The below sections disclose interesting novelties of the operator hierarchy.
Almost all hierarchies in popular and scientific publications are mixtures of operator and non-operator systems, suggesting that the inconsistencies are not recognised as a problem. Inconsistent hierarchies being the rule, I expect that quite a few readers of this section may have difficulty too in understanding the significance of solving the inconsistency problem in hierarchies. They have been educated to accept 'hierarchy' as an approximate concept indicating loosely structured ranges from smaller to bigger, less to more organised, etc.
How, then, can the operator hypothesis help us to bring some clarity in the discussion about hierarchy? To start with, it is useful to explain that the operator hierarchy distinguishes five major types of hierarchy:
Of these types of hierarchy only A, B and D are strict in the sense that a certain system type always occupies one and the same level in the indicated hierarchy. The internal hierarchies of options C and E are normally less strict. With respect to the organisation of organisms, the main reason is that it frequently includes elements that are not part of the sequence of first-next closures. For example organelles in cells and organs in multicellular organisms have evolved after the emergence of the cell and the multicellular organism. They can be regarded as internal differentiations. Each organelle and organ shows its proper internal hierarchy that is characterized by the levels of differentiation that its organisation has reached. With respect to the organisation of ecosystems, any use of hierarchy in interactions must be considered tentative. A good example is a food chain. This is hardly ever strict, because organism rarely feed strictly and only from precisely the first-lower level in the chain. Similarly, there are problems with defining the limits to populations/species. An if organisms are ranked according to the substrate they use, for example a moss that grows on a leaf of a bromeliad, that grows on a branch of a tree, this 'hierarchy' is vulnerable to changes, for example when the moss also is able to grow directly on the bark of the tree. In conclusion I would advocate that it is impossible to create strict hierarchies for interactions in ecosystems for any of the dimensions construction, information, energy and displacement.
The existence of a layered hierarchy is a classical topic in evolution science. A typical example is the layering that includes elementary particles, atoms, cells, etc. Another example is the hierarchy from geosphere to biosphere and noosphere. Where these approaches sometimes have difficulties with defining their layering, the operator hypothesis solves this problem by using one closure types to define the beginning and the next closure type to define the end of the layers such as the superstring layer, the superstring hypercycle layer, the hadron layer, the atom layer, the cell layer and the memon layer.
The Darwinian approach to evolution is ruled by two basic processes: diversification and selection. This implies that parental organisms must survive long enough under the given selection pressures to give birth to a number of offspring with varying representations of the parental genes. Subsequently, the gene- and environment based phenotypes of the offspring determine the individual chance on survival.
The operator hypothesis rephrases these processes in a way that generalises their use from organisms to all operators and adds one additional rule to create a more general framework for evolution:
So far, scientists have discussed the evolutionary importance of hypercyclic dynamics mainly in relation to the origin of life. The works of Maturana (1970), Eigen and Schuster (1971) and Kauffman (1993) have attracted much attention to the second order catalytic cycle that creates autocatalysis. Autocatalysis means "self-catalysis" and implies the existence of a set of enzyme reactions in which the product of each reaction is an enzyme that catalyses another reaction, such that, after one round of catalytic steps all enzymes in the set have been copied. This mutual remaking can be regarded as a circular pattern that connects all enzymes in the set. Because each enzyme reaction also represents a small reaction circle by itself (in which a product is formed after which the enzyme is released again), a cycle of cycles arises: the catalytic hypercycle.
But a hypercyclic set of enzymes does not define its proper boundaries. It "floats" in the surrounding chemical soup and can only gain individuality when a kind of system limit, an "interface", becomes part of the process circle. Only with such an interface, does the system become recognisable as individual. The interface specifies the domain of the network's operations and defines the system as a unit. Such a closed, autocatalytic system configuration has been christened an "autopoietic" system by Maturana and Varela (autopoiesis means 'self-making').
The idea of a hypercycle with boundary/interface forms an integral part of the operator hypothesis. Each major transition specifies a step in system organisation that includes the formation of a hypercyclic interaction pattern and one additional emergent property that is typical for that major transition and which lends the system an interface. For the hadrons, this is the quark hypercycle with the confinement as a strong binding principle. For the atoms, this is the hadron hypercycle with the electron shell as the interface. For the cell, this is the autocatalytic enzyme cycle with the cell membrane as the interface. Finally, for the "brain" this is the hypercyclic neuron network with the sensors as activation and perception interface.
As far as I can judge from published scientific work, the operator hypothesis seems to represent the first theory that is based on a generalised use of hypercyclic interactions with interface as the basis for the major evolutionary transitions in (meta-)evolution. In a less explicit form, there exist a few publications that point in this direction. Capra (The Web of Life, 1996, page 99) refers to the physicist Geoffrey Chew who " formulated his so-called bootstrap hypothesis about the composition and interactions of subatomic particles, which sounds quite similar to the concept of autopoiesis, about a decade before Maturana first published his ideas. According to Chew, strongly interacting particles, or "hadrons", form a network of interactions in which "each particle helps to generate other particles, which in turn generate it" (in Capra 1975). Capra rejects the hadron as an autopoietic system for two reasons. One, "hadrons are potential "bound states" of each other in the probabilistic sense of quantum theory, which does not apply to Maturana's "organisation of the living". Two, a network of subatomic particles interacting through high-energy collisions cannot be said to be autopoietic because it does not form any boundary." (Capra, The Web of Life, 1996, page 99).
The latter rejections may be caused by a strict focus on formative interactions as the basis of autopoiesis and an inflexible interpretation of the boundary concept. The operator hypothesis uses a different approach to transitions, where major transitions (the ones that also are responsible for the emergence of the autopoiesis of the cell) are based on two requirements: a hypercycle and the first-next interface closure. This avoids the obligatory use of a specific hypercycle and boundary definition, but accepts the two closures of a major transition as to create the required unifying principles. The first step of the major transition in the operator hypothesis creates the hypercyclic interactions, for example those between hadrons in the atom nucleus, between molecules in the cell and between CALM's in the memon. The second step of the major transitions causes the membrane of the cell as first-next closure, the electron shell of the atom and the quark-gluon interactions that create the quark confinement of the hadron.
Of course, Maturana and Varela have recognised the closed structure of interactions in the brain. But as far as can be understood from their texts, the brain was regarded as an organ of a living organism, and was not considered to be the emergent structure defining a new, higher complexity operator type.
For those that have read the paper by Szathmary and Smith (Nature 1995) the words "major evolutionary transitions" may appear confusing. Szathmary and Smith have used this concept in relation to transitions in the genetical/cellular organisation of organisms. Yet, in the viewpoint of the operator hierarchy, it is to be preferred to regard as major transitions only those transitions in system configuration, that include an hypercycle step (the confusion caused by the different interpretations of "major transitions" is discussed in the Discussion section). As different studies on evolutionary transitions are based on different scales of observation, confusion about "major" and "minor" transitions will probably continue to exist in the future.
Often it is assumed that a strict hierarchy should be based on one and the same production rule for creating any next entity from a preceding one. This may be true for large whirls in water that include smaller whirls that include still smaller whirls, etc. However, this all too simple approach seems not to work for evolution. Instead, the operator hierarchy advances on this matter by using first-next closure and by postulating major and minor transitions. Major and minor transitions form a practical way to deal with the differences between closure steps. For example, the transitions from atoms to molecules and from molecules to the cell represent quite different closures.
The strictness of the approach may be the most interesting aspect of the operator hierarchy. Of course, other authors have created hierarchies that could be extrapolated. What may be considered innovative about the operator hierarchy, is that it is restricted to operators and that these are ranked rigidly on the basis of the first-next possible closure.
The idea of extrapolation is not new. For example, in the fifties the French philosopher Teilhard de Chardin made predictions of the future of evolution on the basis of a complexity hierarchy. De Chardin must be considered to have been quite ahead of his time, in a philosophical sense, because he distinguished between 'true' and 'other' systems, and based his predictions purely on the 'true' systems. Such an approach parallels the distinguishing of operators and interaction systems. Actually, I only recognised these aspects in Teilhard de Chardin's theory, because I read his work after I created the basis for the operator hypothesis. Otherwise I could well have overlooked the importance of his realisations on this point. However admirable his insight in system hierarchy, the investigations by Teilhard de Chardin suffered from the limited knowledge of low complexity systems (quarks) at that time and a lack of precision in his description of the rules for major transitions. This resulted in the integration of populations (as interaction systems) into the hierarchy, which I consider a mistake. Also his desire to place his ideas in a religious context has not made his work popular amongst many scientists.
The operator hierarchy can be regarded as an improvement of Teilhard de Chardin's approach. By first creating a precise hierarchy, it can formulate extrapolations on the basis of the strict pattern in complexity increases that are related to major and minor transitions. An important philosophical consequence of this strictness is that the operator hierarchy rejects the extrapolation towards populations as the next stage in evolution, because this would imply the inclusion of an interaction system in the set of operators. The readers that are acquainted with the system hierarchy literature will know that De Chardin is not alone. There exist many old, but also many recent approaches, in which populations form an integral part of the system hierarchies presented.
Many scientists write about hierarchies in a rather loose way. I first experienced this during my ecotoxicology studies, where a generally used hierarchy runs from atoms to molecules, organelles, cells, organs, organisms, populations, communities and ecosystems. Another hierarchy that I consider as sloppy, is the one that is used commonly in astronomy, ranging from quarks to hadrons, atoms, molecules, planets, stars and galaxies. Let me point out some sudden jumps in the lines of reasoning that plague these hierarchies.
A. The first aspect in these hierarchies that can be regarded as scientifically problematic concerns the chronology in which evolution evolved the different elements in the hierarchy. From molecules, evolution had to create cells first, before organelles could take shape and develop into complex entities. From cells, evolution created first multicellular beings, before it made any sense to create organs. Turchin (1995) has conceptualised this diversification of internal organisation that follows after the formation of a higher level unit by formulating the "law of the branching growth of the penultimate level". It states that after the formation of a control system C, controlling a number of subsystems Si, the Si will tend to multiply and differentiate.
In an evolutionary context it is interesting to note that only after the formation of a mechanism controlling the Si does it become useful to increase the variety of the Si (Heylighen 19$$). As they represent a kind of secondary, internal diversification, organelles and organs are better not included in any (upwardly directed) chronological evolution hierarchy. They should be dealt with as aspects of the internal organisation of cells and multicellular organisms. I feel strengthened in this perspective because the exclusion of organelles and organs from an ontogenetic evolution hierarchy is also a fundamental aspect of the ideas of Prof. Kornet (Leiden University). Kornet studies the evolution of system types on the basis of the filling of potential slots in system state space. How many potential slots are there, how many are filled and where are the gaps?
B. A second aspect concerns the fact that I consider many of the proposed hierarchies to be 'corrupt'. This viewpoint has its origin in the requirement (of the operator hierarchy) that each operator type holds exactly one -and only one- position in the hierarchy. It should never be possible to include or exclude a transition between two operator types and thereby change the position of the higher level operators. Let me illustrate the effect of this requirement by discussing the following question. Often people ask me whether the hierarchy should include the step from multicellular organisms to populations instead of the step from multicellular beings to neural networks. Indeed, the step from individual organisms towards populations of mating organisms (which must not yet show a hypercyclic neural network!) would involve one emergent property. Yet, the individuals in a population show no unifying system limit -the interface- for the mating interactions, which is the reason that they form an interaction system. When considering organisms with brains, it is simply against the rules of the operator hierarchy to regard the formation of a population as the next step. The reason is that such a step would not involve the first next emergent property above multicellularity, because the neural network already holds this position.
C. Finally, there is a third general aspect that is problematic in many published hierarchies. This involves the mixing of operators and interaction systems in one and the same hierarchy. Atoms, molecules, cells and multicellular organisms are operators. Populations, communities, ecosystems, planets, stars and galaxies are interaction systems. It is a fundamental aspect of the operator hierarchy that these two groups of entities require a separate treatment and must not be placed in the same hierarchy.
A question that people often ask is how ecosystems and life on other planets in the universe will look like and whether more intelligent organisms than us may exist somewhere else. The operator hierarchy shows that the evolution of system types on the basis of closures limits the possibilities for evolutionary system types to those realised by the operators. This implies that either the operator hierarchy shows major flaws, or that the same range of subsequent operators determines the path of evolution in the entire universe. This statement is at least partly supported by the astronomic observations that -as far as observable- other galaxies contain the same multi-atoms and lower operators as our galaxy. Tests are not yet possible on the predictions that life on other planets, when found, will also show a cellular basis and that intelligence, wherever it may be found, will also be based on hypercyclic neural networks. Such networks may also consist of technical equivalents of neurons allowing for similar multivariate computing as in neural networks. Note that the operator hypothesis does not give any rules for predicting the exact construction of the autocatalytic processes in the cells of extraterrestrial organisms. Neither does it give clues for the body-shape of organisms on other planets. Accordingly the operator hypothesis can never be used to predict numbers of legs, size, colour, growth rate, etc. Such aspects can nevertheless be deduced from the local selection pressures, when these are known.
The principles behind the operator hierarchy are of the all-or-nothing type, which offers clear handles for refuting the hypothesis. Here I give two examples (and two more in the FAQ's section).
One, it should never be possible to skip or add a level in the hierarchy. Using molecules as an example, it should not be possible to form them directly from hadrons without the necessity to construct atoms first. The reason is that each transition must represent precisely the one and only closure (involving a hypercycle dimension) that follows immediately on the preceding one. If only a single transition can be found where the hierarchy could be "stretched" with an additional, intermediate closure step, or could be "compressed" by deleting a superfluous closure step, the whole idea would not be viable.
Two, the suggested repeating of stages must be strict. For example, multi-stages, such as the hadrons, the molecules, and the (strictly) multicellular organisms, must always form the basis for the closure that defines the (hyper-)cyclic dynamics of the next primary operator. If only a single situation can be found where this is not true, the whole idea must be considered wrong (aspects that allow the refuting of the hypothesis are also discussed in the FAQ's section of this text).
Of course, the above rigour in rejecting the theory must be weighed against the stage of its development. I consider the operator hypothesis as a theory in development and expect improvements in the mathematical description of the indicated system types, their type properties and the comparison of the closure configurations between layers.