Intrododuction: is artificial life possible?
When posing the question "is artificial life possible?", our immediate answer is that on the one hand: of course it is - people make it, and indeed very interesting and even breathtaking structures have already been constructed, such as `aminats', self-reproducing patterns and the other things, we have seen already. In this sense we are forced to take artificial life as a fact (at least as a fact about a new branch of research), nearly in the same way that the philosopher Kant took the theoretical physics of his days, Newtonian physics, as a matter of fact, and then asked: What are the conditions of possibility for this kind of theoretical science? On the other hand: The situation differs from Kant's. Artificial Life does not confront us with an analogy of theoretical mechanics within the field of biology. We face a curious situation: It is not obvious to the majority of biologists that Artificial Life is possible at all, at least in the purely computational sense of `software life'. Probably, most biologists would never call these artificial constructs `living'. Why not? Because the intuitive notions of life and living systems within biology implies, among other things, that living beings are a result of a long, ongoing evolutionary process that have created autonomous organisms, single-celled and multi-celled, that are highly organized, open (non-equilibrium), material thermodynamic systems based on metabolism and some kind of genetic information supported by macromolecules, that only metaphorically resemble a computer program. It is not that biologists do not think there are some general principles in their field, some kind of `logic of life' (cf. F. Jacob20) or universal forms of the processes that characterizes living phenomena. The genetic code and the structure of heredity is an example. But for biologists, life is not a question of pure form, or formal processes; one might characterize the biological way of looking at things as life seen as a formal-and-material phenomenon.
So the question about the possibility of artificial life immediately raises three other questions; (1) what counts as `artificial life'; (2) what is `real life' after all (and what kind of biology do we invent); and (3) after what criteria can we claim not only to model, modify and experiment with existing life, but also to realize, i.e. `synthesize' life, or different modes of living behaviour. The modeling situation should be considered more closely when simulating formal models of natural systems and artificial universes. Let us first shortly state our basic opinion and simple conjectures on these questions before we proceed to give the full arguments:
1: Artificial Life is many things
That Artificial Life is not a unitary field of research but include very different phenomena is fairly obvious. There are at least these different ideas of what constitute an artificial living system (for a more methodologically oriented classification, see Taylor34):
I) Trivial versions of `artificial' `life':
a. Alife as different (mathematical, conceptual, physical) models of living systems. This is a rather trivial (or `weak') version of the Alife research programme: Everybody seems to agree upon the possibility of modeling living phenomena, these models can be computational or not. However, even here, a closer look reveals disagreement with respect to the adequacy of the formal, computational approach, even conceived of as just models (not the real thing). If we chose computational (or if you like: informational) models, is that just for representational convenience, or is it because we think that the thing modeled is also in some sense computational, or informational? This non-trivial question is not yet clarified.
b. Artificially modified living organisms (e.g., by gene splicing or cell fusion). Domestic animals and food crops are life modified by humans, and thus `artificial' systems, produced for the purpose of man.
II) Non-trivial versions of Alife: (This is Alife as `realized life' de novo, or by non-biological means).
1. Alife as computerlife. I.e., computational systems with emergent lifelike phenomena in a range of complexity that in the eye of the beholder seems to approach Nature's own organisms. (This is the `strong version' of Alife). Many levels of life and even chemistry (cf. `algorithmic chemistry') is included in this concept.
2. Alife as animats (and robots). This is a branch of neocybernetics.
2a. A subgroup is `evolutionary robotics', a vision of man-made creation of autonomous systems, that can live a life of their own by exploiting material and energy-ressources to maintain, rebuilt and `reproduce' their own kind; eventually as semi-autonomous agents that still depend on human society as a source of components for rebuilding and reproduction of their own kinds.
2b. `Weak version robotic Alife': In this group we find robots and animats built for technical purposes which are seen to behave in a `lifelike' manner. This, however, is recognized to be a by-product of our interpretation, the behaviour of these systems represents a category quite distinct from the behaviour of the carbon-based biological cells and organisms.
3. Chemical Alife, i.e., attempts to make real material systems with lifelike characteristics, eventually as in vitro models of prebiotic processes; primitive metabolic systems; Eigen hypercyclic systems; replicating micelles, etc. The goal is to turn in vitro experiments into life in vivo de novo.
Now, one problem with all these individually interesting disciplines is that their integration into a coherent framework of investigation is still very weak. The skeptic will say that they in principle have so little in common that integration might never be achieved (compare Belew3). The common ideas of self-organization, emergence and related concepts are vague and ambiguous. In the long run, it may be a problem for a research program not to study a coherent set of phenomena, but something that may be fundamentally different categories of systems that do not have much in common, except some broad methodological common principles. For the present, it is hardly known to which extent there is general agreement about a set of principles that may constitute `the hard core' of the Alife research programme. So Artificial Life seems to be quite different categories of phenomena. What about real life?
2: Real life as a multiple phenomenon
It is sometimes said that we all have some basic intuitions of what biological life is because, unlike stars and galaxies, we are ourselves living beings and know life `from within'. But can one be so certain about the givenness of this intuition? Surely, we have a `view from within'; but that is not a concept of life (it is rather a qualitative aspect of living consciousness). Have humans beings always been thinking of life as a unitary phenomenon? Obviously not.
`Primitive' (which frankly reads non-occidental) animistic thinking often describes the whole world and its parts as living, but this does not discriminate life in our modern sense. In later and more systematic natural philosophies we find concepts, such as the Psyche in Aristotle, which might be compared with a modern generic concept of life as a set of distinct characteristics (or formal properties) unique to living beings as opposed to non-living matter. (The psyche in Aristotle was in fact a diffentiated level-specific concept, distinguishing the vegetative, the animate and the specific human psyche, a valuable idea, even in modern accounts of psychogenesis12).
In the middle ages, there was still no science of biology in the modern sense but a lot of categorizing activity, and Nature was understood as distinct domains or Kingdoms. There were no unifying concepts of life. According to Foucault, life as a general category with a socially valid meaning did not exist, except perhaps, as one character in the universal distribution of beings or `the Great Chain of Being'. Up to the end of the eighteenth century, only living beings existed, forming "several classes, in the series of all things in the world" (Foucault15 p.160).
The generic concept of life was first developed by some natural historians in the late sixteenth century (such as J. Blumenbach, F. Vicq d'Azyr, A.-L. de Jussieu and L.J.M. Daubenton) who promoted the idea that organization was such an important distinct feature that separated the living from the inorganic nature, and that this difference was more fundamental than the difference between the animal and plant kingdoms. In the following century, the degree of organization became an important key to the study of a natural (as opposed to arbitrary) classification of the order of living Nature. Lamarck temporalized the static view of a chain of being and offered the revolutionary vision that the more complex could have originated from the less complex. In 1802 he coined the term biology, by which he wanted to denote the study of all pertaining to "living bodies, their organization, their developmental processes and their structural complexity" (G. Treviranus and K.F. Burdach independently invented the same term in 1800). Both Treviranus and Lamarck implied that they have identified a new field of research rather than give a new name to an old. In Lamarck it was a part of his struggle against the `imperialism' of the mathematical physicists whose ideas intruded every field and rejected the validity of the methods of natural history at that time. Biology became widely known as one of the `higher sciences' through the works of August Comte in the 1830s, and biology in the modern sense began to take form in the last part of this century, especially after Darwin and the new physiology.
During this whole period, one can find incredible variation as to what was seen to constitute the `basic facts' of living phenomena. We will not deal this complicated story. Instead, we shall put forward the idea that Artificial Life can be seen as a deconstruction of our present rational conceptions of life as a unitary phenomenon, constituted by a single universal set of `generic' properties. (The term deconstruction is borrowed from literary criticism30 and originates in the philosophy of Jacques Derrida, who hoped for `deconstructing' western metaphysics since Plato by so to speak undermine its foundation from within by its own concepts, oppositions and ideas. Deconstruction is both destructive and constructive, but at the same time neither, because Derrida questions the idea that critical reading or construction of alternatives can proceed in a language that is not from the beginning infected by metaphysical ideas. Here, we do not claim to use the term in the original derridaean sense). Alife research reveals that our concept of life is not a single one as we wish to think, and that no simple set of fundamental criteria can decide the status of our models and constructs when these are already embedded in specific preconceptions of what constitutes the aliveness of natural and artificial creatures. This `deconstructive move' is a consequence of the inquiry of fundamental Alife research. It may help one to realize that at least the following different `conceptual models' of life as a biological phenomenon exist: An old idea about the organism as living animal; the scientific idea of the cell as the simplest living thing; life as an abstract phenomenon; and life in the cybernetic sense as a machine process that can be made by natural selection or by an engineer. Other ideas of life exist as well, but the focus is here restricted to the more-or-less rational ones.
We normally think of life in the biological sense as having something to do with `good old fashioned biological organisms' (GOFBO), either single cells, or made up of cells, these having a metabolism, constituted by specific macromolecules, etc. But this is already `too much'; we do not need all these details if we are interested in simply drawing a boundary between the living and nonliving world. First and foremost, we have the old prototypic concept of life as a cluster of characteristics, more or less motivated by our knowledge of biology. There are many versions of this prototypical GOFBO concept (e.g., Mayr28, Farmer & Belin13). Life has irritability; metabolism; it can self-reproduce, feed and develop; it is vulnerable to illness and death. A given instance may not have all of these properties, but it will have many.
We can then go on to see what is implied by these properties such as self-reproduction or metabolism. To do so we have to consult the disciplines of biology and acquire knowledge of cells, membranes, enzyme systems, genetic coded information and other vital structures and processes. If anything can be said to be alive, it will have to be organized on the biological level as a cell or as a system of cells (even viruses require a cell as a necessary part of their cycle of existence, and should thus be considered as a pathological subcomponent of the cell). Thus the next step is a more specific conception of life described at a lower level (the cell and its macromolecular organization). We call this concept of life MOMACE: modern macromolecular-based cells. Molecular biologists seldom care to define life -- they know it when they have it, and they know that its complexity is immense when compared with ordinary organic chemistry.
Logically, the two concepts are not equivalent, there is no simple connection between the prototypic old concept of life and the modern concept that explicitly or implicitly involves the existence of cells. Already here we can see that biology of our time has not one, but two conceptions of life. In fact, Sagan33 drew attention to five different definitions of life, based on physiology, metabolism, biochemistry, genetics and thermodynamics. Now, if we want to construct life artificially by abstracting its logical form (to use von Neumann's35 and Langton's24 words), and subsequently realize this form in other media, it is most likely that we get two different things depending on our point of departure.
From the first concept, we get neo-cybernetic life: animats, robots and other lifelike devices29, i.e. ROLI: robotic life. That is, machines that are living in the sense of being seemingly autonomous in their movements, with sensors and effectors and an internal structure that coordinates input information and output behaviour. (This is of course not autonomy in the strict sense of a cell as a `component system'21 or an `autopoietic system'27).
What do we get from the definition taken from molecular biology? It is not quite clear. Biologically, this definition is more fundamental. Attempts to `realize its content artificially' would lead to a material copy of a cell. Maybe we first have to create `chemical artificial life' before we can make a complete artificial cell. But if an artificial material cell -- if we really want it to be living (in the sense of being an autonomous self-reproducing metabolising unit) -- has to be made up of the same kind of biochemical compounds as a natural cell (the same types of compounds such as DNA, proteins, carbohydrates, etc.), then it will probably be just another instance of the same kind. The point in making it will in some sense disappear, provided that it will have the same level of complexity. It will be merely a replica. Of course, there is a point in trying to create a primitive self-maintaining version of a metabolising cell-system (2, [8) if possible.
One might say that we should make a formal version of the cell, eventually realized in a kind of cellular automata model23 in two or three dimensions, realizing all the formal properties of the physical cell in the cellular-automata space (whatever we mean by formal properties in this context). There has been attempts to formalize the property of self-reproduction (though only with success for trivial instances of self-reproduction, cf. Kampis21), and this approach could be extended to other properties of life. This is precisely the idea of `strong Alife': any lifelike phenomenon can be realized in other media, because life is a question of form, not constituent materials; it is an abstract phenomenon, a form or coherent process-structure; an informational structure emerging from lower-level local interactions. But what is revealed here is that this notion functions as a separate intuitive conceptual model of life that we might call ABLI: abstract life.
So life seems to be a multiple of phenomena if we list these conceptual models of life, some of which are directly connected with the ideas of the Alife research program: (1) Good-Old-Fashioned Biological Organisms (GOFBO), i.e., life as a list of properties known partly from the common sense of daily life, partly from the life sciences. Most often this is life conceived of as animals -- thus GOFBA: Good-Old-Fashioned Biological Animals. (2) Modern Macromolecular-based Cells (MOMACE) as characterized by molecular biology: You know it when you have it in your test tube. (3) Abstract Life (ABLI), i.e., life as a space-time pattern that `realizes' some formal properties of biosystems either within a biochemical medium, or in a symbolic formal space. (4) Robotic Life (ROLI), i.e., neo-cybernetic life, animats, nano-robotic life and so on. One could even add (5) CYBERlife; the idea of creating lifelike structures in a Virtual Reality to which we can relate through hyper-media; and (6) other non-scientific definitions and conceptions of life.
From a point of view of traditional biology (as the study of general principles of life) this is rather surprising. Artificial Life may help us to see that the idea of universality of the fundamental principles of life may be a presupposition, a metaphysical prejudice with a questionable basis. Traditional biology has been haunted by a lot of dualisms and metaphysical contradictions (31, 36) pertaining to the methods of investigation as well as the subject matter: the dualisms between structure and process, form and function, part and whole, inheritance and environment, contingency and necessity, holism and reductionism, vitalism and mechanism, energy and information, concept and metaphor. The construction of Artificial Life may help to dissolve these dualisms, or combine or reinvent them in more fruitful ways, thus giving rise to new ideas about the nature of living beings. In this perspective Artificial Life can be seen as a new way of `reading' the science of biology. We may call it a deconstructive reading: Alife actuates a deconstruction of the Good-Old-Fashioned-Biological Life. The very opposition between living and dead nature, the organismic and the inorganic domain -- that has been constitutive for the whole science of biology since its definition in the beginning of the nineteenth century -- may dissolve or be be reconstructed in a new framework, inspired by insights gained from Artificial Life as well as other disciplines that may reveal new common principles for living as well as non-living organization.
3: Are there criteria for "valid" Alife constructions?
But even if the `universal' conception of life has to be deconstructed as a metaphysical presupposition, and even if `real life' is not a unitary phenomenon, aren't we stock with some criteria for the usefulness and validity of Alife systems compared with natural systems? Or, do we embrace the methodological credo of philosophers as Paul Feuerabend that `anything goes'? How do we prevent the field from degenerating into mere technicalities or becoming a business of developing new computer tools and toys and games? If Alife extends the field of biology to `life-as-it-could-be' by the constructive creation of any imaginable artificial universes, then how do we know `life-as-it-could-never-be'?
Here, it becomes apparent that the evaluation of the artificially constructed `possible life' has to take recourse to one of the mentioned ideas of what constitute the generic properties of life, eventually expressed as a definition of life. And then, if we define life from a point of view of molecular biology/MOMACE, where life is seen as a cell-bound biochemical phenomenon with material as well as formal properties, it is clear that the computational approach can never hope to realize living processes, but only to model life. The `strong version' of Alife will fail.
Strong version of Alife seems more or less to assume that GOFBO as well as MOMACE are out-dated and really without any theoretical foundation -- GOFBO is very close to a common sense `folk-biological' conception of life, and MOMACE is not theoretically satisfying either, with no universal validity; it is a so-called `carbon-chauvinistic' conception of life. In fact, we do not know if the presence of CHNOPS (not to speak of proteins or nucleic acids) is a universal requirement for the emergence of `lifelike' phenomena other places in the universe. And the raison d'etre of `strong Alife' is precisely to overcome the shortcomings of present theoretical biology: That it is based on one single example.
So if Alife research want to invent or construct `life-as-it-could-be', there is this hurdle: In principle one can simulate, any process on a computer (there may be specific limits to simulability of complex systems, but let us assume general simulability for the sake of the argument); then how do we know if a new artificial phenomenon constitutes life as it could be in a possible material world? How do we put realistic physical constraints on evolution of behaviour and learning in models? And how do we know if the virtual reality, that we have constructed, constitutes instances of possible `life' or a complicated but purely non-living physical universe? We have seen many interesting `self-organizing' phenomena in complex non-linear but purely physical systems that in some respects behave life-like. But nobody claim these phenomena to constitute genuine life.
As our ultimate standards for what constitute interesting lifelike phenomena in a virtual universe (possible life), we only have our pre-scientific ideas and traditional biological intuitions of what makes up real life. An objection would be that we do have a solution for that problem, namely a list of agreed upon criteria of the presence of living processes. However, this seems to be a list of problems, rather than a key to the solution. Let us consider an example, the list from Farmer and Belin13 which comprises the following set of properties:
Life (as defined by Farmer & Belin):
Apart from the fact that such lists will always be somewhat arbitrary and express ones chosen frame of description, is is not complete. An important property is added here: life as an autonomous phenomenon. This criterion reflects the evolutionary fact that life is not a pre-designed but a naturally evolved phenomenon, and the ecological fact that life is usually not dependent upon us for its existence, so an artificially created organism should be able to go on living a life of its own within a natural environment. Even domesticated animals, which cannot be sure to be able to do that, nevertheless have a reminiscent inherited degree of autonomy and a potential for colonizing other habitats. The authors want the list to be specific for life and do not include growth: Growth is not a specific property; "there are many inanimate structures such as mountains, crystals, clouds, rust, or garbage dumps that have the ability to grow. Many mature organisms do not grow." (13, p.818). But exactly the same sort of obstacles applies to the other properties. But there are other problems as well.
The first criterion can be interpreted to capture the constant turnover of constituent material in any living organism. A large part of the material of our bodies is replaced within a few years, so the `stuff' changes over time but the `pattern' that it is incorporated into is the same. The turnover is described in detail by biochemistry as metabolism, which is the fourth criterion. Another interpretation is that the first criterion expresses the idea of the medium-independence of life, i.e., life as a formal (informational, functional, or form-) property24. This idea seems to be at odd with an immediate intuition nourished by molecular biology9 that life is a process found in a set of concrete material systems -- living cells -- and that it should be studied in close connection with the study of the material components that make up these systems. Furthermore, this intuition tells that the physical properties of these systems impose constraints on the set of possible forms of life that can be realized by this set. E.g., properties of the double lipid layer of the cell membrane and the various membrane-bound proteins determine what kind of material substances between the organism and the external environment are allowed to be exchanged, thus constraining the set of possible inputs to the general metabolism of the cell. Another example is gene regulation: In order to study mechanisms of gene regulation, one has to look at the way the `information' is being `processed' at the level of macromolecular properties of ribosomes, DNA, mRNA etc. Here one cannot separate the `form' of the process from the molecular `workings' of the system9. That does not mean that life could not exist in other media composed of other materials (Farmer & Belin notes that it is "easy to conceive of other forms of life, in different media, with a variety of different reproductive and developmental mechanisms,"13 p.817), but these materials will impose other constraints on the actual properties of this `other life'. What is non-existent in computational Alife is the study of what kind of physical/chemical constraints that harness the lives of the various computer organisms. As long as the latter are only programs, deficit of other constraints than the abstract computational ones, they do not have the reality-character of natural organisms.
The second criterion of life, self-reproduction (SR) is important, but it invalidates as a candidate for a true instance any example of Artificial Life -- whether it is ABLI's computer organisms (Langton's self-reproducing loop for example23, 24) or the various devices of ROLI. This does not detract from the value of these examples, on the contrary, it negatively shows the power of real non-trivial SR! We shall not give detailed arguments (5, 21) only state that SR (in the full-fledged sense of what an amoeba-cell does when it grows and divides itself into two autonomous living beings) is not achieved yet by artificial means. One must distinguish replication of information (replication of DNA in a cell or the replication of a spoken message) from self-reproduction. Biochemical replication is a necessary but not sufficient condition for self-reproduction. Furthermore, the formal machine SR is equivalent to copying and propagation of an informational structure, but of course it does not involve the reproduction of the physical machine that supports the process; in short: it is a formal model of (a specific theory) of the process, not the phenomenon itself.
Natural self-reproduction is complete in the sense that the information needed for guiding the process is fully contained in and integrated with the cell or organism being reproduced. In a computational (machine) model of SR (whether it is based on `universal construction' as in von Neumann35, or on more elegant designs such as the loop structure of Langton23,24) the `reproduced' entities -- visualised on a screen as specific configurations of automata states duplicating themselves -- do not really as intended contain all the information needed for determining the process of reproduction. From a purely formal view this might be the case, but the physical machine (that realizes the process and which is not reproduced) supports the embedding universe of the reproducing automata and acts as a co-determiner of the process, but is not itself determined by it. One might try to overcome this difficulty by simulating the physical machine in a higher level model of a self-reproducing system (as suggested by von Neumann), but in such a model, there is still an additional external machine whose determination does not depend on the process of reproduction. The information responsible for `self-reproduction' is not completely localised within the configuration, and the external additional specification (by the embedding `universe' and supporting machine) is equally important for the process21. In an autonomous living system, we cannot make the distinction between the entity being reproduced and an ultimate machine whose properties do not depend on the process of reproduction and which is not reproduced itself. DNA is not an external `knowledge' or `description' of the cell, but forms an integral part of the very system; the informational determination is a tacit activity that expresses this information causally (as emphasized by Kampis and Csányi22). It is the intrinsic and causal property of the cell that explains why real SR is complete, while modeled SR involves external sign-relations between observer and the system modeled.
Robotic SR has not, as far as we know, been achieved. One can probable some day construct machines that drive through a supermarket of components, collect and assemble these to make new machines of the same sort. But this sort of ROLI-SR is very different from SR in the biological sense, which is coupled to a process of macromolecular component-production in a network of processes which maintain the cell/organism in the very same process as new subunits is produced (cf. Kampis's component-systems and Maturana & Varela's autopoietic systems). In contrast, ROLI-SR is based on `allopoietic' production of the components to the SR-supermarket of the machines. Again: This does not mean that the problem of ROLI-SR is not interesting. On the contrary: The idea of colonising the Moon with a society of machines that have the right complexity to maintain and reproduce themselves should be investigated, and the reasons why it eventually may be in principle (and not just in practice) impossible to realize should be made explicit (probably we have here the whole `frame problem' of Artificial Intelligence blown up to its ultimate dimension).
The other criteria make other troubles11 not to be discussed here. A fundamental problem common for all criteria when used in the context of computational `strong Alife' is, that they are really not criteria for life in the usual sense (of GOFBO or MOMACE), but that they already represent another concept of life, namely ABLI, and thus their relevance as a kind of `conceptual anchor cable' to the physical world of known plants and animals is dubious. "But hesitate," the Alife objection might say, "we didn't want them to be criteria for carbon-based life in the normal sense! We wanted to create new forms of life; life forms in other media." --But that doesn't help. They are not useful at all for evaluating the strong claim of possible construction of life in a formal domain, because these criteria derive from another world than the world of formal properties, and they do not seem to make sense in the latter domain. One should not forget that the strong version of Alife -- that human beings can create life out of non-living artifacts -- is really a radical claim. Alife is not yet life, if it ever be. One could be tempted to say that what is being studied in Artificial Life for the present, at least in the computational part of the research program, is quite another object: It is not even life as an abstract phenomenon, it is the life of abstract concepts ascribed to a specific interpretation of formal computational structures. However, one should remember that contemporary biology does not have to be the only source of systematic knowledge of life, and that neither the concept of life nor the concept of computation are that clear.
What is biological computation?
The idea of changing a system's state as a kind of computational updating process is so obvious to computer scientists that they often tend to see other systems as well changing state in this way. The brain computes its next states; every single cell of the body takes as input various messenger molecules from other cells and computes which other molecules to be synthesized, etc. If information is intrinsic to life, it is important to ask if this information (e.g., the genetic information in the cell's DNA, or the supposed propagating patterns of conformational switches in the cytoskeleton16) is involved in computation-like processes. This question remains unresolved. An accompanying paper11 deals with the origin of computational powers in natural systems, the `grounding' of semantical information and Langton's cellular automata approach to the origin of computation. What these discussions reveal is that the very concept of computation is not necesserily so well-defined as normally conceived of, and we shall shortly sketch why.
In a sense, we simply face different kinds of computations realized in various systems: One kind has the normal intentional structure known from human and machine-mediated human computation (we can define a computer as an interpreted, formal, automatic system17), another kind is not conceptual but is found to take place in living cells, and a third one which under special circumstances may occur in physical nature as a self-organizing phenomenon which can be modelled in the abstract space of cellular automata. One could add an additional kind which may not even deserve the name of computation but which characterises a highly advanced form of mathematical reasoning that cannot -- due to the limitations inherent in formal systems -- be done merely by computational or algorithmic approaches, e.g., reasoning about the truth value (true/false) of some propositions in number theory which, by Gödel's incompleteness theorem, can be shown to be undecidable in a given formal system19. Instead of kinds of computation, we prefer to talk of four different concepts of computation (coc.1-4), that can be listed as
coc 1. The formal, or algorithmic, concept of computation, which has its theoretical footing in the notion of a Universal Turing Machine7.
coc. 2. An informal, intuitionistic, or `mathematical' concept of
computation (and in general: reasoning about numbers) that is not bounded by
the known limitations of formal systems. It points simply to the fact that
mathematics cannot be reduced to automatic manipulation of symbol tokens; there
is more to numbers (and hence, to computing) than the properties that can be
accounted for by formal theories of computation.
(A rude indication of the difference between coc.1 and coc.2 is the number pi. You can give an algorithm for generating the decimal expansion of pi, to get an approximal value expressed as a rational number with a decimal fraction which may be arbitrarily long, within the limits of the physical possible. This number, however, is not pi -- in that sense, no human being have ever `seen' pi. The algorithm is, so to speak, just the `translation' of the mathematical concept of an irrational and transcendental number to a computationally convenient expression of it. Strictly speaking, one cannot compute pi but only some of its approximations.)
coc. 3. A biological concept of computation. This seems to be a quasi-theoretical concept that can be understood in many ways, for example, as problem solving by learning and adaptability6; as molecular processing of information in cells (1, 16); or as computation by neural networks.
coc. 4. A physical concept of computation, that might be non-representationalistic. The entities that co-operate in computational enterprises are patterns that can transmit, store and modify information (14, 25, 26), but these patterns seemingly do not have to `stand for' anything, as long as no functional constraints are imposed from a higher level.
How these different concepts of computation relate to each other is not clear, and has not as far as we know been analysed yet. From a formal point of view (cf. coc.1), or from an anthropocentric, conceptual perspective (that might embrace coc.2), one is not forced to accept the notion of non-representational computation (coc.4). From an biological perspective (coc.3), there is a point in restricting language- and concept-dependent processes (such as formal and mathematical computation) to the level of human society which is outside the realm of biology, and to preserve the term `information' for more simple kinds of sign-transfer. One may easily be lead to a `restrictivist' approach to computation and dismiss non-doctrinary notions (coc.3 and 4) because they are not specifiable within a formal setting. The fact that important research have been devoted to understand the principal physical limits on computation4 is not in conflict with such a formalistic stance. The study of these physical limits (on formal computation) do not imply `a physical concept of computation' in the sense of coc.4, but is concerned with, for instance, how fast and energetic `cheap' one can realize formal computations in physical devices. In spite of the restrictivistic temptation, it is too preliminary to ascribe explanatory monopoly to just one theory of computation, especially as we are seeing a lot of interesting approaches in computer science and Artificial Life coming up with new material; e.g., Rasmussen, Knudsen and Feldberg32. As these authors observe, "a useful computation theory for natural systems has yet to be formulated" (p.220, ibid.).
We need a general theory of realized computation in natural systems, and neither Artificial Life simulations nor theoretical computer science nor physics or biology provide such a theory yet. Philosophical reflections may help to clarify epistemological and model-theoretic issues and to frame the functional properties of biological information within a greater evolutionary frame.
1. Albrecht-Buehler, Guenter. "Is Cytoplasm Intelligent Too?" Cell and Muscle Motility 6 (1985): 1-21.
2. Bagley, R.J., J.D. Farmer, S.A. Kauffman, N.H. Packard, A.S. Perelson and I.M. Stadnyk. "Modeling Adaptive Biological Systems." BioSystems 23 (1989): 113-138.
3. Belew, R.K. "Artificial Life: a Constructive Lower Bound for Artificial Intelligence." IEEE Expert 6(1) (1991): 8-14, 53-59.
4. Bennett, Charles H. and Rolf Landauer. "The Fundamental Physical Limits of Computation." Scient. Amer. 253 (1) (1985): 48-56.
5. Cariani, Peter. "On the Design of Devices with Emergent Semantic Functions." Ph.D. dissertation, Department of Systems Science, State University of New York at Binghamton, Ann Arbor: University Microfilms, 1989.
6. Conrad, Michael. "Molecular Computing." In: Advances in Computers, vol. 31, edited by Marchall C. Yovits, 235-324. London: Academic Press, 1990.
7. Davis, Martin (1978): "What is a computation?" In: Mathematics Today: Twelve Informal Essays, edited by Lynn Arthur Steen, 241-267. New York: Springer-Verlag, 1978.
8. Dyson, F. Origins of Life. Cambridge: Cambridge University Press, 1985.
9. Emmeche, C. "The Problem of Medium-Independence in Artificial Life." In: Complexity, Chaos, and Biological Evolution. NATO ASI Series B 270, edited by Erik Mosekilde and Lis Mosekilde, 247-257. New York: Plenum, 1991.
10. Emmeche, C. "Modeling Life: a Note on the Semiotics of Emergence and Computation in Artificial and Natural Living Systems." In: Biosemiotics: The Semiotic Web 1991, edited by Thomas A. Sebeok and Jean Umiker-Sebeok, 77-99. Berlin: Mouton de Gruyter, 1992.
11. Emmeche, C. "Life as a multiverse phenomenon: the biosemiotics of computation" (unpublished). [a part of this paper later published as Emmeche (1994): "The computational notion of life",Theoria - Segunda Epoca 9 (21): 1-30. ]
12. Engelsted, Niels "What is the Psyche and How did it Get Into the World?" In: Essays in General Psychology, edited by N. Engelsted, L. Hem and J. Mammen, 13-48. Aarhus: Aarhus University Press, 1989.
13. Farmer, J. Doyne and Aletta d'A. Belin. "Artificial Life: the Coming Evolution." In: Artificial Life II. Santa Fe Institute Studies in the Sciences of Complexity, Proc. Vol. X, edited by Christopher G. Langton, Charles Taylor, J. Doyne Farmer and Steen Rasmussen, 815-838. Redwood City, Calif.: Addison-Wesley, 1992.
14. Forrest, Stephanie, ed. Emergent Computation (special issue), Physica D 42 (1990).
15. Foucault, M. The Order of Things. London: Tavistock, 1970.
16. Hameroff, S., S. Rasmussen and B. Månsson. "Molecular Automata in Microtubules: Basic Computational Logic of the Living State?" In: Artificial Life. Santa Fe Institute Studies in the Sciences of Complexity, Proc. Vol.6, edited by C.G. Langton, 521-553. Redwood City, Calif.: Addison-Wesley, 1989.
17. Haugeland, J. Artificial Intelligence: The very idea. Cambridge, Mass.: MIT Press, 1985.
18. Hoffmeyer, J. & C. Emmeche. "Code-Duality and the Semiotics of Nature", In: On Semiotic Modeling, edited by Myrdene Anderson & Floyd Merrell, 117-166. Berlin: Mouton de Gruyter, 1991.
19. Hofstadter, Douglas R. Gödel, Escher, Bach: an Eternal Golden Braid. London: The Harvester Press, 1979.
20. Jacob, François. The Logic of Life. New York: Vintage Books, 1973.
21. Kampis, Georg. Self-modifying Systems in Biology and Cognitive Science. New York: Pergamon Press, 1991.
22. Kampis, G. and V. Csányi. "Life, Self-Reproduction and Information: Beyond the Machine Metaphor." Journal of theoretical Biology 148 (1991), 17-32.
23. Langton, C. G. "Studying artificial life with cellular automata." Physica D 22 (1986): 120-149.
24. Langton, Christopher G. "Artificial Life." In: Artificial Life. Santa Fe Institute Studies in the Sciences of Complexity, Proc. Vol.6, edited by C.G. Langton, 1-47. Redwood City, Calif.: Addison-Wesley, 1989.
25. Langton, Chris G. "Computation at the Edge of Chaos: Phase Transitions and Emergent Computation." Physica D 42 (1990): 12-37.
26. Langton, Christopher G. "Life at the Edge of Chaos." In: Artificial Life II. Santa Fe Institute Studies in the Sciences of Complexity, Proc. Vol. X, edited by Christopher G. Langton, Charles Taylor, J. Doyne Farmer and Steen Rasmussen, 41-91. Redwood City, Calif.: Addison-Wesley, 1992.
27. Maturana, Humberto R. and Francisco J. Varela. Autopoiesis and Cognition. Boston Studies in the Philosophy of Science Vol. 42. Dordrecht: D. Reidel, 1980.
28. Mayr, Ernst. The Growth of Biological Thought. Cambridge, Mass.: The Belknap Press of Harvard University Press, 1982.
29. Meyer, Jean-Arcady and Stewart W. Wilson, eds. From Animals to Animats. Cambridge, Mass.: The MIT Press, 1991.
30. Norris, Christopher. Deconstruction: Theory and Practice. London: Routledge, 1991.
31. Oyama, Susan. The Ontogeny of Information. Developmental Systems and Evolution. Cambridge: Cambridge University Press, 1985.
32. Rasmussen, Steen, Carsten Knudsen, and Rasmus Feldberg. "Dynamics of Programmable Matter." In: Artificial Life II. Santa Fe Institute Studies in the Sciences of Complexity, Proc. Vol. X, edited by Christopher G. Langton, Charles Taylor, J. Doyne Farmer and Steen Rasmussen, 211-254. Redwood City, Calif.: Addison-Wesley, 1992.
33. Sagan, Carl. "Life." In: The Encyclopaedia Britannica, 15th ed., Macropaedia vol. 10. London: William Benton, 1973.
34. Taylor, Charles E. "`Fleshing Out' Artificial Life II" In: Artificial Life II. Santa Fe Institute Studies in the Sciences of Complexity, Proc. Vol. X, edited by Christopher G. Langton, Charles Taylor, J. Doyne Farmer and Steen Rasmussen, 25-38. Redwood City, Calif.: Addison-Wesley, 1992.
35. von Neumann, John. Theory of Self-Reproducing Automata, edited and completed by A. W. Burks. Urbana: University of Illinois Press, 1966.
36. Woodger, J.H. Biological Principles: A Critical Study. London: Kegan Paul, 1929.