Informational Branching Universe

This paper suggests an epistemic interpretation of Belnap’s branching space-times theory based on Everett’s relative state formulation of the measurement operation in quantum mechanics. The informational branching models of the universe are evolving structures defined from a partial ordering relation on the set of memory states of the impersonal observer. The totally ordered set of their information contents defines a linear “time” scale to which the decoherent alternative histories of the informational universe can be referred—which is quite necessary for assigning them a probability distribution. The “historical” state of a physical system is represented in an appropriate extended Hilbert space and an algebra of multi-branch operators is developed. An age operator computes the informational depth of historical states and its standard deviation can be used to provide a universal information/energy uncertainty relation. An information operator computes the encoding complexity of historical states, the rate of change of its average value accounting for the process of correlation destruction inherent to the branching dynamics. In the informational branching models of the universe, the asymmetry of phenomena in nature appears as a mere consequence of the subject’s activity of measuring, which defines the flow of time-information.     

Quantum Particles as Conceptual Entities: A Possible Explanatory Framework for Quantum Theory

We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum particles interact with ordinary matter, nuclei, atoms, molecules, macroscopic material entities, measuring apparatuses,  in a similar way to how human concepts interact with memory structures, human minds or artificial memories. We analyze the most characteristic aspects of quantum theory, i.e. entanglement and non-locality, interference and superposition, identity and individuality in the light of this new interpretation, and we put forward a specific explanation and understanding of these aspects. The basic hypothesis of our framework gives rise in a natural way to a Heisenberg uncertainty principle which introduces an understanding of the general situation of ‘the one and the many’ in quantum physics. A specific view on macro and micro different from the common one follows from the basic hypothesis and leads to an analysis of Schrödinger’s Cat paradox and the measurement problem different from the existing ones. We reflect about the influence of this new quantum interpretation and explanatory framework on the global nature and evolutionary aspects of the world and human worldviews, and point out potential explanations for specific situations, such as the generation problem in particle physics, the confinement of quarks and the existence of dark matter.     

Philosophical Issues and their Implications for the Systems Architect

Many system architects select their system methodologies without explicit consideration of the philosophical perspectives that impact their decisions. This paper describes how the concepts of ontology and epistemology apply in systems science. Ontology is how we specify terms of reference for existence, allowing us to understand the theory of existence via an ‘existence framework’. Epistemology, the theory of knowledge, allows us to explore new models and theories of knowledge acquisition so the best system-based methodologies can be deployed to solve complex system problems. After introducing these concepts, the paper presents system science issues and assesses the impact of ontological, axiological and epistemological perspectives on system methodology selection, research, system design and deployment. An ontological viewpoint such as realism, as an objective view is contrasted versus nationalism, a personal perceptional view. An epistemological viewpoint is explored comparing knowledge as a product of sensory perception or rational reflection. The paper’s significant contribution is that it helps system architects understand that their philosophical views of systems science impact their system methodology choices.     

The Issue of “Closure” in Jagers op Akkerhuis’s Operator Theory

Attempts to define life should focus on the transition from molecules to cells and the “closure” aspects of this event. Rather than classifying existing objects into living and non-living entities I believe the challenge is to understand how the transition from non-life to life can take place, that is, the how the closure in Jagers op Akkerhuis’s hierarchical classification of operators, comes about.     

Symmetries and Symmetry-Breakings: The Fabric of Physical Interactions and the Flow of Time

This short note develops some ideas along the lines of the stimulating paper by Heylighen (Found Sci 15 4(3):345–356, 2010a). It summarizes a theme in several writings with Francis Bailly, downloadable from this author’s web page. The “geometrization” of time and causality is the common ground of the analysis hinted here and in Heylighen’s paper. Heylighen adds a logical notion, consistency, in order to understand a possible origin of the selective process that may have originated this organization of natural phenomena. We will join our perspectives by hinting to some gnoseological complexes, common to mathematics and physics, which may shed light on the issues raised by Heylighen.     

The Constructive Realist Account of Science and Its Application to Ilya Prigogine’s Conception of Laws of Nature

Sciences are often regarded as providing the best, or, ideally, exact, knowledge of the world, especially in providing laws of nature. Ilya Prigogine, who was awarded the Nobel Prize for his theory of non-equilibrium chemical processes—this being also an important attempt to bridge the gap between exact and non-exact sciences [mentioned in the Presentation Speech by Professor Stig Claesson (nobelprize.org, The Nobel Prize in Chemistry 1977)]—has had this ideal in mind when trying to formulate a new kind of science. Philosophers of science distinguish theory and reality, examining relations between these two. Nancy Cartwright’s distinction of fundamental and phenomenological laws, Rein Vihalemm’s conception of the peculiarity of the exact sciences, and Ronald Giere’s account of models in science and science as a set of models are deployed in this article to criticise the common view of science and analyse Ilya Prigogine’s view in particular. We will conclude that on a more abstract, philosophical level, Prigogine’s understanding of science doesn’t differ from the common understanding.

Coherence of Our Best Scientific Theories

Putnam in Realism in mathematics and Elsewhere, Cambridge University Press, Cambridge (1975) infers from the success of a scientific theory to its approximate truth and the reference of its key term. Laudan in Philos Sci 49:19–49 (1981) objects that some past theories were successful, and yet their key terms did not refer, so they were not even approximately true. Kitcher in The advancement of science, Oxford University Press, New York (1993) replies that the past theories are approximately true because their working posits are true, although their idle posits are false. In contrast, I argue that successful theories which cohere with each other are approximately true, and that their key terms refer. My position is immune to Laudan’s counterexamples to Putnam’s inference and yields a solution to a problem with Kitcher’s position.     

On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions

We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely related to the definition in BISH of ‘locally compact’. Possible approaches to this problem are discussed. Topology seems to be a key to understanding many issues. We offer several new simplifying axioms, which can form bridges between the various branches of constructive mathematics and classical mathematics (‘reuniting the antipodes’). We give a simplification of basic intuitionistic theory, especially with regard to so-called ‘bar induction’. We then plead for a limited number of axiomatic systems, which differentiate between the various branches of mathematics. Finally, in the appendix we offer BISH an elegant topological definition of ‘locally compact’, which unlike the current definition is equivalent to the usual classical and/or intuitionistic definition in classical and intuitionistic mathematics, respectively.     

Development (and Evolution) of the Universe

I distinguish Nature from the World. I also distinguish development from evolution. Development is progressive change and can be modeled as part of Nature, using a specification hierarchy. I have proposed a ‘canonical developmental trajectory’ of dissipative structures with the stages defined thermodynamically and informationally. I consider some thermodynamic aspects of the Big Bang, leading to a proposal for reviving final cause. This model imposes a ‘hylozooic’ kind of interpretation upon Nature, as all emergent features at higher levels would have been vaguely and episodically present primitively in the lower integrative levels, and were stabilized materially with the developmental emergence of new levels. The specification hierarchy’s form is that of a tree, with its trunk in its lowest level, and so this hierarchy is appropriate for modeling an expanding system like the Universe. It is consistent with this model of differentiation during Big Bang development to view emerging branch tips as having been entrained by multiple finalities because of the top-down integration of the various levels of organization by the higher levels.     

Intelligent Choice of the Number of Clusters in K-Means Clustering: An Experimental Study with Different Cluster Spreads

The issue of determining “the right number of clusters” in K-Means has attracted considerable interest, especially in the recent years. Cluster intermix appears to be a factor most affecting the clustering results. This paper proposes an experimental setting for comparison of different approaches at data generated from Gaussian clusters with the controlled parameters of between- and within-cluster spread to model cluster intermix. The setting allows for evaluating the centroid recovery on par with conventional evaluation of the cluster recovery. The subjects of our interest are two versions of the “intelligent” K-Means method, ik-Means, that find the “right” number of clusters by extracting “anomalous patterns” from the data one-by-one. We compare them with seven other methods, including Hartigan’s rule, averaged Silhouette width and Gap statistic, under different between- and within-cluster spread-shape conditions. There are several consistent patterns in the results of our experiments, such as that the right K is reproduced best by Hartigan’s rule – but not clusters or their centroids. This leads us to propose an adjusted version of iK-Means, which performs well in the current experiment setting.     

同构实在论与模型认识论——为罗素的结构实在论辩护

在科学实在论和反实在论的长期的反复的哲学争论中,二十世纪初创建的结构实在论(Structur-alrealism)的学说,最近已成为"科学实在论最有辩护力的形式"(〔1〕,p.1),且"近年来重新进入科学哲学的主流"(〔2〕,p.151)。结构实在论被公认的创始人是著名哲学家罗素。他认为客观事物,特别是不可观察的客体的内部性质是不可认识的,但它的结构可以通过同构关系被人们的感性经验和科学模型认识。本文作者对事物的内部性质不可知持一种保留态度,但对他的通过同构关系认识物质世界的结构持一种赞成的态度,并依罗素的主张将这个观点称为同构实在论,从现象世界与客观世界的同构关系,同态对应在科学理论的模型中的作用和通过建模认识世界的模型这三个方面为罗素的同构实在论和由此决定的认识论辩护,并将它改进为同态实在论,以便更好地说明模型的认识论。     

The Foundational Role of Ergodic Theory

The foundation of statistical mechanics and the explanation of the success of its methods rest on the fact that the theoretical values of physical quantities (phase averages) may be compared with the results of experimental measurements (infinite time averages). In the 1930s, this problem, called the ergodic problem, was dealt with by ergodic theory that tried to resolve the problem by making reference above all to considerations of a dynamic nature. In the present paper, this solution will be analyzed first, highlighting the fact that its very general nature does not duly consider the specificities of the systems of statistical mechanics. Second, Khinchin’s approach will be presented, that starting with more specific assumptions about the nature of systems, achieves an asymptotic version of the result obtained with ergodic theory. Third, the statistical meaning of Khinchin’s approach will be analyzed and a comparison between this and the point of view of ergodic theory is proposed. It will be demonstrated that the difference consists principally of two different perspectives on the ergodic problem: that of ergodic theory puts the state of equilibrium at the center, while Khinchin’s attempts to generalize the result to non-equilibrium states.     

On the Equivalence of Cohen’s Kappa and the Hubert-Arabie Adjusted Rand Index

It is shown that one can calculate the Hubert-Arabie adjusted Rand index by first forming the fourfold contingency table counting the number of pairs of objects that were placed in the same cluster in both partitions, in the same cluster in one partition but in different clusters in the other partition, and in different clusters in both, and then computing Cohen’s κ on this fourfold table. The author thanks Willem Heiser, Mark de Rooij, Marian Hickendorff and three anonymous reviewers for their helpful comments and valuable suggestions on earlier versions of this article. Published online xx, xx, xxxx.     

Towards a Hierarchical Definition of Life,the Organism,and Death

Despite hundreds of definitions, no consensus exists on a definition of life or on the closely related and problematic definitions of the organism and death. These problems retard practical and theoretical development in, for example, exobiology, artificial life, biology and evolution. This paper suggests improving this situation by basing definitions on a theory of a generalized particle hierarchy. This theory uses the common denominator of the “operator” for a unified ranking of both particles and organisms, from elementary particles to animals with brains. Accordingly, this ranking is called “the operator hierarchy”. This hierarchy allows life to be defined as: matter with the configuration of an operator, and that possesses a complexity equal to, or even higher than the cellular operator. Living is then synonymous with the dynamics of such operators and the word organism refers to a select group of operators that fit the definition of life. The minimum condition defining an organism is its existence as an operator, construction thus being more essential than metabolism, growth or reproduction. In the operator hierarchy, every organism is associated with a specific closure, for example, the nucleus in eukaryotes. This allows death to be defined as: the state in which an organism has lost its closure following irreversible deterioration of its organization. The generality of the operator hierarchy also offers a context to discuss “life as we do not know it”. The paper ends with testing the definition’s practical value with a range of examples.     

Comparison tests for dendrograms: A comparative evaluation

Classifications are generally pictured in the form of hierarchical trees, also called dendrograms. A dendrogram is the graphical representation of an ultrametric (=cophenetic) matrix; so dendrograms can be compared to one another by comparing their cophenetic matrices. Three methods used in testing the correlation between matrices corresponding to dendrograms are evaluated. The three permutational procedures make use of different aspects of the information to compare dendrograms: the Mantel procedure permutes label positions only; the binary tree methods randomize the topology as well; the double-permutation procedure is based on all the information included in a dendrogram, that is: topology, label positions, and cluster heights. Theoretical and empirical investigations of these methods are carried out to evaluate their relative performance. Simulations show that the Mantel test is too conservative when applied to the comparison of dendrograms; the methods of binary tree comparisons do slightly better; only the doublepermutation test provides unbiased type I error. Les arbres utilisés pour illustrés les groupements sont généralement représentés sous la forme de classifications hiérarchiques ou dendrogrammes. Un dendrogramme représente graphiquement l’information contenue dans la matrice ultramétrique (=cophénétique) correspondant à la classification. Dès ultramétriques correspondantes. Nous comparons trois méthodes permettant d’évaluer la signification statistique du coefficient de correlation mesuré entre deux matrices ultramétriques. Ces trois tests par permutations tiennent compte d’aspects différents pour comparer des dendrogrammes: le test de Mantel permute les feuilles de l’arbre, les méthodes pour arbres binaires permutent les feuilles et la topologie, alors que la procédure à double permutation permute les feuilles, la topologie et les niveaux de fusion des dendrogrammes comparés. L’efficacité relative des trois méthodes est évaluée empiriquement et théoriquement. Nos résultats suggèrent l’utilisation préférentielle du test à double permutation pour la comparaison de dendrogrammes: le test de Mantel s’avère trop conservateur, tandis que les méthodes pour arbres binaires ne sont pas toujours adéquates.

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This work was supported by NSERC grant no. A7738 to Pierre Legendre and by a NSERC scholarship to F.-J. Lapointe.     

Understanding Pluralism in Climate Modeling

To study Earth’s climate, scientists now use a variety of computer simulation models. These models disagree in some of their assumptions about the climate system, yet they are used together as complementary resources for investigating future climatic change. This paper examines and defends this use of incompatible models. I argue that climate model pluralism results both from uncertainty concerning how to best represent the climate system and from difficulties faced in evaluating the relative merits of complex models. I describe how incompatible climate models are used together in ‘multi-model ensembles’ and explain why this practice is reasonable, given scientists’ inability to identify a ‘best’ model for predicting future climate. Finally, I characterize climate model pluralism as involving both an ontic competitive pluralism and a pragmatic integrative pluralism.     

<Emphasis Type="Italic">k</Emphasis>-Adic Similarity Coefficients for Binary (Presence/Absence) Data

k-Adic formulations (for groups of objects of size k) of a variety of 2-adic similarity coefficients (for pairs of objects) for binary (presence/absence) data are presented. The formulations are not functions of 2-adic similarity coefficients. Instead, the main objective of the the paper is to present k-adic formulations that reflect certain basic characteristics of, and have a similar interpretation as, their 2-adic versions. Two major classes are distinguished. The first class is referred to as Bennani-Heiser similarity coefficients, which contains all coefficients that can be defined using just the matches, the number of attributes that are present and that are absent in k objects, and the total number of attributes. The coefficients in the second class can be formulated as functions of Dice’s association indices. The author thanks Willem Heiser and three anonymous reviewers for their helpful comments and valuable suggestions on earlier versions of this article.     

The Arrow of Time and Meaning

All the attempts to find the justification of the privileged evolution of phenomena exclusively in the external world need to refer to the inescapable fact that we are living in such an asymmetric universe. This leads us to look for the origin of the “arrow of time” in the relationship between the subject and the world. The anthropic argument shows that the arrow of time is the condition of the possibility of emergence and maintenance of life in the universe. Moreover, according to Bohr’s, Poincaré’s and Watanabe’s analysis, this agreement between the earlier-later direction of entropy increase and the past-future direction of life is the very condition of the possibility for meaningful action, representation and creation. Beyond this relationship of logical necessity between the meaning process and the arrow of time the question of their possible physical connection is explored. To answer affirmatively to this question, the meaning process is modelled as an evolving tree-like structure, called “Semantic Time”, where thermodynamic irreversibility can be shown. Time is the substance I am made of. Time is a river which sweeps me along, but I am the river ; it is a tiger which destroys me, but I am the tiger ; it is a fire which consumes me, but I am the fire. – (Jorge Luis Borges)