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) Действия на компании във връзка с персонала през последния месец (да / не)

2) Действия на дружествата във връзка с персонала през последния месец (факт в%)

3) Страховете

4) Най -големите проблеми пред моята страна

5) Какви качества и способности използват добрите лидери при изграждането на успешни екипи?

6) Google. Фактори, които влияят на ефективността на екипа

7) Основните приоритети на търсещите работа

8) Какво прави шефа страхотен лидер?

9) Какво прави хората успешни на работа?

10) Готови ли сте да получавате по -малко заплащане, за да работите дистанционно?

11) Съществува ли егеизмът?

12) Възрастът в кариерата

13) Агеизъм в живота

14) Причини за възрастта

15) Причини, поради които хората се отказват (от Анна жизненоважно)

16) ДОВЕРИЕ (#WVS)

17) Оксфордско проучване за щастие

18) Психологическо благополучие

19) Къде ще бъде следващата ви най -вълнуваща възможност?

20) Какво ще направите тази седмица, за да се грижите за психичното си здраве?

21) Живея, мисля за миналото, настоящето или бъдещето си

22) Меритокрация

23) Изкуствен интелект и края на цивилизацията

24) Защо хората отлагат?

25) Разлика между половете в изграждането на самочувствие (IFD Allensbach)

26) Xing.com Оценка на културата

27) „Петте дисфункции на екип“ на Патрик Ленсиони “

28) Емпатията е ...

29) Какво е от съществено значение за ИТ специалистите при избора на оферта за работа?

30) Защо хората се съпротивляват на промяната (от Siobhán McHale)

31) Как регулирате емоциите си? (От Nawal Mustafa M.A.)

32) 21 умения, които ви плащат завинаги (от Йеремия Тео / 赵汉昇)

33) Истинската свобода е ...

34) 12 начина за изграждане на доверие с другите (от Джъстин Райт)

35) Характеристики на талантлив служител (от Института за управление на таланти)

36) 10 ключа за мотивиране на вашия екип

37) Алгебра на съвестта (от Владимир Льофевр)

38) Три различни възможности на бъдещето (от д-р Клеър У. Грейвс)

39) Действия за изграждане на непоклатимо самочувствие (от Сурен Самарчян)

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.

Страховете

Графики Корелация

VUCA

Критична стойност на коефициента на корелация

Нормално разпространение, от Уилям Сили Госет (студент) r = 0.0317

Не нормално разпределение, от Spearman r = 0.0013

Показват само резултати > r = 0.0317

Разпределение	Не нормално	Не нормално	Не нормално	Нормално	Нормално	Нормално	Нормално	Нормално
Всички въпроси Всички въпроси Най-големият ми страх е
Най-големият ми страх е
Answer 1	-	Слаба положителна 0.0537	Слаба положителна 0.0288	Слаб отрицателен -0.0175	Слаба положителна 0.0948	Слаба положителна 0.0381	Слаб отрицателен -0.0178	Слаб отрицателен -0.1563
Answer 2	-	Слаба положителна 0.0194	Слаб отрицателен -0.0048	Слаб отрицателен -0.0385	Слаба положителна 0.0655	Слаба положителна 0.0495	Слаба положителна 0.0106	Слаб отрицателен -0.0982
Answer 3	-	Слаб отрицателен -0.0001	Слаб отрицателен -0.0084	Слаб отрицателен -0.0449	Слаб отрицателен -0.0445	Слаба положителна 0.0485	Слаба положителна 0.0742	Слаб отрицателен -0.0207
Answer 4	-	Слаба положителна 0.0433	Слаба положителна 0.0291	Слаб отрицателен -0.0232	Слаба положителна 0.0163	Слаба положителна 0.0367	Слаба положителна 0.0226	Слаб отрицателен -0.0996
Answer 5	-	Слаба положителна 0.0277	Слаба положителна 0.1291	Слаба положителна 0.0108	Слаба положителна 0.0745	Слаба положителна 0.0012	Слаб отрицателен -0.0177	Слаб отрицателен -0.1783
Answer 6	-	Слаб отрицателен -0.0015	Слаба положителна 0.0058	Слаб отрицателен -0.0607	Слаб отрицателен -0.0094	Слаба положителна 0.0255	Слаба положителна 0.0844	Слаб отрицателен -0.0363
Answer 7	-	Слаба положителна 0.0113	Слаба положителна 0.0348	Слаб отрицателен -0.0657	Слаб отрицателен -0.0305	Слаба положителна 0.0521	Слаба положителна 0.0686	Слаб отрицателен -0.0532
Answer 8	-	Слаба положителна 0.0657	Слаба положителна 0.0728	Слаб отрицателен -0.0255	Слаба положителна 0.0124	Слаба положителна 0.0386	Слаба положителна 0.0153	Слаб отрицателен -0.1345
Answer 9	-	Слаба положителна 0.0757	Слаба положителна 0.1605	Слаба положителна 0.0066	Слаба положителна 0.0612	Слаб отрицателен -0.0063	Слаб отрицателен -0.0492	Слаб отрицателен -0.1822
Answer 10	-	Слаба положителна 0.0764	Слаба положителна 0.0669	Слаб отрицателен -0.0124	Слаба положителна 0.0271	Слаба положителна 0.0365	Слаб отрицателен -0.0130	Слаб отрицателен -0.1348
Answer 11	-	Слаба положителна 0.0634	Слаба положителна 0.0526	Слаб отрицателен -0.0075	Слаба положителна 0.0096	Слаба положителна 0.0264	Слаба положителна 0.0242	Слаб отрицателен -0.1270
Answer 12	-	Слаба положителна 0.0450	Слаба положителна 0.0944	Слаб отрицателен -0.0323	Слаба положителна 0.0307	Слаба положителна 0.0343	Слаба положителна 0.0260	Слаб отрицателен -0.1530
Answer 13	-	Слаба положителна 0.0725	Слаба положителна 0.0947	Слаб отрицателен -0.0389	Слаба положителна 0.0265	Слаба положителна 0.0443	Слаба положителна 0.0144	Слаб отрицателен -0.1631
Answer 14	-	Слаба положителна 0.0820	Слаба положителна 0.0897	Слаб отрицателен -0.0030	Слаб отрицателен -0.0122	Слаба положителна 0.0060	Слаба положителна 0.0135	Слаб отрицателен -0.1213
Answer 15	-	Слаба положителна 0.0549	Слаба положителна 0.1265	Слаб отрицателен -0.0334	Слаба положителна 0.0119	Слаб отрицателен -0.0153	Слаба положителна 0.0242	Слаб отрицателен -0.1157
Answer 16	-	Слаба положителна 0.0732	Слаба положителна 0.0242	Слаб отрицателен -0.0373	Слаб отрицателен -0.0398	Слаба положителна 0.0729	Слаба положителна 0.0169	Слаб отрицателен -0.0774

Експорт към 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

Собственик на продукта SaaS SDTEST®

Валерий получава квалификация социален педагог-психолог през 1993 г. и оттогава прилага знанията си в управлението на проекти.
Валерий получава магистърска степен и квалификация за ръководител на проекти и програми през 2013 г. По време на магистърската си програма той се запознава с Пътната карта на проекта (GPM Deutsche Gesellschaft für Projektmanagement e. V.) и Spiral Dynamics.
Валерий е автор на изследване на несигурността на V.U.C.A. концепция, използваща спирална динамика и математическа статистика в психологията, и 38 международни проучвания.

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