Discussion points and frequently asked questions

Discussion is not only good for communication, but it also helps to formulate the hypothesis in a more precise way. It is therefore with pleasure that I present some discussion points that were gathered from remarks by enthusiastic or critical readers with a wide range in professional backgrounds.

  1. The operator hierarchy is based on analogies
  2. Evolution is random and not predetermined
  3. Evolution does not necessarily involve progress
  4. No planets, stars, galaxies in your hierarchy
  5. The operator hierarchy selects the system types included
  6. Your 'strict' hierarchy is based on different transition types
  7. You use circular reasoning by defining operators in terms of operators
  8. There may be undiscovered intermediate stages
  9. You neglect the environment in which the operators evolve
  10. The earth is an operator
  11. Your definitions determine your hierarchy
  12. Interactings between organisms will create the next operator
  13. Populations should be the complexity level above organisms
  14. The concept of an "operator" already exists in physics
  15. Your major evolutionary transitions differ from Szathmary and Smith
  16. Computers cannot become intelligent
  17. The operator hypothesis is not a quantitative hypothesis
  18. The operator hypothesis is not a refutable hypothesis
  19. A much simpler scheme would do
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1. 'How can you seriously believe in a hierarchy that is based on analogies and not on mechanistic insight in the transitions?'

Analogies are used in many branches of science. For example, the number xx consist of two identical characters. In analogy, the numbers 11, 22, 33, etc. consist of two identical digits (x being 1, 2 and 3, respectively). Of course, systems are not numbers, but the recognition process in the operator hierarchy works in a similar way, although with different counting-steps and different similarities.

Numbers are the result of counting-steps based on a minimal numerical measure: the number 1 (at least for the set of natural numbers). The operator hierarchy counts evolutionary levels on the basis of a minimal transition measure: the first-next closure.

Similarity of numbers can be based on a simple xx analogy. The recognition of similar types of emergent properties requires a description of an abstract process/structure in such a way that it can be recognised independently of the kind of modules that perform it. For example, quarks link to form hadrons, atoms link to form molecules and cells link to form multicellular beings. With respect to the formation of these three system types the operator hypothesis recognises the same kind of functional relationships that form the same kind of major structure. To be more precise, each of the latter three examplesowe their highest emergent property to a recurrent interaction between the preceding highest-level operator type.

My aim with the above example is to show that the operator hypothesis is based on a counting process that works in a similar way as the numerical counting process. What differs are the kind of units (numbers vs. emergent properties) and the measure for the minimum unit-distance (the number 1 vs. the minimal emergent property that causes closure). The example also shows that the use of analogies in the operator hierarchy does not differ from the use of analogies in numerical approaches.

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2. 'Evolution does not follow a predetermined path! How can you propose a scheme without acknowledging the random processes in evolution?'

Like most biologists I fully recognise that the evolution of organisms is based on diversification and selection. Diversification is the result of mutations and reshuffling of the genetic material that is passed on to the offspring. Selection occurs as soon as the offspring show differences in their ability to survive and reproduce in a given environment. The resulting lineages of survivors can be regarded as a continuously branching tree, thephylogenetic tree or ' tree of live '.

The diversification and selection processes in organisms can also be recognised for other operators. Reactions between fundamental particles in the early universe, for example, allowed for diversification on the basis of random impacts between quarks that led to the formation of a broad range of different types of hadrons. Yet, under the ambient conditions that are required for their formation, the life of most of the mesons (two quarks) and baryons (three quarks) is extremely limited. Only the more stable survived.

Diversification at the hadron level was not based on genes, but on the chance that certain quarks met in the quark soup. Likewise, selection in a quark environment does not involve predators or peers, but is largely based on the stability of the newly formed hadrons.

I fully recognise the randomness of the diversification processes in evolution and the importance of the internal stability of a system in relation to its interactions with its local environment. In addition to this, the focusing on transitions in system organisation allows me to recognise within this chaotic and undirected branching process a series of well-defined transition events. These events are the major and minor evolutionary transitions that are described in the operator hierarchy. The recognition of the transitions in the operator hierarchy is based on system complexity and is, therefore, not directly related to the branching process. For example, multicellularity may arise in different branches of thephylogenetic tree (unrelatedtaxa) and it may occur early in one branch and late in another (unrelated moments). The operator hypothesis gives no information about the when and where multicellularity may arise in an evolutionary tree.

In contrast to this uncertainty stands the certainty that a higher complexity than single celled units must involve some form of multicellular units. Thus, where the branching of thephylogenetic tree may be regarded unpredictable, I regard it as fully predictable which type of transitions in system complexity potentially may occur on any branch.

In conclusion it can be said that evolution follows a branching path and that transitions in system complexity occur showing a strict sequence. To me, therefore, evolution connects minor probabilistic steps with a large predetermined main-structure.

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3. 'In your approach you suggest that evolution always leads to more complex systems. If this is true, how can it be that primitive organisms such as bacteria are still so successful and that some parasites even show a decrease in complexity over generations during their evolutionary adaptation to a host?'

I agree with the vision that the evolution of organisms and other systems does not necessary lead to higher complexity. A fundamental mechanism of evolution is the diversification and subsequent selection of the formed systems in relation to an ambient environment.

Some environments may select for more, others for less complex system types. With respect to organisms, I like to refer to a discussion that was published by Christian Damgaard and me inOikos (1999, 87: 609-614). The discussion part of this paper analyses complexity decrease and increase as two extremes of a broad spectrum of possibilities.

At the one end of this spectrum we find the situation where competition is absent. This applies to environments where resources are limited due to abiotic causes and the organisms experience a random chance on mortality. An example hereof is the above discussed, well-stirred chemostat with algae (an example was presented in that paper in which half the volume of a chemostat with unicellular algae was exchanged with fresh water every 20 minutes, such that algae with a generation time that exceeds 20 minutes would be diluted from the culture). The highest resource dominance in these situations is reached by the organism reproducing the fastest. It will be clear that this requirement acts as a severe constraint on complexity increase.

The other end of the spectrum is formed by situations in which the environment is experienced as relatively stable, or stable in its variability, and in which the availability of resources as well as mortality are mainly determined by competitive interactions. In a competitive environment a lower complexity in the sense of less phenotypic possibilities, in combination with lower efficiency necessarily causes lower resource dominance, and will be selected against. Accordingly, evolutionary disadvantage can only be avoided by any combination of changes in complexity and efficiency yielding a net increase in resource dominace of a unit. . Although it may not be the most likely to occur, an especially favourable combination in the light of selection is that of complexity increase in combination with efficiency increase.

The above discussion shows that depending on the circumstances complexity in organisms may increase and decrease. The operator hierarchy looks at complexity increase from a different angle. The reason is that it limits its analyses to closures .

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4. Of course you know of the existence of galaxies, stars, planets. How can you seriously propose a general evolution approach that does not include these systems?

I realise that a proposal for a general evolutionary hypothesis that is only based on operators (and related interfaces and pre-operators) may give the impression that it is incomplete when it does not include such important systems as stars, galaxies, planets, etc. Yet, the operator hierarchy has good reasons for focusing on operators and regarding the other systems as environmental background. Of course this background is required as the medium that offers the material and the conditions for the transition towards the next operator. Yet, this does not mean that the medium can be regarded as the next operator.

The reason why the medium cannot become the next operator is that every transition in the operator hierarchy is based exclusively on the first-next emergent property that creates the first-next system showing closure.

To explain this in more detail, I will imagine a hypothetical planet that is formed from single atoms kept together by gravity. Such a 'pure' planet can be regarded as a lump of aggregated atoms. Its existence does not depend on any more complexity than the gravitational aggregation of atoms. As it is not obligatorily based on the first-next closure relationship between the atoms, the planet is not a next level operator and has to be kept out of the hierarchy.

Similar explanations can be given for the exclusion of other systems, such as meteors, comets, planets, galaxies, ecosystems, factories, cars, radio's, non-memic computers, etc. etc.

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5. It would lend your hypothesis more credibility if you could prove that you have not selected the systems in the operator hierarchy to fit the regularity you mean to observe.

This question can be answered by referring to the rules I have used for creating the operator hierarchy. These rules cannot be altered freely to include or exclude specific systems that would fit 'better' in the hierarchy. Any change of the rules affects the full construction of the operator hierarchy. Consequently, any next operator cannot be chosen opportunistically. What are the rules on which the operator hierarchy is based?

The most fundamental aspect of the operator hypothesis is hierarchy. All operators can be defined in a stepwise, hierarchical way as structures that are based on an increasing number of complexity steps above a 'most primitive system'. The indication of a most primitive system is a consequence of the hierarchy, and is characterised by the fact that it has only its proper structure as the emergent property that lends the system an interface separating the system from the environment.

To create the operator hierarchy I have made use of the following major rule: assuming that the quarks/gluons can serve as the most primitive system, every transition in the operator hierarchy must comply with the first-next closure criterion. This demand excludes any in between systems and assures that the next system with an emergent property also is the first-next possibility. As a consequence any next system cannot be selected freely.

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6. 'It is confusing that on the one hand you propose a strict hierarchy, which on the other hand consists of seemingly quite different kinds of transitions'.

Some people get puzzled when they find out that the operator hierarchy seems to include several transition types. This gives them the impression that the operator hierarchy is not a strict scheme.

The recognition of different transition types is the result of the fact that the operator hierarchy works in two steps.

  • Step one. The hierarchy uses first-next closure to recognise a long hierarchy of operators.

  • Step two. The systems in the hierarchy are grouped according to similar closure types. This second step requires a new analysis at an elevated level of abstraction, focusing on the interaction patterns between the elements, and not on the particular elements that are involved. For example, the binding of atoms on the basis of recurrent interactions between their electron shells to create a multi-atomary unit (a molecule) can be regarded as a transition of single elements towards a multi-particle system state of these elements. This abstract interaction pattern can also be recognised in the binding of cells on the basis of membrane interactions to form a multicellular organism.

    I believe that using different types of emergent properties, of which each can be associated with a certain transition type, is not a problem. In fact, it represents a solution to a problem: the problem that no study ever has found a single transition type that can cover all steps in the various evolutionary hierarchies that have been published.

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    7. 'You reasoning is circular because you define operators in terms of other operators'.

    Due to the hierarchical construction sequence that underlies all operators, the definition of any operator will always depend on a long sequence of preceding operators, in principle until the most primitive system is reached. This is not a circular reasoning because each step concerns the construction of a higher level operator that depends on that of a lower level operator. In fact, the recurrent definition of all the operators is a marked advantage of the operator hierarchy. It assures a continuous and strict ranking.

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    8. 'What proof do you have that no intermediate stages exist between the operators that you use in the operator hierarchy?

    All the transitions in the operator hierarchy are based on the rule of "first-next possible closure". This implies that every step -by definition- must be the first-next possibility to create the next, new type of functional closure and the next, new type of structural closure. This rule implies that all steps are strict, unless mistakes have been made in their interpretation. The discovery of an additional step that has to be included or a superfluous step that can be deleted would debunk the operator hierarchy.

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    9. 'Even if you do not include stars, planets, etc. in your hierarchy, you must agree, that they play a major role in the formation of your operators.Why then do you pay so little attention to these environmental conditions?'

    Indeed, the operator hypothesis pays little attention to the environments that allow for the formation of the respective operators. This is a consequence of the fact that the operator theory focuses strictly and only on first-next possible closures. For example the formation of multi-atoms (molecules consisting of covalently bound atoms) requires an environmental temperature that is low enough (less than 30000K) to assure that the bonds between the electron shells of the participating atoms are not continuously disrupted by high-energy interactions with surrounding particles. A whole range of various other conditions exist for every specific transition in the operator hierarchy. The operator theory recognizes that such conditions are important for scaffolding the formation of the operators. Meanwhile it remains focused on first-next closures.

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    10. 'The earth is an operator; it shows an interface, the atmosphere, and shows hypercyclic interactions in ecosystems.'

    This idea is sometimes suggested by people that use an organistic interpretation of the Gaia hypothesis. I regret to say that this kind of question is the result of a fundamental misunderstanding of the operator theory. The operator hierarchy is based -step by step- on a sequence of first-next possible closures. The atmosphere is not an interface caused by a first-next closure, nor do ecosystems or populations show a hypercyclic structure that is the result of a first-next possible closure. For this reason planets (Gaia), ecosystems and populations, can by no means become elements in the operator hierarchy.

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    11. 'Your conclusions are a lucky result of the way in which you define the steps in evolution. Anyone else could come up with another hierarchy by using other definitions.'

    Indeed, anyone who would use other definitions would necessarily create a different hierarchy. The strength of the present hierarchy is that it offers logical alternatives for things I regard as inconsistencies in other approaches, such as a mixed use of operators and interaction systems and the presence of levels that can be included or taken out at will without that this would damage the ranking.

    As I explained earlier, the structure of the operator hierarchy is not just a "lucky" result, but an outcome that is based on the strict application of first-next possible closure, which shows a direct link with theories about topological types.

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    12. 'You show that interactions between hadrons create atoms and interactions between molecules create cells. Does the same logic not imply that interactions between multicellulars, such as are found in populations and society, will one day create a new unit that consists of co-operating organisms?'

    To answer this question I stress that the operator hierarchy expects multicellular units to create a hypercyclic interaction pattern and obtain an interface before they can form the next operator. This process is analogous to the way in which hadrons (multi-fundamental particle units) interact in a quark environment to form a nucleus (hypercyclic interaction pattern) that obtains an interface (the electron shell), and the way in which molecules (multi-atomary units) interact in an atom/molecule environment to form the autocatalytic set (hypercyclic interaction pattern) that obtains an interface (the cell membrane).

    In the operator hierarchy the wording multicellular unit refers to units of recurrently interacting and physically connected cells. This does not imply that these units are organisms. The multicellular environment in fact corresponds quite directly to the environment within an organism. The definition of the operator hypothesis thus indeed points away from the formation of any next stage on the basis of co-operating organisms.

    There is a fundamental reason for this: the first-next closure demand of the operator hierarchy. According to this demand, any transition should be based on the first-next closure involving the hypercycle. This demand assures that the hierarchy only includes the most efficient closures, or in other words, there is always exactly one way to reach the next operator. This demand prevents corruption of the hierarchy.

    In analogy with the transitions from hadrons to atoms and from atoms to cells, the transition from a cellular multistage to the next primary operator should form a multicellular unit in the most efficient way showing the following two properties. The unit should (A) show hypercyclic interactions based on multicellular units, and (B) show an interface that mediates the hypercyclic interactions.

    The first-next closure viewpoint implies that because the latter requirements can take place in the within-organism environment it has simply become superfluous to involve whole animals. The reason is that within-animal interactions always represent a more direct step, because this leaves the whole animal out of the discussion. And, because the within-animal route represents the most direct route, it is the only route the operator hierarchy allows and accepts. Any other route would imply a less strict, quasi-hierarchical construction.

    That the transitions from hadrons to atoms and from atoms to cells involve interactions between separate operators I regard as a result of the fact that evolution seems not to have had any possibility at these primitive levels to already make use of within-operator interactions. Thus, at these levels, between operator interactions do involve the most efficient pathway.

    In relation to this aspect it should be mentioned that hypercyclic neural networks in a cellular vehicle (together forming the organism with brains) form an interesting turning point in evolution. For the first time a multistage has developed that shows enough structural complexity to let the next primary operator emerge within it, rather than having to be based on interactions between separate multi-operators.

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    13. 'Why are populations not the next stage above multicellular organisms?'

    This question has at least in part been answered when I discussed the question why interacting organisms (population/society) are not an operator. The main argument against the suggestion that populations can be operators is that between-organism interactions become a hierarchical side path (in the sense of the operator hierarchy) as soon as within-organism interactions can produce the hypercyclic dynamics and interface required for any next operator above the multicellular level.

    Another argument against this suggestion comes from the fact that the sequence structure of the operator hierarchy is based on elements that are both functional and physical units. Populations represent no structural units. Accordingly, they can never form the basis for any evolutionary transition towards a next operator.

    The suggestion must also be rejected that populations form an intermediate hypercyclic stage, comparable to the atom nucleus, the autocatalytic set and the hypercyclic neural network. If we talk about organisms that do not show hypercyclic neural network, the suggestion would have to be rejected because it is the formation of the internal hypercyclic neural network that forms the first-next closure. If we talk about organisms that do show a hypercyclic neural network, the suggestion would have to be rejected because these organisms already show higher emergent properties than multicellularity, namely a memon structure, due to which the formation of a population does no longer represent a first-next closure.

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    14. 'What made you decide to name your units, 'operators'? It will cause confusion with the operator concepts used in physics, mathematics and telephone companies.'

    I have right from the start (which is 1992) realised that the word operator is used in mathematics, physics and telephone companies. Yet, I have chosen the word operator, because it brings to me a direct feeling of a system that operates as a unit in an environment. It shows dynamics and interactions and does this on the basis of a clearly recognisable, own emergent organisation.

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    15. 'Other authors have already defined the concept of 'major evolutionary transitions'. It is confusing that you introduce a different interpretation.'

    In 1995, Szathmary and Maynard Smith published a paper in Nature with the title: The major evolutionary transitions. They use this concept also in their book 'The origins of life' (1999). As a consequence I got questions from people that why the operator hierarchy does not use the major transition concept in the same way as Szathmary and Smith. To bring some clarity, I will start with citing from page 17 of the book 'The origins of life' where Szathmary and Smith give a summary of major transitions:

    A. From replicating molecules to populations of molecules in protocells

    B. From independentreplicators to chromosomes

    C. From RNA as gene-and-enzyme to DNA genes and protein enzymes

    D. From bacterial cells (prokaryote) to cells with nuclei and organelles

    E. From asexual clones to sexual populations

    F. From single-celled organisms to animals, plants and fungi

    G. From solitary individuals to colonies with non-reproductive castes (ants, bees and termites)

    H. From primate societies to human societies and language

    First of all I like to stress that all above 8 points concern transitions that are relevant for the evolution of organisms. But because the operator hierarchy covers a broader range of systems it looks at minor and major transitions in a different way. I will give a short explanation of how the operator hierarchy would view the above eight transitions (major transitions of Szathmary and Smith between brackets followed by the Operator viewpoint).

    A. (From replicating molecules to the cell) The major transition from catalytic molecules to the cell

    B. (From independentreplicators to chromosomes) An internal differentiation that falls under the law of the branching growth of the penultimate level as formulated by Turchin.

    C. (From RNA to DNA) Again an internal differentiation that falls under the law of the branching growth of the penultimate level as formulated by Turchin.

    D. (From prokaryotes to eukaryotes) In the operator hierarchy this represents a minor transition that involves the closure type of Hypercycle Mediating Interface. The presence of a nucleus is essential. The presence of organelles and/or endosymbionts represents an internal differentiation as formulated by Turchin.

    E. (From asexual to sexual) This represents a transition via which single operators are unified by mating behaviour into a mating group (the population) that shares the genes in a gene-pool. This transition relates to a specific kind of interaction system .

    F. (From unicellular to multicellular) In their example Szathmary and Smith indicate a transition from single-celled organisms to animals, plants and fungi. From the viewpoint of the operator hypothesis this way of phrasing implies the mixing of systems of various levels. Single celled organisms may either be bacteria or eucaryote cells. Also animals, on the one hand, and plants and fungi on the other, belong to different levels in the operator hierarchy, namely the (eucaryote) multicellular level and the memic level.

    G. (From individuals to colonies with non-reproductive castes) This transition refers to a special kind of interaction system in which genetic control forms the organising principle. The individuals of the non-reproductive castes can be regarded as the extended phenotype of the gene of the queen (and sometimes also the king) of the colony.

    H. (From primate to human societies) Here, the emphasis in Szathmary and Smith is on the development of language as an interaction mechanism that allows the construction of societies. In the operator hierarchy this is not present as a transition. Al memons, which means primates and humans alike, possess various ways of communicating that they may possess in different levels of perfection. This allows social behaviour in a gradient from an occasional clumsy social interaction to the exchange of highly sophisticated abstract concepts. In the operator hierarchy this represents a transition towards a specific, memically organised interaction system.

    The above shows that while there are quite a few differences in mechanisms explaining the major transitions in the list of Szathmary and Smith, it is easy to assign each of the eight examples to a particular transition type in the operator hierarchy. It seems therefore, that the operator approach offers a more structural way of dealing with major transitions, minor transitions, transitions based on internal differentiation and transitions based on the creation of interaction systems. For this reason I advocate to use of the operator hierarchy as a basis for indicating transition types.

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    16. 'Computers have no feelings and have to be programmed. Why do you expect that they ever may form the next level in evolution and gain dominance over an intelligent race like humans?'

    In my opinion there exist many misconceptions about the potential of technical intelligence. For instance, the expectation that intelligence can, or even must be programmed. People that use this reasoning always ask questions such as how can we ever create programmes that are sufficiently flexible and creative to allow a computer to take part in city traffic, to play children games or to understand the underlying levels of information in speeches of politicians. I think the answer is simple: Firstly we cannot do this and secondly it is not necessary. The reason is that human beings are intelligent even though they never have been programmed. They owe their intelligence to a specific neural structure with sensory interface and many years of learning by experience.

    According to the operator hierarchy, human beings owe their intelligence to a hypercyclic neural network, such as also produces various degrees of intelligence in animals. In analogy, the operator hierarchy predicts that any technical system with a similar neural structure will show intelligence without being programmed.

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    17. 'The operator hypothesis you propose is philosophical rather than quantitative. Yet what we need in system research is science, not philosophy.'

    As a modeller I have experience with the importance of a quantitative approach. I have worked with time series models and with toxicological simulation models that require a strict quantitative practice. I have also learned that the art of modelling is in formulating the right model structure.

    Also when creating the operator hierarchy, I experienced that the formulation of the model structure represented the main challange. The reason is that the hierarchy results from emergent properties. For modellers emergent properties imply difficult transitions, because they cause a change of the entire model structure by introducing a new property that has to be quantified with new parameters and has to be measured in new units. For example, an enzymatic model that is useful for quantifying catalytic processes must be markedly restructured to model cellular reproduction of an organism. In enzymatic models, the cell as a structural unit is simply not defined.

    All emergent properties in the operator approach imply changes in the structure of the systems involved. But how can you quantify structure? In particular, how to quantify the change from one structure to another?

    This general problem of emergent properties is discussed by Holland in his recent book 'Emergence' (Holland, 1998). I strongly support his proposal for a solution by defining emergent properties on the basis of special models called constrained generating procedures (CGP's). With respect to CGP models, Holland (1998) says: The models are dynamic, hence procedures; the mechanisms that underpin the model generate the dynamic behaviour; and the allowed interactions between the mechanisms constrain the possibilities, in the way that the rules of a game constrain the possible board configurations. Thus, when basic functional elements, the mechanisms, create a constrained interaction pattern, a new system is created which, as an individual entity, may show unprecedented functional properties: the emergent properties.

    In line with the reasoning by Simon (1962) and Holland (1998) a CGP shows persistent dynamics, and may act as a building block for the creation of higher level CGP's. In the latter case, CGP's can be used as the building blocks of multilevel CGP hierarchies. This is exactly the way in which the operator hypothesis deals with building blocks and emergent properties. By selecting persistent physical building blocks that themselves can act as the building blocks for the next level system, such as atoms, molecules, cells, etc. a continuous hierarchy can be created. On the basis of CGP's it is possible to formulate a mathematical description for any emergent property, as is discussed in chapter 7 of Holland (1998).

    Furthermore, a few words to those whom expect quantitative predictions from the present approach. In principle I regard the presence of a hypercycle as a quantitative aspect, namely as the prediction of a specific CGP, the structure of which can be quantified in terms of the links between the contributing mechanisms.Further quantitative predictions are not aimed at in the operator approach. Aspects regarded as quantitative, such as the weight, colour or DNA structure, are not even relevant in the context of the operator hierarchy. The weight may help to describe a particular atom 'species' but different atoms can vary considerably in weight, ranging from helium to the trans-Urane elements. A specific weight, therefore, is not a group property. Another example is given by unicellular organisms. These change weight/colour/precise DNA structure during their lives and/or between generations. Again, the weight/colour/DNA is not a group property, but their existence as an autocatalytic cell is.

    The observations that all species of atoms are atoms and all species of unicellular organisms are unicellular organisms are based on common properties shared by all members of the group. These group properties form the focus of the operator hypothesis, irrespective of whether these are considered qualitative or quantitative.

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    18. 'The operator hierarchy is not a hypothesis because it is neither based on refutable statements nor does it lead to refutable predictions.'

    Although the operator hierarchy may be regarded as a description of an existing sequence of transitions and systems, it offers a whole range of statements that are fundamental to the hypothesis and can be refuted in some way or another. These aspects have been discussed in the section 'A refutable hypothesis'.

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    19. 'The operator hierarchy is unnecessarily complex. It is quite easy to see that a much simpler scheme can be used instead'.

    Instead of the full operator hierarchy that is proposed in the present site several simpler scenarios can be imagined. One of the most obvious scenarios is the one that only recognises multistages and the immediately following next operator This is based on the assumption that after a multistage, nature has no choice but to create a next unit system, which again can be used to create a next multistage. Such an approach would include the hadrons, the atoms and molecules, the bacteria and multicellulars, the latter including plants and animals alike. Ranking systems this way has some interesting consequences. First, either all multicellular beings would have to be prokaryotes, since no additional transition between bacteria and multicellularity is recognised or prokaryotic and eucaryotic life would be judged as showing no difference. Another consequence would be, that with multicellularity (now including the organisation of memons as being of the same level as that of plants!), the scheme comes to a halt, because what could there be above? Probably, this scenario would suggest something like a multi-multi-cellular organism (a 'multi-organism'), or simply place the population on top of the hierarchy. I hope to have shown clearly in the above texts that such an approach is in sharp conflict with the strict system reasoning advocated in this site.

    But what happens if we elaborate the approach a bit to propose a scheme that also includes hypercycles following the multistages (the pre-operator hypercyclic sets). Now the hierarchy would run across the following layers: 1. elementary particles, hadrons and atomary nuclei, 2. Atoms, molecules and autocatalytic sets, 3. Cells, multicellular beings, and hypercyclic neural networks, and 4. Neural networks with interfaces (the memons). I hope that with me, many readers will agree that this looks nice, and in a way familiar. It even is rather explicit, as it separates the realm of biology into a layer of cellular life, and a layer of memic life. Yet, the system transition involved in the emergence of eucaryotic life is left out of the discussion. And, how will we classify the additional closure, when in the future a programmed memon arises that can copy its proper brain structure? As it is not a multistage, it can only be placed in the class of normal (hardwired) memons, which implies that a class is created with systems showing various levels of functional closure. Putting together prokaryotic and eucaryotic cells or hard and sorfwired memons feels uneasy if our goal was to include in the same box only system with an identical level of complexity, as measured in closures.

    Under the latter scenario, it is furthermore hard to find arguments why the elementary particles (superstring based entities such as quarks and gluons) should not be given a position in the sequence from atomary nuclei, down to hadrons and elementary particles. To be able to suggest that the fundamental particles may have to be placed in two separate layers ( the superstrings and the syperstring hypercycles), one really needs to start working with the operator hypothesis in all its detail. How this works I have explained in this site. Meanwhile, a full hierarchy recognising interfaces and hypercycles solves the just mentioned problems with the classification of the prokaryote/eucaryote cells and harwired/softwired memons.

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