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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 [1] 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 [2], 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: gordana.dodig-crnkovic@mdh.se

computation apply ranging from classical Turing Machine

theories of [3] to steps beyond in [4][5][6] to interactive

computing of [7], and natural computing in different variations

[8][9][10][11] to the view that computing is a natural science

[12][13].

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/

computation?

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

information/ computation.

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

ELECTRONIC COMPUTERS

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 [14]. 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. [15] 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

and division.

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)

ISBN: 978-1-908187-31-4

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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. [16]

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

in [17].

At the same time computational modelling of human brain in

The Human Brain Project [18] 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 [11] 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.

[19][8][9][20] That led Denning [12] 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. [21][22]

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. [23]

4 COMPUTATION IN CLOSED VS. OPEN

SYSTEMS

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 [24] 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.

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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.

[25] 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

INTERACTIVE COMPUTING

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 [26] 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, [27].

Interestingly, Bohan Broderick [28] 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 [27] 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 [7]:

- 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.

6 CONCURRENCY

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. [26][12][29][24] 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 [30] 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 [29]:

“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” [17] 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. [37] 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

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exactly. Continuous systems with non-linear feedback loops may

be chaotic and impossible to approximate discretely, even over

short time scales, see [37] and [24].

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-

SYMBOLIC COMPUTATION

Among many discussions concerning concepts of

computation, a prominent place is given to the controversy about

the continuous/discrete vs. analogue/digital computation. [31]

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

system).

Trenholme [32] 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 simulation.

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.” [32]

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

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 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.“ [33]

Consequently, our brains use non-symbolic computing

internally in order to manipulate relevant external

symbols/objects.

In the words of MacLennan [34], 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

OF MATHEMATICIANS

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 [35] is missing in

biology, according to Gelfand as quoted by Chaitin, see [36].

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

brains. [37]

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. [24][37] As an

illustration see [38] on parasitic computing that implements

computation on the communication infrastructure of the Internet.

Real world computation is physical.

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Cooper in his article Turing's Titanic Machine? [39]

diagnoses the limitations of the Turing machine model and

identifies the following ways for overcoming those limitations:

− Embodiment invalidating the `machine as data' and

universality paradigm.

− 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

effectivity.

− 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. [40]

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-

CONSISTENCY

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. [41]

Turing machine is assumed always to be in a well defined

state. [24] 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.” [42]

Open, interactive and asynchronous systems have special

requirements on logic. Goldin and Wegner [27] and Hewitt [24]

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

MATTER/ENERGY

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

communication technology.

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 [43] 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” [44] 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 [47]. 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 [23] 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)

informational structures.

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

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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”. [45] For more details on current

research, see the special issue of the journal Information

dedicated to matter/energy and information [46], 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 [47] 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.

11 INFO-COMPUTATIONALISM

As a result of a synthesis of the idea of computing nature

(naturalist computationalism/ pancomputationlism) [22][48][49]

[50][51] with the informational structural realism [43][52] (the

view that nature represents a complex informational structure for

a cognizing agent), the framework of info-computationalism is

construed [21]. 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.” [19] 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.

[53] 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 [23], which in its turn changes that

original informational structure obeying/implementing/realizing

physical laws.

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 [] ]]]

structures.

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

scales. [22][44][45]

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

7

Maturana and Varela who take it to be synonymous with life.

[54][55]. All living organisms possess some degree of cognition

and for the simplest ones like bacteria cognition consists in

metabolism and (my addition) locomotion. [21] 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

NATURAL SCIENCE

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. [54][55] 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. [23][48][49]

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 [56] 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.” [57]

ACKNOWLEDGMENTS

The author would like to acknowledge insightful comments of

two anonymous reviewers and numerous instructive discussions

with Mark Burgin on different models of computation.

REFERENCES

[1] A. M. Turing, “Computing Machinery and Intelligence,” Mind,

vol. 59, pp. 433–460, 1950.

[2] A. Hodges, Turing. A Natural philosopher. London: Phoenix,

1997.

[3] A. M. Turing, “On computable numbers, with an application to

the Entscheidungs problem,” Proceedings of the London

Mathematical Society, vol. 42, no. 42, pp. 230–265, 1936.

[4] B. J. Copeland, “What is computation?,” Synthese, vol. 108, no. 3,

pp. 335–359, 1996.

[5] M. Burgin, Super-Recursive Algorithms. New York: Springer-

Verlag New York Inc., 2005, pp. 1–320.

[6] M. Burgin and G. Dodig-Crnkovic, “Information and

Computation – Omnipresent and Pervasive,” in Information and

Computation, New York/London/Singapore: World Scientific Pub

Co Inc, 2011, pp. vii –xxxii.

[7] D. Goldin, S. Smolka, and P. Wegner, Eds., Interactive

Computation: The New Paradigm. Berlin, Heidelberg: Springer,

2006.

[8] S. Stepney, S. L. Braunstein, J. A. Clark, A. M. Tyrrell, A.

Adamatzky, R. E. Smith, T. R. Addis, C. G. Johnson, J. Timmis,

P. H. Welch, R. Milner, and D. Partridge, “Journeys in Non-

Classical Computation I: A Grand Challenge for Computing

Research,” Int. J. Parallel Emerg. Distr. Syst., vol. 20, pp. 5–19,

2005.

[9] S. Stepney, S. L. Braunstein, J. A. Clark, A. M. Tyrrell, A.

Adamatzky, R. E. Smith, T. R. Addis, C. G. Johnson, J. Timmis,

P. H. Welch, R. Milner, and D. Partridge, “Journeys in Non-

Classical Computation II: Initial Journeys and Waypoints,” Int. J.

Parallel Emerg. Distr. Syst., vol. 21, pp. 97–125, 2006.

[10] S. B. Cooper, B. Löwe, and A. Sorbi, New Computational

Paradigms. Changing Conceptions of What is Computable.

Springer Mathematics of Computing series, XIII. Springer, 2008.

[11] G. Rozenberg, T. Bäck, and J. N. Kok, Eds., Handbook of Natural

Computing. Berlin Heidelberg: Springer, 2012.

[12] P. Denning, “Computing is a natural science,” Communications of

the ACM, vol. 50, no. 7, pp. 13–18, 2007.

8

[13] P. Denning, “What is computation?: Editor’s Introduction,”

Ubiquity, no. October, pp. 1–2, 2010.

[14] A. Clark and D. Chalmers, “The Extended Mind,” Analysis, vol.

58, no. 1, pp. 7 – 19, 1998.

[15] J. Marchant, “In search of lost time.,” Nature, vol. 444, no. 7119,

pp. 534–8, 2006.

[16] “The History of Computing Project web page,” 2012. [Online].

Available: http://www.thocp.net/index.html.

[17] Y. Wang, “The Theoretical Framework of Cognitive Informatics,”

Int’l J. of Cognitive Informatics and Natural Intelligence, vol. 1,

no. 1, pp. 1–27, 2007.

[18] H. Markram, “The blue brain project,” Nature reviews.

Neuroscience, vol. 7, no. 2, pp. 153–60, Feb. 2006.

[19] G. Rozenberg and L. Kari, “The many facets of natural

computing,” Communications of the ACM, vol. 51, pp. 72–83,

2008.

[20] S. Stepney, “The neglected pillar of material computation,”

Physica D: Nonlinear Phenomena, vol. 237, no. 9, pp. 1157–

1164, 2008.

[21] G. Dodig-Crnkovic and V. Mueller, “A Dialogue Concerning Two

World Systems: Info-Computational vs. Mechanistic,”

Information and Computation. World Scientific Pub Co Inc,

Singapore, pp. 149–84, 2009.

[22] Y. Wang, “On Abstract Intelligence: Toward a Unifying Theory

of Natural, Artificial, Machinable, and Computational

Intelligence,” Int. J. of Software Science and Computational

Intelligence, vol. 1, no. 1, pp. 1–17, 2009.

[23] G. Dodig-Crnkovic, “Physical Computation as Dynamics of Form

that Glues Everything Together,” Information, vol. 3, no. 2, pp.

204–218, 2012.

[24] C. Hewitt, “What is computation? Actor Model versus Turing’s

Model,” in A Computable Universe, Understanding Computation

& Exploring Na-ture As Computation, H. Zenil, Ed. World

Scientific Publishing Company/Imperial College Press, 2012.

[25] G. Dodig-Crnkovic and M. Burgin, “Unconventional Algorithms:

Complementarity of Axiomatics and Construction,” Entropy, vol.

14, no. 11, pp. 2066–2080, 2012.

[26] P. Wegner, “Interactive foundations of computing,” Theoretical

computer science., vol. 192, no. 2, 1998.

[27] D. Goldin and P. Wegner, “Paraconsistency of Interactive

Computation,” in PCL 2002 (Workshop on Paraconsistent

Computational Logic, 2002, pp. 109–118.

[28] P. Bohan Broderick, “On Communication and Computation,”

Minds and Machines, vol. 14, no. 1, pp. 1 – 19, 2004.

[29] S. Abramsky, “Information, Processes and Games,” in Philosophy

of Information, J. Benthem van and P. Adriaans, Eds. Amsterdam,

The Netherlands: North Holland, 2008, pp. 483–549.

[30] V. Schachter, “How Does Concurrency Extend the Paradigm of

Computation?,” Monist, vol. 82, no. 1, pp. 37–58, 1999.

[31] C. J. Maley, “Analog and digital, continuous and discrete,” Philos.

Stud, vol. 155, pp. 117–131, 2010.

[32] R. Trenholme, “Analog Simulation,” Philosophy of Science, vol.

61, no. 1, pp. 115–131, 1994.

[33] W. J. Freeman, “The neurobiological infrastructure of natural

computing: Intentionality,” New Mathematics and Natural

Computing, NMNC, vol. 5, no. 1, pp. 19–29, 2009.

[34] B. MacLennan, “Natural computation and non-Turing models of

computation,” Theoretical computer science., vol. 317, no. 1,

2004.

[35] E. Wigner, “The Unreasonable Effectiveness of Mathematics in

the Natural Sciences,” Communications in Pure and Applied

Mathematics, vol. 13, no. 1, 1960.

[36] G. Chaitin, “Mathematics, Biology and Metabiology,” 2009.

[Online]. Available:

http://www.umcs.maine.edu/~chaitin/jack.html.

[37] A. Sloman, “The Irrelevance of Turing machines to AI,” in

Computationalism – New Directions (M. Scheutz, Ed.),

Cambridge, Mass: MIT Press, 2002, pp. 87–127.

[38] A.-L. Barabasi, V. W. Freeh, H. Jeong, and J. Brockman,

“Parasitic computing,” Nature, vol. 412, pp. 894–897, 2001.

[39] S. B. Cooper, “Turing’s Titanic Machine?,” Communications of

the ACM, vol. 55, no. 3, pp. 74–83, 2012.

[40] H. Zenil, Ed., A COMPUTABLE UNIVERSE. Understanding

Computation & Exploring Nature As Computation. Singapore:

World Scientific Publishing Company/Imperial College Press,

2012.

[41] J. Hintikka, “Logic as a Theory of Computability,” APA

Newsletter on Philosophy and Computers, vol. 11, no. 1, pp. 2–5,

2011.

[42] G. Priest and K. Tanaka, “Paraconsistent Logic,” The Stanford

Encyclopedia of Philosophy. Zalta, Edward N., 2013.

[43] L. Floridi, “A defense of informational structural realism,”

Synthese, vol. 161, no. 2, pp. 219–253, 2008.

[44] G. Bateson, Steps to an Ecology of Mind: Collected Essays in

Anthropology, Psychiatry, Evolution, and Epistemology.

University Of Chicago Press, 1972, pp. 448–466.

[45] J. A. Wheeler, “Information, physics, quantum: The search for

links,” in Complexity, Entropy, and the Physics of Information, W.

Zurek, Ed. Redwood City: Addison-Wesley, 1990.

[46] G. Dodig-Crnkovic, “Information and Energy/Matter,”

Information, vol. 3, no. 4, pp. 751–755, 2012.

[47] G. Dodig-Crnkovic and R. Giovagnoli, “Natural/Unconventional

Computing and its Philosophical Significance,” Entropy, vol. 14,

pp. 2408–2412, 2012.

[48] G. Dodig-Crnkovic, “Info-computationalism and Morphological

Computing of Informational Structure,” in Integral Biomathics, A.

Simeonov, P., Smith, L. and Ehresmann, Ed. Berlin, Heidelberg: ,

2012.

[49] G. Dodig-Crnkovic, “The Info-computational Nature of

Morphological Computing,” in Theory and Philosophy of

Artificial Intelligence, SAPERE., V. C. Müller, Ed. Berlin:

Springer, 2012, p. forthcoming.

[50] G. Dodig-Crnkovic and R. Giovagnoli, Computing Nature. Berlin

Heidelberg: Springer.

[51] G. Dodig-Crnkovic, “Significance of Models of Computation

from Turing Model to Natural Computation,” Minds and

Machines,, vol. 21, no. 2, pp. 301–322, 2011.

[52] K. M. Sayre, Cybernetics and the Philosophy of Mind. London:

Routledge & Kegan Paul, 1976.

[53] A. M. Turing, “The Chemical Basis of Morphogenesis,”

Philosophical Transactions of the Royal Society of London, vol.

237, no. 641, pp. 37–72, 1952.

[54] H. Maturana, Biology of Cognition. Ft. Belvoir: Defense

Technical Information Center, 1970.

[55] H. Maturana and F. Varela, Autopoiesis and cognition: the

realization of the living. Dordrecht Holland: D. Reidel Pub. Co.,

1980.

[56] I. Prigogine, The End of Certainty: Time, Chaos and New Laws of

Nature. New York: The Free Press, 1997.

[57] S. Hawking, “Gödel and the end of Physics.” [Online]. Available:

http://www.damtp.cam.ac.uk/events/strings02/dirac/hawking/.