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:

1) Радње предузећа у вези са особљем у последњем мјесецу (да / не)

2) Радње предузећа у односу на особље у последњем мјесецу (чињеница у%)

3) Страхови

4) Највећи проблеми са којима се суочавају моја земља

5) Које квалитете и способности користе добри лидери користе се приликом изградње успешних тимова?

6) Гоогле. Фактори који утичу на ефикасност тима

7) Главни приоритети тражилаца посла

8) Шта шефа чини сјајном вођом?

9) Шта људи чини успешним на послу?

10) Да ли сте спремни да даљите мање платите да даљински радите?

11) Да ли агеизам постоји?

12) Агеизам у каријери

13) Агеизам у животу

14) Узроци агеризма

15) Разлози због којих људи одустају (Анна Витал)

16) Поверење (#WVS)

17) Окфорд Хаппинесс Анкета

18) Психолошко благостање

19) Где би била ваша следећа најузбудљивија прилика?

20) Шта ћете радити ове недеље да бисте се бринули на ментално здравље?

21) Живим размишљајући о својој прошлости, садашњем или будућности

22) Меритократија

23) Вештачка интелигенција и крај цивилизације

24) Зашто људи одлажу?

25) Родна разлика у изградњи самопоуздања (ИФД Алансбацх)

26) Xing.com Процена културе

27) Патрицк Ленциони'с "Пет дисфункција тима"

28) Емпатија је ...

29) Шта је неопходно за ИТ стручњаке у избору понуде за посао?

30) Зашто се људи одупиру променама (од Сиобхан Мцхале)

31) Како регулишете своје емоције? (од Навал Мустафа М.А.)

32) 21 Вештине које вам плаћају заувек (од јеремиах тео / 赵汉昇)

33) Права слобода је ...

34) 12 начина за изградњу поверења са другима (Јустин Вригхт)

35) Карактеристике талентованог радника (од стране Института за управљање талентовима)

36) 10 тастера за мотивисање вашег тима

37) Алгебра савести (Владимир Лефевр)

38) Три различите могућности будућности (др. Цларе В. Гравес)

39) Акције за изградњу непоколебљивог самопоуздања (Сурен Самарцхиан)

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.

Страхови

цхартсКорелација

VUCA

Критична вредност коефицијента корелације

Нормална дистрибуција, Виллиам Сеали Госсет (Студент) r = 0.0312

Нон нормална дистрибуција, од стране Спеарман-а r = 0.0013

Прикажи само резултате > r = 0.0312

Дистрибуција	Не нормално	Не нормално	Не нормално	Нормалан	Нормалан	Нормалан	Нормалан	Нормалан
Сва питања Сва питања Мој највећи страх је
Мој највећи страх је
Answer 1	-	Слабо позитивно 0.0545	Слабо позитивно 0.0255	Слаб негативан -0.0189	Слабо позитивно 0.0953	Слабо позитивно 0.0407	Слаб негативан -0.0164	Слаб негативан -0.1576
Answer 2	-	Слабо позитивно 0.0188	Слаб негативан -0.0047	Слаб негативан -0.0404	Слабо позитивно 0.0634	Слабо позитивно 0.0516	Слабо позитивно 0.0121	Слаб негативан -0.0972
Answer 3	-	Слаб негативан -0.0023	Слаб негативан -0.0060	Слаб негативан -0.0442	Слаб негативан -0.0401	Слабо позитивно 0.0487	Слабо позитивно 0.0745	Слаб негативан -0.0262
Answer 4	-	Слабо позитивно 0.0450	Слабо позитивно 0.0339	Слаб негативан -0.0273	Слабо позитивно 0.0157	Слабо позитивно 0.0415	Слабо позитивно 0.0240	Слаб негативан -0.1058
Answer 5	-	Слабо позитивно 0.0236	Слабо позитивно 0.1276	Слабо позитивно 0.0104	Слабо позитивно 0.0764	Слабо позитивно 0.0002	Слаб негативан -0.0163	Слаб негативан -0.1762
Answer 6	-	Слабо позитивно 0.0003	Слабо позитивно 0.0053	Слаб негативан -0.0607	Слаб негативан -0.0078	Слабо позитивно 0.0237	Слабо позитивно 0.0840	Слаб негативан -0.0368
Answer 7	-	Слабо позитивно 0.0112	Слабо позитивно 0.0333	Слаб негативан -0.0634	Слаб негативан -0.0307	Слабо позитивно 0.0510	Слабо позитивно 0.0682	Слаб негативан -0.0528
Answer 8	-	Слабо позитивно 0.0649	Слабо позитивно 0.0718	Слаб негативан -0.0250	Слабо позитивно 0.0108	Слабо позитивно 0.0407	Слабо позитивно 0.0150	Слаб негативан -0.1343
Answer 9	-	Слабо позитивно 0.0771	Слабо позитивно 0.1597	Слабо позитивно 0.0069	Слабо позитивно 0.0610	Слаб негативан -0.0046	Слаб негативан -0.0526	Слаб негативан -0.1821
Answer 10	-	Слабо позитивно 0.0776	Слабо позитивно 0.0629	Слаб негативан -0.0125	Слабо позитивно 0.0229	Слабо позитивно 0.0378	Слаб негативан -0.0111	Слаб негативан -0.1316
Answer 11	-	Слабо позитивно 0.0626	Слабо позитивно 0.0522	Слаб негативан -0.0075	Слабо позитивно 0.0089	Слабо позитивно 0.0299	Слабо позитивно 0.0212	Слаб негативан -0.1269
Answer 12	-	Слабо позитивно 0.0416	Слабо позитивно 0.0934	Слаб негативан -0.0319	Слабо позитивно 0.0338	Слабо позитивно 0.0339	Слабо позитивно 0.0245	Слаб негативан -0.1527
Answer 13	-	Слабо позитивно 0.0713	Слабо позитивно 0.0947	Слаб негативан -0.0374	Слабо позитивно 0.0282	Слабо позитивно 0.0439	Слабо позитивно 0.0113	Слаб негативан -0.1627
Answer 14	-	Слабо позитивно 0.0827	Слабо позитивно 0.0885	Слаб негативан -0.0015	Слаб негативан -0.0133	Слабо позитивно 0.0076	Слабо позитивно 0.0115	Слаб негативан -0.1211
Answer 15	-	Слабо позитивно 0.0579	Слабо позитивно 0.1221	Слаб негативан -0.0316	Слабо позитивно 0.0084	Слаб негативан -0.0129	Слабо позитивно 0.0243	Слаб негативан -0.1153
Answer 16	-	Слабо позитивно 0.0717	Слабо позитивно 0.0218	Слаб негативан -0.0374	Слаб негативан -0.0404	Слабо позитивно 0.0745	Слабо позитивно 0.0151	Слаб негативан -0.0741

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

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

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

2023.10.13

FearpersonqualitiesprojectorganizationalstructureRACIresponsibilitymatrixCritical ChainProject Managementfocus factorJiraempathyleadersbossGermanyChinaPolicyUkraineRussiawarvolatilityuncertaintycomplexityambiguityVUCArelocatejobproblemcountryreasongive upobjectivekeyresultmathematicalpsychologyMBTIHR metricsstandardDEIcorrelationriskscoringmodelGame TheoryPrisoner's Dilemma

Валерий Косенко

Власник производа СааС СДТЕСТ®

Валерии је 1993. године стекао квалификацију социјалног педагога-психолога и од тада примењује своја знања у управљању пројектима.
Валерии је магистрирао и стекао квалификацију менаџера пројекта и програма 2013. Током магистарског програма упознао се са Планом пута пројекта (ГПМ Деутсцхе Геселлсцхафт фур Пројектманагемент е. В.) и Спирал Динамицс.
Валерии је аутор истраживања неизвесности В.У.Ц.А. концепт који користи спиралну динамику и математичку статистику у психологији и 38 међународних анкета.

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