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) Амалҳои ширкатҳо дар робита ба кадрҳо дар моҳи охир (ҳа / не)

2) Амалҳои ширкатҳо дар робита ба кадрҳо дар моҳи гузашта (далел дар%)

3) Тарс

4) Мушкилоти бузургтарин бо кишвари ман

5) Кадом хислатҳо ва қобилиятҳо ҳангоми сохтани дастаҳои муваффақ истифода мебаранд?

6) Google. Омилҳое, ки ба самаранокии гурӯҳ таъсир мерасонанд

7) Афзалиятҳои асосии Ҷустуҷӯ

8) Роҳбарро пешвои бузург месозад?

9) Чӣ одамонро дар ҷои кор муваффақ мегардонад?

10) Шумо барои гирифтани музди камтар барои кор кардан омодаед?

11) Аҳамият вуҷуд дорад?

12) Синнуобар дар касб

13) Синну сол дар ҳаёт

14) Сабабҳои синну сол

15) Сабабҳои чаро одамонро таслим мекунанд (аз ҷониби Вала

16) Боварӣ (#WVS)

17) Тадқиқоти хушбахтии Оксфорд

18) Варақаи равонӣ

19) ФАЪОЛИЯТИ ИСТИФОДАИ ИСТИФОДАИ ИСТИФОДАИ ИСТИФОДАИ ИСТИФОДАИ ИСТИФОДАИ ИСТИФОДАИ ИСТИФОДАИ ИСТИФОДАИ МЕГӮЯД?

20) Ин ҳафта шумо барои солимии рӯҳии худ чӣ кор мекунед?

21) Ман дар бораи гузаштаи гузашта, ҳозира ва оянда фикр мекунам

22) Маллокократ

23) Зеҳнии сунъӣ ва охири тамаддун

24) Чаро мардум ба поймол мешаванд?

25) Тафовути гендерӣ дар сохтани эътимод ба худбоварӣ (IFD AFD

26) Xing.com Арзёбии фарҳанг

27) Патрик Ленси "Панҷ ҳолати бемории даста"

28) Ҳамдардӣ ...

29) Барои мутахассисони он дар интихоби пешниҳоди кор чӣ қадар муҳим аст?

30) Чаро одамон ба тағирот муқобилат мекунанд (аз ҷониби SIOBHáN MCHALE)

31) Чӣ тавр шумо эҳсосоти худро танзим мекунед? (аз ҷониби nawal m.a.)

32) 21 Малакае, ки шуморо то абад пардохт мекунанд (аз ҷониби Ирмиё teo / 赵汉昇)

33) Озодии воқеӣ ...

34) 12 Роҳҳои эҷоди эътимод бо дигарон

35) Хусусиятҳои корманди боистеъдод (аз ҷониби Донишкадаи идоракунии талант)

36) 10 тугмачаҳо барои ҳавасманд кардани дастаи худ

37) Алгебраи виҷдон (аз ҷониби Владимир Лефебвр)

38) Се имконияти мушаххаси оянда (аз ҷониби доктор Клэр В. Грейвс)

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.

Тарс

Диаграммаҳои Таносуби

VUCA

Арзиши интиқодии коэффитсиенти коррелятсионӣ

Тақсимоти муқаррарӣ, ки аз ҷониби Вилям Веллети баҳрӣ (донишҷӯ) r = 0.033

Тақсимоти муқаррарӣ, аз ҷониби Spearman r = 0.0013

Танҳо натиҷа нишон диҳед > r = 0.033

Тащсимот	Начандон	Начандон	Начандон	Муқаррарӣ	Муқаррарӣ	Муқаррарӣ	Муқаррарӣ	Муқаррарӣ
Ҳама саволҳо Ҳама саволҳо Тарси бузургтарини ман аст
Тарси бузургтарини ман аст
Answer 1	-	Заифи мусбат 0.0532	Заифи мусбат 0.0292	Заифи манфӣ -0.0175	Заифи мусбат 0.0919	Заифи мусбат 0.0301	Заифи манфӣ -0.0114	Заифи манфӣ -0.1523
Answer 2	-	Заифи мусбат 0.0208	Заифи манфӣ -0.0014	Заифи манфӣ -0.0431	Заифи мусбат 0.0641	Заифи мусбат 0.0449	Заифи мусбат 0.0130	Заифи манфӣ -0.0931
Answer 3	-	Заифи манфӣ -0.0053	Заифи манфӣ -0.0130	Заифи манфӣ -0.0406	Заифи манфӣ -0.0456	Заифи мусбат 0.0474	Заифи мусбат 0.0793	Заифи манфӣ -0.0204
Answer 4	-	Заифи мусбат 0.0427	Заифи мусбат 0.0328	Заифи манфӣ -0.0200	Заифи мусбат 0.0158	Заифи мусбат 0.0306	Заифи мусбат 0.0217	Заифи манфӣ -0.0980
Answer 5	-	Заифи мусбат 0.0255	Заифи мусбат 0.1255	Заифи мусбат 0.0143	Заифи мусбат 0.0732	Заифи манфӣ -0.0019	Заифи манфӣ -0.0196	Заифи манфӣ -0.1747
Answer 6	-	Заифи манфӣ -0.0027	Заифи мусбат 0.0074	Заифи манфӣ -0.0629	Заифи манфӣ -0.0074	Заифи мусбат 0.0199	Заифи мусбат 0.0835	Заифи манфӣ -0.0324
Answer 7	-	Заифи мусбат 0.0110	Заифи мусбат 0.0371	Заифи манфӣ -0.0688	Заифи манфӣ -0.0227	Заифи мусбат 0.0471	Заифи мусбат 0.0650	Заифи манфӣ -0.0523
Answer 8	-	Заифи мусбат 0.0693	Заифи мусбат 0.0825	Заифи манфӣ -0.0321	Заифи мусбат 0.0139	Заифи мусбат 0.0351	Заифи мусбат 0.0147	Заифи манфӣ -0.1369
Answer 9	-	Заифи мусбат 0.0643	Заифи мусбат 0.1659	Заифи мусбат 0.0082	Заифи мусбат 0.0699	Заифи манфӣ -0.0136	Заифи манфӣ -0.0513	Заифи манфӣ -0.1826
Answer 10	-	Заифи мусбат 0.0760	Заифи мусбат 0.0730	Заифи манфӣ -0.0219	Заифи мусбат 0.0254	Заифи мусбат 0.0318	Заифи манфӣ -0.0138	Заифи манфӣ -0.1318
Answer 11	-	Заифи мусбат 0.0571	Заифи мусбат 0.0514	Заифи манфӣ -0.0099	Заифи мусбат 0.0077	Заифи мусбат 0.0206	Заифи мусбат 0.0308	Заифи манфӣ -0.1211
Answer 12	-	Заифи мусбат 0.0373	Заифи мусбат 0.1013	Заифи манфӣ -0.0357	Заифи мусбат 0.0357	Заифи мусбат 0.0243	Заифи мусбат 0.0296	Заифи манфӣ -0.1524
Answer 13	-	Заифи мусбат 0.0621	Заифи мусбат 0.1036	Заифи манфӣ -0.0438	Заифи мусбат 0.0273	Заифи мусбат 0.0414	Заифи мусбат 0.0176	Заифи манфӣ -0.1608
Answer 14	-	Заифи мусбат 0.0703	Заифи мусбат 0.1007	Заифи мусбат 9.54E-5	Заифи манфӣ -0.0088	Заифи манфӣ -0.0011	Заифи мусбат 0.0084	Заифи манфӣ -0.1174
Answer 15	-	Заифи мусбат 0.0554	Заифи мусбат 0.1349	Заифи манфӣ -0.0418	Заифи мусбат 0.0179	Заифи манфӣ -0.0165	Заифи мусбат 0.0219	Заифи манфӣ -0.1181
Answer 16	-	Заифи мусбат 0.0581	Заифи мусбат 0.0255	Заифи манфӣ -0.0388	Заифи манфӣ -0.0407	Заифи мусбат 0.0654	Заифи мусбат 0.0283	Заифи манфӣ -0.0714

Содирот ба 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

Валерий Косенко

Соҳибгоҳи маҳсулот Саас Пет Лоиҳаи SDTEST®

Валериӣ ҳамчун педагологи иҷтимоӣ дар соли 1993 тахассус ва равоншинос дар соли 1993 баланд буд ва аз он вақт дониши ӯро дар идоракунии лоиҳа истифода бурд.
Валерии дараҷаи магистр ва лоиҳаи мудири барномаро дар соли 2013 ба даст овард. Ҳангоми барномаи устои худ, ӯ бо лоиҳаи КОРВАТ РОЙГОН РОЙГОН РОЙГОН РОЙГОН РОЙГОН РОЙГОН РОЙГОН РОЙГОНИ ХИЗМАТРАСОНИДАНИ ХИЗМАТ ГРИЛКХАТИ ИСТИФОДАИ ХИЗМАТ.
Валерий тестҳои гуногуни дадамикаи гуногунро гирифт ва донишу таҷрибаи ӯ барои мутобиқ кардани нусхаи кунунии SDTest буд.
Валерии муаллифи огоҳии номуайянии V.U.c.a мебошад. Консепсия бо истифода аз динамикаи спиралӣ ва математикии психология, зиёда аз 20 пурсишҳои байналмилалӣ.

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