1. Complexity, individuation and function in ecology Part I, sec 2 Individuation, dynamical realism and Emergence of properties and levels Prof. John Collier http://web.ncf.ca/collier/ (Departamento de Filosofia, Universidade de Kwazulu-Natal, África do Sul. Pesquisador Visitante do Laboratório de Ensino, Filosofia e História das Ciências (LEFHBio), Programa Ciência sem Fronteiras)

2. Outline 1.Individuation and autonomy a.A dynamical approach to identity and diversity in complex systems. In Paul Cilliers, Rika Prieser eds. Complexity, Difference and Identity: an Ethical Perspective. 2010 Berlin: Springer.A dynamical approach to identity and diversity in complex systemsComplexity, Difference and Identity: an Ethical Perspective 2.Hierarchy and downward causation (is an oversimplified model with many pitfalls) – Two notions of biological hierarchy (ISHPSSB 2011)Two notions of biological hierarchy 3.Heterarchy and networks – Lecture notes 4.Individuation of levels a.Collier, John. 2003. Hierarchical Dynamical Information Systems With a Focus on Biology. Entropy, 5 : 100-124. Hierarchical Dynamical Information Systems With a Focus on Biology 5.Emergence (a few remarks – more detail in next lecture) a.Collier, John. 2008. A dynamical account of emergence. Cybernetics and Human Knowing. 15 no. 3-4: 75-86.A dynamical account of emergence. b.Collier, John. Emergence in dynamical systems. Submitted 2013.Emergence in dynamical systems

3. A Dynamical Approach to Individuation Dynamical Realism: Anything that is real is either dynamical or can be explained in dynamical terms, where something is dynamical if it involves forces and flows. Advantages: testable criteria for reality through interactions, processes are the main objects of investigation, causal models are ensured. Individuation must then be a dynamical property, but must also satisfy the logical and metaphysical conditions for individuality. I call this property cohesion.

4. Dynamical systems Mathematical version: Anything involving change (with respect to time, but this can be generalized to other parametres). A differential or a delta. Physical version: System describable in terms of forces and flows. Possibly linear, but more often networks. Flows can be of anything material that moves, forces are anything that constrains movement.

5. Dynamical realism Anything that is real is dynamical, or can be understood dynamically. 1.Individuation, cohesion, closureIndividuationcohesionclosure 2.Empirical access, interactivism 3.Organized complexityOrganized complexity 4.EmergenceEmergence 5.FunctionalityFunctionality 6.IntentionalityIntentionality

6. Cohesion The dynamical property that individuates something, whether a thing or property. Grounded in the logical condition of identity. But is peculiar (individual) for each thing (though it may be generic for kinds of things). It has an empirical component that must be discovered and tested. It requires dynamical closure, so we have a test of whether we have taken what we need into consideration.

7. Logical conditions: identity Any criterion of individuation, such as cohesion, must satisfy the requirements of identity, A = B. These are: – Logical condition, same for all things – Equivalence relation: symmetric, transitive, closed – A = B implies that B has every property that A has, and vice versa But this is pretty trivial, nonetheless, and criterion of individuation must satisfy these conditions. Closure is very significant.

8. Unity relation U(A) Unity is the relation among the parts of a thing A such that: a.If a and b are parts of A, then aUb, and bUa (symmetric) b.If a and b are parts of A, then aUb and bUc implies aUc (transitive) c.By a. and b., U is an equivalence relation d.U(A) is the closure of U, given any initial part. e.By a. to d., U(A) contains all and only the parts of A.

9. Defined versus Natural Unity The unity U of some things is nominal, defined or chosen by us: – A set is determined by those things that satisfy a condition C, e.g., the set of natural numbers – A system is a set of related or interacting components that is individuated from other systems by those relations or interactions. – A tree is a plant over 4 meters tall. The unity U of other things is natural; U must have an empirical and testable aspect, not predefined but discovered: – A quartz crystal, whose parts and interactions must be discovered – A dynamical system is a set of interacting components that is characterized and individuated from other systems by its dynamical interactions. – Gold has atomic number 79.

10. C(A), dynamical unity Cohesion C(A) is the unity relation U(A) for dynamical entities, such that: 1.All parts aCb are dynamical for all a,b in C 2.C is dynamical Simple (extreme) examples of cohesion a quartz crystal the closure of intermolecular interactions gives the boundary of the crystal, external interactions being much weaker than internal interactions a gas in a box the cohesion of the box defines the boundaries of the gas.

11. Nature of Cohesion Note that in each case the cohesion is not absolute; it is a matter of degree. We should expect difficult intermediate cases. Cohesion can differ in strength in different dimensions (factors) We really need a cohesion profile to individuate an object Cohesion both unifies a dynamical object, and distinguishes it from other dynamical objects (the “dividing glue”). Thus, it is effective as a criterion of individuation. Also, being dynamical, it is testable. Its real strength, however, is in the way it forces us to look for dynamical closure whenever we want to claim that something is individuated. This is especially significant in the case of autonomy.

12. Basic properties of Cohesion B1: Cohesion comes in degrees and dimensions. – a direct consequence of its being grounded in forces and flows, which come in varying kinds, dimensions and strengths. Cohesion, then, must also accommodate kinds, dimensions and strengths. B2: Cohesion must involve a balance of the intensities of centrifugal and centripetal forces and flows that favors the inward, or centripetal. – This balance cannot be absolute, but must be likely over the boundaries of the cohesive entity. Just as there are intensities of forces and flows that must be balanced, there are, due to fluctuations, propensities of forces and flows that show some statistical distribution in space and time (or other relevant dynamical dimensions). – The asymmetry of the balances implies a distinction between inner and outer, consistent with the role of cohesion in individuating something from its surroundings.

13. Derived properties of Cohesion A1: In general, a dynamical system will display a mix of cohesive and non-cohesive properties. From B1 only certain forces and flows matter, and they matter to different degrees; not all forces and flows matter, e.g., fluctuations. A2 Cohesion is not just the presence of interaction. From B2 and A1. A3 A property is cohesive only where there is appropriate and sufficient restorative interaction to stabilize it. From A2, B2. A4: Cohesiveness is perturbation-context dependent with system properties varying in their cohesiveness as perturbation kinds and strengths are varied. From A1, A3. A5: The interactive cohesive support (closure) of nominally system properties may extend across within-system, system-environment and within-environment interactions. Given the characterization of cohesion as a condition of a certain form of balance that has closure. A6: Cohesion characterizes all properties, including higher order process properties, that are interaction-stabilized against relevant perturbations. From A5: cohesion is not to be confined to stability of first order properties like rock shape, kite. E.g., a flock of birds flying around a column.

14. Organizational cohesion Systems can be cohesive due not only to energetic bindings, but also due to their organization. In my last lecture I argued that pattern was important to understanding biology, since boundary conditions are highly specific, and small energy changes can lead to large shifts in behaviour. This means that cohesion in biology is mostly grounded in organization. In the past I have called this sort of cohesion autonomy, but it isn’t clear that we want to call ecosystems autonomous. Nonetheless, looking at autonomy will help in understanding what a function can be for the “sake of”. Organization is both local and larger scale, implying levels of organization. This is also a consequence of logical depth.

15. Some characteristics of autonomy Autonomy is both open and closed, like all cohesion. Autonomy requires conditions that explain closure, but permit openness (like all cohesion, it comes in degrees). Furthermore, autonomy is closely related to individuality and self- governance, the combination of the two yielding independent functionality through the organized interaction of processes. Varela (1979) invokes a duality between structure and organization that follows from the complete informational closure of organization. In autonomy processes and their interactions, which are themselves further processes, form the fundamental basis, and organization is a direct property of this network of processes. This implies a hierarchy of processes and levels of organization. There is no duality between the informational and the causal on this model, because organization is a kind of form (see previous lecture).

16. Autonomy is a special type of cohesion. Cohesion is maintained actively though the contributions of component processes to the continued existence of the system, either directly, or through intermediate processes. This places certain restrictions on what sort of organized system might be autonomous. It should be obvious that neither a rock nor a gas in a box are autonomous, since they are not active in any sense. To be active requires doing work. Doing work, in turn, requires the existence of non- equilibrium conditions – this means that there must be available resources to make use of. I cannot stress too much that autonomy is impossible unless there are sufficient resources available for use. An autonomous system must be internally differentiated, that is, it cannot be in a uniform steady state, but must have a number of internal states that are dynamically accessible. This requires a certain flexibility that systems whose cohesion is based in high energy differentials cannot maintain, so we can expect it to be characteristic of autonomous systems that energy is not their primary concern, but rather. We require only that the internal organizational closure is greater than the interactive closure. (Centripetal forces > centrifugal forces). Comparing degrees of organization is non-trivial.

17. In summary, autonomy requires: 1.non-equilibrium conditions 2.internal dynamical differentiation 3.hierarchical and interactive process organization 4.incomplete closure 5.openness to the world 6.openness to infrastructural inputs The existence of autonomy, like any cohesion, is identical to the corresponding process closure, and is not something complementary to, or over and above, this closure.

18. Natural Hierarchies Any hierarchy must have a hierarchy property that orders the hierarchy into levels. The hierarchy property must, therefore, exist at each and every level. By dynamical realism, natural hierarchies must have a hierarchy property that is either dynamical or definable in dynamical terms. Dynamical hierarchies are determined by part- whole, where the parts and wholes are each individuated by cohesion.

19. Dynamical Hierarchies Levels must be cohesive if they are dynamical, or else they would not be naturally individuated. Since levels are cohesive, the same basic properties B1 and B2, and the same six principles A1-A6 set out above apply. Structural and process levels may co-exist, and generally do co-exist and inter-twine. – Process levels may occur across structural levels, such as the respiratory process which occurs across the sub-cellular, multi-cellular organ and multi- organ levels correlating sub-cellular activity with both pulmonary and cardio- vascular activities, and conversely. – Furthermore, levels may be more or less transitory, especially in living and similar non-stationary systems where structures and lower order process constraints are continually changing to suit the context. – Thus we must reject any simple picture of a system as a single series of universal, permanent levels, like floors of a building, and recognize instead a web of partial levels, each level holding only within some domain, itself perhaps a function of system state (including history).

20. Two types of hierarchies Class, types – Real or nominal – Hierarchy type fits all levels of hierarchy and determines containment, e.g., substance, function, science Component, spatial containment, token – Real of nominal (e.g., things vs. aggregates – Wimsatt, dynamical systems vs. sets) – Whole – component relation determines containment These two kinds of hierarchies are sometimes unconsciously conflated (e.g. the physical components of something are referred to as its physical level, and then sometimes this slides into discussion of type properties of the physical, applied back to discussion of the components in terms of a type level)

21. Typical Biological Hierarchy Physical Chemical Macromolecules (especially genetic) Cells Organs Organisms Populations Ecologies Species Higher Taxa ISHPSSB Salt Lake City 2011

22. Cohesion in individual hierarchies Each level has cohesion of its own; it is not merely an aggregate (Collier Entropy, 2003) – E.g., cells have their own cohesion – This constrains the activities of their chemical components (not to mention, of their immediate environment – cohesive closure is not complete, and may extend beyond the usual boundaries of the cohesive entity) Cohesion exerts “downward causation”. – This is not simply the effect of the lower level components (Paul Humphreys: fusion) However different hierarchies can criss-cross and interact with each other (heterarchy).

23. Structural versus functional decomposition We can decompose biological entities (and other things with teleological properties) into both functional and structural parts. These decompositions need not correspond – Consider decomposition of airplane versus bird into functions of lift and propulsion. Although structural parts are restricted by function, and structure can tell a lot about function and contributions to function, I believe function is primary in biology (and in other teleological entities).

24. Example: Immune System The immune system is not contained within specific parts of the body, but is spread out and uses parts of things like cells, cells them selves, and so on in very complex ways. So there is no simple way to decompose the immune system structurally in a way the corresponds to typical structural decompositions of the body (organ, cell, cellules, etc.). However, if it is regarded functionally, as a sort of organ, it is on a par with other organs like the heart, the skin, the nervous system, and so on. But this suggests that the relevant aspects of these other organs for decomposition is not structural, but functional.

25. Example: The Cheetah A good example for the importance of organization because – genetic variance is very low, so differences cannot be reduced to genes – viability envelope is small, so functional constraints are tight Hierarchical organization starts at the chemical level, and continues up through physiology and organs, condensing in the cheetah, and then branching out into environmental factors. The intersection of the genetic and ecological hierarchies in the individual cheetah means that the organism plays a dual role, ecological and genetic. The two roles are not the same, nor are their closure conditions. This account focuses on the ecological.

26. Cheetah: respiration – fermentation and oxidative phosphoralysation (Krebs) cycles. Consider fermentation, over which there was a long debate as to whether it was a biological or purely chemical phenomenon. Fermentation is possible outside cells, but it is not maintained for long. The first chemical models assumed a simple linear process; later more complex linear models were tried. It turns out that the chemical process required early elements later in the process, making it non-linear. This means that there is feedback in the process, in which at least some elements cycle in a closed way. In fermentation in the muscle, glucose is the input, and lactic acid the output. If the process is laid out linearly, there are two places where ADP enters and ATP leaves, one place where ATP enters and ADP leaves, and one place each where nicotinamide andenine (NAD) leaves and NAD+ enters and the contrary. Closing these open loops at the ends requires that products of the process are needed earlier as inputs. This makes the process indecomposable. Note also that an extra ATP molecule is formed, which is used by the muscle for energy, and reduced to ADP, increasing the scope of the cycle. The history of respiration and oxidative phosphoralysation is similar, with the final model the familiar Krebs cycle, which both has cyclic properties like fermentation and also shows similar connections to other processes. The main difference is that fermentation builds up lactic acid, which cannot be removed from the cells quickly enough, and eventually reduces the efficiency of the process. The Krebs cycle is less efficient in producing power, but it uses oxygen, and produces easily removable carbon dioxide and water as waste products.

32. Implications for the cellular level and above A process is closed if and only if it requires no inputs or outputs at the level at which it is defined. Clearly, fermentation and respiration are not closed, since they require an input of glucose directly into the process itself, at the same level as the process occurs, despite the loops in the process. This requires control of cellular mechanisms to improve transport, but it also requires control of other organs and behaviour. Even at the chemical level, enzymes facilitate the process, with 10 aiding glycolysis alone. This is possible only in a cellular environment. The excess ATP is used for energy, in muscle cells for contraction. In the Cheetah, which requires high speeds for chases, the fermentation stage allows these speeds for short times. After lactic acid builds up, the system switches over to the Kerbs cycle, which does not allow such high muscle activity. This has implications for the cheetah’s behaviour: – It requires a relatively short chase to be likely to be successful. – Thus, it slowly stalks its prey, and then attacks quickly from a close distance. – It also prefers more vulnerable prey, which will require less expenditure of energy.

33. Some consequent adaptations Further adaptations involve the training of cubs with increasingly difficult prey, and eventual cooperation with the mother in stalking and attacking prey. This learning process allows adaptation to local conditions at the behavioural level. The interactive closure with the environment allows much more flexibility for different conditions of local vegetation and prey. Cheetahs are successful in roughly 50% of their attacks, which is close to the level required for their survival, so these adaptations are especially important. Interestingly, the training of cubs must be carried out well within the viability envelope of the cheetah. Too close to the edges, and the cubs would not survive. The adult cheetah typically lives much closer to the edges of its niche much of the time.

34. Physiological coadaptations A second consideration is that the fermentation and Krebs cycles require inputs of sugar and oxygen and removal of waste. This is done through transfer through the cell walls, and transportation from the gut and to the lungs. A large efficient heart aids this process. When oxygen is required efficient lungs are helpful, and the ability to achieve high heart rates is essential. The molecular processes are hardly closed processes, but are coordinated and integrated with other organs and behavioural processes.

35. Neurological coadaptations Much of the control of the cheetah’s behaviour, both autonomic and intentional, is governed by the nervous system. Although nerves do not reproduce in an adult animal, they continually change their connections and levels of neurotransmitters at synapses (learning). These changes can be passed on socially by training cubs. Even the basic structure of the nervous system and its relation to behaviour is far more complex than might be expected.

37. Some notes on reduction Type reductions are ontological deflations – where there were many, we see that there are only few or perhaps one (Collier and Hooker). Individual reductions are of wholes to parts. – Only possible completely if the wholes are aggregates. These two types of reduction are sometimes confused (e.g., Kim) so that ontological deflation is taken to imply whole-part reduction. This does not hold in general (consider fusion, spontaneous self-organization, emergence).

38. Emergence Sometimes used to mean something that is merely unexpected: – The emergence of the internet – The emergence of a new scientific discipline – The emergence of a new political party – “Emergent computation” These cases have no implication of more than surprise (to us) and typically complicatedness. It is not the traditional philosophical notion

39. The philosophical notion of emergence Goes back to Aristotle, but the concept without the name appears in J.S. Mill: – A living body cannot be understood as a mere summing up of the separate actions of its components – Basic physical laws were not violated, but new laws impose further restrictions The word comes from G. H. Lewes (1875): – the emergent is incommensurable with its components and cannot be reduced to their sum or their difference

40. Bénard Cells: A Model Dissipative System A useful starting point for discussing the properties of dissipative structures and emergence. Both the simplifications involved in the Bénard cells and the possibilities that are nonetheless allowed are remarkable. Bénard cells form when a viscous fluid is heated between two planes (or plates, to eliminate surface effects) in a gravitational field. The formation of the cells depends on the type of fluid, its depth, and the temperature gradient. There is a critical value of the Rayleigh number at which fluctuations in the density of the fluid overcome the viscosity faster than they are dissipated. These fluctuations are amplified and give rise to a macroscopic circular current: dissipative structures called Bénard cells are formed.

41. Mathematical treatment of Bénard convection where P is the Prandtl number and R is the Rayleigh number:

42. Intuitive treatment The equations are solved by making the convection and conduction motions equal – this gives the critical Rayleigh number – where convection starts. Several simplifying assumptions are required. Intuitively, there are fluctuations in density in the system. These fluctuations are larger the higher the temperature. There is also viscosity that creates cohesion among the molecules of the fluid (or we may think of the fluid as intrinsically cohesive). As the temperature gradient is increased, there are larger regions of greater and lesser density. These regions are either buoyant or the opposite, respectively. The viscosity of the fluid holds these regions together against their tendency to disperse thermodynamically. As the regions grow larger, this tendency overcomes the dispersive tendency, and the buoyant regions float upwards, while the denser regions sink. Because of the close constraints on the experimental conditions, regular cells form.

43. Dynamical conditions for emergence The system must be nonholonomic, implying the system is nonintegrable (this ensures nonreducibility). The system is energetically (and/or informationally) open (boundary conditions are dynamic). The characteristic rate of at least one property of the system is of the same order as the rate of the non- holonomic constraint (radically nonHamiltonian). If at least one of the properties is an essential property of the system, the system is essentially non-reducible; it is thus an emergent system. I will explain these in more detail next lecture.

44. Conclusions We can only interact with dynamical properties, so these place the limit on what we can take as real. Cohesion is the dynamical version of individuation. Autonomy is the organizational version of cohesion. What contributes to autonomy is real. Cohesion also defines levels in individual hierarchies. In some cases levels are also autonomous. Biological systems are nonreducible and hierarchical. Biological hierarchies are multiple (not simple) and interact with each other in complex ways. Lower level and higher level processes constrain each other.