Monday, January 30, 2012
Input-Output Symmetry, Process-Configuration Reflexivity, Endomorphic-Ectomorphic Duality
Image: Walter J. Freeman
Consciousness, Intentionality, and Causality:
"There is one more thing I would like to leave you with. Notice that quantum symmetry restores a kind of ‘input-output symmetry’ since as well as being able to combine or ‘multiply’ information you can also uncombine or ‘comultiply’ it. All the rules are symmetric between the two. It means that you can take a computation with quantum symmetries as flow charts, turn the chart upside down, and you have another valid computation with the roles of multiplication and comultiplication flipped. If such quantum symmetry ‘duality’ ideas are fully manifested in quantum gravity they would, I argue in my chapter of the book, be related to a deep duality between quantum spacetime and gravity or between the macro world and the micro world. This also suggests some deep ideas about reversing time, which the small margins of this blog are too small to contain (to paraphrase Fermat)…"
"The forefather of biological category theory is Robert Rosen. I haven’t had a chance to look at his work yet, but for an easy (for Café regulars) introduction to some of his ideas, try Juan-Carlos Letelier et al. Organizational invariance and metabolic closure. In particular, it discusses the representation of enzyme metabolism by arrows in categories, taking into account the thesis:
Organisms are closed to efficient causes.
In this case, the thesis translates to the idea that there must be an internal process to repair or replace the enzymes which are metabolising the input molecules. So not only do we have processes mapping inputs to outputs. There must also be processes mapping outputs to the original process effectors. The paper explains conditions on evaluation maps.
I would imagine that a higher proportion of biologists are bewildered by this kind of work than their physicist colleagues by similar work in their field."
"The idea of duality is not too difficult to understand, although there are very non-trivial applications. The idea of duality refers to the possibility that there might be two descriptions for the same thing. It is quite obvious that this occurs often. The two descriptions might be very easily related, as in the following example."
"Process theory is a commonly used form of scientific research study in which events or occurrences are said to be the result of certain input states leading to a certain outcome (output) state, following a set process.
Process theory holds that if an outcome is to be duplicated, so too must the process which originally created it, and that there are certain constant necessary conditions for the outcome to be reached. When the phrase is used in connection with human motivation, process theory attempts to explain the mechanism by which human needs changes. Some of the theories that fall in this category are expectancy theory, equity theory, and goal setting.
In management research, process theory provides an explanation for 'how' something happens and a variance theory explains 'why'.
Some theorists claim that all natural processes have complex phases in which the output state of the process is not determined by the input states of the processes. The condition is defined by Robert Rosen as being "complex".
Central to process theory is the rigorous avoidance of the "historical fallacy", also known as the "psychological fallacy". It has been defined as: “A set of considerations which hold good only because a completed process is read into the content of the process which conditions this completed result."  In other words, the fallacy is committed when something is read into a process which comes about only as a result of that process."
"Unified Theory of Information (UTI) Research Group - Association for the Advancement of Information Sciences
UTI Research Group is a non-profit organization that aims at the advancement of reflection and discourse in academia and society about the role of Information, communication, media, technology, and culture in society. It works for building a better understanding and for dialogue in information science, communication and media studies, and science and technology studies (STS). It is interested in advancing critical ideas, approaches, methods, and research that are needed for establishing a global sustainable information society.
UTI Research Group is the publisher of tripleC - Cognition, Communication, Co-operation: Open Access Journal for a Global Sustainable Information Society, which focuses on transdisciplinary research on information, communication, media, technology, and culture. It also engages in critical research on the role of information, communicaiton, media, technology, and culture in 21st century society and publishes research reports and books."
Information Operators in Categorical Information Spaces:
Theory of information: fundamentality, diversity and unification (Google eBook)
"This work is aimed at a demonstration that in contrast to physics, which is still in search for a unified theory and is striving to get particles that are the most elementary, in mathematics such a theory exists. It is the theory of named sets. It is demonstrated in this paper that the construction of a named set allows one to systematize all approaches to foundation of mathematics. Evidence is provided that named set is the most fundamental concept and structure of mathematics as it underlies other fundamental concepts and structures: sets, logical, algorithmic/computational, and categorical structures and entities. Although named sets are closely related to ordinary sets, existence of independent axiomatics of the theory of named sets demonstrates that named sets are not only conceptually more fundamental than sets, but also are independent in the logical setting."
"Mental models are representations in the mind of real or imaginary situations.
Scientists sometimes use the term "mental model" as a synonym for "mental representation", but it has a narrower referent in the case of the theory of thinking and reasoning. The idea that people rely on mental models can be traced back to Kenneth Craik’s suggestion in 1943 that the mind constructs "small-scale models" of reality that it uses to anticipate events."
"Cognitive science is one area where the difference between models and modelling tends to become blurred. A central question of cognitive science is how we represent facts or possibilities in our minds. If one formalises these mental representations, they become something like ‘models of phenomena’. But it is a serious hypothesis that in fact our mental representations have a good deal in common with simple set-theoretic structures, so that they are ‘models’ in the model-theoretic sense too. In 1983 two influential works of cognitive science were published, both under the title Mental Models. The first, edited by Dedre Gentner and Albert Stevens, was about people's ‘conceptualizations’ of the elementary facts of physics; it belongs squarely in the world of ‘modelling of phenomena’. The second, by Philip Johnson-Laird, is largely about reasoning, and makes several appeals to ‘model-theoretic semantics’ in our sense. Researchers in the Johnson-Laird tradition tend to refer to their approach as ‘model theory’, and to see it as allied in some sense to what we have called model theory."
"Since I shall be referring to my book More Than Life Itself (Louie 2009) many times, I shall henceforth use the canonical symbol ML in its stead. Likewise, same as their usage in ML, the symbol LI shall denote Robert Rosen’s book Life Itself (Rosen 1991), and the symbol EL shall denote his book Essays on Life Itself (Rosen 2000). It is appropriate to recall the theme and offer a pre´cis of ML here, before I comment on the preceding essays that discuss it. ML represents a synergy of the mathematical theories of categories, lattices, and modelling, and the result is a synthetic biology that provides a characterization of life. On this journey in relational biology, one meets a cast and crew of mathematical and biological characters. They include partially ordered sets, lattices, simulations, models, Aristotle’s four causes, graphs, categories, simple and complex systems, anticipatory systems, and Rosen’s metabolism-repair systems. Along the way, I recast Rosen’s theorems from LI on a rigorously mathematical footing, and present an alternate set of proofs."
"BASIC CONCEPTS OF NATURAL RELATIONSHIP
1. Nature is best imagined in terms of interconnected and holarchical relationships between explicit and implicit forms.
2. The explicit form is an observable (measurable or classifiable) material existence that might otherwise be described in terms of energy and matter.
3. The implicit form is the reflection or specification of an explicit form. The implicit form (analogous to a ‘formal system’ in mathematics) may be thought to exist in contextually related systems. That relation establishes what we call the organization” of a system.
4. The relationship between explicit and implicit forms is a “modeling relation” as described by Robert Rosen. That relation defines natural complexity. The explicit and implicit forms, when recognized in this relation, account for all that we can know or infer symbolically of the natural world.
5. Modeling relations exist in nature itself, not just in our study of nature. Consequently, we not only employ our own modeling relations when studying nature, but we can actually study nature in terms of modeling relations, which can thus be taken as fundamental theoretical units of analysis at all scales in all systems.
6. Modeling relations are information relations in the sense that each related system ‘encodes’ to or ‘decodes’ from one system’s organization to the other’s. In this precise weay, systems can be said to ‘interact’ (i.e., to act together and between each other). In the general case, such encodings and decodings are not exact, being necessarily comprised of abstracted patterns (of observation or interaction) that are determined by the nature of their interaction. It is logically impossible for two different systems to interact in all ways they are capable of, that necessarily implying an infinite number of abstractions. Abstraction is thus, by its nature, a feature of the explicit (material) world It is a unique measurement of a unique state in existence at the time (or as a result of measurement) in a given space-time reference.
7. The classical world of mechanisms is a special case of general relational complexity. It is the case where explicit and implicit forms are equivalent; where any system and its implicit ‘model’ (which may exist in any related system, including self), contain the same organization, pattern, or specification; where causality in the explicit material world can be said to correspond with implication in the implicit world. In this highly reduced reality, without any isolated causal sub-systems, a set of precise general physical laws can explain behavior.
8. Given (7), the case of mechanism is, therefore, an ideal case that can only be approximated in explicit nature. The scientific description of a mechanism thus describes an abstracted aspect of nature; one that the behavior of the natural system may come very close to, but will never correspond to completely at all scales and conditions. Though not detectable under observed conditions where a classical mechanism may seem quite predictable, natural complexity — natural relationship — remains nevertheless latent. There are no true realizations of a mechanism in the explicit world.
9. Organisms represent a different case of general relational complexity. It is the case where five functional mappings combine to produce a self-entailed organization (isolated causal system) that performs the functions of metabolism and repair (including reproduction). Two unentailed mappings of these relations, one each from its metabolism and repair components, connect the organism with its environment. Reproduction and repair entail the organism structurally with its environment as a defined material system (defined by its genetic code, its pattern of material organization). Metabolism entails the organism with its environment through the natural selection of its function in the environment (its behavior). The organism thus participates functionally and structurally in its outer surroundings. Ref: Kineman dissertation
10. The obvious presence and predictable persistence of a general mechanical (classical) world of observable states, arises from the collective effect of multiple (complex) modeling relations, to the extend that their interactions are un-isolated from the general system of interactions.
11. The obvious elaboration or enhancement of complexity in organisms, especially more intricately evolved organisms, (i.e., those that incorporate a greater number of functions) is made possible by their causal isolation from the general reality (10). The causally closed organization of M-R systems (9), isolates the internal causalities, producing internally closed modeling relations that are therefore not strictly predictable from knowledge of the general external causal laws and entailments. Organisms thus invent their own laws in an isolated internal reality. Such internal systems thus may comprise sophisticated models that, through the organism’s relationships with environment (9) can adapt to persistent conditions in anticipatory ways and thus to cause the lineage of organisms (physogeny) to evolve. Such evolution can therefore be driven by environmental conditions and unique patterns generated by the independent behavior of internal models. To the extent that such models may be said to involve, produce, or correspond with psychological phenomena (obviously of similar type to implicit realities), consciousness and choice may then be said to affect evolution in combination with the effects of environmental selection. Conscious evolution of humans is thus a logical reality, and this capacity must be considered to exist on a continuum from non-organism to highly developed organism.
12. Modeling relations, as the presumed ‘reality’ of nature and appropriate method for analyzing its complexity are thus to be considered ontological entities. They are assumed components of living nature in that they comprise a fundamental way of thinking about nature. As such, this view of nature is more general than the mechanistic view, underlying classical, complex, and living systems; but not more general in the case of living systems than needed to capture true complexity. As ontological models they are capable of representing the origin of natural systems and their laws: they provide a conceptual bridge across traditional duality, without compromising known science on the one hand (e.g., of mechanisms) and obvious unexplained phenomena on the other (e.g., of living nature). Unlike mechanistic theory, relational theory is capable of dealing with origins, and thus systems that originate themselves to whatever degree (adaptive and evolutionary systems). This ontology extends directly to epistemological and empirical elements, which are the modeling relation’s ‘encodings’ and ‘decodings’; corresponding respectively to ‘structure’ and ‘function.’"
"33. WOLTJER, ROGIER: SUPPORTING CONTROL THROUGH
In this paper we discuss the utility of the concept of constraint in the design of support systems for process control. The paper draws upon concepts from the book on the 1985 NATO ASI meeting on Intelligent Decision Support in Process Environments and adds current Cognitive Systems Engineering (CSE) concepts. Our focus is the roles of Joint Cognitive Systems and the recognition of constraints in process control. First, the stance of Cognitive Systems Engineering (CSE) is discussed. Second, the inadequacy of the classical option generation and evaluation paradigm of decision support is is contrasted to the CSE approach of striving for joint cognitive systems to retain control. Third, the important concepts of time and goals are briefly discussed. Fourth, the theory of supporting control through the recognition of constraints is outlined. Last, the concepts discussed are applied in three domains where the application of CSE is particularly appropriate: command and control, driving, and aviation safety.
33.1 Purpose and control
We take the stance of Cognitive Systems Engineering (CSE). A cognitive system (Hollnagel & Woods, 2005) is a system that can control its behavior on the basis of experience towards its goals. The term Joint Cognitive System (JCS) means here that control is accomplished by an ensemble of cognitive systems and (physical and social) artifacts that exhibit goal-directed behavior. In the areas of interest to CSE, typically one or several persons (controllers) and one or several support systems are part of a JCS, which in a complex environment is jointly engaged in some sort of process control.
To control a process is to steer the behavior of the process. Thus, when considering the design of support systems for process control, it is useful to consider the theory of cybernetics, meaning steermanship, the science of control. According to cybernetics pioneers Rosenblueth, Wiener, and Bigelow (1943), purposeful behavior is behavior that can be interpreted as goal-directed, on the basis of feedback and prediction. Hollnagel & Woods (2005) also state that being in control means knowing what has happened and what will happen."
"Today designing smart systems—which include smart objects, buildings, and cities—is more important, and more difficult, than ever, as the complexity of our projects and our world rises dramatically. Fortunately we can learn much about designing systems (aka networks) from our millions of years ofexperience designing things (nodes). Autodesk’s Jon Pittman will discuss essential digital design techniques such as digital models and “experiencing things before they are real, as well as how technologies such asreality capture, sensors, smart grids, and advanced visualizations, simulations, and analysis can help us do a better job of designing the smart systems needed to power an increasingly complicated world."
"…Each step of implementation created a new situation; and the new situation provided a starting point for fresh activity" - H. A. Simon, "The sciences of the artificial", 1991.p.163
"Usually, socio-economic systems are percieved as evolving systems, although their modelers claim their difficulty to design stable, teachable and workable models of such phenomena, particularly when they must admit that they do not know the laws which eventually govern the local or global evolution of those phenomena: How can they design predictive models of the behavior of social systems, when this evolving behavior is affected at each step by the expectations and reactions of the various actors involved in the process?
"The theorems of game theory and rational expectations have added a new hazard to be faced by designers of social and economic models aimed at prediction" conclude H.A. Simon, who add:
"More than forty years of intensive research leaves us with the firmly established conclusion that there is no unequivocal definition of rationality under conditions of mutual outguessing".
The modeling process of a socio economic evolving system needs some preliminary and explicit considerations on the reasoning process involved in such design."
"In this paper, we elaborate on the fundamental characteristics of ecological ontologies, and draw attention to the importance of space and time in the structure of these ontologies. First, we argue that a key to the specification of eco-ontologies is the notion of teleological organization grounded in a notion of recursion. Second, we introduce the notion of roles to characterize the generalized and interactive teleological aspects of ecological systems. Third, we also introduce a preliminary set of temporal and spatial concepts intended to represent ecological space and time in the formalization of eco-ontologies. Fourth, we show how some
important epistemological constraints on cognition are fundamentally ecological in nature. This work is informed by Kant’s investigations into the foundations of biology, by the hermeneutic investigations of Heidegger and Gadamer, and by mathematical investigations into recursive logic and their application to biology by Spencer-Brown, Maturana, Varela, and Kauffman."
Keywords: ecology, ontology, space, time, epistemology
"The algebra of boundaries is novel, and is not incorporated within existing mathematical systems. Boundary mathematics provides a unique opportunity to observe formal structure rising out of literally nothing, without recourse to, or preconceptions from, the existing logical, set theoretic, numeric, relational, geometric, topological, or categoric formal systems that define modern mathematics."
"By repeated contraction, expansion, and analogy, any theory can be converted into any other. Multiple contractions would reduce a (closed) theory to the empty (top) theory at the top of the lattice. The top theory is the closure of the empty theory – it contains only tautologies or logical truths; i.e., expressions that are true in all models (it is “true of everything”). Multiple expansions would reduce a (closed) theory to the full inconsistent theory at the bottom of the lattice. The full inconsistent theory is the closed theory consisting of all expressions; i.e., expressions that are true in no models (it is “true of nothing”)."
Rational Souls, Recursive Teleology, Mirror Neurons, Symbolic Systems, Extension Transference
The periods of the Solenoid of Semeiosis are:
Semeiosis and autopoiesis
Semiosis is autopoietic (Maturana and Varela, 1973, p. 78), i.e. it produces itself from a fundamental complementarity between structure and function.