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) Акыркы айда персоналга карата компаниялардын иш-аракеттери (ооба / жок)

2) Акыркы айда персоналга карата компаниялардын иш-аракеттери (фактыларында факт)

3) Коркуу

4) Менин өлкөмдүн эң чоң көйгөйлөрү

5) Ийгиликке жеткенде, жакшы лидерлер кандай сапаттар жана жөндөмдөр колдонушат?

6) Гугл. Команданын таасирин тийгизген факторлор

7) Жумуш издөөчүлөрдүн негизги артыкчылыктары

8) Чоң жол башчыга эмне жардам берет?

9) Жумушта адамдарды ийгиликтүү кылат?

10) Алыстан иштөө үчүн азыраак акы алууга даярсызбы?

11) Аланизм барбы?

12) Карьерада АГЕНЦИЯЛЫК

13) Жашоодо

14) Араизмдин себептери

15) Адамдар багынып беришинин себептери (Анна Витал тарабынан)

16) Ишенүү (#WVS)

17) Оксфорд бактылуу

18) Психологиялык жыргалчылык

19) Сиздин кийинки эң кызыктуу мүмкүнчүлүгүңүз кайда болмок?

20) Ушул жуманы психикалык ден-соолугуңузга кам көрүү үчүн эмне кыласыз?

21) Мен өткөн, азыркы же келечек жөнүндө ойлонуп жашайм

22) Meritociace

23) Жасалма интеллект жана цивилизациянын аягы

24) Эмне үчүн адамдар создуктурушат?

25) Өзүн-өзү ишенимди курууда гендердик айырма (IFD Алленич)

26) Xing.com маданият баалоо

27) Патрик Ленционинин "команданын беш дисфунттери"

28) Боорукердик ...

29) Жумуш сунушун тандоодо бул адистер үчүн эмне үчүн маанилүү?

30) Эмне үчүн адамдар өзгөрүүгө каршы турушат (Сиобан МакХейлдин)

31) Сезимдериңизди кандайча жөнгө саласыз? (Навал Мустафа М.А.)

32) 21 Сизди түбөлүккө төлөп берген жөндөмдөр (Жеремия Тео / 赵汉昇)

33) Чыныгы эркиндик бул ...

34) Башкаларга ишеним өрчүтүүнүн 12 жолу (Джастин Райт)

35) Таланттуу кызматкердин мүнөздөмөлөрү (таланттуу башкаруу институту тарабынан)

36) Командаңызды түрткү берүү үчүн 10 ачкыч

37) Абийир алгебрасы (Владимир Лефебвр тарабынан)

38) Келечектин үч өзгөчө мүмкүнчүлүгү (доктор Клэр В. Грейвс тарабынан)

39) Өзүнө ишенимди бекемдөө боюнча аракеттер (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.

Коркуу

ЧарттарСалыштырмалуу

VUCA

Корреляция түрү	Сызыктуу (Пирсон) Сызыктуу (Пирсон) Сызыктуу эмес (Спирмен)
Корреляция коэффициентинин критикалык мааниси	Нормалдуу бөлүштүрүү, William Sealy Gosset (студент) Нормалдуу бөлүштүрүү, William Sealy Gosset (студент) Нормалдуу эмес бөлүштүрүү, Спарман	Натыйжаларды гана көрсөтүү > r = 0.029

Бөлүштүрүү	Кадимки эмес	Кадимки эмес	Кадимки эмес	Нормалдуу	Нормалдуу	Нормалдуу	Нормалдуу	Нормалдуу
Бардык суроолор Бардык суроолор Менин эң чоң коркунучум
Менин эң чоң коркунучум
Answer 1	-	Алсыз позитив 0.0429	Алсыз позитив 0.0189	Алсыз терс -0.0194	Алсыз позитив 0.0971	Алсыз позитив 0.0362	Алсыз терс -0.0081	Алсыз терс -0.1493
Answer 2	-	Алсыз позитив 0.0167	Алсыз позитив 0.0065	Алсыз терс -0.0354	Алсыз позитив 0.0582	Алсыз позитив 0.0448	Алсыз позитив 0.0113	Алсыз терс -0.0962
Answer 3	-	Алсыз терс -0.0054	Алсыз позитив 0.0053	Алсыз терс -0.0440	Алсыз терс -0.0462	Алсыз позитив 0.0411	Алсыз позитив 0.0795	Алсыз терс -0.0241
Answer 4	-	Алсыз позитив 0.0366	Алсыз позитив 0.0289	Алсыз терс -0.0226	Алсыз позитив 0.0207	Алсыз позитив 0.0329	Алсыз позитив 0.0276	Алсыз терс -0.1013
Answer 5	-	Алсыз позитив 0.0169	Алсыз позитив 0.1275	Алсыз позитив 0.0119	Алсыз позитив 0.0794	Алсыз терс -0.0030	Алсыз терс -0.0087	Алсыз терс -0.1804
Answer 6	-	Алсыз позитив 0.0065	Алсыз позитив 0.0202	Алсыз терс -0.0625	Алсыз терс -0.0146	Алсыз позитив 0.0178	Алсыз позитив 0.0881	Алсыз терс -0.0420
Answer 7	-	Алсыз позитив 0.0139	Алсыз позитив 0.0480	Алсыз терс -0.0680	Алсыз терс -0.0387	Алсыз позитив 0.0425	Алсыз позитив 0.0743	Алсыз терс -0.0514
Answer 8	-	Алсыз позитив 0.0643	Алсыз позитив 0.0891	Алсыз терс -0.0166	Алсыз позитив 0.0062	Алсыз позитив 0.0290	Алсыз позитив 0.0135	Алсыз терс -0.1386
Answer 9	-	Алсыз позитив 0.0674	Алсыз позитив 0.1614	Алсыз позитив 0.0085	Алсыз позитив 0.0549	Алсыз терс -0.0146	Алсыз терс -0.0434	Алсыз терс -0.1727
Answer 10	-	Алсыз позитив 0.0701	Алсыз позитив 0.0597	Алсыз терс -0.0113	Алсыз позитив 0.0167	Алсыз позитив 0.0437	Алсыз терс -0.0041	Алсыз терс -0.1326
Answer 11	-	Алсыз позитив 0.0575	Алсыз позитив 0.0612	Алсыз позитив 0.0028	Алсыз позитив 0.0085	Алсыз позитив 0.0192	Алсыз позитив 0.0187	Алсыз терс -0.1277
Answer 12	-	Алсыз позитив 0.0411	Алсыз позитив 0.1022	Алсыз терс -0.0340	Алсыз позитив 0.0313	Алсыз позитив 0.0248	Алсыз позитив 0.0296	Алсыз терс -0.1508
Answer 13	-	Алсыз позитив 0.0722	Алсыз позитив 0.0951	Алсыз терс -0.0322	Алсыз позитив 0.0201	Алсыз позитив 0.0317	Алсыз позитив 0.0209	Алсыз терс -0.1575
Answer 14	-	Алсыз позитив 0.0850	Алсыз позитив 0.0886	Алсыз терс -0.0020	Алсыз терс -0.0257	Алсыз позитив 0.0061	Алсыз позитив 0.0131	Алсыз терс -0.1116
Answer 15	-	Алсыз позитив 0.0553	Алсыз позитив 0.1253	Алсыз терс -0.0257	Алсыз позитив 0.0072	Алсыз терс -0.0188	Алсыз позитив 0.0258	Алсыз терс -0.1181
Answer 16	-	Алсыз позитив 0.0691	Алсыз позитив 0.0339	Алсыз терс -0.0302	Алсыз терс -0.0534	Алсыз позитив 0.0616	Алсыз позитив 0.0197	Алсыз терс -0.0682

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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

Продукт ээси SaaS SDTEST®

Валерий 1993-жылы социалдык педагог-психолог квалификациясын алган жана андан бери өз билимин долбоорлорду башкарууда колдонот.
Валерий 2013-жылы магистр даражасын жана долбоордун жана программанын менеджеринин квалификациясын алган. Магистрдик программасынын жүрүшүндө ал Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) жана Spiral Dynamics менен таанышкан.
Валерий V.U.C.A-нын белгисиздигин изилдөөнүн автору. психологияда Spiral Dynamics жана математикалык статистиканы колдонуу менен концепция жана 38 эл аралык сурамжылоо.

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