Problem decomposability as a factor in complexity of the dimensional change card sort task

According to cognitive complexity and control (CCC) theory complexity depends on number of levels of a hierarchy of rules. According to relational complexity (RC) theory complexity is a function of the number of related variables in the task, and the most difficult tasks are those in which there is a constraint on decomposition into simpler subtasks. One hundred and twenty, 3–6-year old children were tested on the standard dimensional change card sort (DCCS) task, or a modified version, the DecompDCCS, in which the dimensions could be decomposed into subtasks. The standard version requires two levels of a hierarchy to be processed, and is ternary relational according to RC theory, whereas the subtasks of the DecompDCCS are binary relational. The DecompDCCS was easier than the DCCS for 3–4 year-olds, but all 5–6 year-olds succeeded on both. The results indicate that decomposability into simpler subtasks, as suggested by RC theory, is a factor in difficulty of DCCS. The role of decomposability in other tasks that are persistently difficult for young children is discussed.     

On Interpreting Chaitin's Incompleteness Theorem

The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin's famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be good measure of the strength of the theory.I exhibit certain strong counterexamples and establish conclusively that the received view is false. Moreover, I show that the limiting constants provided by the theorem do not in any way reflect the power of formalized theories, but that the values of these constants are actually determined by the chosen coding of Turing machines, and are thus quite accidental.     

顿悟问题解决过程中抑制解除理论有效性的实验研究

本研究以Puzzle任务为材料,对135名高二学生特定线索下的操作水平进行测查,结果表明：（1）表征的抑制解除理论对顿悟问题解决的机制具有一定的解释效力,表现为总体上经历了高操作失败次数的被试在线索敏感性上明显高于未经历操作失败次数的被试。（2）而被试在特定阶段的操作水平未出现朝向解决目标的线性增长而是出现停滞的现象证明了问题的表征复杂性对抑制解除的过程存在制约作用,使其宏观上表现为渐进-停滞-跃升的变化模式。     

Information‐Theoretic Measures Predict the Human Judgment of Rhythm Complexity

To formalize the human judgment of rhythm complexity, we used five measures from information theory and algorithmic complexity to measure the complexity of 48 artificially generated rhythmic sequences. We compared these measurements to human prediction accuracy and easiness judgments obtained from a listening experiment, in which 32 participants guessed the last beat of each sequence. We also investigated the modulating effects of musical expertise and general pattern identification ability. Entropy rate and Kolmogorov complexity were correlated with prediction accuracy, and highly correlated with easiness judgments. A logistic regression showed main effects of musical training, entropy rate, and Kolmogorov complexity, and an interaction between musical training and both entropy rate and Kolmogorov complexity. These results indicate that information‐theoretic concepts capture some salient features of the human judgment of rhythm complexity, and they confirm the influence of musical expertise on complexity judgments.     

LÉVY HIERARCHY IN WEAK SET THEORIES

We investigate the interactions of formula complexity in weak set theories with the axioms available there. In particular, we show that swapping bounded and unbounded quantification preserves formula complexity in presence of the axiom of foundation weakened to an arbitrary set base, while it does not if the axiom of foundation is further weakened to a proper class base. More attention is being paid to the necessary axioms employed in the positive results, than to the combinatorial strength of the positive results themselves.     

社会认知复杂性的量化指标及其关系

在Kelly个人构念理论的基础上,Bieri提出用构念的分化程度衡量个体社会认知复杂性的思路,并具体用从不同构念上评价每个角色时评分的匹配个数作为复杂性的最化指标。此后,研究者从不同分析思路提出了一系列新的复杂性指标,如根据对构念的相关分析所得组内相关、RMS、SMC等,基于因素分析所得第一因素解释率、主要因素个数及其解释率等,冲突分析所得整体冲突百分比,此外还有MPP、LPP、ASO等各种Fiedler分数。本研究以402名初中一二年级青少年为被试。采用库格测验收集数据,以Gridstat4．0、Excel、SPSSl0．0等软件统计数据,分析了上述各种复杂性指标的内在关联,为同类研究选择使用这些指标提供了依据。     

Representations of Complexity: How Nature Appears in Our Theories

In science we study processes in the material world. The way these processes operate can be discovered by conducting experiments that activate them, and findings from such experiments can lead to functional complexity theories of how the material processes work. The results of a good functional theory will agree with experimental measurements, but the theory may not incorporate in its algorithmic workings a representation of the material processes themselves. Nevertheless, the algorithmic operation of a good functional theory may be said to make contact with material reality by incorporating the emergent computations the material processes carry out. These points are illustrated in the experimental analysis of behavior by considering an evolutionary theory of behavior dynamics, the algorithmic operation of which does not correspond to material features of the physical world, but the functional output of which agrees quantitatively and qualitatively with findings from a large body of research with live organisms.     

复杂性理论及其问题

Complexity theories are on the way to establish a new worldview—processes instead of objects, history and uniqueness of everything instead of repetition and lawlikeness are the elements. These theories from deterministic chaos via the dissipative structures, the theory of catastrophes, self organization and synergetics are mathematical models, connected with a new understanding of science. They are characterized by new fundamental commitments of sciences. But at the same time, they are characterized by epistemic boundaries. During my stay as a visiting professor at Dalian University of Technology in September 2006, I had the opportunity to deliver parts of this paper at North-Eastern University at Shenyang and at Beijing Normal University; a first draft has been presented at the IV. Russian Congress of Philosophy, May 2005, Moscow, and published as congress material as Knowledge and Society, edited by Ilya Kassavine, Moscow: Kanon 2005, 178–189.     

The Humanizing Brain: An Introduction

The rediscovery of the sacred needs to take into account the neural underpinnings of faith and meaning and also draw on the insights of the emerging discipline of complexity studies, which explore a tendency toward adaptive self-organization that seemingly is inherent in the universe. Both neuroscience and complexity studies contribute to our understanding of the brain's activity as it transforms raw stimuli into recognizable patterns, and thus "humanizes" all our perceptions and understandings. The brain is our physical anchor in the natural environment— and its human capacities orbit us into the emerging world of culture (including religion), which provides a template for the brain's function of making sense of an ambiguous reality. The humanizing brain holds together scientific causality and religious meaning, working both bottom-up (linking the physical and the experiential) and top-down (beginning with the whole of things, or God). These processes we know as "mind" (experienced as intentionality, subjective consciousness, empathy, imagination, memory, adaptability). We maintain that such processes are not only subjective but built into "the way things really are." Thus, they carry the most privileged information about the nature of reality to which we human beings have access. For not only are we humans observers and logicians, but we are embedded in the larger reality; and as we strive to make sense of it all, we become both Homo sapiens and Homo religiosus .     

认知复杂性与意识水平:Zelazo理论述评

Zelazo等人提出的认知复杂性和控制理论、意识水平模型认为可在问题解决框架内理解执行功能,且执行功能的变化可根据儿童形成和使用的最大规则复杂性的变化来描述,而规则复杂性的变化可根据儿童意识水平的变化来解释。Zelazo的理论提出后受到不少研究者的关注,但也存在一些问题和不足。     

Multiple routes to mind wandering: Predicting mind wandering with resource theories

Three experiments examine individual (attentional capacity) and task-related characteristics leading to mind wandering, and the effect of mind wandering on task performance. Drawing on resource theories, we tested interactive nonlinear effects of these predictors, manipulating task demand using math tests of varying difficulty (Exp 1: N = 143, three levels between-subjects; Exp 2: N = 59, three levels within-subjects; Exp 3: N = 133, four levels within-subjects). Results confirmed that mind wandering was most frequent during extreme task demand levels, although the effect varied somewhat between experiments. Additionally, results from Experiment 3 and an integrated analysis demonstrated that people with relatively higher attentional capacity were less likely to mind wander as task demand increased. Moreover, mind wandering was more detrimental to performance as task demand increased across all experiments. Our findings build on past research by demonstrating the importance of accounting for interactions and nonlinear effects of task demand and attentional capacity in mind wandering research.     

Abstract: Scenario Planning,Art or Science?

This article will argue that there is a science of scenario planning; or at least a logos, a logic, a scenariology. Scenario planning is not predictive. But a good set of scenarios, scientifically developed, can reliably and predictably change minds. Scenario planning is both art and science. In joining the club of the sciences, scenario planning calls for a new kind of membership, or a new kind of science, one that, following Stuart Kauffman, relies on the importance of story. Hegel tells us that all stories, all narratives include a conflict between desire and the law, intention, and necessity. Scenarios provide a way for communities to frame their intentions. They thereby effect “downward causality” on the present in order to project the present toward a preferred future. In fulfilling the promise of this new kind of science, scenario planning breaks with positivistic science, but without falling into a postmodern nihilism. Without setting out to do so, the discipline of scenario planning introduces us to a new epistemology, a new way of knowing the truth. Drawing on pragmatism, Wittgenstein, and Richard Rorty, this article reaches the conclusion that, for scenario planners, the future replaces objectivity as the horizon for justification. What is true? We'll see.     

The influence of relational complexity and strategy selection on children's reasoning in the Latin Square Task

The present study focused on children's deductive reasoning when performing the Latin Square Task, an experimental task designed to explore the influence of relational complexity. Building on Birney, Halford, and Andrew's (2006) research, we created a version of the task that minimized nonrelational factors and introduced new categories of items. The results of two experiments conducted with school-aged children yielded an apparent dilution of complexity effects and suggest that specific inferential strategies can reduce the relational complexity that children need to process. A theoretical account is proposed emphasizing the influence of adaptive selection of strategies that mediate processing capacity constraints in reasoning development.     

应用复杂科学理论对穴位进行实验研究和定量计算

近年来,一些研究者根据复杂性科学理论研究的最新成果,对穴位的复杂性进行了实验研究和分析计算.就有关复杂科学对穴位的研究进行了概述和讨论,并认为研究穴位的本质可采用复杂性科学方法.     

Deterministic Chaos and Computational Complexity: the Case of Methodological Complexity Reductions

Some problems rarely discussed in traditional philosophy of science are mentioned: The empirical sciences using mathematico-quantitative theoretical models are frequently confronted with several types of computational problems posing primarily methodological limitations on explanatory and prognostic matters. Such limitations may arise from the appearances of deterministic chaos and (too) high computational complexity in general. In many cases, however, scientists circumvent such limitations by utilizing reductional approximations or complexity reductions for intractable problem formulations, thus constructing new models which are computationally tractable. Such activities are compared with reduction types (more) established in philosophy of science. This revised version was published online in August 2006 with corrections to the Cover Date.     

10～12岁儿童在平衡秤任务上的规则使用及其复杂性

以256名10～12岁儿童为被试,采取规则评估方法探讨了儿童在平衡秤任务上的规则使用类型及其年龄特点,并尝试使用认知复杂性和控制理论对此加以分析和解释.结果表明:(1)除了Siegler所谓的四种规则和补偿规则以外,儿童还使用了规则ⅢA和距离规则,其中规则ⅢA并不特指单一的规则,而是代表儿童在掌握了规则Ⅲ之后向更高级的规则Ⅳ发展的不稳定期和过渡期;(2)10～12岁儿童中使用规则Ⅲ的人数显著多于使用补偿规则的人数,对此认知复杂性和控制理论能够提供较好的解释;(3)规则Ⅰ仍是10～12岁儿童使用的主要规则,并非Siegler认为的主要是4、5岁儿童使用此规则.     

个体认知方式与材料复杂性对视空间工作记忆的影响

采用计算机呈现的Corsi积木点击任务,探讨了不同认知方式个体对材料的路径、结构和数量复杂性不同的视空间工作记忆的广度。研究结果表明：（1）场独立性认知方式是影响视空间工作记忆广度的一个重要的个别差异变量,在路径复杂或呈现的材料结构随机的条件下,场独立者的视空间工作记忆广度明显高于场依存者;（2）材料呈现的路径、数量是影响视空间记忆广度的重要因素,在路径简单或数量少的情况下被试的视空间记忆广度要明显得高     

Canada 2001: Alternative futures for the Canadian communities

The global “problématique humaine” is described in terms of the “grand issues” of population, resources, development in the rich and poor countries, and the environment. Three competing paradigms about the future and their implications for the Canadian communities are examined, and a model is offered showing interrelationships between the different Canadian communities, organizational levels, and various societal/environmental activities. A comprehensive programme of future‐oriented studies is proposed.

This article is a shortened version of a monograph to appear as one of a series entitled Queen's Studies of the Future of the Canadian Communities, published by the Institute of Intergovernmental Relations, Queen's University, Kingston, Ontario. The research was funded by the Donner Canadian Foundation.