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.

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Here are reports of polls which SDTEST^® makes:

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12) Ubudala emsebenzini

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14) Izimbangela zokuguga

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16) Themba (#WVS)

17) Ucwaningo lwenjabulo ye-Oxford

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35) Izici zesisebenzi esinethalente (ngesikhungo Sokulawulwa Kwethalente)

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38) Amathuba Amathathu Ahlukene Esikhathi Esizayo (nguDkt. Clare W. Graves)

39) Izenzo Zokwakha Ukuzethemba Okungenakunyakaziswa (ngu-Suren Samarchyan)

40)

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.

Ukwesaba

Amashadi Ukuhlanganisa

VUCA

Inani Ebucayi Coefficient ukuhlanganisa

Ukusatshalaliswa okujwayelekile, ngoWilliam Sealy Gosset (umfundi) r = 0.0318

Ukusatshalaliswa okungajwayelekile, nguSpyman r = 0.0013

Khombisa imiphumela kuphela > r = 0.0318

Ukuhlephula	Okungajwayelekile	Okungajwayelekile	Okungajwayelekile	-Ngokwejwayelekile	-Ngokwejwayelekile	-Ngokwejwayelekile	-Ngokwejwayelekile	-Ngokwejwayelekile
Yonke imibuzo Yonke imibuzo Ukwesaba kwami okukhulu
Ukwesaba kwami okukhulu
Answer 1	-	Omuhle engaqinile 0.0524	Omuhle engaqinile 0.0258	Negative engaqinile -0.0180	Omuhle engaqinile 0.0949	Omuhle engaqinile 0.0355	Negative engaqinile -0.0146	Negative engaqinile -0.1537
Answer 2	-	Omuhle engaqinile 0.0175	Negative engaqinile -0.0058	Negative engaqinile -0.0387	Omuhle engaqinile 0.0669	Omuhle engaqinile 0.0494	Omuhle engaqinile 0.0116	Negative engaqinile -0.0969
Answer 3	-	Negative engaqinile -0.0035	Negative engaqinile -0.0091	Negative engaqinile -0.0441	Negative engaqinile -0.0435	Omuhle engaqinile 0.0477	Omuhle engaqinile 0.0747	Negative engaqinile -0.0199
Answer 4	-	Omuhle engaqinile 0.0412	Omuhle engaqinile 0.0255	Negative engaqinile -0.0229	Omuhle engaqinile 0.0192	Omuhle engaqinile 0.0353	Omuhle engaqinile 0.0246	Negative engaqinile -0.0990
Answer 5	-	Omuhle engaqinile 0.0227	Omuhle engaqinile 0.1271	Omuhle engaqinile 0.0109	Omuhle engaqinile 0.0770	Negative engaqinile -0.0005	Negative engaqinile -0.0175	Negative engaqinile -0.1774
Answer 6	-	Negative engaqinile -0.0055	Omuhle engaqinile 0.0042	Negative engaqinile -0.0622	Negative engaqinile -0.0080	Omuhle engaqinile 0.0249	Omuhle engaqinile 0.0863	Negative engaqinile -0.0354
Answer 7	-	Omuhle engaqinile 0.0084	Omuhle engaqinile 0.0331	Negative engaqinile -0.0656	Negative engaqinile -0.0297	Omuhle engaqinile 0.0523	Omuhle engaqinile 0.0696	Negative engaqinile -0.0522
Answer 8	-	Omuhle engaqinile 0.0629	Omuhle engaqinile 0.0710	Negative engaqinile -0.0267	Omuhle engaqinile 0.0130	Omuhle engaqinile 0.0379	Omuhle engaqinile 0.0184	Negative engaqinile -0.1339
Answer 9	-	Omuhle engaqinile 0.0711	Omuhle engaqinile 0.1602	Omuhle engaqinile 0.0072	Omuhle engaqinile 0.0643	Negative engaqinile -0.0106	Negative engaqinile -0.0484	Negative engaqinile -0.1819
Answer 10	-	Omuhle engaqinile 0.0740	Omuhle engaqinile 0.0656	Negative engaqinile -0.0150	Omuhle engaqinile 0.0292	Omuhle engaqinile 0.0321	Negative engaqinile -0.0123	Negative engaqinile -0.1359
Answer 11	-	Omuhle engaqinile 0.0629	Omuhle engaqinile 0.0524	Negative engaqinile -0.0098	Omuhle engaqinile 0.0104	Omuhle engaqinile 0.0253	Omuhle engaqinile 0.0247	Negative engaqinile -0.1270
Answer 12	-	Omuhle engaqinile 0.0433	Omuhle engaqinile 0.0921	Negative engaqinile -0.0338	Omuhle engaqinile 0.0335	Omuhle engaqinile 0.0331	Omuhle engaqinile 0.0257	Negative engaqinile -0.1540
Answer 13	-	Omuhle engaqinile 0.0687	Omuhle engaqinile 0.0957	Negative engaqinile -0.0396	Omuhle engaqinile 0.0304	Omuhle engaqinile 0.0408	Omuhle engaqinile 0.0151	Negative engaqinile -0.1630
Answer 14	-	Omuhle engaqinile 0.0781	Omuhle engaqinile 0.0884	Negative engaqinile -0.0003	Negative engaqinile -0.0096	Omuhle engaqinile 0.0050	Omuhle engaqinile 0.0138	Negative engaqinile -0.1228
Answer 15	-	Omuhle engaqinile 0.0539	Omuhle engaqinile 0.1269	Negative engaqinile -0.0339	Omuhle engaqinile 0.0148	Negative engaqinile -0.0172	Omuhle engaqinile 0.0237	Negative engaqinile -0.1160
Answer 16	-	Omuhle engaqinile 0.0690	Omuhle engaqinile 0.0248	Negative engaqinile -0.0372	Negative engaqinile -0.0385	Omuhle engaqinile 0.0703	Omuhle engaqinile 0.0205	Negative engaqinile -0.0792

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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

Umnikazi Womkhiqizo i-SaaS SDTEST®

U-Valerii waqeqeshelwa ukuba yisazi sezengqondo zezenhlalo ngo-1993 futhi usesebenzise ulwazi lwakhe ekuphathweni kwephrojekthi.
U-Valerii uthole iziqu ze-Master kanye neziqu zephrojekthi kanye nomphathi wohlelo ngo-2013. Phakathi nohlelo lwakhe lwe-Master, wajwayelana ne-Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) kanye ne-Spiral Dynamics.
U-Valerii ungumbhali wokuhlola ukungaqiniseki kwe-V.U.C.A. umqondo usebenzisa iSpiral Dynamics kanye nezibalo zezibalo kupsychology, kanye namavoti angama-38 amazwe ngamazwe.

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