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)

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

Чарттар Салыштырмалуу

VUCA

Корреляция коэффициентинин критикалык мааниси

Нормалдуу бөлүштүрүү, William Sealy Gosset (студент) r = 0.0331

Нормалдуу эмес бөлүштүрүү, Спарман r = 0.0013

Натыйжаларды гана көрсөтүү > r = 0.0331

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 0.0563	Алсыз позитив 0.0317	Алсыз терс -0.0161	Алсыз позитив 0.0907	Алсыз позитив 0.0298	Алсыз терс -0.0126	Алсыз терс -0.1537
Answer 2	-	Алсыз позитив 0.0216	Алсыз позитив 0.0002	Алсыз терс -0.0458	Алсыз позитив 0.0654	Алсыз позитив 0.0445	Алсыз позитив 0.0124	Алсыз терс -0.0937
Answer 3	-	Алсыз терс -0.0035	Алсыз терс -0.0111	Алсыз терс -0.0421	Алсыз терс -0.0456	Алсыз позитив 0.0466	Алсыз позитив 0.0786	Алсыз терс -0.0201
Answer 4	-	Алсыз позитив 0.0435	Алсыз позитив 0.0353	Алсыз терс -0.0181	Алсыз позитив 0.0145	Алсыз позитив 0.0301	Алсыз позитив 0.0197	Алсыз терс -0.0979
Answer 5	-	Алсыз позитив 0.0299	Алсыз позитив 0.1279	Алсыз позитив 0.0136	Алсыз позитив 0.0730	Алсыз терс -0.0007	Алсыз терс -0.0207	Алсыз терс -0.1746
Answer 6	-	Алсыз терс -0.0004	Алсыз позитив 0.0082	Алсыз терс -0.0629	Алсыз терс -0.0078	Алсыз позитив 0.0193	Алсыз позитив 0.0830	Алсыз терс -0.0318
Answer 7	-	Алсыз позитив 0.0122	Алсыз позитив 0.0381	Алсыз терс -0.0686	Алсыз терс -0.0242	Алсыз позитив 0.0471	Алсыз позитив 0.0636	Алсыз терс -0.0513
Answer 8	-	Алсыз позитив 0.0698	Алсыз позитив 0.0849	Алсыз терс -0.0321	Алсыз позитив 0.0146	Алсыз позитив 0.0345	Алсыз позитив 0.0130	Алсыз терс -0.1368
Answer 9	-	Алсыз позитив 0.0665	Алсыз позитив 0.1674	Алсыз позитив 0.0092	Алсыз позитив 0.0691	Алсыз терс -0.0128	Алсыз терс -0.0528	Алсыз терс -0.1812
Answer 10	-	Алсыз позитив 0.0778	Алсыз позитив 0.0755	Алсыз терс -0.0180	Алсыз позитив 0.0231	Алсыз позитив 0.0346	Алсыз терс -0.0146	Алсыз терс -0.1298
Answer 11	-	Алсыз позитив 0.0584	Алсыз позитив 0.0524	Алсыз терс -0.0096	Алсыз позитив 0.0081	Алсыз позитив 0.0199	Алсыз позитив 0.0318	Алсыз терс -0.1197
Answer 12	-	Алсыз позитив 0.0380	Алсыз позитив 0.1042	Алсыз терс -0.0352	Алсыз позитив 0.0357	Алсыз позитив 0.0254	Алсыз позитив 0.0286	Алсыз терс -0.1515
Answer 13	-	Алсыз позитив 0.0644	Алсыз позитив 0.1057	Алсыз терс -0.0448	Алсыз позитив 0.0268	Алсыз позитив 0.0416	Алсыз позитив 0.0169	Алсыз терс -0.1600
Answer 14	-	Алсыз позитив 0.0717	Алсыз позитив 0.1026	Алсыз терс -0.0006	Алсыз терс -0.0089	Алсыз терс -0.0012	Алсыз позитив 0.0080	Алсыз терс -0.1168
Answer 15	-	Алсыз позитив 0.0549	Алсыз позитив 0.1375	Алсыз терс -0.0420	Алсыз позитив 0.0178	Алсыз терс -0.0160	Алсыз позитив 0.0216	Алсыз терс -0.1180
Answer 16	-	Алсыз позитив 0.0591	Алсыз позитив 0.0273	Алсыз терс -0.0386	Алсыз терс -0.0399	Алсыз позитив 0.0653	Алсыз позитив 0.0282	Алсыз терс -0.0708

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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

Продукт ээси Саас үй жаныбары Долбоорунун СТТЕСТ®

Валерий 1993-жылы социалдык педагогок-психолог катары квалификацияланган жана анын билимин долбоорду башкарууда колдонгон.
Валерий 2013-жылы магистрдик даражасын жана программалык менеджер квалификациясын алган. Ал мырзасынын программасы учурунда ал долбоордун программасы менен тааныш болгон (GPM Deutsche Gesellschaft für projektmanagement д. V.) жана спираль динамикасы.
Валерии ар кандай спираль динамикасын сынап көрдү жана STTESTдин учурдагы версиясын ылайыкташтыруу үчүн өзүнүн билимин жана тажрыйбасын колдонгон.
Valerii V.u.c.a белгисиздикти изилдөө автор. спираль динамикасын жана психологиядагы математикалык статистика менен, 20дан ашык эл аралык сурамжылоолорду колдонуп, түшүнүк.

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