Theory of mind and relational complexity

Cognitive complexity and control theory and relational complexity theory attribute developmental changes in theory of mind (TOM) to complexity. In 3 studies, 3-, 4-, and 5-year-olds performed TOM tasks (false belief, appearance-reality), less complex connections (Level 1 perspective-taking) tasks, and transformations tasks (understanding the effects of location changes and colored filters) with content similar to TOM. There were also predictor tasks at binary-relational and ternary-relational complexity levels, with different content. Consistent with complexity theories: (a) connections and transformations were easier and mastered earlier than TOM; (b) predictor tasks accounted for more than 80% of age-related variance in TOM; and (c) ternary-relational items accounted for TOM variance, before and after controlling for age and binary-relational items. Prediction did not require hierarchically structured predictor tasks.

An analysis of relational complexity in an air traffic control conflict detection task

Theoretical analyses of air traffic complexity were carried out using the Method for the Analysis of Relational Complexity. Twenty-two air traffic controllers examined static air traffic displays and were required to detect and resolve conflicts. Objective measures of performance included conflict detection time and accuracy. Subjective perceptions of mental workload were assessed by a complexity-sorting task and subjective ratings of the difficulty of different aspects of the task. A metric quantifying the complexity of pair-wise relations among aircraft was able to account for a substantial portion of the variance in the perceived complexity and difficulty of conflict detection problems, as well as reaction time. Other variables that influenced performance included the mean minimum separation between aircraft pairs and the amount of time that aircraft spent in conflict.

Relational time for systems of oscillators

Using an elementary example based on two simple harmonic oscillators, we show how a relational time may be defined that leads to an approximate Schrodinger dynamics for subsystems, with corrections leading to an intrinsic decoherence in the energy eigenstates of the subsystem.

Toy model for a relational formulation of quantum theory

In the absence of an external frame of reference-i.e., in background independent theories such as general relativity-physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is twofold. First, we demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental. Second, we describe how the original non-relational theory approximately emerges from the fully relational theory when reference systems become semi-classical. Our technique is motivated by a Bayesian approach to quantum mechanics, and relies on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, our model circumvents the problem of the collapse of the wave packet as the probability interpretation is only ever applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of spin networks introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semiclassical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.

Developing relational navigation to effectively understand software

Effective comprehension of complex software systems requires understanding of both the individual documents that represent software and the complex relationships that exist within and between documents. Relationships of all kinds play a vital role in a software engineer's comprehension of, and navigation within and between, software documents. User-determined relationships have the additional role of enabling the engineer to create and maintain relational documentation that cannot be generated by tools or derived from other relationships. We argue that for a software development environment to effectively support the understanding of complex software systems, relational navigation must be supported at both the document-focused (intra-document) and relation-focused (inter-document) levels. The need for a relation-focused approach is highlighted by an evaluation of an existing document-focused relational interface. We conclude with the requirements for a relation-focused approach to relational navigation. These requirements focus on the user's perspective when interacting with a collection of related documents. We define the requirements for a software development environment that effectively supports the understanding of the software documents and relationships that define a complex software system.