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.

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36) 10 kle pou motive ekip ou a

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.

Pè

Charts Korelasyon

VUCA

Kritik valè de koyefisyan an korelasyon

Distribisyon nòmal, pa William Sealy Gosset (Elèv) r = 0.0353

Distribisyon ki pa nòmal, pa Spearman r = 0.0014

Montre rezilta sèlman > r = 0.0353

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

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