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

Врста корелације	линеарно (Пеарсон) линеарно (Пеарсон) Нелинеарни (Спеарман)
Критична вредност коефицијента корелације	Нормална дистрибуција, Виллиам Сеали Госсет (Студент) Нормална дистрибуција, Виллиам Сеали Госсет (Студент) Нон нормална дистрибуција, од стране Спеарман-а	Прикажи само резултате > r = 0.0294

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 0.0475	Слабо позитивно 0.0210	Слаб негативан -0.0214	Слабо позитивно 0.1000	Слабо позитивно 0.0342	Слаб негативан -0.0105	Слаб негативан -0.1505
Answer 2	-	Слабо позитивно 0.0187	Слабо позитивно 0.0032	Слаб негативан -0.0357	Слабо позитивно 0.0611	Слабо позитивно 0.0475	Слабо позитивно 0.0094	Слаб негативан -0.0987
Answer 3	-	Слаб негативан -0.0032	Слабо позитивно 0.0012	Слаб негативан -0.0418	Слаб негативан -0.0473	Слабо позитивно 0.0442	Слабо позитивно 0.0770	Слаб негативан -0.0240
Answer 4	-	Слабо позитивно 0.0403	Слабо позитивно 0.0305	Слаб негативан -0.0241	Слабо позитивно 0.0198	Слабо позитивно 0.0336	Слабо позитивно 0.0227	Слаб негативан -0.0988
Answer 5	-	Слабо позитивно 0.0218	Слабо позитивно 0.1265	Слабо позитивно 0.0068	Слабо позитивно 0.0828	Слабо позитивно 0.0008	Слаб негативан -0.0119	Слаб негативан -0.1822
Answer 6	-	Слабо позитивно 0.0065	Слабо позитивно 0.0165	Слаб негативан -0.0621	Слаб негативан -0.0123	Слабо позитивно 0.0193	Слабо позитивно 0.0850	Слаб негативан -0.0406
Answer 7	-	Слабо позитивно 0.0137	Слабо позитивно 0.0441	Слаб негативан -0.0686	Слаб негативан -0.0370	Слабо позитивно 0.0461	Слабо позитивно 0.0730	Слаб негативан -0.0518
Answer 8	-	Слабо позитивно 0.0592	Слабо позитивно 0.0827	Слаб негативан -0.0228	Слабо позитивно 0.0102	Слабо позитивно 0.0380	Слабо позитивно 0.0151	Слаб негативан -0.1380
Answer 9	-	Слабо позитивно 0.0693	Слабо позитивно 0.1576	Слабо позитивно 0.0039	Слабо позитивно 0.0606	Слаб негативан -0.0095	Слаб негативан -0.0453	Слаб негативан -0.1750
Answer 10	-	Слабо позитивно 0.0719	Слабо позитивно 0.0590	Слаб негативан -0.0104	Слабо позитивно 0.0204	Слабо позитивно 0.0416	Слаб негативан -0.0075	Слаб негативан -0.1319
Answer 11	-	Слабо позитивно 0.0595	Слабо позитивно 0.0536	Слаб негативан -0.0006	Слабо позитивно 0.0093	Слабо позитивно 0.0242	Слабо позитивно 0.0192	Слаб негативан -0.1254
Answer 12	-	Слабо позитивно 0.0400	Слабо позитивно 0.0990	Слаб негативан -0.0371	Слабо позитивно 0.0337	Слабо позитивно 0.0296	Слабо позитивно 0.0290	Слаб негативан -0.1509
Answer 13	-	Слабо позитивно 0.0727	Слабо позитивно 0.0967	Слаб негативан -0.0350	Слабо позитивно 0.0235	Слабо позитивно 0.0341	Слабо позитивно 0.0169	Слаб негативан -0.1581
Answer 14	-	Слабо позитивно 0.0832	Слабо позитивно 0.0882	Слаб негативан -0.0023	Слаб негативан -0.0189	Слабо позитивно 0.0039	Слабо позитивно 0.0120	Слаб негативан -0.1127
Answer 15	-	Слабо позитивно 0.0553	Слабо позитивно 0.1247	Слаб негативан -0.0264	Слабо позитивно 0.0096	Слаб негативан -0.0189	Слабо позитивно 0.0270	Слаб негативан -0.1193
Answer 16	-	Слабо позитивно 0.0646	Слабо позитивно 0.0299	Слаб негативан -0.0306	Слаб негативан -0.0487	Слабо позитивно 0.0642	Слабо позитивно 0.0190	Слаб негативан -0.0672

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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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