessity (“computational”),
eventually representing them either in a sub-symbolic, or in a symbolic form. This
foundational task can be performed, by the newborn discipline of theoretical formal
ontology.” Proposed ontology is based on the information-theoretic approach in quan-
tum physics and cosmology, the information-theoretic approach of dissipative QFT
(Quantum Field Theory) and the theoretical cognitive science.
Freeman [30] characterizes accurately the relationship between physical/sub-
symbolic and logical/symbolic level in the following:
“Human brains intentionally direct the body to make symbols, and they use the
symbols to represent internal states. The symbols are outside the brain. Inside the
brains, the construction is effected by spatiotemporal patterns of neural activity
that are operators, not symbols. The operations include formation of sequences of
neural activity patterns that we observe by their electrical signs. The process is by
neurodynamics, not by logical rule-driven symbol manipulation. The aim of simu-
lating human natural computing should be to simulate the operators. In its simplest
form natural computing serves for communication of meaning. Neural operators
implement non-symbolic communication of internal states by all mammals, in-
cluding humans, through intentional actions. (…) I propose that symbol-making
operators evolved from neural mechanisms of intentional action by modification
of non-symbolic operators.“ (emphasis added)
Consequently, our brains use non-symbolic computing internally in order to ma-
nipulate relevant external symbols!
So in what way is physical computation/natural computation important vis-à-vis
Turing machine model? One of the central questions within computing, cognitive
science, AI and other related fields is about computational modeling (and simulating)
of intelligent behaviour. What can be computed and how? It has become obvious that
we must have richer models of computation, beyond Turing machines, if we are to
efficiently model and simulate biological systems. What exactly can we learn from
nature and especially from intelligent organisms?
It has taken more than sixty years from the first proposal of Turing test he called
the ”Imitation Game", described in Turing [31] p. 442, to the Watson machine win-
ning Jeopardy. That is just the beginning of what Turing believed one day will be
possible - a construction of computational machines capable of generally intelligent
behavior as well as the accurate computational modeling of the natural world. So
there are several classes of problems that deserve our attention when talking about
computing nature.
To ”compute” nature by any kind of computational means, is to model and/or simu-
late the behaviors of natural systems by computational means. Watson is a good ex-
ample. We know that we do not function like Watson or like chess playing programs
that take advantage of brute force algorithms to search the space of possible states.
We use our experience, ”gut feeling” and ”fingertip-feeling”/ ”fingerspitzengefühl”
that can be understood as embodied, physical, sub-symbolic information processing
mechanisms we acquire by experience and use when necessary as automatized hard-
ware-based recognition tools.
To compute “nature” means to interpret natural processes, structures and objects as
a result of natural computation which is in general defined as information processing.
This implies understanding and modeling of physical agents, starting from the very
fundamental level via several emergent levels of chemistry, biology, cognition and
extended cognition (social and augmented by computational machinery).
At the moment we have bits and pieces of the picture – COMPUTING nature, that
is computational modeling of nature and computing NATURE, that is nature under-
stood in itself as a computational network of networks.
5 The Relationship Between Human Representation, Animal
Representation and Machine Representation
We would like to highlight the relevance of the relationship between human repre-
sentation and machine representation to show the main issues concerning “functional-
ism” and “connectionism”. We propose to discuss the notion of “representation” be-
cause an important challenge for AI is to simulate not only the “phonemic” and “syn-
tactic” aspects of mental representation but also the “semantic” aspect. Traditionally,
philosophers use the notion of “intentionality” to describe the representational nature
of mental states namely intentional states are those that “represent” something, be-
cause mind is directed toward objects. We think that it is important to consider the
relevance of “embodied cognition” for contentful mental states (see, for instance, the
classical thought experiment of the “Chinese room” introduced by Searle to criticize
the important results of the Turing test, [32]).
The challenge for AI is therefore to approximate to human representations i.e. to
the semantic content of human mental states. There are two competing interpretations
of mental representations relevant for AI. The first focuses on the discreteness of
mental representations and the second focuses on their inter-relation [33]. The first
corresponds to the symbolic paradigm in AI, according to which mental representa-
tions are symbols. Proponents of the symbolic representation point on a semantic that
rests on the relation between tokens of the symbol and objects of representation. The
intentional mechanism functions in a way that the content of a symbol does not de-
pend on the content of other symbols. In this sense, each symbol is discretely con-
ferred with its intentional content. The second corresponds to connectionism in AI,
according to which mental representations are distributed patterns. Proponents of this
view intend the way in which a mental representation is conferred with its intentional
content as mediated by relations with other representations. The virtue of connection-
ism as presented in the neural networks resides in the fact that the categories repre-
sented admit borderline cases of membership. As regards the composition of mental
representations, it reveals itself to be the complex, contextually modulated interaction
of patterns of activation in a highly interconnected network. We aim to describe the
main aspects of the two approaches to make clear: the mechanisms characterizing the
different way by which representations are conferred with their intentional content;
the nature and structure of the categories represented and the ways in which mental
representations interact.
The task to consider the similarity between human and artificial representation
could involve the risk of skepticism about the possibility of “computing” this mental
capacity. If we consider computationalism as defined in purely abstract syntactic
terms then we are tempted to abandon it because human representation involves “real
world constrains”. But, a new view of computationalism could be introduced that
takes into consideration the limits of the classical notion and aims at providing a con-
crete, embodied, interactive and intentional foundation for a more realistic theory of
mind [25]. We would like to highlight also an important and recent debate on “digital
representation” [34] that focus on the nature of representations in the computational
theory of mind (or computationalism). The starting point is the nature of mental rep-
resentations, and, particularly, if they are “material”. There are authors such as Clark
who maintain that mental representation are material [35] while others like Speaks
think that thought processes use conventional linguistic symbols [36]. The question of
digital representation involves the “problem of physical computation” [37] as well as
the necessity of the notion of representation [38] so that we only have the problem of
how to intend the very notion of representation [39, 40]. But, there is also the possi-
bility of understanding computation as a purely physical procedure where physical
objects are symbols processed by physical laws on different levels of organization
that include “every natural process” in a “computing universe” [41]. In this context,
we need a plausible relation between computation and information. Info-
computational naturalism describes the informational structure of the nature i.e. a
succession of level of organization of information. Morphology is the central idea in
the understanding of the connection between computation and information. It pro-
ceeds by abstracting the principles via information self-structuring and sensory-motor
coordination. The sensory-motor coordination provides an “embodied” interaction
with the environment: information structure is induced in the sensory data, thus facili-
tating perception, learning and categorization.
Among the possibilities to compute human representational processes, Basti in this
volume proposes a natural account from the field of formal ontology. In particular, he
implements the so-called “causal theory of reference” in dynamic systems.
We think it is necessary to find a plausible philosophical strategy to consider the
capacities that are common to human and machine representation (Giovagnoli in this
volume). Analytic Pragmatism that is represented by the American philosopher
Brandom [42] suggests relevant ideas to describe human, animal and artificial capaci-
ties for representing the external world. It is easier to start with the human case and so
to describe discursive practices and to introduce norms for deploying an autonomous
vocabulary, namely a vocabulary of a social practice (science, religion etc.). These
norms are logical and are at the basis of an “inferential” notion of representation. But,
inference in this sense, recalling Frege, is material. Brandom refuses the explanation
of representation in terms of syntactical operations as presented by “functionalism” in
“strong” artificial intelligence (AI or GOFAI). He does not even accept weak AI
(Searle), rather he aims to present a “logical functionalism” characterizing his analytic
pragmatism. According to Brandom, we are not only creatures who possess abilities
such as to respond to environmental stimuli we share with thermostats and parrots but
also “conceptual creatures” i.e. we are logical creatures in a peculiar way and we need
a plausible view to approach human capacities.
Very interesting results are offered by Arriola-Rios and Demery et al. who discuss
in this book how salient features of objects can be used to generate compact represen-
tations in animals and robots, later allowing for relatively accurate reconstructions
and reasoning. They would like to propose that when exploration of objects occurs for
forming representations, it is not always random, but also structured, selected and
sensitive to particular features and salient categorical stimuli of the environment.
They introduce how studies into artificial agents and into natural agents are comple-
mentary by emphasizing some findings from each field.
Along this line, Bull, Holley, De Lacy Costello and Adamatzky present initial re-
sults from consideration of using Turing’s dynamical representation within unconven-
tional substrate – networks of Belousov-Zhabotinsky vehicles – designed by an imita-
tion based i.e. cultural approach. Over sixty years ago, Alan Turing presented a sim-
ple representation scheme for machine intelligence namely a discrete dynamical sys-
tem network of two-input NAND gates. Since then only a few other explorations of
these unorganized machines are known. As the authors underscore in their paper, it
has long been argued that dynamic representations provide numerous useful features,
such as an inherent robustness to faults and memory capabilities by exploiting the
structure of their basins of attraction:
“For example, unique attractors can be assigned to individual system
states/outputs and the map of internal states to those attractors can be constructed
such that multiple paths of similar states lead to the same attractor. In this way,
some variance in the actual path taken through states can be varied, e.g., due to er-
rors, with the system still responding appropriately. Turing appears to have been
thinking along these lines also”.
6 Conclusions, Open Problems and Future Work
“It turns out to be better to use the world as its own model.” Brooks [43]
As already argued, we enjoy and appreciate what Wigner named “the unreasonable
efficiency of mathematics in natural sciences” [44] – except for biology. Time is right
to address biology at last and try to find out how best to use computation to model and
simulate behavior of biological systems. In this context it can never be overempha-
sized that:"nothing in biology makes sense except in the light of evolution" – an in-
sight made by the evolutionary biologist Dobzhansky [45]. In order to model (simu-
late) evolution we need generative models (as demonstrated by e.g. Epstein [10] and
Wolfram [46]), capable of producing complex behaviors starting from simple struc-
tures and processes (rules).
Of all biological phenomena, cognition (the ability of living organisms to process
information beyond simple reactivity) seems to be the most puzzling one, as in more
complex organisms it is related to complex phenomena such as mind, intelligence and
mental (thought) processes. Cognition in highly developed organisms indeed looks
like a miracle if one does not take into account that it took enormous time in nature to
develop, in the process of evolution, through the variety of biological structures and
processes.
For the future work it remains to reconstruct the details of evolution of life in terms
of information and computation. This especially goes for the evolution of nervous
system and brains in animals and thus the development of complex cognitive capaci-
ties (such as intelligence). This understanding of the evolution and development of
organisms in terms of information and computation will lead to improved understand-
ing of underlying mechanisms of morphological computing as information self-
structuring [47] Through the reverse engineering of evolution of various capacities in
organisms we will be able both to deeper understand how organisms function through
the detailed computational models and simulations (such as in Human Brain/Blue
Brain project). At the same time we will learn to compute in novel and more powerful
ways (such as in IBM’s project of Cognitive Computing).
Here is the list of some important questions to answer in the framework of natural
computation (information processing in physical systems).
Generative modeling of the evolution and development of physical structures of the
universe, starting with minimum assumptions about primordial universe in terms of
information and computation, based on actor (agent) networks exchanging infor-
mation (messages).
Generative modeling of hierarchical structure of emergent layers of organization
in physical systems in terms of natural computing. Modeling of the process in which
the whole constraints its parts and showing how its (higher level) properties emerge.
Using natural computation to program nano-devices and applying it to universally
programmable intelligent matter. (MacLennan)[48]
Understanding and describing of the evolution and development of living organ-
isms on earth within the framework of natural computation (morphological computa-
tion, self-organization of informational structures through computational processes –
concurrent computational processes, modeled as above.
Understanding intelligence and consciousness, in terms of information and compu-
tation. Explaining how representations (symbolic level) emerge from sub symbolic
information processes. Understanding how exactly our brains process information,
learn and act in terms of information and natural computation on different levels of
organization. Working out the connections between connectionist networks/dynamic
systems and symbol manipulation, sub-symbolic and symbolic information pro-
cessing.
Explaining how physics connects to life and how the fact that we evolved from
physical matter defines the ways we interact with the universe and form our concepts
and actions (observer problem in epistemology). Find out info-computational mecha-
nisms involved in DNA control of cellular processes.
Answering questions for which natural computationalism is especially suitable
framework, such as: why is the genetic difference between humans and other animals
smaller than we imagined before genome sequencing? How does the evident differ-
ence between humans and apes developed, given our social communication system as
computational infrastructure that acts as a basis of human social intelligence estab-
lished by natural computing? All of those questions can be framed in terms of infor-
mation and natural computation and we are looking forward to see them addressed as
the field of natural computing and study of computing nature develop.
From all above proposed research a richer notion of computation will emerge,
which in its turn will help in the next step to better address natural phenomena as
computations on informational structures. As Penrose in the Foreward to [15] states:
“(S)ome would prefer to define “computation” in terms of what a physical object
can (in principle?) achieve (Deutsch, Teuscher, Bauer and Cooper). To me, however,
this begs the question, and this same question certainly remains, whichever may be
our preference concerning the use of the term “computation”. If we prefer to use this
“physical” definition, then all physical systems “compute” by definition, and in that
case we would simply need a different word for the (original Church-Turing) mathe-
matical concept of computation, so that the profound question raised, concerning the
perhaps computable nature of the laws governing the operation of the universe can be
studied, and indeed questioned.”
It seems apt to conclude that nature indeed can be seen as a network of networks of
computational processes and what we are trying is to compute the way nature does,
learning its tricks of the trade. So the focus would not be computability but computa-
tional modeling. How good computational models of nature are we able to produce
and what does it mean for a physical system to perform computation, computation
being implementation of physical laws.
It is evident that natural computing/ computing nature presents a new natural phi-
losophy of generality and scope that largely exceed natural philosophy of Newton’s
era, presented in his Philosophiae Naturalis Principia Mathematica. Natural computa-
tion brings us to the verge of a true paradigm shift in modeling, simulation and con-
trol of the physical world, and it remains to see how it will change our understanding
of nature and especially living nature and humans, societies and ecologies.
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