Mathematical Psychology

This project investigates mathematical psychology's historical and philosophical foundations to clarify its distinguishing characteristics and relationships to adjacent fields. Through gathering primary sources, histories, and interviews with researchers, author Prof. Colin Allen - University of Pittsburgh [1, 2, 3] and his students Osman Attah, Brendan Fleig-Goldstein, Mara McGuire, and Dzintra Ullis have identified three central questions:

What makes the use of mathematics in mathematical psychology reasonably effective, in contrast to other sciences like physics-inspired mathematical biology or symbolic cognitive science?
How does the mathematical approach in mathematical psychology differ from other branches of psychology, like psychophysics and psychometrics?
What is the appropriate relationship of mathematical psychology to cognitive science, given diverging perspectives on aligning with this field?

Preliminary findings emphasize data-driven modeling, skepticism of cognitive science alignments, and early reliance on computation. They will further probe the interplay with cognitive neuroscience and contrast rational-analysis approaches. By elucidating the motivating perspectives and objectives of different eras in mathematical psychology's development, they aim to understand its past and inform constructive dialogue on its philosophical foundations and future directions. This project intends to provide a conceptual roadmap for the field through integrated history and philosophy of science.

The Project: Integrating History and Philosophy of Mathematical Psychology

This project aims to integrate historical and philosophical perspectives to elucidate the foundations of mathematical psychology. As Norwood Hanson stated, history without philosophy is blind, while philosophy without history is empty. The goal is to find a middle ground between the contextual focus of history and the conceptual focus of philosophy.

The team acknowledges that all historical accounts are imperfect, but some can provide valuable insights. The history of mathematical psychology is difficult to tell without centering on the influential Stanford group. Tracing academic lineages and key events includes part of the picture, but more context is needed to fully understand the field's development.

The project draws on diverse sources, including research interviews, retrospective articles, formal histories, and online materials. More interviews and research will further flesh out the historical and philosophical foundations. While incomplete, the current analysis aims to identify important themes, contrasts, and questions that shaped mathematical psychology's evolution. Ultimately, the goal is an integrated historical and conceptual roadmap to inform contemporary perspectives on the field's identity and future directions.

The Rise of Mathematical Psychology

The history of efforts to mathematize psychology traces back to the quantitative imperative stemming from the Galilean scientific revolution. This imprinted the notion that proper science requires mathematics, leading to "physics envy" in other disciplines like psychology.

Many early psychologists argued psychology needed to become mathematical to be scientific. However, mathematizing psychology faced complications absent in the physical sciences. Objects in psychology were not readily present as quantifiable, provoking heated debates on whether psychometric and psychophysical measurements were meaningful.

Nonetheless, the desire to develop mathematical psychology persisted. Different approaches grappled with determining the appropriate role of mathematics in relation to psychological experiments and data. For example, Herbart favored starting with mathematics to ensure accuracy, while Fechner insisted experiments must come first to ground mathematics.

Tensions remain between data-driven versus theory-driven mathematization of psychology. Contemporary perspectives range from psychometric and psychophysical stances that foreground data to measurement-theoretical and computational approaches that emphasize formal models.

Elucidating how psychologists negotiated to apply mathematical methods to an apparently resistant subject matter helps reveal the evolving role and place of mathematics in psychology. This historical interplay shaped the emergence of mathematical psychology as a field.

The Distinctive Mathematical Approach of Mathematical Psychology

What sets mathematical psychology apart from other branches of psychology in its use of mathematics?

Several key aspects stand out:

Advocating quantitative methods broadly. Mathematical psychology emerged partly to push psychology to embrace quantitative modeling and mathematics beyond basic statistics.
Drawing from diverse mathematical tools. With greater training in mathematics, mathematical psychologists utilize more advanced and varied mathematical techniques like topology and differential geometry.
Linking models and experiments. Mathematical psychologists emphasize tightly connecting experimental design and statistical analysis, with experiments created to test specific models.
Favoring theoretical models. Mathematical psychology incorporates "pure" mathematical results and prefers analytic, hand-fitted models over data-driven computer models.
Seeking general, cumulative theory. Unlike just describing data, mathematical psychology aspires to abstract, general theory supported across experiments, cumulative progress in models, and mathematical insight into psychological mechanisms.

So while not unique to mathematical psychology, these key elements help characterize how its use of mathematics diverges from adjacent fields like psychophysics and psychometrics. Mathematical psychology carved out an identity embracing quantitative methods but also theoretical depth and broad generalization.

Situating Mathematical Psychology Relative to Cognitive Science

What is the appropriate perspective on mathematical psychology's relationship to cognitive psychology and cognitive science? While connected historically and conceptually, essential distinctions exist.

Mathematical psychology draws from diverse disciplines that are also influential in cognitive science, like computer science, psychology, linguistics, and neuroscience. However, mathematical psychology appears more skeptical of alignments with cognitive science.

For example, cognitive science prominently adopted the computer as a model of the human mind, while mathematical psychology focused more narrowly on computers as modeling tools.

Additionally, mathematical psychology seems to take a more critical stance towards purely simulation-based modeling in cognitive science, instead emphasizing iterative modeling tightly linked to experimentation.

Overall, mathematical psychology exhibits significant overlap with cognitive science but strongly asserts its distinct mathematical orientation and modeling perspectives. Elucidating this complex relationship remains an ongoing project, but preliminary analysis suggests mathematical psychology intentionally diverged from cognitive science in its formative development.

This establishes mathematical psychology's separate identity while retaining connections to adjacent disciplines at the intersection of mathematics, psychology, and computation.

Looking Ahead: Open Questions and Future Research

This historical and conceptual analysis of mathematical psychology's foundations has illuminated key themes, contrasts, and questions that shaped the field's development. Further research can build on these preliminary findings.

Additional work is needed to flesh out the fuller intellectual, social, and political context driving the evolution of mathematical psychology. Examining the influences and reactions of key figures will provide a richer picture.

Ongoing investigation can probe whether the identified tensions and contrasts represent historical artifacts or still animate contemporary debates. Do mathematical psychologists today grapple with similar questions on the role of mathematics and modeling?

Further analysis should also elucidate the nature of the purported bidirectional relationship between modeling and experimentation in mathematical psychology. As well, clarifying the diversity of perspectives on goals like generality, abstraction, and cumulative theory-building would be valuable.

Finally, this research aims to spur discussion on philosophical issues such as realism, pluralism, and progress in mathematical psychology models. Is the accuracy and truth value of models an important consideration or mainly beside the point? And where is the field headed - towards greater verisimilitude or an indefinite balancing of complexity and abstraction?

By spurring reflection on this conceptual foundation, this historical and integrative analysis hopes to provide a roadmap to inform constructive dialogue on mathematical psychology's identity and future trajectory.

The SDTEST^®

The SDTEST^® is a simple and fun tool to uncover our unique motivational values that use mathematical psychology of varying complexity.

The SDTEST^® helps us better understand ourselves and others on this lifelong path of self-discovery.

Here are reports of polls which SDTEST^® makes:

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Below you can read an abridged version of the results of our VUCA poll “Fears“. The full version of the results is available for free in the FAQ section after login or registration.

Rädsla

diagram Korrelation

VUCA

Kritiska värdet av korrelationskoefficienten

Normal Distribution, av William Sealy Gosset (Student) r = 0.0353

Icke normal distribution, av Spearman r = 0.0014

Visa endast resultat > r = 0.0353

Distribution	Icke normal	Vanligt	Icke normal	Vanligt	Vanligt	Vanligt	Vanligt	Vanligt
Alla frågor Alla frågor Min största rädsla är
Min största rädsla är
Answer 1	-	Svagt positivt 0.0297	Svagt positivt 0.0298	Svagt negativt -0.0106	Svagt positivt 0.0970	Svagt positivt 0.0325	Svagt negativt -0.0019	Svagt negativt -0.1558
Answer 2	-	Svagt positivt 0.0188	Svagt positivt 0.0076	Svagt negativt -0.0360	Svagt positivt 0.0711	Svagt positivt 0.0387	Svagt positivt 0.0082	Svagt negativt -0.1011
Answer 3	-	Svagt positivt 0.0026	Svagt negativt -0.0170	Svagt negativt -0.0443	Svagt negativt -0.0458	Svagt positivt 0.0547	Svagt positivt 0.0808	Svagt negativt -0.0270
Answer 4	-	Svagt positivt 0.0332	Svagt positivt 0.0285	Svagt negativt -0.0006	Svagt positivt 0.0155	Svagt positivt 0.0276	Svagt positivt 0.0105	Svagt negativt -0.0917
Answer 5	-	Svagt positivt 0.0122	Svagt positivt 0.1193	Svagt positivt 0.0095	Svagt positivt 0.0721	Svagt positivt 0.0057	Svagt negativt -0.0083	Svagt negativt -0.1687
Answer 6	-	Svagt positivt 0.0044	Svagt positivt 0.0005	Svagt negativt -0.0582	Svagt negativt -0.0004	Svagt positivt 0.0210	Svagt positivt 0.0830	Svagt negativt -0.0418
Answer 7	-	Svagt positivt 0.0242	Svagt positivt 0.0368	Svagt negativt -0.0521	Svagt negativt -0.0234	Svagt positivt 0.0403	Svagt positivt 0.0568	Svagt negativt -0.0597
Answer 8	-	Svagt positivt 0.0707	Svagt positivt 0.0781	Svagt negativt -0.0244	Svagt positivt 0.0140	Svagt positivt 0.0303	Svagt positivt 0.0137	Svagt negativt -0.1334
Answer 9	-	Svagt positivt 0.0564	Svagt positivt 0.1531	Svagt positivt 0.0127	Svagt positivt 0.0769	Svagt negativt -0.0136	Svagt negativt -0.0495	Svagt negativt -0.1752
Answer 10	-	Svagt positivt 0.0711	Svagt positivt 0.0700	Svagt negativt -0.0127	Svagt positivt 0.0246	Svagt positivt 0.0363	Svagt negativt -0.0156	Svagt negativt -0.1273
Answer 11	-	Svagt positivt 0.0542	Svagt positivt 0.0488	Svagt positivt 0.0086	Svagt positivt 0.0078	Svagt positivt 0.0162	Svagt positivt 0.0315	Svagt negativt -0.1248
Answer 12	-	Svagt positivt 0.0281	Svagt positivt 0.0929	Svagt negativt -0.0325	Svagt positivt 0.0361	Svagt positivt 0.0276	Svagt positivt 0.0365	Svagt negativt -0.1482
Answer 13	-	Svagt positivt 0.0643	Svagt positivt 0.0916	Svagt negativt -0.0418	Svagt positivt 0.0237	Svagt positivt 0.0425	Svagt positivt 0.0239	Svagt negativt -0.1558
Answer 14	-	Svagt positivt 0.0697	Svagt positivt 0.1017	Svagt positivt 0.0149	Svagt negativt -0.0062	Svagt negativt -0.0087	Svagt negativt -0.0002	Svagt negativt -0.1161
Answer 15	-	Svagt positivt 0.0603	Svagt positivt 0.1299	Svagt negativt -0.0379	Svagt positivt 0.0163	Svagt negativt -0.0091	Svagt positivt 0.0164	Svagt negativt -0.1204
Answer 16	-	Svagt positivt 0.0691	Svagt positivt 0.0221	Svagt negativt -0.0305	Svagt negativt -0.0515	Svagt positivt 0.0750	Svagt positivt 0.0187	Svagt negativt -0.0696

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[1] https://twitter.com/wileyprof

[2] https://colinallen.dnsalias.org

[3] https://philpeople.org/profiles/colin-allen

2023.10.13

Valerii Kosenko

Produktägare SaaS Pet Project SDTest®

Valerii var kvalificerad som en social pedagog-psykolog 1993 och har sedan dess tillämpat sin kunskap i projektledning.
Valerii erhöll en magisterexamen och projekt- och programchefskvalificeringen 2013. Under sitt masterprogram blev han bekant med Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) och spiraldynamik.
Valerii tog olika spiraldynamiktester och använde sin kunskap och erfarenhet för att anpassa den aktuella versionen av SDTest.
Valerii är författaren för att utforska osäkerheten i V.U.C.A. Koncept med spiraldynamik och matematisk statistik i psykologi, mer än 20 internationella undersökningar.

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