Complex Adaptive Systems, Cognitive Apparatuses, Life-after-Google-Post Church-Turing-Thesis-Architectures and All That Jazz.

This video (3 minutes and 15 seconds long) discusses 
the difference between complex adaptive systems 
with the emergence property and 
biological systems that manage their destiny.        

Prologue:

Jazz is an example of a complex adaptive system where individual members participate with their local talent that results in a surprising global harmony.?All that Jazz is a metaphor that describes the thesis, antithesis and the synthesis involved in the process.?Current understanding of information processing is undergoing a synthesis and the Jazz metaphor seems very appropriate.?This post describes my own attempt to?understand information processing structures both in the physical and digital realms and their evolution. I sincerely appreciate any critique or comments. They only further the progress of science and its application to solve business problems today.

Complex Adaptive Systems:

The universe consists of complex adaptive systems (CAS) and we humans are the most evolved CAS of all. A CAS is a system in which a perfect understanding of the individual parts does not automatically convey a perfect understanding of the whole system's behavior. A CAS is a network of individual elements interacting with each other and its environment. Each element (living or non-living) exhibits a specific behavior and may be composed of subnetworks of elements providing a composed behavior. The whole is more complex than its parts, and more complicated and meaningful than the aggregate of its parts. It takes energy to process information, sustain its structure and exhibit the intended behavior. Various systems adapt different strategies to use matter and energy to sustain order in the face of fluctuations caused by internal or external forces. The second law of thermodynamics comes into play because of matter and energy involvement which states that "there is no natural process the only result of which is to cool a heat reservoir and do external work." In more understandable terms, this law observes the fact that the useable energy in the universe is becoming less and less. Ultimately there would be no available energy left. Stemming from this fact we find that the most probable state for any natural system is one of disorder. All-natural systems degenerate when left to themselves.

An adaptive system refuses to be ‘left to itself’ and develops self-organizing patterns to reconfigure the structure to compensate for the deviations of behavior due to fluctuations.?Thus function, structure, fluctuations, sensory perception, awareness and reconfiguration processes play key roles in the evolution of CAS. Physical and chemical structures exhibit complex adaptive behaviors resulting phase transitions and chemical reactions.?In responding to environmental temeperature fluctuations, water becomes ice or vapor.?In response to external magnetic field, iron filings change their behavior and align themselves to change the magnetic properties. Another example is the depolarization of the membrane of a nerve cell where a charged cellular system is driven far from equilibrium by the difference in charg density on the two sides of the membrane. An ant colony exhibits the behaviors of collaboration and competition although individual ant behavior is tightly preprogrammed to respond very simply and directly to chemical signals. Financial, immune and global ecosystems also exhibit complex adaptive behaviors where local actions without global knowledge result in often, surprising and unexpected outcomes.

The study of complex adaptive systems in the last couple of decades has given us a deeper understanding of their properties and resulted in predicting how information propagates in social networks, how the evolving individual components which compose themselves into network of networks, develop redundant and resilient properties

Cognition and Information Processing Structures:

In nature, the most resilient and efficient systems that compose themselves into highly scalable organisms are biological systems. Biological systems are unique in that they have managed to develop cognitive apparatuses that take information processing to a higher level with the ability to facilitate sentience (the ability to sense and feel), intelligence (the ability to process information) and resilience (using the information to rearrange the structure and facilitate its management using the cognitive apparatuses). These apparatuses take the form of genes and neurons and their ability to observe, process, model, reason about and take action has enabled them to model themselves and their interaction with their environments. Figure 1 shows the cognitive and physical structures.

Figure?1: The relationship between matter, energy, information, knowledge and data.

Cognitive abilities exist in all biological systems with varying degree.?As this quote from Charles Darwin says “the difference in mind between man and the higher animals, great as it is, certainly is one of degree and not of kind.” According to Maturna and Varela [1] “A cognitive system is a system whose organization defines a domain of interaction in which it can act with relevance to the maintenance of itself, and the process of cognition is the actual (inductive) acting or behaving in the domain. Living systems are cognitive systems, and living as a process is a process of cognition. This statement is valid for all organisms, with or without a nervous system.”

According to Wikipedia, "cognition is considered as the ability of adaptation in a certain environment. That definition is not as strange as it seems at first glance: for example, one is considered to have a good knowledge of Mathematics if they can understand and subsequently solve a Mathematical problem. That is, one can recognize the mathematical entities, their interrelations and the procedures used to view other aspects of the relevant phenomena; all these, are the domain of Mathematics. And one with knowledge of that domain, is one adapted to that domain, for they can tweak the problems, the entities and the procedures within the certain domain.

Cognition emerges as a consequence of the continuous interaction between the components of the system and its environment. The continuous interaction triggers bilateral perturbations; perturbations are considered problems – therefore the system uses its functional differentiation procedures to come up with a solution (if it doesn't have one handy already through its memory). Gradually the system becomes "adapted" to its environment – that is it can confront the perturbations so as to survive. The resulting complexity of living systems is cognition produced by the history of bilateral perturbations within the system/environment schema.”

Cognition enables complex physical structures to evolve, adapt and become autopoietic. The term autopoiesis refers to a system capable of reproducing and maintaining itself. “An autopoietic machine is a machine organized (defined as a unity) as a network of processes of production (transformation and destruction) of components which: (i) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produced them; and (ii) constitute it (the machine) as a concrete unity in space in which they (the components) exist by specifying the topological domain of its realization as such a network.”

Digital Information Processing Structures:

In biological systems, cognition is embodied in physical structures and is encoded in its cell that enables its functions, structure and fluctuation management.?As Waldrop Mitchell points out in his book on complexity, “The DNA was actually the foreman in charge of construction. In effect, DNA was a kind of molecular -scale computer that directed how the cell was to build itself and repair itself and interact with the outside world.” Each cell can divide and differentiate itself into muscle cells, brain cells, liver cells, and all other kinds of cells that make up a new born. Each different type of cell corresponds to a different pattern of activated genes. In figure 2. We represent the embodied cognition in the human genome that that senses, models, reasons and manages both physical and mental structures (using the mind, brain, and body structures).

The digital structures are made possible by the human cognitive abilities and the implementation of cognitive representations of the physical world using physical structures such as computers, networks and storage devices. Current information technologies are implemented as physical structures implementing the models of the physical and mental structures using the digital genes and digital neurons.?They are modeled and managed by the human.?Figure 2 shows the digital structures and their implementation using physical structures such as computer, networks and storage devices.

Figure 2: Digital Information Processing Structures with Digital Genes and Neurons made possible by Church-Turing Thesis and conceived by the human cognitive abilities

John von Neumann’s stored program implementation of the Turing machine provides a physical implementation of a cognitive apparatus to represent and transform knowledge structures that are created by physical or mental worlds in the form of data structures representing the domain under consideration. Figure 2 shows the implementation of Turing Machines as cognitive apparatuses with locality and the ability to form information processing structures where information flows from one apparatus to another with a velocity defined by the medium. These implementations have allowed us to develop current state of the art of information processing structures using digital computing machines.

Symbolic computing in the form of executable tasks allows us to process a list of formal, mathematical rules or a sequence of event driven actions such as modeling, simulation, business workflows, interaction with devices, etc. The digital computing machine, in essence, acts as a “cognitive apparatus” to implement cognitive functions described as easily described tasks. We call this a digital Gene.?In addition, algorithms are designed to mimic the neural networks in the brain and process information. The neural network model allows computers to understand the world in terms of a hierarchy of concepts to perform tasks that are easy to do "intuitively", but are hard to describe formally or a sequence of event driven actions such as recognizing spoken words or faces. We call the neural network implementations as digital neurons.

The digital computing structures with digital genes and neurons have allowed many paradigms of computation, including Mainframe, PC, Network, Internet, Distributed Computing, Grid Computing, Cloud Computing, Machine Learning and Deep Learning. However, the limitation of current state of the art is pointed out by Cockshott et al., in their book “Computation and its limits” with the concluding paragraph “The key property of general-purpose computer is that they are general purpose. We can use them to deterministically model any physical system, of which they are not themselves a part, to an arbitrary degree of accuracy. Their logical limits arise when we try to get them to model the part of the world that includes themselves.” The Turing’s system is limited to single, sequential processes and is not amenable for expressing dynamic concurrent processes where changes in one process can influence changes in other processes while the computation is still in progress in those processes. This is an essential requirement for describing cognitive processes. Concurrent and asynchronous task execution and regulation require a systemic view of the context, constraints, communication and control where the identities, autonomic behaviors and associations of individual components also must be part of the description.

The thesis of this post is that sentience, resilience and intelligence are the results of information processing structures that various systems design and develop to manage their own state evolution in an optimal way by minimizing entropy in spite of a natural tendency for entropy to increase.?They do this by creating physical structures that sense, model, monitor and evolve their states to establish equilibrium between their internal states and the environment with which they interact. Matter and energy and physical, chemical and biological information processing structures that exploit their transformation rules enabled sentience, resilience and intelligence in the physical world.

We argue that we can model both physical and mental structures using structural machines, cognizing oracle[1] agents and the knowledge structures along with the cognitive apparatuses (digital genes and neurons) that enable flow of information from one knowledge structure to another.?These digital structures implementing the structural machines allow us to design and develop sentient, resilient and intelligent systems with models that include both themselves and the physical structures they are made up of and interact with.

Post-Church-Turing-Thesis and Life-after-Google Information Processing Architecture:

Taking the cues from the embodied cognition in biological systems, we propose the infusion of cognitive behaviors into digital computing structures and implement self-managing patterns that provide resiliency and efficiency at scale. The limitation of current computing model is the inability of including the computing infrastructure itself in the model of the computing structure that models and manages the physical world. In addition to the self-referential circularity of the Turing computing model, the Church-Turing thesis boundaries are challenged when rapid non-deterministic fluctuations drive the demand for resource readjustment in real-time without interrupting the service transactions in progress. This is more pronounced in the case of distributed computing structures that are composed of concurrent and asynchronous functions contributing to a common goal as in the case of business process automation tasks. The information processing structure in this case utilizes software components executed in hardware components from multiple infrastructure providers with local management systems enabling the deployment, operation and maintenance of the computation workloads on their infrastructure in the form of a cloud or a datacenter. The information processing system, in effect, behaves as complex autonomous system and is prone to emergent behavior in the face of strong fluctuations.?For example, when the system is subject to sudden fluctuations in the demand for computing resources or sudden decrease due to failure of some components, the system will experience severe deviation from its mission unless the resources are restored and the inconsistencies resulting from the local components being in different states are resolved.

Adapting the lessons learned from biological cognitive systems with self-managing patterns, we assert that the digital information processing structures must also become autonomous and predictive by including cognitive apparatuses that model themselves and their behaviors along with the information processing tasks at hand. Figure 3 shows the infusion of cognition into digital computing structures using the structural machine approach described by Prof. Mark Burgin.

Figure 3: Infused cognition in digital information processing structures

Cognitive apparatuses that sense, model and monitor, reason and manage the digital computing structure allow encoding the information to deploy, monitor and manage the computing processes with local autonomy and global coordination.?True intelligence involves generalizations from observations, creating models, deriving new insights from the models through reasoning. In addition, human intelligence also creates history and uses past behaviors and experience in making the decision. The cognitive overlay we propose in this paper provides a means to encode the information and the means to execute the processes required to understand the goals of the computational structure, available resources and the means to execute end to end deployment, monitoring and management to maintain homeostasis. In short, the new digital genome provides a means to create an autopoietic machine.

New mathematics of named sets, knowledge structures, cognizing oracles and the structural machines:

The theory of knowledge and the theory of information articulated by Professor Burgin states that information is encapsulated in named sets (objects), their attributes in the form of data and the intrinsic and ascribed knowledge of these objects in the form of relationships, algorithms and processes which, makeup the foundational blocks for information processing. Information processing structures utilize knowledge in the form of algorithms and processes that transform one state (determined by a set of data) of the object to another with a specific intent. Information structures and their evolution using knowledge and data determine the flow of information.

The use of the new mathematics detailing named sets, knowledge structures, structural machines, the theory of oracles and digital Information processing structures is discussed by Burgin and Mikkilineni. The long and short of it is that cognitive behaviors can be infused into digital information processing structures to implement self-managing patterns. Figure 4 shows an architecture to infuse cognition and create a self-managing workload that provides self-healing, self-scaling, self-protection and self-reconfiguration to address fluctuations in demand for or the availability of computing resources in a distributed network of autonomous cloud resources with global supervision and mediation without disrupting the functional behavior of the digital information processing structure.

Figure 4: Digital information processing structures with infused cognition using digital neurons and genes.

Epilogue:

I am a physicist by training and learnt from my mentor and thesis advisor Prof. Walter Kohn (Nobel Laureate 1998) that applying lessons learned from one field to another field results in surprising rewards. My accidental journey into information processing systems started with many mentors at AT&T Bell Labs before it was dismantled and continued thereafter in Bellcore, US WEST and few startups.?My quest to improve efficiency and resiliency of information processing at scale continued through my interactions with computer scientists, philosophers and mathematicians and resulted in a publication in the Turing Centenary conference proceedings in 2012.?There I was pointed to the need for a cognitive control overlay by Prof. Roger Penrose and Prof. Peter Wegner. Finally, my association with Prof. Mark Burgin and Prof. Gordana Dodig Crncovic has resulted in the application of structural machines to develop cognitive information processing systems and go beyond Deep Learning to build non-Markovian reasoning systems to solve some key issues in current information processing systems well-articulated by George Gilder in his book “Life after Google.”

At Golden Gate University, some graduate students are implementing solutions to few business issues identified by few companies using the new approach. There will be publications on how we use current hardware and software technologies to infuse cognition into existing systems without disrupting their current operations.

I am surprised to see how physics (information processing structures are amenable to many body theories) where phase space evolution of computing structures determines stability, emergence and chaos depending on the nature and strength of fluctuations. I am equally surprised at how the new mathematics and physics indeed provide a new architecture that addresses some of the long-standing issues in distributed computing and lays to rest much of the dogma about Church-Turing thesis. More importantly, the new approach points a way to solve very key issues of privacy, security, data governance in current implementations of information services and improves efficiency, resiliency at scale without a fork-lift.

I conclude this post with this observation from John von Neumann (1948).

“It is very likely that on the basis of philosophy that every error has to be caught, explained, and corrected, a system of the complexity of the living organism would not last for a millisecond. Such a system is so integrated that it can operate across errors. An error in it does not in general indicate a degenerate tendency. The system is sufficiently flexible and well organized that as soon as an error shows up in any part of it, the system automatically senses whether this error matters or not. If it doesn’t matter, the system continues to operate without paying any attention to it. If the error seems to the system to be important, the system blocks that region out, bypasses it, and proceeds along other channels. The system then analyzes the region separately at leisure and corrects what goes on there, and if correction is impossible the system just blocks the region off and by-passes it forever. The duration of operability of the automation is determined by the time it takes until so many incurable errors have occurred, so many alterations and permanent bypasses have been made, that finally the operability is really impaired. This is completely different philosophy from the philosophy which proclaims that the end of the world is at hand as soon as the first error has occurred.”

References

I am listing here (for the benefit of graduate students who want to go beyond what their thesis advisors know) the references from a paper under preparation with Prof. Mark Burgin describing both the theory and implementation of cognitive information processing structures. They pretty much cover both the theory and the implementation as we know today.

[1]????Maturana, Humberto R./Varela, Francisco J. (1980): Autopoiesis and Cognition. The Realization of the Living. Dordrecht: Reidel, p. 13.

[2]????Yang, A. & Shan, Y. (eds) (2008) Intelligent Complex Adaptive Systems, IGI Publishing,Hershey, PA.

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[5]????Choi, Thomas Y., Kevin J Dooley, and Manus Rungtusanatham (2001), "Supply Networks and Complex Adaptive Sysems: Control Versus Emergence, "Journal of Operations Management, Vol. 19, No. 3, pp. 351-66

[6]????Miller, J., & Page, S. (2007). Complex adaptive Systems: An introduction to computational models of social life, Princeton, NJ: Princeton University Press.

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[10]??Waldrop, W. Mitchell 1992 Complexity: The Emerging Science at the Edge of Order and Chaos. New York: Touchstone.

[11]??Burgin, M. (2011). Information in the structure of the world, International Journal “Information Theories and Applications”, Vol. 18, Number 1.

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[13]??Prigogine, I. and Stengers, I. Order out of Chaos, Bantam Books, Toronto/New York/London,1984

[14]??Burgin, Mark. 2017. "The General Theory of Information as a Unifying Factor for Information Studies: The Noble Eight-Fold Path." Proceedings 1, no. 3: 164.

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[16]??P. Cockshott, L. M. MacKenzie and G. Michaelson, “Computation and Its Limits,” Oxford University Press, Oxford, 2012.

[17]??R. Mikkilineni, "Going beyond Computation and Its Limits: Injecting Cognition into Computing," Applied Mathematics, Vol. 3 No. 11A, 2012, pp. 1826-1835. doi: 10.4236/am.2012.331248.

[18]??Burgin, M.; Adamatzky, A. Structural machines and slime mold computation. Int. J. Gen. Syst. 2017, 45, 201–224. [CrossRef] 5.

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[20]??Burgin, M. 2016. Theory of Knowledge: Structures and Processes; World Scientific Books: Singapore.

[21]??Burgin, M. and Mikkilineni, R. (2018) Cloud computing based on agent technology, super -recursive algorithms, and DNA, Int. J. Grid and Utility Computing, v. 9, No. 2, pp.193–204.

[22]??Rao Mikkilineni, Giovanni Morana and Mark Burgin, "Oracles in Software Networks: A New Scientific and Technological Approach to Designing Self-Managing Distributed Computing Processes", Proceedings of the 2015 European Conference on Software Architecture Workshops (ECSAW '15), 2015.

[23]??Burgin, M. (2020) Information Processing by Structural Machines, in Theoretical Information Studies: Information in the World, pp. 323–371

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[33]??Burgin M. Nonlinear Phenomena in Spaces of Algorithms, International Journal of Computer Mathematics, 2003a, v. 80, No. 12, pp. 1449-1476?????

[34]??Burgin, M. Structural Reality, Nova Science Publishers, New York, 2012

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[43]??Burgin, M. and Bratalskii, E. (1986) The principle of asymptotic uniformity in complex system?modelling,?in?Operation Research and Automated Control Systems, Kiev: Institute of Cybernetics, pp. 115-122????[in Russian]

[44]??Burgin, M. and Debnath, N. Reusability as Design of Second-Level Algorithms, in Proceedings of the ISCA 25th International Conference “Computers and their Applications” (CATA-2010), ISCA, Honolulu, Hawaii, 2010, pp. 147-152??????

[45]??Burgin, M. and Gupta, B. Second-level Algorithms, Superrecursivity, and Recovery Problem in Distributed Systems, Theory of Computing Systems, v. 50, No. 4, 2012, pp. 694-705????

[46]??Burgin, M., Eberbach, E., & Mikkilineni, R. (2019). Cloud Computing and Cloud Automata as A New Paradigm for Computation. Computer Reviews Journal, 4, 113-134. Retrieved from https://purkh.com/index.php/tocomp/article/view/459.

[47]??R. Mikkilineni and G. Morana, "Post-Turing Computing, Hierarchical Named Networks and a New Class of Edge Computing," 2019 IEEE 28th International Conference on Enabling Technologies: Infrastructure for Collaborative Enterprises (WETICE), Napoli, Italy, 2019, pp. 82-87, doi: 10.1109/WETICE.2019.00024.

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[1] Theory of oracles built by Mark Burgin is a far-reaching generalization of the concept proposed by Alan Turing.