Why Do Psychologists Not Use Mathematical Models to Express Their Theories?
Why Do Psychologists Not Use Mathematical Models to Express Their Theories?
The perception that psychologists rarely employ mathematical models in their theories is, in fact, an outdated one. Despite the widely held belief that most psychologists forgo numerical approaches, there is a thriving subfield that utilizes mathematical models to deepen our understanding of cognitive processes and human behavior. To debunk this myth, we explore the reasons behind the misconception and highlight the substantial and ongoing contributions of psychologists to mathematical psychology.
History and Development of Mathematical Psychology
The Society for Mathematical Psychology was established in 1964, two years before the first issue of the Journal of Mathematical Psychology was published in January of that year. This indicates the initial enthusiasm for applying mathematical modeling to psychological theories. As evidenced by the 2008 paper titled Mathematical Psychology: Prospects for the 21st Century, the field has evolved significantly over time. The authors, led by James Townsend, discuss the advancements and future directions of mathematical psychology, emphasizing its importance in psychological research.
Key Figures in Mathematical Psychology
One of the most notable figures in the field is Ben Goertzel, who holds a PhD in Dynamical Chaos Theory and has made significant contributions to mathematical psychology. In his early research, Goertzel specialized in complex and nonlinear models, demonstrating that mathematical approaches can be powerful tools in understanding psychological phenomena. His work exemplifies the intersection between dynamical systems and human cognition, highlighting the recurring themes in mathematical psychology.
Contemporary Applications of Mathematical Models in Psychology
In the contemporary context, the number of mathematical models of cognitive processes is growing exponentially. A recent study by Palminteri, Wyart, and Koechlin (2017) highlights this trend, presenting a comprehensive overview of advancements in the field. These models are not only making psychological theories more precise but are also enabling researchers to derive testable predictions. The primary objective of formalizing theories mathematically is to enhance our understanding of cognitive processes and to ensure that our ideas are logically consistent and empirically verifiable.
The Role of Formalization in Psychological Theories
Formalizing a theory mathematically is essential for several reasons. First, it allows for a rigorous and systematic examination of theoretical claims. When a theory is expressed in mathematical terms, it becomes easier to identify and correct any logical inconsistencies, thereby improving the robustness of the theory. Second, formalization facilitates the derivation of testable predictions. These predictions can be used to guide further empirical research, leading to a more comprehensive understanding of the phenomena being studied. Finally, mathematical models often provide a clearer and more precise description of cognitive processes, making it easier for other researchers to replicate and build upon the work.
Thematic Conceptual Introduction to Mathematical Modeling of Cognition
A recent blog post from the European Journal of Psychology Students titled A Conceptual Introduction to Mathematical Modeling of Cognition provides a valuable resource for both students and researchers. The post discusses the exponential growth of mathematical models in cognitive research and aims to demystify the approach to understanding the mind through mathematical modeling. The author argues that formalizing a theory mathematically helps to clarify the theoretical underpinnings and derive actionable predictions.
Conclusion
The persistent notion that psychologists avoid mathematical models seems to stem from a misunderstanding or outdated impression. Modern psychological research increasingly relies on mathematical models to express and test theories. The contributions of pioneering researchers like Ben Goertzel and the ongoing advancements in mathematical psychology underscore the importance and relevance of these methods. As the field continues to evolve, the use of mathematical models in psychology will undoubtedly play an even more significant role in advancing our understanding of human cognition and behavior.