The Internal and External Problems of String Theory: A Philosophical View

String theory is at the moment the only advanced approach to a unification of all interactions, including gravity. But, in spite of the more than 30 years of its existence, it does not make any empirically testable predictions, and it is completely unknown which physically interpretable principles could form the basis of string theory. At the moment, “string theory” is no theory at all, but rather a labyrinthic structure of mathematical procedures and intuitions. The only motivations for string theory consist in the mutual incompatibility of the standard model of quantum field theory and of general relativity as well as in the metaphysics of the unification program of physics, aimed at a final unified theory of all interactions, including gravity. The article gives a perspective on the problems leading to and resulting from this situation.

The conjunction fallacy and interference effects

In the present article we consider the conjunction fallacy, a well known cognitive fallacy experimentally tested in cognitive science, which occurs for intuitive judgments. We show that the quantum formalism can be used to describe, in a very simple way, this fallacy, in terms of interference effect. We provide evidence that the quantum formalism leads quite naturally to violations of the joint probability rule of classic probability when considering the estimated probability of the conjunction of two events. By defining the concept of maximal conjunction error, we find a good agreement with experimental results. Thus we suggest that in cognitive science the formalism of quantum mechanics can be used to describe a quantum regime, where the cognitive fallacies and heuristics are valid.     

Projective expected utility

Motivated by several classic decision-theoretic paradoxes, and by analogies with the paradoxes which in physics motivated the development of quantum mechanics, we introduce a projective generalization of expected utility along the lines of the quantum-mechanical generalization of probability theory. The resulting decision theory accommodates the dominant paradoxes, while retaining significant simplicity and tractability. In particular, every finite game within this larger class of preferences still has an equilibrium.     

Quantum mechanics, interference, and the brain

In this paper we discuss the use of quantum mechanics to model psychological experiments, starting by sharply contrasting the need of these models to use quantum mechanical nonlocality instead of contextuality. We argue that contextuality, in the form of quantum interference, is the only relevant quantum feature used. Nonlocality does not play a role in those models. Since contextuality is also present in classical models, we propose that classical systems be used to reproduce the quantum models used. We also discuss how classical interference in the brain may lead to contextual processes, and what neural mechanisms may account for it.     

Techniques for rotating two or more loading matrices to optimal agreement and simple structure: A comparison and some technical details

Matrices of factor loadings are often rotated to simple structure. When more than one loading matrix is available for the same variables, the loading matrices can be compared after rotating them all (separately) to simple structure. An alternative procedure is to rotate them to optimal agreement, and then compare them. In the present paper techniques are described that combine these two procedures. Specifically, five techniques that combine the ideals of rotation to optimal agreement and rotation to simple structure are compared on the basis of contrived and empirical data. For the contrived data, it is assessed to what extent the rotations recover the underlying common structure. For both the contrived and the empirical data it is studied to what extent the techniques give well matching rotated matrices, to what extent these have a simple structure, and to what extent the most prominent parts of the different loading matrices agree. It was found that the simple procedure of combining a Generalized Procrustes Analysis (GPA) with Varimax on the mean of the matched loading matrices performs very well on all criteria, and, for most purposes, offers an attractive compromise of rotation to agreement and simple structure. In addition to this comparison, some technical improvements are proposed for Bloxom's rotation to simple structure and maximum similarity.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author. The author is obliged to René van der Heijden for assistance in programming the procedures in the simulation study reported in this paper, and to Jos ten Berge, three anonymous reviewers and an associate editor for helpful comments on an earlier version of this paper.     

More on EM for ML factor analysis

We address several issues that are raised by Bentler and Tanaka's [1983] discussion of Rubin and Thayer [1982]. Our conclusions are: standard methods do not completely monitor the possible existence of multiple local maxima; summarizing inferential precision by the standard output based on second derivatives of the log likelihood at a maximum can be inappropriate, even if there exists a unique local maximum; EM and LISREL can be viewed as complementary, albeit not entirely adequate, tools for factor analysis.This work was partially supported by the Program Statistics Research Project at Educational Testing Service.     

Discovery algorithms for hierarchical relations

Two algorithms based on a latent class model are presented for discovering hierarchical relations that exist among a set ofK dichotomous items. The two algorithms, stepwise forward selection and backward elimination, incorporate statistical criteria for selecting (or deleting) 0–1 response pattern vectors to form the subset of the total possible 2 ^k vectors that uniquely describe the hierarchy. The performances of the algorithms are compared, using computer-constructed data, with those of three competing deterministic approaches based on ordering theory and the calculation of Phi/Phi-max coefficients. The discovery algorithms are also demonstrated on real data sets investigated in the literature.     

Quantum sortal predicates

Sortal predicates have been associated with a counting process, which acts as a criterion of identity for the individuals they correctly apply to. We discuss in what sense certain types of predicates suggested by quantum physics deserve the title of ‘sortal’ as well, although they do not characterize either a process of counting or a criterion of identity for the entities that fall under them. We call such predicates ‘quantum-sortal predicates’ and, instead of a process of counting, to them is associated a ‘criterion of cardinality’. After their general characterization, it is discussed how these predicates can be formally described. To Patrick Suppes on his 80th birthday.     

Object‐Label‐Order Effect When Learning From an Inconsistent Source

Learning in natural environments is often characterized by a degree of inconsistency from an input. These inconsistencies occur, for example, when learning from more than one source, or when the presence of environmental noise distorts incoming information; as a result, the task faced by the learner becomes ambiguous. In this study, we investigate how learners handle such situations. We focus on the setting where a learner receives and processes a sequence of utterances to master associations between objects and their labels, where the source is inconsistent by design: It uses both “correct” and “incorrect” object‐label pairings. We hypothesize that depending on the order of presentation, the result of the learning may be different. To this end, we consider two types of symbolic learning procedures: the Object‐Label (OL) and the Label‐Object (LO) process. In the OL process, the learner is first exposed to the object, and then the label. In the LO process, this order is reversed. We perform experiments with human subjects, and also construct a computational model that is based on a nonlinear stochastic reinforcement learning algorithm. It is observed experimentally that OL learners are generally better at processing inconsistent input compared to LO learners. We show that the patterns observed in the learning experiments can be reproduced in the simulations if the model includes (a) an ability to regularize the input (and also to do the opposite, i.e., undermatch) and (b) an ability to take account of implicit negative evidence (i.e., interactions among different objects/labels). The model suggests that while both types of learners utilize implicit negative evidence in a similar way, there is a difference in regularization patterns: OL learners regularize the input, whereas LO learners undermatch. As a result, OL learners are able to form a more consistent system of image‐utterance associations, despite the ambiguous learning task.     

An Optimized Design of Choice Experiments: A New Approach for Studying Decision Behavior in Choice Task Experiments

In this paper, we present a new approach for the optimal experimental design problem of generating diagnostic choice tasks, where the respondent's decision strategy can be unambiguously deduced from the observed choice. In this new approach, we applied a genetic algorithm that creates a one‐to‐one correspondence between a set of predefined decision strategies and the alternatives of the choice task; it also manipulates the characteristics of the choice tasks. In addition, this new approach takes into account the measurement errors that can occur when the preferences of the decision makers are being measured. The proposed genetic algorithm is capable of generating diagnostic choice tasks even when the search space of possible choice tasks is very large. As proof‐of‐concept, we used this novel approach to generate respondent‐specific choice tasks with either low or high context‐based complexity that we operationalize by the similarity of alternatives and the conflict between alternatives. We find in an experiment that an increase in the similarity of the alternatives and an increase in the number of conflicts within the choice task lead to an increased use of non‐compensatory strategies and a decreased use of compensatory decision strategies. In contrast, the size of the choice tasks, measured by the number of attributes and alternatives, only weakly influences the strategy selection. Copyright © 2014 John Wiley & Sons, Ltd.