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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12) Ubudala emsebenzini

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25) Umehluko wobulili ekwakheni ukuzethemba (IFD Allensbach)

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30) Kungani abantu bemelana noshintsho (nguSiobhán Mchale)

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32) Amakhono angama-21 akukhokhela kuze kube phakade (nguJeremiah Teo / 赵汉昇)

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35) Izici zesisebenzi esinethalente (ngesikhungo Sokulawulwa Kwethalente)

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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.

Ukwesaba

Amashadi Ukuhlanganisa

VUCA

Inani Ebucayi Coefficient ukuhlanganisa

Ukusatshalaliswa okujwayelekile, ngoWilliam Sealy Gosset (umfundi) r = 0.0353

Ukusatshalaliswa okungajwayelekile, nguSpyman r = 0.0014

Khombisa imiphumela kuphela > r = 0.0353

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

Thekelisa MS Excel

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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 Wemikhiqizo iSaas Pet Project SDTEST®

UValerii wafaneleka njengodokotela wezengqondo wezenhlalo - ngo-1993 futhi usekusebenzise ulwazi lakhe ekuphathweni kwephrojekthi.
UValerii wathola iziqu ze-master kanye nephrojekthi kanye nemenenja yohlelo ngo-2013. Ngesikhathi sohlelo lwenkosi yakhe, wajwayela i-Project RoadMap (GPM Deutsche GesellSchaft Für projektnagement e. V.) kanye nama-Spiral Dynamics. V.) kanye ne-Spiral Dynamics. V.) kanye ne-Spiral Dynamics. V.) kanye ne-Spiral Pynamics
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