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)

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

цхартс Корелација

VUCA

Критична вредност коефицијента корелације

Нормална дистрибуција, Виллиам Сеали Госсет (Студент) r = 0.0329

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

Прикажи само резултате > r = 0.0329

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 0.0566	Слабо позитивно 0.0332	Слаб негативан -0.0170	Слабо позитивно 0.0912	Слабо позитивно 0.0308	Слаб негативан -0.0153	Слаб негативан -0.1537
Answer 2	-	Слабо позитивно 0.0223	Слабо позитивно 0.0011	Слаб негативан -0.0442	Слабо позитивно 0.0639	Слабо позитивно 0.0464	Слабо позитивно 0.0120	Слаб негативан -0.0960
Answer 3	-	Слаб негативан -0.0031	Слаб негативан -0.0104	Слаб негативан -0.0407	Слаб негативан -0.0463	Слабо позитивно 0.0475	Слабо позитивно 0.0779	Слаб негативан -0.0213
Answer 4	-	Слабо позитивно 0.0437	Слабо позитивно 0.0357	Слаб негативан -0.0197	Слабо позитивно 0.0161	Слабо позитивно 0.0311	Слабо позитивно 0.0187	Слаб негативан -0.0987
Answer 5	-	Слабо позитивно 0.0296	Слабо позитивно 0.1300	Слабо позитивно 0.0124	Слабо позитивно 0.0749	Слабо позитивно 0.0014	Слаб негативан -0.0231	Слаб негативан -0.1771
Answer 6	-	Слаб негативан -0.0008	Слабо позитивно 0.0090	Слаб негативан -0.0613	Слаб негативан -0.0070	Слабо позитивно 0.0196	Слабо позитивно 0.0803	Слаб негативан -0.0321
Answer 7	-	Слабо позитивно 0.0118	Слабо позитивно 0.0401	Слаб негативан -0.0693	Слаб негативан -0.0246	Слабо позитивно 0.0471	Слабо позитивно 0.0623	Слаб негативан -0.0505
Answer 8	-	Слабо позитивно 0.0697	Слабо позитивно 0.0875	Слаб негативан -0.0316	Слабо позитивно 0.0155	Слабо позитивно 0.0346	Слабо позитивно 0.0098	Слаб негативан -0.1373
Answer 9	-	Слабо позитивно 0.0679	Слабо позитивно 0.1707	Слабо позитивно 0.0105	Слабо позитивно 0.0676	Слаб негативан -0.0138	Слаб негативан -0.0545	Слаб негативан -0.1821
Answer 10	-	Слабо позитивно 0.0793	Слабо позитивно 0.0772	Слаб негативан -0.0208	Слабо позитивно 0.0242	Слабо позитивно 0.0343	Слаб негативан -0.0152	Слаб негативан -0.1300
Answer 11	-	Слабо позитивно 0.0590	Слабо позитивно 0.0559	Слаб негативан -0.0071	Слабо позитивно 0.0082	Слабо позитивно 0.0205	Слабо позитивно 0.0266	Слаб негативан -0.1213
Answer 12	-	Слабо позитивно 0.0405	Слабо позитивно 0.1050	Слаб негативан -0.0363	Слабо позитивно 0.0361	Слабо позитивно 0.0253	Слабо позитивно 0.0277	Слаб негативан -0.1522
Answer 13	-	Слабо позитивно 0.0655	Слабо позитивно 0.1056	Слаб негативан -0.0439	Слабо позитивно 0.0270	Слабо позитивно 0.0417	Слабо позитивно 0.0152	Слаб негативан -0.1601
Answer 14	-	Слабо позитивно 0.0728	Слабо позитивно 0.1049	Слаб негативан -0.0002	Слаб негативан -0.0088	Слаб негативан -0.0007	Слабо позитивно 0.0061	Слаб негативан -0.1187
Answer 15	-	Слабо позитивно 0.0561	Слабо позитивно 0.1378	Слаб негативан -0.0415	Слабо позитивно 0.0178	Слаб негативан -0.0162	Слабо позитивно 0.0194	Слаб негативан -0.1176
Answer 16	-	Слабо позитивно 0.0606	Слабо позитивно 0.0308	Слаб негативан -0.0348	Слаб негативан -0.0421	Слабо позитивно 0.0642	Слабо позитивно 0.0250	Слаб негативан -0.0717

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

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

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

2023.10.13

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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