A mathematical theory of strong emergence using multiscale variety

We argue conceptually and then demonstrate mathematically that it is possible to define a scientifically meaningful notion of strong emergence. A strong emergent property is a property of the system that cannot be found in the properties of the system's parts or in the interactions between the parts. The possibility of strong emergence follows from an ensemble perspective, which states that physical systems are only meaningful as ensembles rather than individual states. Emergent properties reside in the properties of the ensemble rather than of any individual state. A simple example is the case of a string of bits including a parity bit, i.e. the bits are constrained to have, e.g., an odd number of ON bits. This constraint is a property of the entire system that cannot be identified through any set of observations of the state of any or all subsystems of the system. It is a property that can only be found in observations of the state of the system as a whole. A collective constraint is a property of the system, however, the constraint is caused when the environment interacts with the system to select the allowable states. Although selection in this context does not necessarily correspond to biological evolution, it does suggest that evolutionary processes may lead to such emergent properties. A mathematical characterization of multiscale variety captures the implications of strong emergent properties on all subsystems of the system. Strong emergent properties result in oscillations of multiscale variety with negative values, a distinctive property. Examples of relevant applications in the case of social systems include various allocation, optimization, and functional requirements on the behavior of a system. Strongly emergent properties imply a global to local causality that is conceptually disturbing (but allowed!) in the context of conventional science, and is important to how we think about biological and social systems. © 2004 Wiley Periodicals, Inc. Complexity 9: 15–24, 2004     

Are beliefs believable? An investigation of college students’ epistemological beliefs and behavior in mathematics

College students’ epistemological belief in their academic performance of mathematics has been documented and is receiving increased attention. However, to what extent and in what ways problem solvers’ beliefs about the nature of mathematical knowledge and thinking impact their performances and behavior is not clear and deserves further investigation. The present study investigated how Taiwanese college students espousing unlike epistemological beliefs in mathematics performed differently within different contexts, and in what contexts these college students’ epistemological beliefs were consistent with their performances and behavior. Results yielded from the survey of students’ performances on standardized tests, semi-open problems, and their behaviors on pattern-finding tasks, suggest mixed consequences. It appears that beliefs played a more reliable role within the well-structured context but lost its credibility in non-standardized tasks.     

RISK-BASED MULTIATTRIBUTE DECISION-MAKING IN PROPERTY AND WATERSHED MANAGEMENT

ABSTRACT. Determining best management systems for properties and evaluating their sustainability at the watershed scale are useful and important aspects of integrated watershed management. Multiattribute decision-making (MADM) is very useful for modeling the selection of best management systems for properties in a watershed. This paper reviews four MADM approaches including utility theory, surrogate worth tradeoff, free iterative search and stochastic dominance with respect to a function (SDWF). Emphasis is on determining how the first three methods could be used to determine the best (most preferred) combinations of attributes and associated management systems for a property. An application of the expected utility method with risk neutral preferences is presented in which farmer's preferences for five attributes are used to rank five farming systems for an agricultural watershed in Missouri. A framework is presented for assessing the sustainability of the best management systems for all properties in a watershed and the cost-effectiveness of policies for enhancing sustainable resource management at the watershed scale.     

Acting with systems intelligence: integrating complex responsive processes with the systems perspective

The systems thinking literature assumes that the concept of a system is useful in management and organizational research. Ralph D. Stacey and his collaborators, however, have questioned this. They have presented the theory of complex responsive processes (CRP) as an alternative to systems thinking. We argue that systems thinking and the CRP perspective are complementary. The CRP illuminates many of the micro-behavioural, local interaction and creativity-related organizational phenomena whereas the systems perspective is useful for other purposes. CRP misses the mark in its criticism of systems thinking. The insights of CRP should and could be incorporated, not switched, with the systems perspective. The systems intelligence perspective, proposed by Hämäläinen and Saarinen, provides a framework to accomplish that. By integrating systems thinking and the CRP model we hope to provide a platform from which it is possible to appreciate the relative merits of the two apparently conflicting strands of thought.     

Ryle and Intentionality

After some opening comments on how I think one should approach the philosophy of mind, I look at what relatively little Gilbert Ryle had to say explicitly about intentionality, that occurring almost exclusively in his several papers on phenomenology. Then, I discuss the notion of intentionality with respect to the doctrines of The Concept of Mind, although neither the word nor the idea, strictly speaking, appears anywhere in the book. Following more exposition of my own views, including an argument I have made for a certain specific theory of intentionality, I close with some reflections on Ryle as a modern-day Aristotelian.     

From Optimizing to Learning: A Development of Systems Thinking for the 1990s

In any subject concerned with rational intervention in human affairs, theory must lead to practice; but practice is the source of theory: neither theory nor practice is prime. We can examine this ‘groundless’ relation by asking what intellectual framework F is applied in what methodology M to what area of application A? If we do this for O.R., systems analysis, systems engineering etc., we see that F and M have changed dramatically between the 1950s and the 1980s, yielding the ‘hard’ and ‘soft’ traditions of systems thinking. The ‘hard’ tradition, based on goal seeking, is examined in the work of Simon and contrasted with the ‘soft’ tradition, based on learning, as exemplified in the work of Vickers and the development of soft systems methodology. The two are complementary, but the relation between them is that the ‘hard’ is a special case of ‘soft’ systems thinking. This analysis makes sense of the recent history of management science and helps to prepare us for the 1990s.     

Price caps

Price-cap regulation of AT&T, which became effective on July 1, 1989, is an example of an idea that made its way from economic theory to institutional practice; in this case the process took about seven years. We describe both price-cap regulation and its predecessor — rate-of-return regulation — with particular regard to their incentive properties. We then give the assumptions and conclusions of a theoretical study (in fact a principal-agent model) that bears on the likely effectiveness of price-cap regulation. In the concluding section we describe some aspects of the progress of this idea from theory to practice, and draw tentative conclusions about the conditions that made it possible for this progress to be successfully completed.The views expressed here are the authors', and not necessarily those of AT&T Bell Laboratories.     

Topological measures,image transformations and self-similar sets

Summary This paper introduces a novel idea: the concept of an image transformation. We also introduce the closely related concept of a quasi-homomorphism, and study the properties of these mathematical objects, and give several examples. In particular we investigate iterated systems of image transformations, which we believe give a more realistic approach to the study of so called self-similar structures in nature than what is obtained by iterated function systems.     

Recalibrating scorecards

Many credit scoring systems depend on scorecards which order applicants by credit risk. However the scorecards may also have other properties with certain scores reflecting certain good:bad odds or differences in scores having the same property throughout the score range. Other properties like positivity of attribute points may be required for palatability or internal marketing reasons. The paper outlines the results of a small survey of what properties scorecard builders require of their scorecards. It then discusses how these properties can be obtained and describes a linear programming formulation which recalibrates scorecards so as to produce the best approximate scorecard with the properties required.     

Veber on knowledge and factuality

The article deals with the development of the philosophy of France Veber (1890–1975), the pupil of Meinong and a main Slovene philosopher. One of the most important threads of Veber’s philosophy is the consideration of knowledge and factuality, which may be seen as a driving force of its development. Veber’s philosophical development is usually divided into three phases: the object theory phase, the phase when he created his philosophy of a person as a creature at the crossing of the natural and the spiritual world, who as an active, not merely passive subject possesses her own causal powers, and the third phase, when he supplemented his earlier philosophy with the theory of a special side of our experience which he called hitting-upon-reality. It is a direct experience of reality, a special kind of intentionality, which is however fundamentally different from presentational intentionality, which alone is taken into account by object theory or phenomenology. The questions of knowledge and factuality are closely connected in Veber’s philosophy since, pace Veber, knowledge is a kind of, we may say, justified experience the object of which is a factual entity. Hence, if we want to understand what knowledge is, we must face the challenge of comprehending factuality. There are five stages to be noted in the development of his epistemology. The first two belong to his object theory phase, the third to his person phase, the fourth is characterised by his distinguishing and exploring truth and validity with regard to the thought about God, and the basis of the fifth phase lies in his theory of hitting-upon-reality. In Introduction to Philosophy and The System of Philosophy, that is in the year 1921, Veber believed that factuality (“truth,”) was a property of the object, which we do present, but we do not present the factuality of this factuality (that is why he distinguishes between the merely objective truths and truths that are in addition transcendental truths). In 1923, in The Problems of Contemporary Philosophy and in the work Science and Religion, he already rejected such a view. There is something that makes things factual, but that is a complete unknown X. Therefore we cannot even say what kind of an entity this factuality is. Some people would probably demand the following formulation: if X is an ultimate mystery, we should not claim even that it is an entity. In The Problems of Presentation Production (1928) Veber claimed that factuality is not a property since this would lead to a regressum ad infinitum. Philosophy (1930) related internally correct experience to personal will. In The Book about God (1934) he developed the thesis that factuality depends on the act of God. In The Question of Reality (1939) he importantly modified, developed and enriched the thesis that we do not present reality with his theory of immediate experience of (hitting upon) factuality.     

Game and decision theory in mathematics education: epistemological, cognitive and didactical perspectives

In the 1950s, game and decision theoretic modeling emerged—based on applications in the social sciences—both as a domain of mathematics and interdisciplinary fields. Mathematics educators, such as Hans Georg Steiner, utilized game theoretical modeling to demonstrate processes of mathematization of real world situations that required only elementary intuitive understanding of sets and operations. When dealing with n-person games or voting bodies, even students of the 11th and 12th grade became involved in what Steiner called the evolution of mathematics from situations, building of mathematical models of given realities, mathematization, local organization and axiomatization. Thus, the students could participate in processes of epistemological evolutions in the small scale. This paper introduces and discusses the epistemological, cognitive and didactical aspects of the process and the roles these activities can play in the learning and understanding of mathematics and mathematical modeling. It is suggested that a project oriented study of game and decision theory can develop situational literacy, which can be of interest for both mathematics education and general education.     

Stability Concepts in Topological Dynamics by Nonstandard Methods

It is known that it is not possible to introduce C⁰ -structural stability for whole systems in topological dynamics. Using the methods of Nonstandard Analysis, we suggest four different purely topological stability concepts for dynamical systems on compact subsets of Rⁿ. Classically these amount to considering the space of all systems on a given subset of Rⁿ as the fundamental entity when deforming a continuous system (instead of the space of all continuous systems as is normally done in topological dynamics). For two of the introduced stability concepts, we will show that all minimal flows are stable in this sense. Besides this, we will show that one of our stability concepts is related to what is called the pseudo orbit tracing property in a recently published book by Aoki and Hiraide and compare some of our results to the theory of dynamical systems as presented there.     

Dragging in a Dynamic Geometry Environment Through the Lens of Variation

What makes Dynamic Geometry Environment (DGE) a powerful mathematical knowledge acquisition microworld is its ability to visually make explicit the implicit dynamism of thinking about mathematical geometrical concepts. One of DGE’s powers is to equip us with the ability to retain the background of a geometrical configuration while we can selectively bring to the fore dynamically those parts of the whole configuration that interest us. That is, we can visually study the variation of an aspect of a DGE figure while keeping other aspects constant, hence anticipating the emergence of invariant patterns. The aim of this paper is to expound the epistemic value of variation of the Dragging tool in DGE in mathematical discovery. Functions of variation (contrast, separation, generalization, fusion) proposed in Marton’s theory of learning and awareness will be used as a framework to develop a discernment structure which can act as a lens to organize and interpret dragging explorations in DGE. Such a lens focuses very strongly on mathematical aspects of dragging in DGE and is used to re-interpret known dragging modalities (e.g., Arzarello et al.) in a potentially more mathematically-relevant way. The exposition will centre about a specific geometrical problem in which two dragging trajectories are mapped out, consequently resulting in a DGE theorem and a visual theorem. In doing so, a new spectral dragging strategy will be introduced that literally allows one to see the drag mode in action. A model for the lens of variation in the form of a discernment nest structure is proposed as a meta-tool to interpret dragging experiences or as a meta-language to relate different dragging analyses which consequently might give rise to pedagogical and epistemological implications.     

Qualitative criteria of admissibility for enforced agreements

It is desirable that artificial agents can help each other when they cannot achieve their goals, or when they profit from social exchanges. In this work we study coalition formation processes supported by enforced agreements and we define two qualitative criteria, the do-ut-des property and the composition property, that establish when a coalition is admissible to be formed. The do-ut-des property is based on a balance between the advantages and the burdens of an agent, when it agrees an enforced agreements. The composition property is a refinement of the do-ut-des property that takes into account also the costs and the risks deriving from the coalition formation process. Two relevant aspects distinguish our approach from the solution criteria developed in cooperative game theory. First, the do-ut-des property and the composition property are not based on an explicit utility function associated to the goals of an agent, and hance they can be used also in that cases in which the importance that agents give to their own goals is unknown. Second, a coalition has all the necessary information to establish if it satisfies the do-ut-des property or the composition property, therefore these two properties can be used in the case not all the space of possible coalitions is known. Luigi Sauro graduated in Physics at the University “Federico II” of Naples in 2001. From February 2002 to July 2002 he was collaborator at the SRA division of the IRST Institute (Trento). He got is Ph.D. in Computer Science from University of Torino in February 2006. Currently he is member of the Natural Language Processing and Agents Group, directed by prof. Leonardo Lesmo. His research interests include social reasoning, coalition formation and coordination in multiagent systems.     

Halfway to Infinity: Systems Theorizing for the Practitioners?

Systems theory is seen as stressing the rational mind (what we think about) to the detriment of the transactional mind (which we use day-to-day). This stress can be harmful to practitioners who must work in practical, transactional worlds. Rather than attempting to be infinitely rational, we propose a position halfway to infinity-rational and transactional combined.Much of systems theory is pleasing to hear and difficult to contradict. Much of the theory is about design of systems, but it is in the often non-rational process of implementation that the real system emerges. Also the theory tells us about systems but not how to identify the `correct' system that our O.R. efforts are impacting. The theory also tells about complexity, but the tools presented for handling it do not seem related to the theory.The halfway position is to build a body of contingent theory from reflection on experience, using systems theory as a framework for thinking rather than a guide for action.     

On the boundedness of outer polyhedral estimates for reachable sets of linear systems

New properties of outer polyhedral (parallelepipedal) estimates for reachable sets of linear differential systems are studied. For systems with a stable matrix, it is determined what the orientation matrices are for which the estimates possessing the generalized semigroup property are bounded/unbounded on an infinite time interval. In particular, criteria are found (formulated in terms of the eigenvalues of the system’s matrix and the properties of bounding sets) that guarantee for previously mentioned tangent estimates and estimates with a constant orientation matrix that either there are initial orientation matrices for which the corresponding estimate tubes are bounded or all these tubes are unbounded. For linear stationary systems, a system of ordinary differential equations and algebraic relations is derived that determines estimates with constant orientation matrices for reachable sets that have no generalized semigroup property but are tangent and also bounded if the matrix of the system is stable.