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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 inducesthe development of technology and natural sciences and viceversa. 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 computationalmodels. It is necessary to extend classical Turing machine modeltowards physical/ natural computation. Important aspects areopenness and interactivity of computational systems, as well asconcurrency of computational processes. The development

proceeds in two directions as a search for new mathematicalstructures beyond algorithms as well as a search for differentmodes of physical computation that are not equivalent to actions

of human executing an algorithm, but appear in physical systemsin which concurrent interactive information processing takes

place. The article presents the framework of info-computationalism as applied on computing nature, where natureis an informational structure and its dynamics (information

processing) is understood as computation. In natural computing,new developments in both understanding of natural systems andin their computational modelling are needed, and those twoconverge 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 (Turings name forTuring machine) simulating a human strictly following analgorithm. But he also devised two other fundamentally differenttheoretical models of computation: neural networks andmorphological computing. In the background for all threemodels we can discern his computational natural philosophy.According to Hodges [2], Turing was a natural philosopher, andnature from patterns on the animal skin to functioning ofhuman brains - was for him possible to understand incomputational terms. Turing lived in a time when computingmachinery still was in its beginnings, and there wascharacteristic dominance of theory over practical devices.

Today on the contrary, it appears that the existing computing

machinery developed faster than the corresponding theory ofcomputation. The consequence is that for different directions ofthe development of computing systems different models of

1School of Innovation, Design and Engineering, Mlardalen University,Sweden. Email: [email protected]

computation apply ranging from classical Turing Machinetheories of [3] to steps beyond in [4][5][6] to interactivecomputing 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 beconfusing. However, the lack of consensus about the nature ofcomputation is not unique and it has the parallel in the currentlack of consensus about the nature of information. Those two arerelated 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 weagree 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 newones, going via phenomena in the real world that we identify asinformation/ computation.

We can compare this situation with the development of otherbasic scientific concepts. Ideas about matter, energy, space andtime have their history. The same is true of the idea of number inmathematics or the idea of life in biology. So, we should not besurprised to notice the development in the theory of computationthat goes along with the development of mathematical methods,new computational devices and new domains of the real worldthat can be modelled computationally.

2 HYSTORY OF COMPUTATION UP TO

ELECTRONIC COMPUTERS

The oldest computational devices were analog. The earliestcalculating tools that humans used were fingers (Latin "digit")and pebbles (Latin calculus) that can be considered as simplemeans of extended human cognition [14]. Tally stick, countingrods and abacus were the first steps towards mechanization ofcalculation. The ancient Greek astronomical analog calculator,Antikythera mechanism, from the second century BC, calculatedthe motions of stars and planets. [15] Among the first knownconstructors of mechanical calculators was Leonardo da Vinci.Pascal invented mechanical calculator that could add andsubtract two numbers directly, and multiply and divide byrepetition, improved by Leibniz who added direct multiplicationand division.

Traditionally, computation was understood as synonymouswith calculation. The first recorded use of the word "computer"was in 1613 to denote apersonwho carried out calculations, andthe word retained the same meaning until the middle of the 20thcentury, when the word "computer" started to assume its currentmeaning, describing a machinethat performs computations.


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Babbage was the first to design a programmablemechanicalcomputer, the general purpose Analytical Engine. The firstelectronic digital computerwas built in 1939 by Atanasoff andBerry and it marks the beginning of the era of digital computing.In 1941 Zuse designed the firstprogrammable computerZ3, alsothe first one based on the binary system. UNIVAC was the firstcomputer capable of running a program from memory. The first

minicomputerPDP was built in 1960 by DEC. Since 1960s theextremely fast growth of computer use was based on thetechnology of integrated circuit/ microchip, which triggered theinvention of the microprocessor, by Intel in 1971. [16]

The progress of computing of course depends both on thedevelopment of hardware and the corresponding development ofsoftware. This includes algorithms, programming languages,compilers and interpreters, operating systems, virtual machines,and so on. Yet a lot of software development was considered asadvanced applications of Turing Machine model. ComputabilityTheory is still based on Turing Machine.

3 BEYOND CONVENTIONAL COMPUTING

MACHINERY: NATURAL COMPUTING

The development of computing, both machinery withprograms and its models, continues. We are accustomed to rapidincrease of computational power, memory and usability ofcomputers, but the limit of miniaturization within the present-day concept of computing is approaching as we are getting closeto quantum dimensions of hardware. One of the ideals ofcomputing ever since the time of Turing is intelligent computing,which would imply machine capable of not only executingmechanical procedure, but even intelligent problem solving.Thus the goal is a computer able to simulate behaviour of humanmathematician, able of making an intelligent insight. Adevelopment of cognitive computingaimed towards human-levelabilities to process/organize/understand information is presentedin [17].

At the same time computational modelling of human braininThe Human Brain Project [18] has for a goal to reveal the exactmechanisms of human brain function that will help usunderstand both how humans actually perform symbol

processing when they follow an algorithm, and also how humanscreate algorithms or models. Those new developments incomputational modelling of brain can be seen as a part of theresearch within the field of natural computing, where naturalsystem performing computation is human brain.

However, natural computing has much broader scope.According to the Handbook of Natural Computing [11] naturalcomputing 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 cellularautomata and neural computation, evolutionary computation,molecular computation, quantum computation, nature-inspiredalgorithms and alternative models of computation.

An important characteristic of the research in naturalcomputing is that knowledge is generated bi-directionally,through the interaction between computer science and naturalsciences. While natural sciences are adopting tools,methodologies and ideas of information processing, computerscience is broadening the notion of computation, recognizinginformation 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 basisfor a unified understanding of phenomena of embodiedcognition, intelligence and knowledge generation. [21][22]

The idea of computing nature has important consequences forour view of computation as information processing thatgeneralizes the idea of algorithm. Computation found in nature isunderstood as a physical process, where nature computes with

physical bodies as objects. Physical laws govern processes ofcomputation, which necessarily appears on many different levelsof organization of physical systems.

Natural computation can be modelled as informationprocessing based on the exchange of information in a network ofagents. An agent is defined as an entity capable of acting in theworld on its own behalf.

One sort of computation is found on the quantum-mechanicallevel where agents are elementary particles, and messages(information carriers) are exchanged by force carriers, anothertype of computation is on the other levels of organization. In

biology, computational processes (information processing) aregoing on in cells, tissues, organs, organisms, and eco-systems,with corresponding agents and message types passed. In

biological computing or social computing the message carriersare complex chunks of information such as molecules, orsentences and the computational nodes (agents) can bemolecules, cells, organisms or groups. [23]

4 COMPUTATION IN CLOSED VS. OPEN

SYSTEMS

As we have seen in Section 2, computational machinery evolvedhistorically from simplest tools of extended human cognition tomechanical computers (calculators) to electronic machines withvacuum tubes and then transistors, to integrated circuits andeventually to microprocessors. During this development ofhardware technologies towards ever smaller, faster and cheaperdevices, the computational principles remained similar: anisolated computing machine calculating a function, executing analgorithm that can be represented by the Turing machine model.

However, since the 1950s computational machinery has beenincreasingly used to exchange information and computersgradually started to connect in networks and communicate. Inthe 1970s computers were connected via telecommunications.The emergence of networking involved a rethinking of the natureof computation and boundaries of a computer. Computeroperating systems and applications were modified to access theresources of other computers in the network. In 1991 CERNcreated the World Wide Web, which resulted in computernetworking becoming a part of everyday life for common

people. By the end of 2011 an estimated 35% of Earth'spopulation used the Internet, according to Wikipedia articleGlobal Internet usage.

With the development of computer networks, twocharacteristics of computing systems have become increasingly

important: parallelism/concurrency and openness both basedon communication between computational units.Comparing new open-system with traditional closed-system

computation models, Hewitt [24] characterizes the Turingmachine model as an internal (individual) framework and hisown Actor model of concurrent computation as an external(sociological) model of computing.


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In order to provide mathematical framework for open-systemmodelling, Burgin and Dodig-Crnkovic analyze methodologicaland philosophical implications of algorithmic aspects ofunconventional/natural computation that extends the closedclassical universe of computation of the Turing machine type.[25] The new model constitutes an open world of algorithmicconstellations, allowing increased flexibility and expressive

power, supporting constructivism and creativity in mathematicalmodelling and enabling richer understanding of computation.The greater power of new types of algorithms also results in thegreater complexity of the algorithmic universe, transforming itinto the algorithmic multiverse. New tools are brought forth bylocal mathematics, local logics and logical varieties.

5 COMPUTATION AS INTERACTION ANDINTERACTIVE COMPUTING

As we have seen in the previous sections, interaction betweencomputational units and processes has become one of the centralissues in computing. In 1998 Wegner developed the interactivemodel of computation [26] which involves interaction, orcommunication, with the environment during computation,

unlikely the traditional Turing machine model of computationwhich goes on in an isolated system. The interactive paradigmincludes concurrent and reactive computations, agent-oriented,distributed and component-based computations, [27].Interestingly, Bohan Broderick [28] argues based on the study oftechnical notions of communication and computation and findsthem practically indistinguishable. The two notions may be keptdistinct if computation is limited to actions within a system andcommunications is an interaction between a system and itsenvironment. Bohan Broderick ascertains.

Goldin and Wegner [27] show, that the paradigm shift fromalgorithms to interactive computation follows the technologyshift from mainframes to networks, and intelligent systems, fromcalculating to communicating, distributed and often even mobiledevices. A majority of the computers today are embedded inother systems and they are continuously communicating witheach other and with the environment. The communicative rolehas definitely prevailed over the initial role of a computer as anisolated calculating machine.

The following characteristics distinguish this new, interactivenotion of computation [7]:

- Computational problem is defined as performing a task, [ina dynamical environment my addition] rather than(algorithmically) producing an answer to a question.

- Dynamic input and output are modelled by dynamic streamswhich are interleaved; later values of the input stream maydepend 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 dynamicallysupplying the computational system with the inputs, andconsuming the output values from the system.

- Concurrency: the computing system (agent) computes inparallel with its environment, and with other agents. (Agents canconsist of agents networks, recursively.)

- Effective non-computability: the environment cannot beassumed to be static or effectively computable. We cannotalways pre-compute input values or predict the effect of thesystem's output on the environment.

6CONCURRENCY

Even though practical implementations of interactivecomputing such as Internet are decades old, a generalfoundational theory, and the semantics and logic of interactivecomputing is still missing. A theoretical foundation analogous towhat Turing machines are for algorithmic computing, is under

development. [26][12][29][24] One important aspect ofinteractive computing is concurrency. In concurrent systemsmultiple agents (processes) interact with each other. In biology,where systems are typically concurrent, the following models ofconcurrent computation are used: Petri nets, Process calculi,Interacting state machines, Boolean networks (especially forgene regulatory networks).

The advantages of concurrency theory that is used to simulateobservable natural phenomena are according to [30] that:

it is possible to express much richer notions of time andspace 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 onewants 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 observerinto the model by allowing certain shifting of the inside-outsidesystem boundary. According to Abramsky [29]:

An important quality of Petris 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 Petris 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 ofhuman, then it seems unavoidable to further develop new modelsof computation, especially interactive computing and naturalcomputing. Living systems are essentially open and in constantcommunication with the environment. New computationalmodels must include interactive, embodied, concurrentcomputation 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 concurrentmachines are asynchronous, and thus not equivalent to Turingmachines. [37] If a machine is composed of asynchronousconcurrently running subsystems, and their relative frequenciesvary randomly, then such a machine cannot be adequatelymodelled by Turing machine.

Turing machines are discrete but can in principle approximatemachines with continuous changes, but cannot implement them


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Cooper in his article Turing's Titanic Machine? [39]diagnoses the limitations of the Turing machine model andidentifies the following ways for overcoming those limitations:

Embodiment invalidating the `machine as data' anduniversality paradigm.

The organic linking of mechanics and emergent outcomesdelivering a clearer model of supervenience of mentality on

brain functionality, and a reconciliation of different levels ofeffectivity.

A reaffirmation of experiment and evolving hardware, forboth AI and extended computing generally.

The validating of a route to creation of new informationthrough interaction and emergence.

Related article by the same author, The Mathematician's Biasand the Return to Embodied Computation, elucidates thedifferences of physical computation compared to universalsymbol manipulation. [40]

From all above it is clear that Turing machine model ofcomputation is an abstraction and idealization. In general, thetrend in computing can be discerned towards extension to moreand 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 ofcomputing is logic. The underlying logic of Turings LogicalCalculating Machine is fully consistent standard logic. Hintikka

proposes Logic as a Theory of Computability, still within thesame classical framework. [41]

Turing machine is assumed always to be in a well definedstate. [24] In contemporary computing machinery, however, weface both states that are not well defined (in the process oftransition) 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 isquite 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 modelinteractive computation, and that classical logic must be robusttowards inconsistencies i.e. must be paraconsistent due to theincompleteness of interaction.

10 INFORMATION/ COMPUTATION AND

MATTER/ENERGY

As pointed out in the introduction, not only the idea ofcomputation is under dynamic development, but similar is trueof the concept of information. Both processes can be seen as aresult of current rapid development of information technology/

computing machinery and our newly acquired insights insciences, largely based on the development of information andcommunication technology.

Even though we are far from having a consensus on theconcept of information, the most general view is that informationis a structure consisting of data. Floridi [43] has the followingdefinition of datum: In its simplest form, a datum can bereduced to just a lack of uniformity, that is, a binary difference.Batesons the difference that makes the difference [44] is adatum in that sense. Information is both the result of observeddifferences (differentiation of data) and the result of synthesis ofthose data into a common informational structure (integration ofdata), as argued by Schroeder in [47]. In the process ofknowledge generation an intelligent agent moves between thosetwo processes differentiation and integration of data. It iscentral to keep in mind that for something to be informationthere must exist an agent from whose perspective this structureis established. Thus information is a network of data pointsrelated from an agents perspective.

There is a distinction between the world as it existsautonomously, independent from any agent, Kantian ding ansich, (thing in itself, nuomenon) and the world for an agent,things as they appear through interactions (phenomena).

Informational realists (like Floridi, Sayre, Vedral) take thereality/world/universe to be information. In [23] I added byanalogy information an sich representative of the ding ansich as apotential information for an agent.

When does this potential information become actualinformation for an agent?

The world in itself is (proto)information that gets actualthrough interactions with agents and huge parts of the universe

are potential information for different kinds of agents fromelementary particles, to molecules, etc. and all the way up tohumans and societies.

Living organisms as complex agents inherit bodily structures(which ultimately are informational structures) as a result of along evolutionary development of species. Those structures areembodied memory of the evolutionary past. They present themeans for agents to interact with the world, get new memories,learn new patterns of behaviour and construct knowledge. Worldvia Hebian learning forms a humans (or an animals)informational structures.

If we say that for something to be information there mustexist an agent from whose perspective this structure isestablished, and we argue that the fabric of the world isinformational, 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 ofinhomogeneities (data), establishing the connections betweenthose data and the data that constitute the agent itself (a particle,a system). There are myriads of agents for whom information ofthe world makes differences (Batesons difference that makesthe 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 informationdynamics is natural computation. When I interact via computer,

photons from the screen reach my retina, and agents are bothphotons and the cells that photon hits and interacts with but alsoall the other parts of the system that transfer and processinformation from my eye to my brain and back to the motorcontrol that controls my fingers that type on the keyboard. I can

also see myself as an agent and my agency in this case isdifferent from the agency of the cells on my retina. In short, thisis 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 andphysicists are already working on reformulating physics in termsof information. This development can be related to theWheelers idea it from bit. [45] For more details on currentresearch, see the special issue of the journal Informationdedicated to matter/energy and information [46], with articles byVedral, Goyal, Brenner, Matsuno and Salthe, Fields, Fiorillo,Yoshitake and Saruwatari, Luhn and Zenil. Furthermore, a recentspecial issue of the journal Entropy addressesnatural/unconventional computing [47] with articles byChiribella, DAriano and Perinotti, Stepney, Ehresmann, DodigCrnkovic and Burgin, Zenil, Gershenson, Marshall andRosenblueth. All contributions explore the space of naturalcomputation 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] (theview that nature represents a complex informational structure fora cognizing agent), the framework of info-computationalism isconstrued [21]. Within info-computationalism the timedevelopment (dynamics) of physical states in nature isunderstood as information processing. Such processes include

self-organization processes, self-assembly, developmentalprocesses, gene regulation networks, gene assembly, protein-protein interaction networks, biological transport networks, andsimilar processes found in nature. The majority of info-computational processes are sub-symbolic and some aresymbolic (in case of agents capable of symbol manipulation).

Within info-computational framework, computation on agiven level of organization presents a realization/actualization ofthe laws that govern interactions between constituent parts.Computation comes with built-in causation. What happens inevery next layer of organization of matter is that a set of rulesgoverning the system switch to the new emergent regime. Itremains yet to be revealed how this process exactly goes on innature, how emergent properties occur. With help of naturalcomputing we may hope to uncover those mechanisms.

In words of Rozenberg and Kari: (O)ur task is nothing lessthan to discover a new, broader, notion of computation, and tounderstand the world around us in terms of information

processing. [19] From the research in complex dynamicalsystems, 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 achemical 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 producingpatterns actually performed computation. Nevertheless, from theperspective of info-computationalism we can argue thatmorphogenesis is a process of morphological computing.Physical process though not computational in the traditionalsense, presents natural (unconventional), morphologicalcomputation. Essential element in this process is the interplay

between the informational structure and the computationalprocess - information self-structuring and informationintegration, both synchronic and diachronic, going on indifferent time and space scales in physical bodies.

Informational structure presents a program that governscomputational process [23], which in its turn changes thatoriginal informational structure obeying/implementing/realizing

physical laws.

Morphology is the central idea in understanding of theconnection between computation (morphological/morphogenetical) and information. What is observed asmaterials on one level of analysis, represents morphology on thelower level, recursively. So water as material presentsarrangements of [molecular [atomic [elementary particle [] ]]]structures.

Info-computational naturalism describes nature asinformational structure a succession of levels of organizationof information. Morphological computing on that informationalstructure leads to new informational structures via processes ofself-organization of information. Evolution itself is a process ofmorphological computation on a long-term scale. It will beinstructive within the info-computational framework to study

processes of self organization of information in an agent (as wellas in population of agents) able to re-structure themselves

through interactions with the environment as a result ofmorphological (morphogenetic) computation.

Cognition can be seen as a result of processes ofmorphological computation on informational structures of acognitive 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 agents body, its nervous (control) system and itsenvironment. Through the embodied interaction with theinformational structures of the environment, via sensory-motorcoordination, information structures are induced in the sensorydata of a cognitive agent, thus establishing perception,categorization and learning.

Essential element in this process is the interplay between theinformational structures and the computational processes -information self-structuring and information integration, both

synchronic and diachronic, going on in different time and spacescales. [22][44][45]

From the simplest cognizing agents such as bacteria to thecomplex biological organisms with nervous systems and brains,the basic informational structures undergo transformationsthrough morphological computation. Here an explanation is inorder regarding cognition which is defined in general way of


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Maturana and Varela who take it to be synonymous with life.[54][55]. All living organisms possess some degree of cognitionand for the simplest ones like bacteria cognition consists inmetabolism and (my addition) locomotion. [21] This process ofinteraction with the environment causes changes in theinformational 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 semanticinformation 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 wemean everything that physically exists not only livingorganisms, animals, plants and microorganisms, geologicalformations, astronomical objects but also machines, humans andhuman societies understood as physical systems in other wordsall that can be described as existing in terms of matter/energyand space/time. Info-computational framework in effect replacesmatter/energy (in space/time) with more basic formulation interms of information/computation (in space/time).

On different levels of physical organization we find differenttypes of natural computation: on quantum level, there is quantumcomputation, on the molecular level there is molecularcomputation, higher up in hierarchy we find nano-computation,networks of proteins are computing in living organisms, DNAcode governs variety of computational processes in cells,metabolic processes are at the same time information processingand they are constitutive of life. Maturana and Varela equatecognition with life. [54][55] Computations of nervous systemsresemble neural network models, living organisms as wholes areregulated on variety of levels and so are ecologies.

Information processing going on in the physical world can bemodelled as computation some of it on continuous flow of

signals, some on discrete signals or symbols, some within livingagents without conscious control, whilst other which proceed vialanguages require conscious living organisms for information to

be processed. Morphological computing can be considered as abasis for all those physical processes that can be studied asinformation 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. Startingwith 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/networkswhich all are in need of better models of computation. Presentaccount highlights several topics of importance for thedevelopment of new understanding of computation and its role inthe physical world: natural computation and the relationship

between the model and physical implementation, interactivity asfundamental for computational modelling of concurrent

information processing systems such as living organisms andtheir networks, and the new developments in mathematicalmodelling needed to support this generalized framework.Besides the Turing machine model as well developed andgenerally established model of computation, variety of newideas, 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 enormousattraction of the idea of final theory of everything (includingsuch 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 oftwo anonymous reviewers and numerous instructive discussionswith Mark Burgin on different models of computation.

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