Systems Research and Behavioral Science 22, 413-430, 2005 LIFE AND SIMPLE SYSTEMS Ron Cottam, Willy Ranson & Roger Vounckx The Evolutionary Processing Group, ETRO Vrije Universiteit Brussel, Brussels, Belgium Communicating author: Ron Cottam ricottam@etro.vub.ac.be Tel/fax: +32 (2) 629.2933 ABSTRACT This last decade has seen the publication of an extensive literature describing, cataloguing and analyzing the ‘emergence’ of complexity. This seems very strange. The creation of a complex assembly is comparatively easy – the difficult job is to generate simplicity from it. So much is this the case, that the only context within which it takes place is that of life itself. Although we naturally imagine life as a dynamic process rather than as a static structure, both of these are critical to its survival. Continuously expanding multi-element assemblies finally lose their cohesion, and split up into separate parts, or restructure themselves to redress their stability by generating a simplified umbrella-level of operation. In large organisms this process may repeat itself, thus creating a multi-leveled selfcorrelating operational hierarchy. It is not obvious how the associated generation of simplicity is initiated, but it appears that such a self-correlating hierarchy is itself alive. Keywords: life, hierarchy, multi-scalar, complexity, simplicity. INTRODUCTION One of the preoccupations of Homo sapiens is, and has been to explain in some way the genesis of life, both in an abstract sense and in the appearance of individual organisms. Over the last century there has been a progressive move away from attributing its origin to some external intelligence and towards attempting an explanation from the bases developed in the natural (i.e. mainly ‘inorganic’) ‘exact’ sciences. Unfortunately, to some extent this has been doomed to failure, as these bases were derived for systems in equilibrium, and life is anything but that! More precisely, the standard scientific scenarios comprise systems which remain in equilibrium because their constituent parts are also in equilibrium, while living systems maintain a temporally limited quasi-equilibrium because their constituent parts are individually far from equilibrium. Within the standard scientific scenarios, Life and Simple Systems 1 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 therefore, a reductive approach can provide reasonable understanding of the relationships which exist across scales, while the application of a reductive scientific approach to living systems merely provides the description of a dead organism, and not a living one. If we are to arrive at a degree of ‘understanding’ of life itself, we are therefore constrained to either adopt a far less mechanistic investigative tool, or to change the formulation of the scientific tools we already possess to take account, at the very least, of this cross-scalar difficulty. Within a traditional scientific discourse, there is a formal separation of static and dynamic aspects of a system. Over the past few decades the investigation of complex phenomena has brought about the beginnings of recognition that this compartmentalization must be relaxed, but it is still less than obvious how this can be achieved without completely abandoning the ‘exact’ nature of the ‘exact’ sciences. Much has been written of late about complexity and the ‘emergence’ of complexity in both inorganic and organic contexts. Unfortunately, the word ‘complexity’ appears in so many guises that it is virtually impossible to use it without attempting some qualification of its meaning. Our own use of the word is close to that implied by Robert Rosen [see, for example, Rosen, 1997; Rosen and Kineman, 2005], but there are dozens of other interpretations [for an overview see, for example, Edmonds, 1997]. It is now fairly commonplace to associate the nature of life with the ‘emergence’ of complexity, and it is certainly the case that the two can be in some way associated, but it is difficult to see how the ‘emergence’ of complexity could be sufficient without a concurrent ‘emergence’ of simplicity to resolve the difficulties which complexity entails. Complexity itself solves no problems, eases no paths, and facilitates no response to stimulus – all these are the purview of simplicity. We suggest that complexity is more the result of development than of ‘emergence’, and that the ‘true’ emergence is, if anything, of simplicity [Cottam et al., 1998a]. The biggest difficulty which science will have to resolve in attempting an understanding of life is the unfamiliar concurrence of complexity and simplicity, where the appearance of a (living) system depends on the context it experiences, which may be very different from the context which scientific study may attribute to it from an external setting. In this paper we will explore the hypothesis that life is essentially a relationship between complexity and simplicity within a unified system. We will regularly fall back on the application of a computational paradigm in our descriptions. This is not to suggest that life consists of ‘computation’ per se, but that in the relationships between complexity and simplicity it provides a useful provisional ‘pictorial’ support in transmitting the ideas we wish to propagate. STATIC AND DYNAMIC ASPECTS OF LIFE It would be difficult to think of life without immediately focusing on its dynamic aspects. The initial perceptional distinction we draw of our surroundings is between stasis and movement, and to a large extent it appears to be living things which move. Our mammalian eyes have developed a degree of pre-neural processing which is mainly directed towards the Life and Simple Systems 2 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 location in our field of view of moving entities whose recognition may be vital to survival. Beyond this simplistic distinction, it becomes less easy to establish criteria for ‘alive or not alive’ which are neither self-referential nor unsatisfactory across a range of timescales. Biology has traditionally concentrated on metabolism and reproduction as distinguishing features, but while these two are certainly necessary for the maintenance and evolution of living forms, it is questionable whether they relate usefully to our personal momentary sense of ‘being alive’. It would appear that these characteristics are more the servants of life than its primitive nature. While we automatically associate life with phenomenological dynamics, its substrate is the structural nature of cells, tissue and organs – whose character appears most amenable to reductive investigation. Even so, we must be careful to what extent we presuppose that there is a one-to-one relationship between a detailed description of the internal processes of living material and the external appearance of its importance on a larger scale. The major difficulty appears to be that structure and process cannot be reductively separated in a living system, and that their relationships depend on the scale from which they are viewed. Our basic viewpoint is that which we have stated elsewhere [Cottam et al., 2003a, 2004a]: if we analyze a dynamic system in terms of the classical separation of time-independent and time-dependent parts, then we adopt the hierarchical form of supposing that dynamics consists of two subsidiary complementary parts, namely structure and its counterpart process. It should be noted that simplification of a binary complement can lead to binary orthogonality, or by more extreme reduction leads to a pair of opposites. Structure and process are complementary in neither of these simplified senses, but in that indicated by Niels Bohr: “The opposite of a correct statement is a false statement… but the opposite of a profound truth may well be another profound truth. We believe that this relationship between time-independent and time-dependent complements predated the large-scale organization of living systems and that it corresponds to the primitive form of consciousness, which is almost but not quite the same as the most primitive form of energy: in large suitably-organized information-processing networks this leads to the high-level consciousness which we ourselves experience [Cottam et al., 1998b]. The most productive route towards an understanding of the grounding of life appears to be by manipulation of the style and the degree of partiality or completeness we attribute to the logic with which we describe phenomena which have implications at more than one scale of an entity. This entails always keeping in mind that complexity engenders simplicity, and that apparent simplicity conceals an underlying complexity. Characteristically, in this context of describing or defining ‘life’, any definition of ‘complexity’ will be a simplified one, and any definition of ‘simple’ will be overly complex! What is “Complexity”? Our references to ‘complexity’ in this paper may be associated with a sense of incompleteness of description, and of consequent analytical difficulties. Life and Simple Systems 3 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 Following Robert Rosen [see, for example, Rosen, 1997], Rosen and Kineman [2005] categorize complexity by “… if there is no way to completely model all aspects of any given system, it is considered ‘non-computable’ and is, therefore, ‘complex’ in this unique sense.” Our own use of the word corresponds to the form of this computational description, but we distinguish between two very different classes of complexity, which may be associated with different styles of incompleteness or approximation. Analog approximation is a reduced representation (i.e. a simplification) of the entire entity under consideration, whose incompleteness or error is ‘fuzzy’ in style1. This corresponds to the more usual use of the word ‘approximate’. For example, the analogue approximation of a digital computer would presumably be rather vague across its entire organization and operation. Digital approximation is a reduced representation (i.e. a simplification) of the entity by reduction in the number of its defined sub-units. Although entirely valid, this style of approximation may appear to be arbitrary in many contexts. For example, the digital approximation of a digital computer could be missing the central processor – raising the question of whether it is still a computer. However, this problem analogously raises its head in specific cases of analog approximation, and it appears to result from ‘intentionally choosing a context which does not fit the (reduced) description’. Description is always by reduction, so it is always possible to choose contexts within which a given description is invalid. The analog and digital approximations of a real-valued parameter are related to each other through process and intention. An analog approximation would be to a degree vague in the definition of each and every digit of its formulation, making it useless to specify its value to more than a particular number of significant figures. A digital approximation, however, would effectively lose one or more of the digits of its formulation, similarly limiting its specification, but by the possible values of that one digit. A nice example of this distinction is the way in which we relate to traditional or digital clocks. We would normally attribute analog approximation to a traditional clock, by suggesting that it shows the ‘right’ time (i.e. it is ‘accurate’) to within a certain (arbitrary) degree. More formally, we would suggest that a digital clock is (also) only ‘right’ to within plus or minus ‘1’ in its least significant digit. While it is possible to (approximately) categorize two types of complexity by associating their incompletenesses with analog and digital approximations, any attempt at a complete definition of complexity runs into precisely (!) the problems which complexity itself engenders. If we look even further into the analog/digital categorization, we find that complexity is often associated either with the digital representation of an analog context, or with the analog representation of a digital context – but not always! It should be noted that this is not the meaning of the word ‘fuzzy’ which is applied in ‘fuzzy logic’, where set membership may be other than 1 or 0, but it is in any case precisely defined. 1 Life and Simple Systems 4 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 While our own use of the word “complex” corresponds to the form of the noncomputability criterion Robert Rosen used in his concept of complexity, the implied content is different, as will be clear from the description above. We are in no way suggesting that nature itself is complex – we do not have enough information to maintain such an absolutist assertion. We are rather attributing complexity to the mismatch between a ‘mode of expression’ of nature and a ‘mode of representation’ of it or, in David Bohm’s terms [1987], a mismatch between nature’s implicate order and our interpretation of its explicate order. This appears to be categorically different from Robert Rosen’s view that nature is complex2. We find it difficult to see that this apparent view could extend beyond belief to measurement. However, we do not imply that it is possible to choose a mode of representation from a single point of view which would permit ‘complete’ modeling of the universe. What is “Simple”? Sadly, not only do we need a sense of ‘simple’ to define ‘complexity’, we also need a sense of ‘complexity’ to define ‘simple’! Fortunately, we can fall back on the computational paradigm to help distinguish between them and give a sense of reality to their difference. In doing so, we can also attribute a meaning to ‘complication’. ‘Simple’ implies ‘easy to compute’ – i.e. feasible to compute, and not taking too much time. ‘Complicated’ implies ‘more of the same’ – i.e. feasible to compute, and longer to compute, but not substantially more difficult: this is similar to Rosen’s [2000] formulation. ‘Complex’, however, implies ultimate incomputability, and that even if an approximation can be obtained it may take infinite time to obtain it. These three ‘implied definitions’ appear to fit reasonably well with Rosennean complexity as referred to by Rosen and Kineman [2006]. However, defining ‘complication’ non-computationally is as tricky as defining complexity, if not more so. Complication is often associated either with the analog representation of an analog context, or with the digital representation of a digital context – but not always! If we accept the usual premise that communication is restricted by relativity, then the temporal ‘snapshot’ of any non-permanent spatially-measurable entity will always exhibit some degree of ‘incomplete’ complexity. Consequently, any multi-elemental system, however small and ‘simple’, will always depend on time to fulfill its system-defining entailments, however simple these are. An obvious immediate conclusion is that neither ‘simple’ nor ‘complicated’ exist outside our own definitions, but this argument gets us nowhere. It is far more relevant that different degrees of ‘incompleteness’ can be envisaged, and that in a hierarchical assembly different So far as we are aware, this was Robert Rosen’s belief. E.g. Judith Rosen (private communication): “in my father's usage, complexity is inherent in the universe”; John Kineman (private communication): “Rosen, I believe, did assert that nature is complex”; Robert Rosen (Rosen, 1997): “Complexity is, I feel, a basic feature of the world, the material world, even the world of physics, the world of machines”. 2 Life and Simple Systems 5 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 scalar levels depend on different optimal (never zero) ‘incompletenesses’ of their samescale entailments for structural or organizational quasi-stability (i.e. fractal degrees of internal freedom). Persistent scalar levels of a system are those which have managed to establish some kind of equilibrium between both the positive and the negative implications of their elemental or procedural ‘vaguenesses’3. Rather than maintaining that complication always has a complex component, it is more interesting to note that persistent scalar levels in a self-correlating hierarchy most probably always constitute simple or complicated selfrepresentations, as they are always computationally viable entities. The stabilization of such levels appears to be associated with the ejection of sufficient complexity into their adjacent inter-scalar regions [Cottam et al., 2003a] to achieve optimal at-least-partially-complex relations with other scales of the system of which they are a part, and although some degree of incomplete-complexity remains, it is of little importance at that scale. QUASI-STABILITY IN EXPANDING SYSTEMS The primary quality of any recognizable entity is its unification. It is easy to bypass this aspect and concentrate on more observable characteristics, but an entity’s unification cannot be ignored if we are to come to any understanding of its nature and operation. A viable characterization of ‘unification’ is provided by comparison between intra-entity correlative organization and entity-environment inter-correlative organization – between cohesion and adhesion [Collier, 1999]. Although the difference between these two for a crystal is substantial, that for a living organism is far higher. This, then, provides us with a major question. How is it that living entities which consist of a multiplicity of strikingly different subordinate parts do not simply disintegrate? Clearly, the individual parts cannot be entirely autonomous, or there would be no reason for them to remain together. But is it just ‘the whole’ which requires the parts, or ‘the parts’ which require the whole, or both? John Collier has provided a resolution to this dilemma [Collier, 1999]. He suggests as an example that through evolution the brain has ceded its biological-support autonomy to the body, in exchange for a gain in information-processing autonomy. This kind of autonomy exchange need not necessarily be complete between two individual parts of an entity, but can spread across the entire assembly, so that in some way all the individual subordinate parts require and are subordinate to all the others. This networked autonomy exchange seems to be a good candidate for the global structure of a living organism, especially as it would be a likely result of survivalist evolution being applied not to complete organisms but to their individual parts. It suggests that an ecosystemic paradigm can be applied not only to an assembly of different species, but also to their internal structures. It is notable that all of the entities we would consider to be alive possess a highly differentiated internal structure, when compared to a crystal, for example. A net result is that the difference in information content between a living entity’s smallest and largest scales is enormous. We may compare this to the change in information content across scales in a crystal, which is virtually zero. This seems at first sight to be a great 3 A term attributable to Stan Salthe. Life and Simple Systems 6 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 disadvantage, as it is primarily the entity as a whole which must respond to external threats, and if its global character requires such an enormous pool of descriptive information, then it must of necessity be slow to react. However, this is not the case. Communication requires effort. It is a central tenet of information processing that faster communication requires more energy. As an integrated assembly of small elements expands, it sooner or later reaches the point where its coherence is insufficient to support rapid communication between all of its different parts, and it is faced with a ‘choice’: disintegrate, or change. Disintegration results in a number of different entities, which is of little interest. But in what way can it change to improve the situation and enable it to remain integrated? Its only option is to partially split up but to also remain partially integrated. In that way, the majority of communication can remain local, with only a limited amount taking place between the new large-scale subordinate parts of the whole. This saves energy which can be applied to increase the cohesion of the whole, but a result is that a new kind of communication appears between different scales of the assembly. Rosen’s modeling relation [Rosen, 1985] refers to just such a situation where one system relates to another through a complementary assembly of dependence and autonomy. Unfortunately, the relationship between adjacent scales of a unified system is massively fractal, in terms both of analog and digital complexity. Kineman [2002] has proposed a multi-scaled nested form of Rosen’s modeling relation, but this in itself is insufficient to represent the multiply-fractal nature of the communicational complexity which resides between different real scales. It should be noted that if it is possible to communicate between adjacent levels of a hierarchy by means of the rationality of either of those scales, then that part of the hierarchy will collapse into a single level, unless its structure is supported by the external imposition of constraints. This form of constrained quasihierarchy corresponds to the structure of a digital computer. The only way to model interscalar transport in a real self-correlating hierarchy is by reference to all the system’s interscalar relationships: this requires bringing into play some kind of nonlocality [Cottam et al., 1998c, 2003a, 2004b]. Information Transport across Scales Analyzing the transport of information between different scales of an entity runs into a major obstacle when it is realized that this cannot follow the same rationality which is operational at one or other of the scales involved. If we consider the generation of a new high-level scale, as was suggested above to increase cohesion, then the stability of that new level depends on condensing an extended description of the interactions between numerous lower-level elements to a far simpler description of their global properties. In short, information must be compressed. The compression of information is analogous to the physical compression of a gas, in that beyond a certain degree of compulsion there will be a phase change to a much more concentrated form (a liquid, in the case of a gas; an abstraction in the case of information) which exhibits different properties from those of the initial content. A case in point is the Life and Simple Systems 7 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 compression of steam. Not only does it first change to water – a polar liquid whose universal-solvent properties are arguably responsible for the development of life – it then changes into ice, which exhibits a series of different forms and properties with increasing pressure. In general, this degree of compression means not only that much detail is lost through phase change, but more seriously that the resultant higher abstracted form does not depend on a description at the lower elemental level, but on what is required by the new higher one. The only way the higher level can indicate this requirement to the elemental level is by downward information-expansive communication, but it has only a sketchy description of the lower level’s character because of the upscale compression. The only way this can operate satisfactorily to produce a pair of levels whose descriptions are coordinated is by a negotiation between the two, leading to autonomy exchange. Autonomy negotiation between adjacent scalar levels requires a stable environment to support it, but this appears at first sight to be absent from the questionable region of compression/expansion between the scales. The creation of a previously nonexistent scalar level above that of an assembly of numerous elements is usually referred to as the ‘emergence’ of a new level. Traditionally, this is attributed to the generation of ‘novelty’ as a result of upward information pressure. Evidence from the physical structure of biological molecules (most particularly of lipids) and from cross-scale information transport in single crystals of gallium arsenide [Cottam et al., 2004a] suggests that the majority of the information transport between different scalar levels of an entity is related to physical or informational structure and not novelty. The successful transmission of low-noise television signals depends on relatively small modulations of predictably-structured sets of carrier frequencies. In a similar manner, it appears that the cross-scale transport of information which leads to novel results requires a strongly structured carrier. This can then provide a stable inter-scalar regime within which the autonomy negotiation can take place. Generating Simplicity through Partial (En-)closure The easiest way to reduce the descriptive complication of an entity is to surround it with a complete barrier and then to establish a limited number of input/output ports through which carefully limited information can be processed. This is exactly what a biological cell does. The lipid cell membrane is penetrated by numerous channels which are each associated with the transfer of specific kinds of information, for example the gap junctions which permit inter-cellular communication. The cell itself also contains numerous organelles, or different functional units, most of whose communication is limited by one or more membranes. The central issue here is how a particular entity maintains suitable relationships in both the up- and down-scale directions: an individual cell must be in some sort of active correlation, not only with its organelles, but also with adjacent cells. Although incoming information may be completely different from outgoing information, the information cycle crossing the membrane in both directions must not only be selfconsistent, but must also be consistent with all of the other cross-scalar cycles within the organism if its viability as a quasi-stable entity is to be maintained. It is the multiply-scalar nature of these cycles which produces a local process closure as well as the spatial enclosure of a cell and ultimately defines the cell’s function in the organism. As a result of Life and Simple Systems 8 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 interaction between these closures, the cell may present itself to its environment in ways which are useful to it, without confusing the issue with detail which is only relevant to its internal processes. On a relatively short timescale, the cell’s lifetime is then controlled by survivalist evolution at its own spatial scale and in relation to that of its ‘ecosystem’, much as Darwinian evolution would proceed at the level of the organism. Low-level Hierarchy As soon as we start to describe ‘a whole’ consisting of ‘elements’ we are entering into the regime of hierarchy. The basic problem of ‘how to correlate different levels’ is independent of the number of levels as there are already two: ‘inside’ and ‘outside’ is sufficient! Consequently, it is virtually impossible to take into consideration ‘how something works’ without invoking hierarchy and its associated advantages and difficulties. However, if there are only a small number of levels, the ‘precision’ of definition of the assembly will be low, as there will not be much pressure towards conformity from one inter-scalar transition acting on another. An example of this is the difficulty in attributing a unique internal mechanism to an entity comprising only a single level of internal operation. Current investigations of the birth of the universe indicate that a couple of minutes after the big bang there were no structures bigger than subatomic particles. At that point the entire universe could be described as a very low-level hierarchy, with subatomic particles at the peak of evolution. Although we can observe now that these same particles have very little freedom of expression, as they can be described by a small set of quantum numbers, there is little reason to suppose that at that time the situation was the same, and we should expect ‘primordial electrons’ to have had a wide range of different properties. At the current age of the universe, electrons are far down the evolutionary fossil record when compared to biological organisms. Consequently, the similarity of electrons can be attributed to downward causal pressure, or ‘slaving’, from the multiplicity of higher-level closure cycles which contribute to the stability of the entire structure. Multi-level Hierarchy The universe as we now experience it constitutes a wide range of observable or modellable scales, from membranes, through superstrings, quarks, elementary particles, nuclei, atoms, molecules, bio-molecules, organelles, cells… right up to organisms and societies. If the arguments we have provided are relevant, we should find that our surroundings are stably based on a majority of inter-scalar information-structural transport. Although in principle a self-correlating multi-scalar hierarchy could be far from quasi-stability, our own experience suggests that this is not the case at scales which are close to our own – if we close our eyes, and then re-open them, the greater proportion of our surroundings remains the same. The result of quasi-stability in a multi-level hierarchy is that the different scalar levels all become very precisely defined, each with its own characteristic structure, rather than being only vaguely internally self-consistent as in a low-level hierarchy. Virtually all the imprecision and vagueness is ejected from the scalar levels themselves into the inter-scalar regions, which become repositories of complexity. A simple example of this can be seen in Life and Simple Systems 9 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 Figure 1, which shows the classical logistic plot for the reproduction of rabbits, given limited food resources: xn1   xn (1  xn ) , xn = number of rabbits in year n, normalized to within 0→1, λ = rabbit fertility, where the different scalar solutions S1-S4 are separated by regions of deterministic chaos. Transit between adjacent scalar levels of a multi-level hierarchy entails passage through an interface which is not only complex, but which contains fractally-alternating regions of both analog and digital complexity. The inter-scalar interfaces are archetypically complex in the sense we referred to earlier – it is not only impossible to completely model them in a formal manner, it is also impossible to model transit through them. It is easy to see why this should be so. Autonomy negotiation within the interfaces depends not only on local properties and processes, but on negotiation in all of the interfaces of the entire scalar assembly. It is only by reference to global properties and processes that a local inter-scalar transit can be specified. Figure 1. The logistic plot: scalar levels S1 – S4 are separated by regions of chaos. Hierarchical stability depends on the imposition of inter-scalar constraints. These may be externally imposed, creating an artificial hierarchy, or they can be the result of hierarchywide auto-correlation of the scalar levels and their interfaces, generating a natural hierarchy – the basis of living organisms. Figure 1 illustrates the scalar levels of an artificial hierarchy, where the appearance of deterministic chaos depends on restriction of the contextual dimensions. Natural hierarchy, however, has a completely different character. Any dimensional constraints are the result of auto-correlation, and extant scalar levels themselves are autonomously generated in such a way that local and global properties approximately coincide within the levels. This is a major characteristic of any natural hierarchy: extant scalar levels correspond to Newtonian potential wells. To see why Life and Simple Systems 10 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 this should be the case, we must first look at how it is possible to distinguish one entity from another and one scale from another. Within the context of universal nonlocality, the restriction on communication speed which results from relativity creates localization [Prigogine and Stengers, 1984; Cottam et al., 1998a], and makes the instantaneous correlation of events in different parts of the universe impossible. Within a multi-level hierarchy, the distinction of one scale from another depends similarly on a restriction in communication speed, but now it is the inter-scalar communication which is relevant. A generalized form of relativity4 applies to any kind of communication, not just to photonic communication. Communication between glial cells in the brain, for example, takes place by calcium ion diffusion [Newman and Zahs, 1997], with a timescale of hundreds of milliseconds for distances of the order of microns. Even at these tiny velocities, relativistic differentiation is significant. Naturally occurring scales develop in regions of a general phase space where local properties are close to global ones. This provides a way to avoid the most serious consequences of relativity, by making sure that events at different locations of the global phase space do not later turn out to have contradicted each other, or to contradict global constraints. Newtonian physics itself is so successful because it mirrors the local-global correspondence of natural scales. This character is entirely absent from the artificial hierarchy of, for example, a digital computer, where the external imposition of quasi-scalar levels completely disengages local operations from global intentions, thus providing a favorable environment for catastrophic crashes. Figure 2. The generalized representation of a natural hierarchy. 4 Note that we refer here to a generalized form of relativity, and not to Einsteinian General Relativity. Life and Simple Systems 11 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 A further major characteristic of natural hierarchy derives from the quasi-autonomy of any particular scalar level from all of the other scales. If a large organism is to survive by successfully confronting external threats, it must be endowed with rapid response mechanisms. The integration of a multitude of individual cells into a higher level representation supports just such a capability, by providing a scaled set of models of the organism in its environment which are conducive to rapid computation and stimulusreaction. Representing Hierarchy There are a number of common ways of illustrating or representing hierarchy. Most of these fall into one of two classes – either scalar hierarchy or specification hierarchy. We do not find that either of these modes of description portrays sufficiently well the properties of a natural hierarchy. Figure 2 illustrates a model hierarchical description [Cottam et al., 1999, 2000], which is far richer than purely scalar or specification descriptions. Each vertical line represents a different scalar level. Every level corresponds to a complete scaled model of the same entity, from the most detailed version on the left to the simplest one on the right. Vertical line length indicates the amount of information which is required to completely describe the entity and its implications at that scale. In its most general form, the extreme left hand side corresponds to perfect nonlocality, while the extreme right hand side corresponds to the perfect localization of formal logic. Consequently, the left hand extreme is completely indescribable, and the right hand extreme is completely inaccessible, corresponding as it does to a formal rationality (e.g. Boolean logic) whose domain of operation is completely self-sufficient. Transit between adjacent scalar levels entails passage through an interface which is not only complex, but which contains fractally-alternating regions of both analog and digital complexity as we indicated earlier (see the simplified representation of Figure 2). A Limit to Expansion All natural organisms are scale-limited in size. Insects, for example, cannot be very large because of the restricted manner in which they distribute oxygen to their internal organs – this is evidenced by the larger-scaled insects which appear in the geological fossil record at around the time that the Earth’s atmosphere contained a higher proportion of oxygen than it does now. In the same way that an expanding system of primitive elements finally loses coherence, an expanding hierarchy will ultimately suffer a similar fate. However, the controlling factor is now not the number of similar elements, but the number of the hierarchy’s scalar levels. Hierarchical cohesion is directly coupled to correlation across the scalar level assembly. If differently scaled levels of the entity are well correlated cohesion will be strong, but if there is a great disparity between different scales the entity will be structurally weak and prone to fragmentation. This illustrates a fundamental distinction between artificial hierarchies, where inter-scalar constraints are externally imposed, and natural hierarchies, whose inter- Life and Simple Systems 12 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 scalar constraints are the result of hierarchy-wide auto-correlation of the scalar levels and their interfaces. It seems likely that the lack of hierarchy-wide auto-correlation in artificial hierarchies will be the biggest block on any attempt to generate artificial intelligence or artificial life. Any expanding information-processing structure will ultimately relativistically ‘fragment’: the central question will always be whether it can be made to generate a coherent hierarchy, or whether it simply and uselessly splits into a number of independent entities. THE HIERARCHICAL MAINTENANCE OF SIMPLICITY AND COMPLEXITY The net result of all of the auto-correlatory activity in a natural hierarchy is to maintain a suitable balance between apparent complexity and apparent simplicity. While it is vital that an organism has available simple models which able it to react swiftly to external threats, it is not necessarily the case that it should appear to be simplistic from an external viewpoint. In an environment where predators or parasites are capable of perceptional and intelligent information processing, it may be that apparent simplicity of reaction is taken as a sign of weakness. Bruce Edmonds [2004] has proposed that this may be at the origin of ‘free will’, and that an apparently ‘irrational’ response to threat may persuade the threat’s originator that it has not sufficiently evaluated its target’s capabilities. James Gunderson5 has found in experiments to implement escape strategies for submarines that simply doing nothing in the face of discovery may ward off further attack – presumably because the attacker is worried that it has not understood what the submariners know or are capable of. This risks opening up the entire question of ‘who defines intelligence, and from which viewpoint’, but suffice it to say in our present context that a wide range of reactive options provides more opportunities than a restricted one, and that the coherently multi-scaled pre-computed scenarios which are available from a natural hierarchy are invaluable for defense and survival. Is a Natural Hierarchy Scalar or Not? Auto-correlation across a natural hierarchy results not only in assuring cohesive stability of the entity, but also in strengthening the self-consistency of individual scalar levels by ejecting an optimal degree of complexity from them into the inter-scalar regions. In principle, it should be possible to satisfactorily approximate process/structure interactions within a single scalar level by a limited set of rules, corresponding to a scalar-dependent rationality. Unfortunately, the rationality associated with each scalar level is then likely to be specific to that level, and it will be impossible to make a simple rational transit between scales through the intermediate complex layers. This is to be expected from the arbitrary negotiated nature of each level’s partial (en-)closure and process closures. To that extent a natural hierarchy is clearly scalar. 5 Private communication. Life and Simple Systems 13 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 However, closer examination reveals that hierarchy-wide inter-level auto-correlation is itself a recognizable characteristic of natural hierarchy (and is not, therefore, associable with artificial hierarchy). As such, the auto-correlation provides a hierarchy-wide indication of the degree to which all the scalar levels are mutually consistent: it creates a hyper-scalar level which appears to be a simplification of the entire assembly. This reveals possibly the most significant aspect of natural hierarchy: it permits an organism to simultaneously operate as a mono-scalar and a multi-scalar entity. Simple logic is presented as required; specific complexity is accessible to match contextual requirements; even more possibilities are available than at first appears to be the case. GENERATING SIMPLICITY One of the major challenges in describing how living organisms operate is to identify the means by which the generation of simplicity is initiated. In common with the majority of physical phenomena, even if it is relatively easy to describe a system’s trajectory once it is in operation, it is virtually impossible to be certain about how that operation began, other than to rely on ‘stochastic processes’. We would ideally like to be able to see a little farther than that! An Immune System Approach The generation of simplicity has a character in common with the usual description of the evolutionary development of the mammal visual system. Although its inception appears to be dependent on the presence of some kind of ‘random’ activity as a source of variation from which selection may be made, this would seem to be far too hit-and-miss an operation to account for reliable directed development within a restricted timescale. Some ‘creative force’ is obviously present, and it can apparently be relied on to ‘deliver the goods’ in a timely manner. Luis Arata [2004] has proposed an interesting possibility, which is linked to the development of self-repairing systems. He suggests that an immune system can be viewed as an imperfect problem-solving mechanism: the autonomous system detects internal malfunctions and tries to fix them on its own, tinkering with all it has at hand. Internal innovation happens when a new type of malfunction is fixed. The system remembers the solution, for use at some future time in an as-yet unknown context, and on that occasion with a quicker response to stimulus. In this sense the system has adapted, it has innovated with respect to its previous capabilities, and learned from this action. An interesting aspect of this process is that the cause of a new type of malfunction may be the result of the system's interaction with a new environment - the immune response mechanism can function as an adaptive drive. Arata’s proposed ‘tinkering’, however, again suffers from the requirement for an as-yet undefined faster-than-stochastic creative generator. Life and Simple Systems 14 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 Figure 3. (a) A number of naturally hierarchical entities within the same environment, and (b) asynchronous auto-correlation across the hierarchy. We propose that the superposition of a number of different natural hierarchies which use the same database may help in solving this problem. Figure 3(a) illustrates the superposition of a number of hierarchically-defined entities within a single unified environment (we have left their multiple scalar levels out of the picture for clarity). In our present case, each of these entities can represent a different multi-scaled model of environmental problems which have already been solved. The aim is to provide a solution to a recognizable but as-yet un-encountered problem. We suggest that this may be achieved by one or a number of mutations of previously existing solutions. The key to creative generation is that although natural hierarchical auto-correlation may be strong, it will never be perfect. Differently scaled representations of an entity will never exactly coincide – otherwise, there is only one scale, and no hierarchy. Correlation between the various scales of a particular entity (e.g. of that shown centrally in Figure 3(a)) will take place asynchronously between all the neighboring pairs of levels, as indicated in Figures 3(b) and 4(a). However, a small degree of non-coincidence between adjacent scales of the particular entity and of its neighbors can now have an important effect. Whereas complete scalar coincidence would mean that auto-correlation is relatively simple across the entire scalar ensemble, if this is not the case there will be scales present where it is less than obvious how to access the adjacent ones, as illustrated in Figure 4(b). The net result can now be a mutation of local scales, by interference in the correlation path of one entity by the scales of another (see Figure 4(c)). We suggest that this mechanism can provide useful generation of new problem solutions by mutation, and help to speed up the creation of new candidates for inclusion in the immune ‘toolbox’ Arata [2004] proposes. Life and Simple Systems 15 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 Figure 4. (a) Auto-correlation in a perfectly aligned natural hierarchy, (b) autocorrelation in a partially misaligned natural hierarchy, and (c) auto-correlation mutation caused by overlapping misaligned scales of two different entities. One other source of mutation is that transit between adjacent scalar levels involves passage through both analog and digital complex regions. It is likely that this process itself can modify the perception of representations between the members of an auto-correlating level pair. Defining “What is Alive” The traditional way of defining ‘what is alive’ is to establish a number of criteria which could distinguish the living from the inanimate (or inplantate?), and then fix those criteria so that they define that ‘what we know is alive, is alive’. Self-referential definitions of this kind are of little use in progressing our understanding of ‘what life is’. Biologists have long used the combination of metabolism and reproduction to define life, but this approach addresses more how an entity evolved to its state of ‘living’ than whether it is alive at this moment. It is, however, possible to derive criteria for living systems from more abstract considerations, and we present two of these below. Protein Bending as the Origin of Life It is reasonable to suppose that the complexities of a living system would not survive the absence of the complex proteins which to a great extent make up the tissue substrate for life. Is it possible that we can use the inception of proteins as a criterion? Starting from a presumption of the big bang, as is intrinsic to evolution of the natural hierarchy representation we presented in Figure 2, the ‘emergence’ of new structure initially took the form of discrete (digital) entities emerging from a continuous (analog) background. From 10-5 seconds after the big bang protons and neutrons were formed (localized) out of quarks, through an intervening complex interface. From 3 minutes later, atomic nuclei were synthesized; from 300,000 years later the first atoms formed; and so on. Life and Simple Systems 16 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 From this point onward, and up to the formation of bio-molecules, it is reasonable to suppose that the vast majority of information which was coded into the created structures could be simplistically represented by the sequence and organization of atoms with respect to each other. The supposition is that this pattern continued up to the generation of the first simple proteins, but that then a new difficulty raised its head. Normally, protein development is referred to locations in sequence space – a multi-dimensional representation of the atomic sequences which can go to making up complicated protein structures - where possible new sequences of atoms can be visualized to see whether a new molecule is ‘feasible’ or not. Unfortunately, this takes no account of the difficulties presented to complicated atomic arrangements which must position themselves in only three spatial dimensions. Even at the current stage of biological development, sequence space is virtually empty, and there are vast numbers of possible but as-yet unrealized protein sequences. However, a modified form of representation which takes account of the real spatial relationships between the parts of a molecule, namely shape space, is already nearly filled up. Andrade [2000] has suggested that this is the reason why protein bending developed, as a way of getting round the limitations imposed on new sequences by their spatial constraints. It is notable that protein bending makes possible the kind of ‘key in a keyhole’ molecular alignments which control much of organic metabolism. The development of protein bending provided bio-systems with the dual analog-digital coding mechanism which is the basis of evolved life. In its most simple form, this consists of DNA as a digital representation and the organism itself as an analog derivative of it. It seems as if the development of protein bending could indicate the genesis of life as we recognize it. Redefining “What is Alive” Further consideration of the implications of natural hierarchy suggests that it is the stabilization of highly multi-scalar entities which indicates the onset of life. This does not contradict our previous conclusion with respect to protein bending – it supports it. A major step in stabilizing a large hierarchy is the organized development of correlated digitalanalog coding which can support inter-scalar information transit through the digital/analog complex interfaces. We suggest that the most significant contribution of hierarchy to sustainable life is that it permits an organism to simultaneously operate as a mono-scalar and a multi-scalar entity. DISCUSSION So, is nature complex? And is its complexity distinguishable from complexity by assembly? Responses to these questions depend, as always, on the contexts within which we decide to ask and answer them. A vital part of any kind of modeling process is to remember that there Life and Simple Systems 17 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 are always at least three participants in the narrative. These may be a natural system, a formal system and an observer; they may be two mutually observing systems and their interface; they may semiotically be an input object-relation, an interface mediation relation and an output interpretant relation [Taborsky, 2005] - but there are always at least three. It is worth remembering that Newtonian mechanics already has problems with the interaction of three distinct entities. And it is easy to forget that a structural ‘snapshot’ of a living system yields no information about its temporal organization, and that recourse to simplistic description demands that all three narrative participants co-exist within one and the same context for a model or state-description to have anything other than ephemeral meaning. Our own approach to modeling, as evidenced in this paper, is in accordance with the evolution of our species, whose first technological successes were at scales related to our human bodies, whether of space, or time, or hardness, or any other observable or measurable phenomenon or property. Only recently have we progressed to investigation, knowledge (or presumption) and control of more extreme scales, of carbon nanotubes, of cosmological black holes, of terrestrial plate tectonics, of microscopic computational devices. Is nature complex? Complexity is certainly in evidence at our own scale, and clearly perceptible as we progress to scales lower or higher than our own, but can we justify suggesting that there is a sense in which it is all-pervasive beyond our limited means of observation? We believe not – we are predisposed to accept our belief that any other conclusion would only be one of belief! There is, however, a sense in which a Rosennean-style incompleteness-complexity enters into every observation we make of our surroundings. With all its failings, Science has managed to demonstrate that any measurements we make depend on the pre-assembly of lower-scaled ‘entities’, whether these are molecules, atoms, protons neutrons and electrons, quarks, superstrings, … . Measurement and subsequent modeling at every stage of this Scientific progression has thrown up predictions of as-yet unmeasured scale. Everything we currently ‘know’ about the physical nature of our universe is portrayed as an assembly. At every scale, relativistic communicative restriction plays its part, making it impossible to obtain complete time-independent information about any assembly of entities. Consequently, in at least this restricted sense, any assembly of entities will exhibit a more or less relevant degree of incompleteness-complexity. This not only applies to large systems, whose complexity may derive from this or other causes, it also applies to complicated and even simple assembled systems: everything ‘is’ complex. Even at the quantum level, Ioannes Antoniou [1995] has demonstrated that when conventional quantum theory is extended to large systems there is a breakdown in logical completeness. The central issue is not one of definition, it is one of relevance to a particular context: is the incompleteness ‘a difference which makes a difference’? 6 This may appear to be something of a quibble, as life is most certainly not associated with minimal degrees of complexity, but it is of prime importance in judging how we decide to model living systems. 6 "...what we mean by information... is a difference which makes a difference." - Gregory Bateson. Life and Simple Systems 18 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 Newtonian mechanics is ridiculously simplistic, but it reproduces very effectively the tendency of nature to create simple representations of complex phenomena, because it reproduces nature’s requirement for ‘computable’ models which exhibit approximate localto-global correlation [Cottam et al., 2004a]. The complexity which is implicit in its simplistic avoidance of questions of temporal completeness is not a serious shortcoming, in so far as it applies to our human scale. The complexity of life is not obviously amenable to generating the rapid responses an organism needs if it is to avoid succumbing to external threats in a hostile environment. Organisms create their own simple models of both themselves and their environments to help them survive. Our own brains implement this strategy (as ‘fear-learning’) through an approximate-but-fast amygdalic bypass to the detailed-but-slow cortical processing [LeDoux, 1992]. Multiple scales provide multiple degrees of organizational complexity, and associated multiple scales of temporally constrained entailment. In general, successful modelling involves recognizing how a difficulty in one part of a model can be relocated to some other part of the model where it can be more easily dealt with. Rosen and Kineman [2006] present a reappraisal of Robert Rosen’s proposition that the complex nature of time and its interaction with biological systems is what allows organisms to develop ‘internal predictive models’ that are built into a living system’s organization, and that these models involve ‘acts of abstraction’ that lie ‘outside the dynamics of the living system’. The natural hierarchy we present in this paper instantiates just such a kind of organization7, and because the rational inhomogeneity of a ‘real’ hierarchy permits, or rather insists on, the partial enclosure of different scales, multi-scalar temporal encoding is now embedded in the structural hierarchy which is characteristic of a reactive organism’s embodiment.8 A major advantage of this reformulation is that it is then possible to call upon modifications of already-existing theory to resolve the thorny problem of inter-scalar transit. A natural hierarchy is essentially birational [Cottam et al., 2004a]: the Newtonian potential wells indicated in Figure 2 form a self-consistent auto-correlated set of scales; the intermediate complex layers form a second one. The former Newtonian set is reductive towards localization (on the right hand side of Figure 2); the complex set is reductive towards nonlocality (on the left), the two yielding an interleaved complementary pair of self-correlated mono-rational hierarchies. Each mono-rational hierarchy acts as a scaled repository of ‘hidden variables’ [Bohm, 1987] for the other, and it seems [Cottam et al., 2003a] that apparently a-rational inter-scalar transits may now be rationally modelled through a generic form of quantum error correction: reformulation of the complex substrate of life as a natural hierarchy pays great dividends! … although it is a moot point whether the ‘acts of abstraction’ lie outside the dynamics of the living system: we prefer to use the word ‘dynamics’ to describe all kinds of temporally significant activities, rather than restricting its use to a small subset of these and therefore placing the ‘acts of abstraction’ outside ‘dynamics’. 7 8 The developmental origin of this research programme lies in AQuARIUM [Langloh et al., 1993] - an architecture which was intended to reproduce the multi-temporal response capabilities of organisms in an optical computer. Life and Simple Systems 19 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 CONCLUSIONS This paper targets the relationship between simple systems and life, which begs the question “What is a simple system?”. We suggest that a simple system is a nominally stable composition of nominally stable ‘sub-elements’, where communication across the entire assembly can take place within a limited and complete set of rationalities9. The maintenance of simplicity within a complex domain requires the application of external constraints, in the manner that a causally-chaotic system may be encouraged to exhibit deterministic chaos by restricting its degrees of freedom (e.g. for the logistic plot of Figure 1, by containing its expression to within two dimensions). In a natural hierarchy individual Newtonian scales experience precisely this kind of externally applied en-closure, which is imposed by adjacent scales of the same entity through their complex mutual interfaces: complexity is a necessary condition for autonomous simplicity! Living organisms depend on their quasi-stable simplistic-system appearances to adequately relate to their environments, but evolution requires that their ‘sub-elements’ can mutate. Whereas simple systems derive stability from that of their basic elements, living systems do so by exploiting the complexity of their organization to circumvent the far less stable nature of their constituents. Rosen began his life’s investigations by asking the question “Why are living things alive?”. We began from within a technological domain by asking “What is a computer?”, which surprisingly, but we now see inevitably, led us towards complexity and life. Two major processes are required for computational survival: decision-making and comparison. Decision-making is locally data-destructive: information is progressively compressed (and locally thrown away) to arrive at a simple computationally-serial decision. Comparison, however, must either be computationally-serial and non-destructive of data, which for large systems is impossibly resource-intensive, or it must proceed in parallel, either through quantum superposition or by a simulation of it [Langloh et al., 1992]. Biological organisms exploit complexity to simulate parallel comparison through chaotic computation [Cottam et al., 1998a]. Karl Pribram [2000] has suggested that this simulation is responsible for memory storage in the complex axonite meshes which couple together neuron outputs and inputs. We have presented elsewhere a network-based relational rationalization of the commonly presumed Descartes-style duality of body and mind [Cottam et al., 2004a]. The coevolution of linearly-scaling direct and quadratically-scaling indirect relations in growing networks ultimately leads to two different quasi-independent externally-interpretable system characters. One corresponds to the normal Scientific view, which depends on formally-rational cross-scale information transport, the other to parts of the holistic system which are inaccessible to a ‘normal Scientific’ viewpoint, and which are associated with the distributed nature of indirect relations. Complete representation of a system’s interactions with its environment requires evaluation of both of these characters. We believe that this 9 This is, of course, a simple model of a simple system. Life and Simple Systems 20 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 bifurcation of system character into dual reductive and holistically-related parts, and the difference in reductively-rational contemplative accessibility to these two characters, has led to the conventionally presumed split between body and mind, where the body is associated with direct ‘Scientific’ bio-systemic relations and the mind is naturally ‘difficult to understand’ from a ‘normally Scientific’ viewpoint which presupposes that all essential system aspects can be related to a single localized platform. We have proposed [Cottam et al. 2004a] that the dual system characters derived from direct and indirect relationships in a large network are equivalent to those more usually associated with formally-rational information processing: as a co-evolution: the direct relationships lead to (reductive) ‘hardware’; the indirect relationships lead to (holistic) ‘software’. The most critical facet of this bifurcation is that of relatedness to a single localized platform, which corresponds to the instantaneous uniqueness of our human consciousness, and to its consequent and somewhat egotistical presumption that an albeit simplified reduction of our environment to a single viewpoint can validly represent natural phenomena. This is arguably a far greater indictment of the conventional Scientific stance than those presented by Rosen [see, for example, Rosen, 1991], most particularly in that it precludes the inter-scalar closures upon which organism survival depends. If we describe a quasi-externally viewed system solely in terms of reductively specified interactions (i.e. in our network analysis the ‘hardware’) we unsurprisingly risk missing out the majority of the systemic character! This conclusion mirrors in many ways Rosen’s conclusions about living systems. However, if we choose to completely discard the reductive system interpretation (the ‘hardware’) we end up with an abstract description which precludes embodiment. Relationship to the Work of Robert Rosen Although, as Rosen points out in Life Itself [1991, page 19], a dead organism is as inanimate as anything; so, to the best of our knowledge, is an un-embodied organization. We require both the reductive and holistic descriptions of a system to successfully interpret its operation: similarly, we require both the reductive and organizational descriptions of a living system to successfully understand its nature. A ‘state-based snapshot’ of a living system can inform us about its architectural embodiment; “entailment without states” [Rosen, 1991] can inform us about its more holistic organization. We are reminded that in his ‘Note to the Reader’, at the beginning of ‘Life Itself’, Rosen [1991, page xviii] commented that when he tried to integrate relational and structural descriptions of the same biological systems they did not seem to want to go together gracefully, but that they must go together, being alternate descriptions of the same systems, the same material reality. Life and Simple Systems 21 Cottam, Ranson and Vounckx, 2005 Systems Research and Behavioral Science 22, 413-430, 2005 It appears to us that the results of Robert Rosen’s investigations and of our own are in not essentially contradictory. Starting from “Why are living things alive?”, Rosen arrived at an appraisal related to the ‘software’ needed for a living system; starting from “What is a computer?”, we arrive at least at the ‘hardware’ architecture for its embodiment. Rosen’s specification for life is in terms of the closure to efficient cause of his replicating (M, R)system [Rosen, 1991, page 244]; our own is in terms of the self-correlatory completeness (i.e. closure) of inhomogeneously-birational multi-scalar natural hierarchy. A natural hierarchy assumes functional inter-relationships and subsumes closure to efficient cause. Rosen’s conclusions about life, however, do not appear to take into account the hierarchical scalarity of living systems which is described in this paper, nor the tendency of scalar levels to eject complexity into their inter-scalar regions in an attempt to improve their computability by ‘becoming’ simple machines. Rosen [1991, page 251] points out that in a replicating (M, R)-system every function is entailed by another function, and that apart from initial input the environment is irrelevant, so far as entailment is concerned. While we would agree with the former assertion that in the natural hierarchy of an organism every function is entailed by another function, recognition that the hierarchy is birational makes the latter claim unlikely, except when pertaining to a simple model of life, for example in Rosen’s [1991, page 251] well-known abstract block diagram 10C.6 of the entailments of a living system. At every level of an organism’s hierarchy there is a locally-scaled environmental complement to its locally-scaled description [Cottam et al., 2003b], which injects environmental entailments into both its own and other adjacent scales. In biological terms, it seems reasonable to attribute at least part of a cell’s efficient cause to the organism of which it is a part, if less obviously vice versa (it is important to note that entailment between biological scales is never unidirectional). It is difficult to see why the birational entity-ecosystem fertilization of entailment should be restricted to taking place only within an organism, and to be excluded from the similar entity-ecosystem relationships it maintains with its external environment. We conclude that auto-correlatory natural hierarchy lies at the root of the development of life, and that its major characteristics correspond to the major requirements of living entities. It seems most likely that the two are inseparable, and that through its inevitable properties a natural hierarchy is alive. The attribute of logical intelligence derives from the inter-scalar complex regions (in a way which is related to semiotic abduction), and that a more global form of intelligence, related to wisdom, derives from correlation between the hyper-scalar levels which are generated from the hierarchy’s entire scalar assembly [Cottam et al., 2003b]. 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