The Development of Models of Computation
with Advances in Technology and Natural Sciences
Gordana Dodig-Crnkovic 1
Abstract. The development of models of computation induces
the development of technology and natural sciences and vice
versa. Current state of the art of technology and sciences,
especially networks of concurrent processes such as Internet or
biological and sociological systems, calls for new computational
models. It is necessary to extend classical Turing machine model
towards physical/ natural computation. Important aspects are
openness and interactivity of computational systems, as well as
concurrency of computational processes. The development
proceeds in two directions – as a search for new mathematical
structures beyond algorithms as well as a search for different
modes of physical computation that are not equivalent to actions
of human executing an algorithm, but appear in physical systems
in which concurrent interactive information processing takes
place. The article presents the framework of info-
computationalism as applied on computing nature, where nature
is an informational structure and its dynamics (information
processing) is understood as computation. In natural computing,
new developments in both understanding of natural systems and
in their computational modelling are needed, and those two
converge and enhance each other.
1 INTRODUCTION: WHAT IS COMPUTING?1
“The idea behind digital computers may be explained by
saying that these machines are intended to carry out any
operations which could be done by a human computer.”
Turing in  p.436
Turing pioneered the development of first digital computers,
based on his Logical Calculating Machine (Turing’s name for
Turing machine) simulating a human strictly following an
algorithm. But he also devised two other fundamentally different
theoretical models of computation: neural networks and
morphological computing. In the background for all three
models we can discern his computational natural philosophy.
According to Hodges , Turing was a natural philosopher, and
nature – from patterns on the animal skin to functioning of
human brains - was for him possible to understand in
computational terms. Turing lived in a time when computing
machinery still was in its beginnings, and there was
characteristic dominance of theory over practical devices.
Today on the contrary, it appears that the existing computing
machinery developed faster than the corresponding theory of
computation. The consequence is that for different directions of
the development of computing systems different models of
1 School of Innovation, Design and Engineering, Mälardalen University,
Sweden. Email: email@example.com
computation apply ranging from classical Turing Machine
theories of  to steps beyond in  to interactive
computing of , and natural computing in different variations
 to the view that computing is a natural science
The existing diversity of ideas about computing can be
confusing. However, the lack of consensus about the nature of
computation is not unique and it has the parallel in the current
lack of consensus about the nature of information. Those two are
related questions and both have two parts:
a) What is it in the world that corresponds to information/
b) How do we model that information/ computation [once we
agree upon what in the world they correspond to]?
The answer to the above is not simple, as concepts are theory-
laden and we use our existing theories in order to formulate new
ones, going via phenomena in the real world that we identify as
We can compare this situation with the development of other
basic scientific concepts. Ideas about matter, energy, space and
time have their history. The same is true of the idea of number in
mathematics or the idea of life in biology. So, we should not be
surprised to notice the development in the theory of computation
that goes along with the development of mathematical methods,
new computational devices and new domains of the real world
that can be modelled computationally.
2 HYSTORY OF COMPUTATION UP TO
The oldest computational devices were analog. The earliest
calculating tools that humans used were fingers (Latin "digit")
and pebbles (Latin “calculus”) that can be considered as simple
means of extended human cognition . Tally stick, counting
rods and abacus were the first steps towards mechanization of
calculation. The ancient Greek astronomical analog calculator,
Antikythera mechanism, from the second century BC, calculated
the motions of stars and planets.  Among the first known
constructors of mechanical calculators was Leonardo da Vinci.
Pascal invented mechanical calculator that could add and
subtract two numbers directly, and multiply and divide by
repetition, improved by Leibniz who added direct multiplication
Traditionally, computation was understood as synonymous
with calculation. The first recorded use of the word "computer"
was in 1613 to denote a person who carried out calculations, and
the word retained the same meaning until the middle of the 20th
century, when the word "computer" started to assume its current
meaning, describing a machine that performs computations.
Author's copy of a text published by The Society for the Study of Artificial Intelligence and the
Simulation of Behaviour http://www.aisb.org.uk in the
Proceedings of The 6th AISB Symposium on Computing and Philosophy: The Scandal of Computation
- What is Computation?. Mark Bishop and Yasemin J. Erden (editors)
Babbage was the first to design a programmable mechanical
computer, the general purpose Analytical Engine. The first
electronic digital computer was built in 1939 by Atanasoff and
Berry and it marks the beginning of the era of digital computing.
In 1941 Zuse designed the first programmable computer Z3, also
the first one based on the binary system. UNIVAC was the first
computer capable of running a program from memory. The first
minicomputer PDP was built in 1960 by DEC. Since 1960s the
extremely fast growth of computer use was based on the
technology of integrated circuit/ microchip, which triggered the
invention of the microprocessor, by Intel in 1971. 
The progress of computing of course depends both on the
development of hardware and the corresponding development of
software. This includes algorithms, programming languages,
compilers and interpreters, operating systems, virtual machines,
and so on. Yet a lot of software development was considered as
advanced applications of Turing Machine model. Computability
Theory is still based on Turing Machine.
3 BEYOND CONVENTIONAL COMPUTING
MACHINERY: NATURAL COMPUTING
The development of computing, both machinery with
programs and its models, continues. We are accustomed to rapid
increase of computational power, memory and usability of
computers, but the limit of miniaturization within the present-
day concept of computing is approaching as we are getting close
to quantum dimensions of hardware. One of the ideals of
computing ever since the time of Turing is intelligent computing,
which would imply machine capable of not only executing
mechanical procedure, but even intelligent problem solving.
Thus the goal is a computer able to simulate behaviour of human
mathematician, able of making an intelligent insight. A
development of cognitive computing aimed towards human-level
abilities to process/organize/understand information is presented
At the same time computational modelling of human brain in
The Human Brain Project  has for a goal to reveal the exact
mechanisms of human brain function that will help us
understand both how humans actually perform symbol
processing when they follow an algorithm, and also how humans
create algorithms or models. Those new developments in
computational modelling of brain can be seen as a part of the
research within the field of natural computing, where natural
system performing computation is human brain.
However, natural computing has much broader scope.
According to the Handbook of Natural Computing  natural
computing is “the field of research that investigates both human-
designed computing inspired by nature and computing taking
place in nature.” It includes among others areas of cellular
automata and neural computation, evolutionary computation,
molecular computation, quantum computation, nature-inspired
algorithms and alternative models of computation.
An important characteristic of the research in natural
computing is that knowledge is generated bi-directionally,
through the interaction between computer science and natural
sciences. While natural sciences are adopting tools,
methodologies and ideas of information processing, computer
science is broadening the notion of computation, recognizing
information processing found in nature as computation.
 That led Denning  to argue that computing
today is a natural science. Natural computation provides a basis
for a unified understanding of phenomena of embodied
cognition, intelligence and knowledge generation. 
The idea of computing nature has important consequences for
our view of computation as information processing that
generalizes the idea of algorithm. Computation found in nature is
understood as a physical process, where nature computes with
physical bodies as objects. Physical laws govern processes of
computation, which necessarily appears on many different levels
of organization of physical systems.
Natural computation can be modelled as information
processing based on the exchange of information in a network of
agents. An agent is defined as an entity capable of acting in the
world on its own behalf.
One sort of computation is found on the quantum-mechanical
level where agents are elementary particles, and messages
(information carriers) are exchanged by force carriers, another
type of computation is on the other levels of organization. In
biology, computational processes (information processing) are
going on in cells, tissues, organs, organisms, and eco-systems,
with corresponding agents and message types passed. In
biological computing or social computing the message carriers
are complex chunks of information such as molecules, or
sentences and the computational nodes (agents) can be
molecules, cells, organisms or groups. 
4 COMPUTATION IN CLOSED VS. OPEN
As we have seen in Section 2, computational machinery evolved
historically from simplest tools of extended human cognition to
mechanical computers (calculators) to electronic machines with
vacuum tubes and then transistors, to integrated circuits and
eventually to microprocessors. During this development of
hardware technologies towards ever smaller, faster and cheaper
devices, the computational principles remained similar: an
isolated computing machine calculating a function, executing an
algorithm that can be represented by the Turing machine model.
However, since the 1950s computational machinery has been
increasingly used to exchange information and computers
gradually started to connect in networks and communicate. In
the 1970s computers were connected via telecommunications.
The emergence of networking involved a rethinking of the nature
of computation and boundaries of a computer. Computer
operating systems and applications were modified to access the
resources of other computers in the network. In 1991 CERN
created the World Wide Web, which resulted in computer
networking becoming a part of everyday life for common
people. By the end of 2011 an estimated 35% of Earth's
population used the Internet, according to Wikipedia article
Global Internet usage.
With the development of computer networks, two
characteristics of computing systems have become increasingly
important: parallelism/concurrency and openness – both based
on communication between computational units.
Comparing new open-system with traditional closed-system
computation models, Hewitt  characterizes the Turing
machine model as an internal (individual) framework and his
own Actor model of concurrent computation as an external
(sociological) model of computing.
In order to provide mathematical framework for open-system
modelling, Burgin and Dodig-Crnkovic analyze methodological
and philosophical implications of algorithmic aspects of
unconventional/natural computation that extends the closed
classical universe of computation of the Turing machine type.
 The new model constitutes an open world of algorithmic
constellations, allowing increased flexibility and expressive
power, supporting constructivism and creativity in mathematical
modelling and enabling richer understanding of computation.
The greater power of new types of algorithms also results in the
greater complexity of the algorithmic universe, transforming it
into the algorithmic multiverse. New tools are brought forth by
local mathematics, local logics and logical varieties.
5 COMPUTATION AS INTERACTION AND
As we have seen in the previous sections, interaction between
computational units and processes has become one of the central
issues in computing. In 1998 Wegner developed the interactive
model of computation  which involves interaction, or
communication, with the environment during computation,
unlikely the traditional Turing machine model of computation
which goes on in an isolated system. The interactive paradigm
includes concurrent and reactive computations, agent-oriented,
distributed and component-based computations, .
Interestingly, Bohan Broderick  argues based on the study of
technical notions of communication and computation and finds
them practically indistinguishable. “The two notions may be kept
distinct if computation is limited to actions within a system and
communications is an interaction between a system and its
environment.” – Bohan Broderick ascertains.
Goldin and Wegner  show, that the paradigm shift from
algorithms to interactive computation follows the technology
shift from mainframes to networks, and intelligent systems, from
calculating to communicating, distributed and often even mobile
devices. A majority of the computers today are embedded in
other systems and they are continuously communicating with
each other and with the environment. The communicative role
has definitely prevailed over the initial role of a computer as an
isolated calculating machine.
The following characteristics distinguish this new, interactive
notion of computation :
- Computational problem is defined as performing a task, [in
a dynamical environment – my addition] rather than
(algorithmically) producing an answer to a question.
- Dynamic input and output are modelled by dynamic streams
which are interleaved; later values of the input stream may
depend on earlier values in the output stream and vice versa.
- The environment of the computation is a part of the model,
playing an active role in the computation by dynamically
supplying the computational system with the inputs, and
consuming the output values from the system.
- Concurrency: the computing system (agent) computes in
parallel with its environment, and with other agents. (Agents can
consist of agents networks, recursively.)
- Effective non-computability: the environment cannot be
assumed to be static or effectively computable. We cannot
always pre-compute input values or predict the effect of the
system's output on the environment.
Even though practical implementations of interactive
computing such as Internet are decades old, a general
foundational theory, and the semantics and logic of interactive
computing is still missing. A theoretical foundation analogous to
what Turing machines are for algorithmic computing, is under
development.  One important aspect of
interactive computing is concurrency. In concurrent systems
multiple agents (processes) interact with each other. In biology,
where systems are typically concurrent, the following models of
concurrent computation are used: Petri nets, Process calculi,
Interacting state machines, Boolean networks (especially for
gene regulatory networks).
The advantages of concurrency theory that is used to simulate
observable natural phenomena are according to  that:
“it is possible to express much richer notions of time and
space in the concurrent interactive framework than in a
sequential one. In the case of time, for example, instead of a
unique total order, we now have interplay between many partial
orders of events--the local times of concurrent agents--with
potential synchronizations, and the possibility to add global
constraints on the set of possible scheduling. This requires a
much more complex algebraic structure of representation if one
wants to "situate" a given agent in time, i.e., relatively to the
occurrence of events originated by herself or by other agents.“
Theories of concurrency are partially integrating the observer
into the model by allowing certain shifting of the inside-outside
system boundary. According to Abramsky :
“An important quality of Petri’s conception of concurrency,
as compared with “linguistic” approaches such as process
calculi, is that it seeks to explain fundamental concepts:
causality, concurrency, process, etc. in a syntax-independent,
“geometric” fashion. Another important point, which may
originally have seemed merely eccentric, but now looks rather
ahead of its time, is the extent to which Petri’s thinking was
explicitly influenced by physics (…).
To a large extent, and by design, Net Theory can be seen as a
kind of discrete physics: lines are time-like causal flows, cuts are
space-like regions, process unfoldings of a marked net are like
the solution trajectories of a differential equation. This acquires
new significance today, when the consequences of the idea that
“Information is Physical”  are being explored in the rapidly
developing field of quantum informatics.”
If the current programme for computation is formulated as
aiming at reconstruction of the computational capabilities of
human, then it seems unavoidable to further develop new models
of computation, especially interactive computing and natural
computing. Living systems are essentially open and in constant
communication with the environment. New computational
models must include interactive, embodied, concurrent
computation processes in order to be applicable not only to
physics but also to biological and social phenomena.
As Sloman shows, 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
concurrently running subsystems, and their relative frequencies
vary randomly, then such a machine cannot be adequately
modelled by Turing machine.
Turing machines are discrete but can in principle approximate
machines with continuous changes, but 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  and .
Theoretical model of concurrent (interactive) computing that
would be the counterpart of 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 proper subset of a more
general interactive, embodied, concurrent computation.
7 DIGITAL VS. ANALOG, DISCRETE VS.
CONTINUOUS AND SYMBOLIC VS. SUB-
Among many discussions concerning concepts of
computation, a prominent place is given to the controversy about
the continuous/discrete vs. analogue/digital computation. 
Some believe in the ultimately discrete nature of physical reality
and deny any true continuum. Some believe that human
cognition can be understood in terms of language and symbol
manipulation. Understanding of nature of symbols has relevance
for understanding of human cognition and information
processing going on in human body (including brain and nervous
Trenholme  describes the relationship of analog vs.
“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
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.” 
Both symbolic and sub-symbolic simulations depend on
causal/analog/physical and symbolic type of computation on
some level of abstraction but in the case of symbolic
computation it is the symbolic level where information
processing is observed. Similarly, even though in the sub-
symbolic model symbolic representation exists at some high
level of abstraction (because language is used for its
description), it is the physical agency and its causal structure
that define computation.
Freeman characterizes accurately the relationship between
physical/sub-symbolic and logical/symbolic level in the
“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 simulating 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, including humans, through intentional actions. (…) I
propose that symbol-making operators evolved from neural
mechanisms of intentional action by modification of non-
symbolic operators.“ 
Consequently, our brains use non-symbolic computing
internally in order to manipulate relevant external
In the words of MacLennan , who emphasizes the
importance of continuous computation for natural systems:
“We propose certain non-Turing models of computation, but
our intent is not to advocate models that surpass the power of
Turing Machines (TMs), but to defend the need for models with
orthogonal notions of power. We review the nature of models
and argue that they are relative to a domain of application and
are ill-suited to use outside that domain. Hence we review the
presuppositions and context of the TM model and show that it is
unsuited to natural computation (computation occurring in or
inspired by nature). Therefore we must consider an expanded
definition of computation that includes alternative (especially
analog) models as well as the TM.“
8 THE UNREASONABLE INEFFECTIVENESS
OF MATHEMATICS IN BIOLOGY AND BIAS
Mathematician’s contribution to the development of the idea of
computing nature is central. Turing was mathematician and an
early proponent of natural computing who put forward two
computational models of physical processes – morphological
computing and neural networks.
In the context of computing nature, living systems are
particularly interesting because of their complexity of
informational processing, but up to now science haven’t been
able to adequately model and simulate the behaviour of even the
simplest living organisms. “The unreasonable effectiveness of
mathematics” observed in physics by Wigner  is missing in
biology, according to Gelfand as quoted by Chaitin, see .
Not many people today would claim that human cognition
(information processing going on in our body, including our
brains) can be adequately modelled 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 running in parallel as
communicating sequential processes exchanging information.
We know today that such a system of Turing machines cannot
produce the most general kind of computation, as truly
asynchronous concurrent information processing going on in our
On the other hand, one may object that IBM’s Watson, the
winner in man vs. machine "Jeopardy!" challenge, runs on
contemporary supercomputer which is claimed to be
implementation of the Turing machine. Yet, Watson is
connected to the Internet, and Internet is not a Turing machine. It
is not even a network of Turing machines. Information
processing going on throughout the Internet includes signalling
and communication based on complex concurrent physical
processes that cannot be sequentialized.  As an
illustration see  on parasitic computing that implements
computation on the communication infrastructure of the Internet.
Real world computation is physical.
Cooper in his article Turing's Titanic Machine? 
diagnoses the limitations of the Turing machine model and
identifies the following ways for overcoming those limitations:
− Embodiment invalidating the `machine as data' and
− The organic linking of mechanics and emergent outcomes
delivering a clearer model of supervenience of mentality on
brain functionality, and a reconciliation of different levels of
− A reaffirmation 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, The Mathematician's Bias
and the Return to Embodied Computation, elucidates the
differences of physical computation compared to universal
symbol manipulation. 
From all above it is clear that Turing machine model of
computation is an abstraction and idealization. In general, the
trend in computing can be discerned towards extension to more
and more physics-inspired instead of idealized, symbol-
manipulating models, which are its subset.
9 LOGIC OF COMPUTING AND PARA-
Besides physical embodiment, one of the important aspects of
computing is logic. The underlying logic of Turing’s Logical
Calculating Machine is fully consistent standard logic. Hintikka
proposes Logic as a Theory of Computability, still within the
same classical framework. 
Turing machine is assumed always to be in a well defined
state.  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.” 
Open, interactive and asynchronous systems have special
requirements on logic. Goldin and Wegner  and Hewitt 
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.
10 INFORMATION/ COMPUTATION AND
As pointed out in the introduction, not only the idea of
computation is under dynamic development, but similar is true
of the concept of information. Both processes can be seen as a
result of current rapid development of information technology/
computing machinery and our newly acquired insights in
sciences, largely based on the development of information and
Even though we are far from having a consensus on the
concept of information, the most general view is that information
is a structure consisting of data. Floridi  has the following
definition of datum: “In its simplest form, a datum can be
reduced to just a lack of uniformity, that is, a binary difference.”
Bateson’s “the difference that makes the difference”  is a
datum in that sense. Information is both the result of observed
differences (differentiation of data) and the result of synthesis of
those data into a common informational structure (integration of
data), as argued by Schroeder in . In the process of
knowledge generation an intelligent agent moves between those
two processes – differentiation and integration of data. It is
central to keep in mind that for something to be information
there must exist an agent from whose perspective this structure
is established. Thus information is a network of data points
related from an agent’s perspective.
There is a distinction between the world as it exists
autonomously, independent from any agent, Kantian ”ding an
sich”, (thing in itself, nuomenon) and the world for an agent,
things as they appear through interactions (phenomena).
Informational realists (like Floridi, Sayre, Vedral) take the
reality/world/universe to be information. In  I added by
analogy ”information an sich” representative of the ”ding an
sich” as a potential information for an agent.
When does this potential information become actual
information for an agent?
The world in itself is (proto)information that gets actual
through interactions with agents and huge parts of the universe
are potential information for different kinds of agents – from
elementary particles, to molecules, etc. and all the way up to
humans and societies.
Living organisms as complex agents inherit bodily structures
(which ultimately are informational structures) as a result of a
long evolutionary development of species. Those structures are
embodied memory of the evolutionary past. They present the
means for agents to interact with the world, get new memories,
learn new patterns of behaviour and construct knowledge. World
via Hebian learning forms a human’s (or an animal’s)
If we say that for something to be information there must
exist an agent from whose perspective this structure is
established, and we argue that the fabric of the world is
informational, the question can be asked: who/what is the agent?
An agent (an entity capable of acting on its own behalf in the
world) can be seen as interacting with the points of
inhomogeneities (data), establishing the connections between
those data and the data that constitute the agent itself (a particle,
a system). There are myriads of agents for whom information of
the world makes differences (Bateson’s “difference that makes
the difference”) – from elementary particles to molecules, cells,
organisms, societies… - all of them interact and exchange
information on different levels of scale and this information
dynamics is natural computation. When I interact via computer,
photons from the screen reach my retina, and agents are both
photons and the cells that photon hits and interacts with but also
all the other parts of the system that transfer and process
information from my eye to my brain and back to the motor
control that controls my fingers that type on the keyboard. I can
also see myself as an agent and my agency in this case is
different from the agency of the cells on my retina. In short, this
is an agent-based (or actor-based) view of natural computation.
The change in the physical world happens through data self-
organization in an agent.
Information processes are governed by laws of physics and
physicists are already working on reformulating physics in terms
of information. This development can be related to the
Wheeler’s idea “it from bit”.  For more details on current
research, see the special issue of the journal Information
dedicated to matter/energy and information , with articles by
Vedral, Goyal, Brenner, Matsuno and Salthe, Fields, Fiorillo,
Yoshitake and Saruwatari, Luhn and Zenil. Furthermore, a recent
special issue of the journal Entropy addresses
natural/unconventional computing  with articles by
Chiribella, D’Ariano and Perinotti, Stepney, Ehresmann, Dodig
Crnkovic and Burgin, Zenil, Gershenson, Marshall and
Rosenblueth. All contributions explore the space of natural
computation and relationships between the physical
(matter/energy), information and computation.
As a result of a synthesis of the idea of computing nature
(naturalist computationalism/ pancomputationlism) 
 with the informational structural realism  (the
view that nature represents a complex informational structure for
a cognizing agent), the framework of info-computationalism is
construed . Within info-computationalism the time
development (dynamics) of physical states in nature is
understood as information processing. Such processes include
self-organization processes, self-assembly, developmental
processes, gene regulation networks, gene assembly, protein-
protein interaction networks, biological transport networks, and
similar processes found in nature. The majority of info-
computational processes are sub-symbolic and some are
symbolic (in case of agents capable of symbol manipulation).
Within info-computational framework, computation on a
given level of organization presents a realization/actualization of
the laws that govern interactions between constituent parts.
Computation comes with built-in causation. What happens in
every next layer of organization of matter is that a set of rules
governing the system switch to the new emergent regime. It
remains yet to be revealed how this process exactly goes on in
nature, how emergent properties occur. With help of natural
computing we may hope to uncover those mechanisms.
In words of Rozenberg and Kari: “(O)ur task is nothing less
than to discover a new, broader, notion of computation, and to
understand the world around us in terms of information
processing.”  From the research in complex dynamical
systems, biology, neuroscience, cognitive science, networks,
concurrency and more, new insights essential for the info-
computational universe may be expected in the years to come.
12 MORPHOLOGICAL COMPUTING.
MEANING GENERATION FROM RAW DATA
TO SEMANTIC INFORMATION
In 1952 Turing wrote a paper on morphogenesis proposing a
chemical model as the explanation of the development of
biological patterns such as the spots and stripes on animal skin.
 Turing did not claim that physical system producing
patterns actually performed computation. Nevertheless, from the
perspective of info-computationalism we can argue that
morphogenesis is a process of morphological computing.
Physical process – though not computational in the traditional
sense, presents natural (unconventional), morphological
computation. Essential element in this process is the interplay
between the informational structure and the computational
process - information self-structuring and information
integration, both synchronic and diachronic, going on in
different time and space scales in physical bodies.
Informational structure presents a program that governs
computational process , which in its turn changes that
original informational structure obeying/implementing/realizing
Morphology is the central idea in understanding of the
connection between computation (morphological/
morphogenetical) and information. What is observed as
materials on one level of analysis, represents morphology on the
lower level, recursively. So water as material presents
arrangements of [molecular [atomic [elementary particle  ]]]
Info-computational naturalism describes nature as
informational structure – a succession of levels of organization
of information. Morphological computing on that informational
structure leads to new informational structures via processes of
self-organization of information. Evolution itself is a process of
morphological computation on a long-term scale. It will be
instructive within the info-computational framework to study
processes of self organization of information in an agent (as well
as in population of agents) able to re-structure themselves
through interactions with the environment as a result of
morphological (morphogenetic) computation.
Cognition can be seen as a result of processes of
morphological computation on informational structures of a
cognitive agent in the interaction with the physical world, with
processes going on at both sub-symbolic and symbolic levels.
This morphological computation establishes connections
between an agent’s body, its nervous (control) system and its
environment. Through the embodied interaction with the
informational structures of the environment, via sensory-motor
coordination, information structures are induced in the sensory
data of a cognitive agent, thus establishing perception,
categorization and learning.
Essential element in this process is the interplay between the
informational structures and the computational processes -
information self-structuring and information integration, both
synchronic and diachronic, going on in different time and space
From the simplest cognizing agents such as bacteria to the
complex biological organisms with nervous systems and brains,
the basic informational structures undergo transformations
through morphological computation. Here an explanation is in
order regarding cognition which is defined in general way of
Maturana and Varela who take it to be synonymous with life.
. All living organisms possess some degree of cognition
and for the simplest ones like bacteria cognition consists in
metabolism and (my addition) locomotion.  This process of
interaction with the environment causes changes in the
informational structures that correspond to the body of an agent,
and its control mechanisms, which define its future interactions
with the world and its inner information processing.
Informational structures of an agent become semantic
information first in the case of highly intelligent agents.
13 DEVELOPMENTS AND PROSPECTS OF
NATURAL COMPUTATION. COMPUTING AS
When we talk about natural computation by “nature” we
mean everything that physically exists – not only living
organisms, animals, plants and microorganisms, geological
formations, astronomical objects but also machines, humans and
human societies understood as physical systems – in other words
all that can be described as existing in terms of matter/energy
and space/time. Info-computational framework in effect replaces
matter/energy (in space/time) with more basic formulation in
terms of information/computation (in space/time).
On different levels of physical organization we find different
types of natural computation: on quantum level, there is quantum
computation, on the molecular level there is molecular
computation, higher up in hierarchy we find nano-computation,
networks of proteins are computing in living organisms, DNA
code governs variety of computational processes in cells,
metabolic processes are at the same time information processing
and they are constitutive of life. Maturana and Varela equate
cognition with life.  Computations of nervous systems
resemble neural network models, living organisms as wholes are
regulated on variety of levels and so are ecologies.
Information processing going on in the physical world can be
modelled as computation – some of it on continuous flow of
signals, some on discrete signals or symbols, some within living
agents without conscious control, whilst other which proceed via
languages require conscious living organisms for information to
be processed. Morphological computing can be considered as a
basis for all those physical processes that can be studied as
information self-structuring. 
14 CONCLUSIONS & FUTURE WORK
”I invite readers not on a visit to an archaeological museum,
but rather on an adventure in science in making”
Prigogine  p. IX
In this article too, a new science in making is presented. Starting
with the short history of computational machinery and models,
presentation focuses on the current state of the art of computing
machinery and complex biological and social systems/networks
which all are in need of better models of computation. Present
account highlights several topics of importance for the
development of new understanding of computation and its role in
the physical world: natural computation and the relationship
between the model and physical implementation, interactivity as
fundamental for computational modelling of concurrent
information processing systems such as living organisms and
their networks, and the new developments in mathematical
modelling needed to support this generalized framework.
Besides the Turing machine model as well developed and
generally established model of computation, variety of new
ideas, still under developments are taking shape and have good
prospects to extend our understanding of computation and its
relationship to physical implementations.
As Stephen Hawking aptly noticed, in spite of enormous
attraction of the idea of final theory of everything (including
such theory of everything computational), the progress goes on:
“Some people will be very disappointed if there is not an
ultimate theory that can be formulated as a finite number of
principles. I used to belong to that camp, but I have changed my
mind. I'm now glad that our search for understanding will never
come to an end, and that we will always have the challenge of
new discovery.” 
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