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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2) Izenzo zezinkampani maqondana nabasebenzi ngenyanga edlule (iqiniso ku-%)

3) Ukwesaba

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7) Izinto ezibaluleke kakhulu zabafuna umsebenzi

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10) Ingabe usukulungele ukuthola inkokhelo encane ukuze usebenze ukude?

11) Ngabe uneminyaka yobudala ukhona?

12) Ubudala emsebenzini

13) Ubudala empilweni

14) Izimbangela zokuguga

15) Izizathu zokuthi kungani abantu bekela (ngu-Anna Vital)

16) Themba (#WVS)

17) Ucwaningo lwenjabulo ye-Oxford

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22) Inhlanganobikhali

23) Ubuhlakani bokufakelwa kanye nokuphela kwempucuko

24) Kungani abantu behlehlisa?

25) Umehluko wobulili ekwakheni ukuzethemba (IFD Allensbach)

26) Ukuhlolwa kwesiko le-Xing.com

27) UPatrick Lenfion's "The Dyssuncess Emihlanu Yeqembu"

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29) Yini ebalulekile kochwepheshe be-IT ekukhetheni umnikelo?

30) Kungani abantu bemelana noshintsho (nguSiobhán Mchale)

31) Ulawula kanjani imizwa yakho? (Ngu-Nawal Mustafa M.A.)

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

33) Inkululeko yangempela ...

34) Izindlela eziyi-12 zokwakha ukwethembana nabanye (nguJustin Wright)

35) Izici zesisebenzi esinethalente (ngesikhungo Sokulawulwa Kwethalente)

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37) I-Algebra Kanembeza (kaVladimir Lefebvre)

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

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 = 0.0335

Ukusatshalaliswa okungajwayelekile, nguSpyman r = 0.0014

Khombisa imiphumela kuphela > r = 0.0335

Ukuhlephula	Okungajwayelekile	Okungajwayelekile	Okungajwayelekile	-Ngokwejwayelekile	-Ngokwejwayelekile	-Ngokwejwayelekile	-Ngokwejwayelekile	-Ngokwejwayelekile
Yonke imibuzo Yonke imibuzo Ukwesaba kwami okukhulu
Ukwesaba kwami okukhulu
Answer 1	-	Omuhle engaqinile 0.0521	Omuhle engaqinile 0.0294	Negative engaqinile -0.0147	Omuhle engaqinile 0.0885	Omuhle engaqinile 0.0316	Negative engaqinile -0.0110	Negative engaqinile -0.1513
Answer 2	-	Omuhle engaqinile 0.0213	Omuhle engaqinile 0.0013	Negative engaqinile -0.0432	Omuhle engaqinile 0.0618	Omuhle engaqinile 0.0453	Omuhle engaqinile 0.0103	Negative engaqinile -0.0918
Answer 3	-	Negative engaqinile -0.0042	Negative engaqinile -0.0116	Negative engaqinile -0.0406	Negative engaqinile -0.0477	Omuhle engaqinile 0.0487	Omuhle engaqinile 0.0767	Negative engaqinile -0.0191
Answer 4	-	Omuhle engaqinile 0.0421	Omuhle engaqinile 0.0350	Negative engaqinile -0.0115	Omuhle engaqinile 0.0112	Omuhle engaqinile 0.0307	Omuhle engaqinile 0.0175	Negative engaqinile -0.0980
Answer 5	-	Omuhle engaqinile 0.0288	Omuhle engaqinile 0.1272	Omuhle engaqinile 0.0146	Omuhle engaqinile 0.0697	Omuhle engaqinile 0.0037	Negative engaqinile -0.0215	Negative engaqinile -0.1746
Answer 6	-	Negative engaqinile -0.0001	Omuhle engaqinile 0.0042	Negative engaqinile -0.0607	Negative engaqinile -0.0115	Omuhle engaqinile 0.0231	Omuhle engaqinile 0.0826	Negative engaqinile -0.0309
Answer 7	-	Omuhle engaqinile 0.0117	Omuhle engaqinile 0.0372	Negative engaqinile -0.0653	Negative engaqinile -0.0283	Omuhle engaqinile 0.0495	Omuhle engaqinile 0.0626	Negative engaqinile -0.0505
Answer 8	-	Omuhle engaqinile 0.0658	Omuhle engaqinile 0.0830	Negative engaqinile -0.0310	Omuhle engaqinile 0.0139	Omuhle engaqinile 0.0334	Omuhle engaqinile 0.0134	Negative engaqinile -0.1322
Answer 9	-	Omuhle engaqinile 0.0660	Omuhle engaqinile 0.1658	Omuhle engaqinile 0.0051	Omuhle engaqinile 0.0691	Negative engaqinile -0.0093	Negative engaqinile -0.0498	Negative engaqinile -0.1820
Answer 10	-	Omuhle engaqinile 0.0758	Omuhle engaqinile 0.0724	Negative engaqinile -0.0173	Omuhle engaqinile 0.0236	Omuhle engaqinile 0.0312	Negative engaqinile -0.0115	Negative engaqinile -0.1263
Answer 11	-	Omuhle engaqinile 0.0577	Omuhle engaqinile 0.0544	Negative engaqinile -0.0075	Omuhle engaqinile 0.0082	Omuhle engaqinile 0.0185	Omuhle engaqinile 0.0293	Negative engaqinile -0.1190
Answer 12	-	Omuhle engaqinile 0.0376	Omuhle engaqinile 0.1007	Negative engaqinile -0.0342	Omuhle engaqinile 0.0296	Omuhle engaqinile 0.0273	Omuhle engaqinile 0.0341	Negative engaqinile -0.1500
Answer 13	-	Omuhle engaqinile 0.0627	Omuhle engaqinile 0.1017	Negative engaqinile -0.0443	Omuhle engaqinile 0.0248	Omuhle engaqinile 0.0434	Omuhle engaqinile 0.0189	Negative engaqinile -0.1576
Answer 14	-	Omuhle engaqinile 0.0732	Omuhle engaqinile 0.1036	Omuhle engaqinile 0.0048	Negative engaqinile -0.0105	Negative engaqinile -0.0039	Omuhle engaqinile 0.0041	Negative engaqinile -0.1157
Answer 15	-	Omuhle engaqinile 0.0539	Omuhle engaqinile 0.1381	Negative engaqinile -0.0424	Omuhle engaqinile 0.0163	Negative engaqinile -0.0147	Omuhle engaqinile 0.0216	Negative engaqinile -0.1173
Answer 16	-	Omuhle engaqinile 0.0590	Omuhle engaqinile 0.0274	Negative engaqinile -0.0375	Negative engaqinile -0.0429	Omuhle engaqinile 0.0687	Omuhle engaqinile 0.0253	Negative engaqinile -0.0698

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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