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 0.0569	Заифи мусбат 0.0313	Заифи манфӣ -0.0161	Заифи мусбат 0.0906	Заифи мусбат 0.0297	Заифи манфӣ -0.0118	Заифи манфӣ -0.1544
Answer 2	-	Заифи мусбат 0.0225	Заифи мусбат 0.0002	Заифи манфӣ -0.0450	Заифи мусбат 0.0644	Заифи мусбат 0.0442	Заифи мусбат 0.0128	Заифи манфӣ -0.0940
Answer 3	-	Заифи манфӣ -0.0030	Заифи манфӣ -0.0116	Заифи манфӣ -0.0411	Заифи манфӣ -0.0465	Заифи мусбат 0.0466	Заифи мусбат 0.0786	Заифи манфӣ -0.0200
Answer 4	-	Заифи мусбат 0.0440	Заифи мусбат 0.0354	Заифи манфӣ -0.0189	Заифи мусбат 0.0150	Заифи мусбат 0.0299	Заифи мусбат 0.0204	Заифи манфӣ -0.0986
Answer 5	-	Заифи мусбат 0.0309	Заифи мусбат 0.1278	Заифи мусбат 0.0137	Заифи мусбат 0.0728	Заифи манфӣ -0.0011	Заифи манфӣ -0.0195	Заифи манфӣ -0.1757
Answer 6	-	Заифи манфӣ -0.0001	Заифи мусбат 0.0086	Заифи манфӣ -0.0623	Заифи манфӣ -0.0085	Заифи мусбат 0.0193	Заифи мусбат 0.0829	Заифи манфӣ -0.0319
Answer 7	-	Заифи мусбат 0.0127	Заифи мусбат 0.0385	Заифи манфӣ -0.0683	Заифи манфӣ -0.0246	Заифи мусбат 0.0468	Заифи мусбат 0.0640	Заифи манфӣ -0.0519
Answer 8	-	Заифи мусбат 0.0700	Заифи мусбат 0.0853	Заифи манфӣ -0.0322	Заифи мусбат 0.0146	Заифи мусбат 0.0344	Заифи мусбат 0.0132	Заифи манфӣ -0.1370
Answer 9	-	Заифи мусбат 0.0670	Заифи мусбат 0.1680	Заифи мусбат 0.0087	Заифи мусбат 0.0692	Заифи манфӣ -0.0132	Заифи манфӣ -0.0518	Заифи манфӣ -0.1822
Answer 10	-	Заифи мусбат 0.0784	Заифи мусбат 0.0758	Заифи манфӣ -0.0199	Заифи мусбат 0.0245	Заифи мусбат 0.0342	Заифи манфӣ -0.0133	Заифи манфӣ -0.1308
Answer 11	-	Заифи мусбат 0.0586	Заифи мусбат 0.0528	Заифи манфӣ -0.0091	Заифи мусбат 0.0074	Заифи мусбат 0.0198	Заифи мусбат 0.0318	Заифи манфӣ -0.1198
Answer 12	-	Заифи мусбат 0.0392	Заифи мусбат 0.1042	Заифи манфӣ -0.0353	Заифи мусбат 0.0357	Заифи мусбат 0.0249	Заифи мусбат 0.0297	Заифи манфӣ -0.1526
Answer 13	-	Заифи мусбат 0.0646	Заифи мусбат 0.1052	Заифи манфӣ -0.0444	Заифи мусбат 0.0266	Заифи мусбат 0.0416	Заифи мусбат 0.0176	Заифи манфӣ -0.1605
Answer 14	-	Заифи мусбат 0.0714	Заифи мусбат 0.1026	Заифи манфӣ -0.0002	Заифи манфӣ -0.0090	Заифи манфӣ -0.0012	Заифи мусбат 0.0086	Заифи манфӣ -0.1174
Answer 15	-	Заифи мусбат 0.0558	Заифи мусбат 0.1369	Заифи манфӣ -0.0419	Заифи мусбат 0.0176	Заифи манфӣ -0.0163	Заифи мусбат 0.0222	Заифи манфӣ -0.1183
Answer 16	-	Заифи мусбат 0.0592	Заифи мусбат 0.0275	Заифи манфӣ -0.0384	Заифи манфӣ -0.0402	Заифи мусбат 0.0652	Заифи мусбат 0.0283	Заифи манфӣ -0.0710

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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