Liane Gabora

A Theory of Concepts and Their Combinations II: A Hilbert Space Representation

The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept. Moreover, a solution to the combination of concepts is proposed. Using the tensor product, a procedure for describing combined concepts is elaborated, providing a natural solution to the pet fish problem. This procedure allows the modeling of an arbitrary number of combined concepts. By way of example, a model for a simple sentence containing a subject, a predicate and an object, is presented.

Contextualizing Concepts using a Mathematical Generalization of the Quantum Formalism

We outline the rationale and preliminary results of using the state context property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used and combined to generate meaning. The quantum formalism was developed to cope with problems arising in the description of (i) the measurement process, and (ii) the generation of new states with new properties when particles become entangled. Similar problems arising with concepts motivated the formal treatment introduced here. Concepts are viewed not as fixed representations, but entities existing in states of potentiality that require interaction with a context—a stimulus or another concept—to ‘collapse’ to an instantiated form (e.g. exemplar, prototype, or other possibly imaginary instance). The stimulus situation plays the role of the measurement in physics, acting as context that induces a change of the cognitive state from superposition state to collapsed state. The collapsed state is more likely to consist of a conjunction of concepts for associative than analytic thought because more stimulus or concept properties take part in the collapse. We provide two contextual measures of conceptual distance—one using collapse probabilities and the other weighted properties—and show how they can be applied to conjunctions using the pet fish problem.

A Theory of Concepts and Their Combinations I: The Structure of the Sets of Contexts and Properties

Purpose – To elaborate a theory for modeling concepts that incorporates how a context influences the typicality of a single exemplar and the applicability of a single property of a concept. To investigate the structure of the sets of contexts and properties. Design/methodology/approach – The effect of context on the typicality of an exemplar and the applicability of a property is accounted for by introducing the notion of “state of a concept”, and making use of the state‐context‐property formalism (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. Findings – The paper proves that the set of context and the set of properties of a concept is a complete orthocomplemented lattice, i.e. a set with a partial order relation, such that for each subset there exists a greatest lower bound and a least upper bound, and such that for each element there exists an orthocomplement. This structure describes the “and”, “or”, and “not”, respectively for contexts and properties. It shows that the context lattice as well as the property lattice are non‐classical, i.e. quantum‐like, lattices. Originality/value – Although the effect of context on concepts is widely acknowledged, formal mathematical structures of theories that incorporate this effect have not been successful. The study of this formal structure is a preparation for the elaboration of a theory of concepts that allows the description of the combination of concepts.

Revenge of the “Neurds”: Characterizing Creative Thought in Terms of the Structure and Dynamics of Memory

There is cognitive, neurological, and computational support for the hypothesis that defocusing attention results in divergent or associative thought, conducive to insight and finding unusual connections, while focusing attention results in convergent or analytic thought, conducive to rule-based operations. Creativity appears to involve both. It is widely believed that it is possible to escape mental fixation by spontaneously and temporarily engaging in a more associative mode of thought. The resulting insight (if found) may be refined in a more analytic mode of thought. The questions addressed here are: (a) How does the architecture of memory support these two modes of thought, and (b) what is happening at the neural level when one shifts between them? Recent advances in neuroscience shed light on this. Activated cell assemblies are composed of multiple neural cliques, groups of neurons that respond differentially to general or context-specific aspects of a situation. I refer to neural cliques that would not be included in the assembly if one were in an analytic mode, but would be if one were in an associative mode, as neurds. It is posited that the shift to a more associative mode of thought is accomplished by recruiting neurds that respond to abstract or atypical microfeatures of the problem or task. Since memory is distributed and content-addressable, this fosters the forging of associations to potentially relevant items previously encoded in those neurons. Thus it is proposed that creative thought occurs not by searching a space of predefined alternatives and blindly tweaking those that hold promise, but by evoking remotely associated items through the recruitment of neurds in a distributed, content-addressable memory.

The Violation of Bell Inequalities in the Macroworld

We show that Bell inequalities can be violated in the macroscopic world. The macroworld violation is illustrated using an example involving connected vessels of water. We show that whether the violation of inequalities occurs in the microworld or the macroworld, it is the identification of nonidentical events that plays a crucial role. Specifically, we prove that if nonidentical events are consistently differentiated, Bell-type Pitowsky inequalities are no longer violated, even for Bohms example of two entangled spin 1/2 quantum particles. We show how Bell inequalities can be violated in cognition, specifically in the relationship between abstract concepts and specific instances of these concepts. This supports the hypothesis that genuine quantum structure exists in the mind. We introduce a model where the amount of nonlocality and the degree of quantum uncertainty are parameterized, and demonstrate that increasing nonlocality increases the degree of violation, while increasing quantum uncertainty decreases the degree of violation.

Cognitive mechanisms underlying the creative process

This paper proposes an explanation of the cognitive change that occurs as the creative process proceeds. During the initial, intuitive phase, each thought activates, and potentially retrieves information from, a large region containing many memory locations. Because of the distributed, content-addressable structure of memory, the diverse contents of these many locations merge to generate the next thought. Novel associations often result. As one focuses on an idea, the region searched and retrieved from narrows, such that the next thought is the product of fewer memory locations. This enables a shift from association-based to causation-based thinking, which facilitates the fine-tuning and manifestation of the creative work.

Concepts and Their Dynamics: A Quantum-Theoretic Modeling of Human Thought

We analyze different aspects of our quantum modeling approach of human concepts and, more specifically, focus on the quantum effects of contextuality, interference, entanglement, and emergence, illustrating how each of them makes its appearance in specific situations of the dynamics of human concepts and their combinations. We point out the relation of our approach, which is based on an ontology of a concept as an entity in a state changing under influence of a context, with the main traditional concept theories, that is, prototype theory, exemplar theory, and theory theory. We ponder about the question why quantum theory performs so well in its modeling of human concepts, and we shed light on this question by analyzing the role of complex amplitudes, showing how they allow to describe interference in the statistics of measurement outcomes, while in the traditional theories statistics of outcomes originates in classical probability weights, without the possibility of interference. The relevance of complex numbers, the appearance of entanglement, and the role of Fock space in explaining contextual emergence, all as unique features of the quantum modeling, are explicitly revealed in this article by analyzing human concepts and their dynamics.

Toward an Ecological Theory of Concepts

Psychology has had difficulty accounting for the creative, context-sensitive manner in which concepts are used. We believe this stems from the view of concepts as identifiers rather than bridges between mind and world that participate in the generation of meaning. This article summarizes the history and current status of concepts research and provides a nontechnical summary of work toward an ecological approach to concepts. We outline the rationale for applying generalizations of formalisms originally developed for use in quantum mechanics to the modeling of concepts, showing how it is because of the role of context that deep structural similarities exist between the two. A concept is defined not just in terms of exemplary states and their features or properties but also by the relational structures of these properties and their susceptibility to change under different contexts. The approach implies a view of mind in which the union of perception and environment drives conceptualization, forging a web of conceptual relations or “ecology of mind.”

The shifting sands of creative thinking: Connections to dual-process theory

Dual-process models of cognition suggest that there are two types of thought: autonomous Type 1 processes and working memory dependent Type 2 processes that support hypothetical thinking. Models of creative thinking also distinguish between two sets of thinking processes: those involved in the generation of ideas and those involved with their refinement, evaluation, and/or selection. Here we review dual-process models in both these literatures and delineate the similarities and differences. Both generative creative processing and evaluative creative processing involve elements that have been attributed to each of the dual processes of cognition. We explore the notion that creative thinking may rest upon the nature of a shifting process between Type 1 and Type 2 dual processes. We suggest that a synthesis of the evidence bases on dual-process models of cognition and of creative thinking, together with developing time-based approaches to explore the shifting process, could better inform the development of interventions to facilitate creativity.

Ideas are Not Replicators but Minds Are

An idea is not a replicator because it does not consist of coded self-assembly instructions. It may retain structure as it passes from one individual to another, but does not replicate it. The cultural replicator is not an idea but an associatively-structured network of them that together form an internal model of the world, or worldview. A worldview is a primitive, uncoded replicator, like the autocatalytic sets of polymers widely believed to be the earliest form of life. Primitive replicators generate self-similar structure, but because the process happens in a piecemeal manner, through bottom-up interactions rather than a top-down code, they replicate with low fidelity, and acquired characteristics are inherited. Just as polymers catalyze reactions that generate other polymers, the retrieval of an item from memory can in turn trigger other items, thus cross-linking memories, ideas, and concepts into an integrated conceptual structure. Worldviews evolve idea by idea, largely through social exchange. An idea participates in the evolution of culture by revealing certain aspects of the worldview that generated it, thereby affecting the worldviews of those exposed to it. If an idea influences seemingly unrelated fields this does not mean that separate cultural lineages are contaminating one another, because it is worldviews, not ideas, that are the basic unit of cultural evolution.