1. Complexity, individuation and function in ecology Part I, sec 3 Emergence of properties and levels Functionality
Prof. John 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 02/09/2013 Emergence (continued) Functionality
Collier, John A dynamical account of emergence. Cybernetics and Human Knowing. 15 no. 3-4:
Collier, John. Emergence in dynamical systems. Submitted 2013.
Functionality
Versions and their problems
Wright, Larry Functions. The Philosophical Review. 82, No. 2. pp
Cummins, Robert Functional Analysis. The Journal of Philosophy. 72, No. 20. pp
Explaining Biological Functionality: Is Control Theory Enough? South African Journal of Philosophy. 2011, 30(4):
Autonomy and functionality
Moreno et al
Collier, J Autonomy and Process Closure as the Basis for Functionality. Annals of the New York Academy of Science.
Collier, J. Simulating autonomous anticipation: The importance of Dubois' Conjecture (ALife X 2006, Biosystems 2008)
Conditions for fully autonomous anticipation (CASYS 2005)
Testing functions – Lecture notes, closure, “for the sake of”

3. Dynamical realism
Anything that is real is dynamical, or can be understood dynamically.
Individuation, cohesion, closure
Empirical access, interactivism
Organized complexity
Emergence
Functionality
Intentionality

4. Dynamical Individuation
Cohesion
The dynamical property that individuates something, whether a thing or property.
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.
Organizational cohesion
Systems can be cohesive due not only to energetic bindings, but also due to their organization.
Cohesion in biology is mostly grounded in organization. It isn’t clear that we want to call ecosystems autonomous. Nonetheless, looking at autonomy will help understand what a function can be for the “sake of”.
Organization is both local and larger scale, so levels of organization. This is also a consequence of logical depth. We should expect this in ecology.

5. Case 1 Autonomy (grounds for functionality in organisms)
Autonomy is closely related to self-governance, yielding independent functionality through the organized interaction of processes.
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).

6. In summary, autonomy requires:
non-equilibrium conditions
internal dynamical differentiation
hierarchical and interactive process organization
incomplete closure
openness to the world
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. We should expect this in other forms of individuation in bioology.

7. Case 2: Species as individuals
If species are individuals, then they should have some form of cohesion.
Many species concepts exist: mate recognition, ecological, gene transfer (biological species concept), phylogenetic (vertical and horizontal cohesion -- Wiley), developmental canalization (Waddington, non-mating species), cohesion concept (Templeton – deficient in my view).
There is a tendency to see something right about each of these concepts, and to promote pluralism about species definitions.
But all of these processes can be involved in species cohesion.
One may dominate, but all may contribute; we need a single species concept with multiple factors.

8. Cohesion concept of Species 1
The meaning of species and speciation, Templeton, 1989
Explicit use of cohesion to define species
Fully gene centred: species determined by gene flow (“intrinsic cohesion mechanisms”), so really a biological species concept at base.
Process oriented, but no explicit distinction between vertical and horizontal cohesion.
No theoretical unification, just a collection of mechanisms (next slide) that confine and separate gene flow
Cohesion both separates species (isolation) and unifies species (facilitation of gene flow)
Speciation as disruption of cohesion

9. Cohesion concept of Species 2
Cohesion mechanisms (Templeton 1989)
Genetic exchangeability
Promotion (facilitation)
Isolation
Demographic exchangeability (constraints from selection and drift)
Replaceability (genetic drift promotes genetic identity)
Displaceability
Selective fixation
Adaptive transitions (natural selection)
constraints on the origin of heritable variation
constraints on the fate of heritable variation
ecological, developmental, historical, population
genetic (all “extrinsic” – to genes, presumably)

10. Some remarks on the phylogenetic and cohesion approaches
Wiley’s approach is more general because it does not specify heredity mechanisms
Templeton’s approach is more operational, but difficult to generalize
Brooks and Wiley regard sexual selection and developmental constraints as internal, whereas Templeton regards sexual selection as a form of natural selection (intrinsic to gene flow), but developmental constraints are extrinsic
The last is a significant difference following from Templeton’s focus on genes alone (and assuming implicitly that selection is on genes, thus intrinsic to gene flow), and Brooks and Wiley’s focus on information flow.

11. The Tautology Problem Gold (2001)
Hey decries this popularly acclaimed definition. He unmasks it as a tautology framed in the ostensibly palpable, yet suffering a lack of utility. Hey urges us to substitute the word “cohesion” with any other word and suggests we will find equal meaning. In other words, cohesion in Templeton is an empty term.
(Ghiselin later made efforts to repair Templeton’s mis-construction by identifying a species as that which is by what it does, specifically defining species as the products of speciation.)

12. The tautology non-problem
The cohesion concept has alternatives that might be correct, e.g., phenetic concepts or essential properties concepts.
But these have proven inadequate and subjective.
The cohesion concept neither endorses or prohibits particular contributions to cohesion. This is an empirical matter.
This empirical matter is testable.

13. Phylogenetic species are cohesion species
Though tautology is a non-problem, if we assume a phylogenetic account of species as historical entities, it is necessary that cohesion is the determiner of species identity.
If we use the cohesion account of species, then the phylogenetic view of species follows.
So the accounts are equivalent if not identical.
As soon as we accept species as individuals, we commit ourselves to a multifaceted cohesion account.
Is there any similar underlying cohesion approach in the ecological literature?

14. Emergence (slight review)
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

15. 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

16. Requirements for emergence
Dynamical account is required as traditional logical conditions are hard to determine.
Dissipation is required, or else the systems will be reducible (see below).
Chaotic behaviour is required for a process to result in emergence. This involves local and nonlocal processes to be arbitrarily close.
This leads to bifurcation points in the system, where it can follow either of two (or more) paths as a result of minimal and uncontrollable (and perhaps nonlocal) perturbations.

17. Bénard Cells: A Model Dissipative Structure
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.

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

19. 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.

20. 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.

21. Biological systems are far from equilibrium
In order to support information flows as the dominant processes in biology, biological systems must exist far from equilibrium.
The basic processes are supported by relatively simple energy flows (internally mostly involving ATP), but are themselves far from simple.
The dynamics of pattern (information flow) is largely decoupled from energy flows, and we can treat the information and energy budgets separately.

22. Biological processes are self-organized
Autopoiesis (Maturana, Varela)
Closure to efficient causation (Rosen)
Self-organization of networks (Kauffman)
Self-organization of biological information flows, including phylogenesis (Brooks and Wiley)
And many others (sensory response, developmental processes, ecological systems, etc)

23. Two kinds of self-organization
There are two kinds of self-organization that are distinctly different (Collier and Hooker). Both are found in biological systems.
Self-reorganization: passive, depends on dissipation only during formation, no emergence or new information. (e.g. self-assembly of molecules, formation of lipid vesicles)
Spontaneous self-organization: active, requires dissipation for maintenance, emergence, new information (e.g. formation of new nodes in networks, various forms of turbulence, etc.)

24. FFECOS’s
Far from equilibrium complexly organized systems (FFECOS’s) are the result of spontaneous self-organization only.
FFECOS’s are such that system laws and boundary conditions cannot be separated (Conrad and Matsuno).
The system can do work on boundary conditions, changing its own dynamics.
This can be (but need not be) in the context of system organization.
This ensures emergence can occur in such systems. And that it may be internally facilitated but not fully controlled.

25. Process is indispensable
Although many systems of biological interest are characterized by pattern, pattern dynamics alone are not sufficient for explanation.
This is because laws and constraints cannot be separated in the formation of FFECOS’s. Both must be taken into consideration.
The only way to do this is to look at the processes from both the top and the bottom, as in Bénard Cells.
For biological systems, the top level is organization.

26. Formation of new nodes
In stable networks, the Onsager reciprocity relations hold (Rashevsky) and the system can be treated with near to equilibrium methods.
However, when new nodes are formed, the dynamics peculiar to FFECOS’s become indispensable.
This happens in growing systems, especially in evolution and development.
In such cases we have no choice but to think in terms of both pattern and process.
This will also apply to ecological systems: stable higher level forms can appear, but the process will be an emergent one.

28. Organization
The basic idea of an organized system is that it is interconnected in complex ways, so that there are both local and non-local effects.
A system can be strictly hierarchical, with either
Such systems are decomposable and are not complexly organized.
Complex organization
involves neither summation nor top down control, but shows an interaction of bottom-up effects and top-down effects
Complexly organized systems cannot be decomposed

29. Predictability (analytic)
A system can be predicted across time if and only if its trajectory can be calculated from its initial and boundary conditions specified within some region of its phase (state) space, together with its equations of motion, to be within some region of phase space at some arbitrary later time.
Specifically, the trajectory of a system is predictable if and only if there is a region η constraining the initial conditions at t0 such that the equations of motion will ensure that the trajectory of the system will pass within some region ε at some time t1, where the region η is chosen to satisfy ε.
Indeterministic systems have probabilistic predictability.
Predictability applies in principle to all closed Hamiltonian (specifically, conservative, holonomic) systems, including those without exact analytical solutions, such as the three body case.

30. Predictability (modelling)
The systems without exact analytical solutions can be numerically calculated in principle for any finite time, if we have a large enough computer. We might call this stepwise computability.
All computations are stepwise computable, but some computations do not terminate.
These computations, however are stepwise computable, and allow, in principle – the required computer might have to be larger than the known universe – the arbitrarily exact computation of a finite later state.
The macrostate of a microsystem can be predicted similarly by composing the trajectories of the microcomponments and averaging to get the expected macrovalues.

31. Requirements for unpredictability
To undermine predictability, at least one of the standard assumptions must go. The assumptions are
1) the system is closed,
2) the system is Hamiltonian, and
3) there exist sufficient computational resources.
The last condition (3) is a shorthand way of saying that the information in all properties of the system can be computed from some set of boundary conditions and physical laws.
Laplace was able to show that the orbits of the major bodies of the Solar System were stable for at least 100 million years, no mean accomplishment for a many-bodied system

32. Interactions of boundaries and system laws
Conrad, Michael and Koichiro Matsuno (1990). The boundary condition paradox: a limit to the university of differential equations. Applied Mathematics and Computation. 37: 67-74
Differential equations provide the major means of describing the dynamics of physical systems in both quantum and classical mechanics. The indubitable success of this scheme suggests, on the surface, that in principle it could be extended to a universal program covering all of nature. The problem is that the essence of a differential equation description is a separation of itself from the boundary conditions, which are regarded as arbitrary.
Note that when the last condition fails, the system is non-holonomic (constraints depend on velocity i.e., there is no function on the n spatial dimensions of the system such that f(x1, … xn, t) = 0). Some non-holonomic systems can be expressed in differential equations that are integrable, but most can not. I call these radically nonHamiltonian.

33. Failure of the independence
Non-Holonomic systems
Basically, energy is not conserved, as in dissipative systems
Boundary conditions and system laws cannot be separated in principle.
Near holonomic we can approximate at one end by step functions, and at the other end by perturbation theory
Radically non-holonomic systems, however, are a problem

34. 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 system has multiple attractors (essential?)
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

35. Violate Laplacean model
Laplace’s assumptions are:
Determinism
No two possible trajectories in the phase space of a system can share a point in phase space.
Predictability
For any property of a system, the values of that property can in principle be predicted with arbitrarily high accuracy for an arbitrarily long time.
Locality
All dynamical properties of a system are fully specified by universal natural laws and parameters defined with convergent accuracy on arbitrarily small spatiotemporal regions.
Determinism is no problem, but predictability and locality fail.

36. An example: Mercury (1)
Before 1965, astronomers believed that, like the Moon, Mercury's rotation matched its orbital period of 88 days.
Mercury is actually in a 3:2 resonance such that Mercury's day is exactly 2/3 of its 88-day year.
It turns out that there are relative energy minima at 1:1, 3:2, 5:2 and so on. Once in one of these local minima, it is unlikely that Mercury could get into one of the other minima, since local forces would keep it into the local minimum in which it has been captured.

37. An example: Mercury (2)
If we don’t assume initial conditions, the phase space gives a 1/3 chance of capture of Mercury in the 3:2 ratio, and 1/2 for the 1:1 ratio, with the other ratios taking up the rest of the chances.
For initial conditions near the even ratios, capture in the respective ratio is very likely, but the system overall is chaotic, and in other regions infinitesimal differences in initial conditions can lead to another ratio.
Specifically, in the phase space of the system, the attractor basins for the different ratios intermingle in certain regions so that for each two points in one basin, there is at least one point between them that is in another basin.
So both predictability and locality fail. The 3:2 ratio is emergent.

38. Observations on Mercury example
The system is dissipative (non-holonomic).
The rate of orbit/rotation ratio formation is similar to the rate of dissipation.
Therefore the property of orbit/rotation formation is radically non-Hamiltonian.
Predictability fails, and locality fails. The latter implies some sort of holism.
Unlike noncomputable Hamiltonian systems, the system reaches a final state in finite time.
Holism and emergence: Dynamical complexity defeats Laplace’s Demon. South African Journal of Philosophy :

39. Some further observations on emergence
Emergent patterns may be stable and analyzable (e.g. Mercury’s harmonics, Bénard Cells).
The processes that form them, though, are not fully analyzable, nor are they reducible.
We can get a good idea of what is happening from understanding the underlying aspects of the system dynamics.
Network dynamics are analyzable if they do not change their nodes, but typically not otherwise.

40. Biological Functionality 1
Teleological account (Wright, Mayr, Millikan, Neander)
The function of T is to F if an only if T exists because it Fs.
A trait T, on this account, is functional if and only if T is an adaptation due to its Fing (T was selected because it Fs).

41. Biological Functionality 2
2. Autonomy account (Kant, Maturana and Varela, Rosen, Bickhard, Christensen, Collier)
Biological autonomy is the organization that constitutes a biological system’s persistence.
Biological function of a trait is its contribution to biological autonomy.
So, biological function is likely to be selected for, if it is stronger than other biological functions.

42. Biological Functionality 3
Both accounts of biological function are grounded in contributions to persistence (survival).
Biological function can fail (e.g., the heart was selected to pump blood, and that is its organizational role, but it can fail to perform this function, undermining survival).
Function has an object that is not present (Deacon), but it must have some sort of representation in the functional system.

43. Biological Functionality 4
The etiological account fails to account for functionality that is not functional enough to survive; the organizational account can handle this.
We can recognize function without knowing etiology (mostly); the organizational account can handle this.
The autonomy account is superior to the etiological account.

44. Biological Information Theory
Information theory is a useful technology for representing biological systems.
More than that, biological processes involve not only matter and energy flows, but also information flows.
The energy and information budgets are to some extent independent.
Thus information theory is more than just instrumentally useful, but has a substantive application within biological systems.
Can we use this to understand control in biological systems, and thus the role of autonomy in functionality?

45. Information Models Communications theory (Shannon)
Network theory (Ulanowicz, Barwise and Seligman, many others)
Control theory (widespread)
Including 1st and 2nd order cybernetics
Infodynamics/Morphodynamics (Salthe, Collier, Brooks and Wiley)
The last involves emergence in information systems.
All of these can be incorporated under the theory of information flow (Barwise and Seligman)

46. Information Flow
Information Flow: The Logic of Distributed Systems, Barwise an Seligman
Defines a channel as an ordered set of morphisms between two classifications and the tokens that fall under them such that the tokens of the second can recover the classification of the first (the logic is not typically symmetric).

47. Information Flow

48. Limits of BIT
Biological information theory is purely syntactic; it has no semantics in itself.
BIT says nothing about function.
BIT deals only with information flows, but has no specification of the way in which these information flows control anything, including other information flows. These ideas are either epiphenomenal, or are further constraints.

49. Organisms are Complex Adaptive Systems
The adaptive part implies that they are cybernetic (origin, Greek word for steering) systems.
Cybernetic systems are control systems that use information to direct other forms of flows (including other information flows).
This suggests that information directing flows is sufficient to explain the behaviour of organisms.

50. 1st Order Cybernetics
Given a distributed network, the mutual information among nodes defines the properties of the relations in the network (Ulanowicz)
Feedback and feedforward allow for control of the information flow through the nodes.
These are specific network organizations

51. Feedback

52. Organisms are autonomous
Cybernetics cannot explain function.
It can explain how a system behaves in terms of the relation of information and flows, but not why.
In order to explain function we need to postulate some sense of something being done for the sake of something.
The what is done is for the sake of the organism that does it, then the organism must have some degree of autonomy.

53. Autonomy requires 2nd order cybernetics
Autonomy is self-regulation.
This implies that the steerer is also steered, i.e., 2nd order cybernetics.
Interestingly, the model of a controller that controls a controller can in principle control anything (Penfold), like an F16.
A controller controlling another controller is like an abstraction of the function of the first level controller. (Hooker, Penfold, Evans)

54. The difference between an E coli and an F16 (1)
F16s don’t represent anything to themselves in any sense and the F16 system itself serves a function within a larger system, so its self-controlling capacities gain their function derivatively.
Furthermore, it could be said that the controller of the F16 uses the airplane to achieve its functions (deadly flight). This symmetry is fatal to our usual understanding of biological function.

55. The difference between an E coli and an F16 2
E coli cells don’t function for anything but themselves. Unlike F16s.
There is also no symmetry: the functions of E coli function for the cell (and perhaps its lineage, but then these are really functions of the lineage), but the cell does not function for its parts.
We need to account for these two properties in explaining biological function.

56. Semiotics to the rescue?
Functionality needs some account of what is special in biological systems. The main point is that it requires that the function is a function for the system, rather than the system serving the functions. The function must be understood in an integrative way.
One way to resolve this is through biosemiotics, which requires that functions are integrated into system organization in a meaningful way.
It isn’t clear how to apply this to species or to ecologies, if it can be done at all. Organisms are special.

57. An example of closure issues
Some birds exhibit “broken wing” behaviour when a predator approaches their nest – they move off on the ground flapping a wing ineffectively.
This distracts the predator, and leads it away from the vulnerable eggs.
This is obviously functional, but what is it for the sake of?
Not the bird, as it puts itself in danger.
Not for the eggs, as they do nothing.
The closure conditions require that the function is a function for the lineage of the bird. That function has the proper closure conditions.
Is the lineage autonomous? It has vertical cohesion, and it depends on organization for its survival, so I would say “yes”.

58. Conclusions – Emergence
Emergence is common in biology, but can lead to stable and analyzable steady states.
The processes leading to these states are not analyzable fully, and the states are not reducible.
If we can learn the underlying processes, then we can guess at likely bifurcation points emergence points as well as likely forms of emergence.
In networks, emergence can occur when the number of nodes changes.
Organization can constrain and even facilitate emergence from the top down.

59. Conclusions – Function
Autonomy is the best analysis of function in organisms. It is multifaceted and complexly organized, and hierarchical
It is not clear how it might apply to other biosystems like species and ecosystems, but we can expect organization to play a role.
Cohesion will still play a central role, and we can expect this to be multifaceted and irreducible.