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 0.0562	Алсыз позитив 0.0311	Алсыз терс -0.0164	Алсыз позитив 0.0903	Алсыз позитив 0.0301	Алсыз терс -0.0120	Алсыз терс -0.1534
Answer 2	-	Алсыз позитив 0.0217	Алсыз позитив 0.0011	Алсыз терс -0.0455	Алсыз позитив 0.0660	Алсыз позитив 0.0440	Алсыз позитив 0.0117	Алсыз терс -0.0942
Answer 3	-	Алсыз терс -0.0034	Алсыз терс -0.0104	Алсыз терс -0.0419	Алсыз терс -0.0451	Алсыз позитив 0.0462	Алсыз позитив 0.0780	Алсыз терс -0.0204
Answer 4	-	Алсыз позитив 0.0436	Алсыз позитив 0.0362	Алсыз терс -0.0177	Алсыз позитив 0.0150	Алсыз позитив 0.0296	Алсыз позитив 0.0189	Алсыз терс -0.0984
Answer 5	-	Алсыз позитив 0.0298	Алсыз позитив 0.1270	Алсыз позитив 0.0133	Алсыз позитив 0.0724	Алсыз терс -0.0002	Алсыз терс -0.0199	Алсыз терс -0.1742
Answer 6	-	Алсыз терс -0.0003	Алсыз позитив 0.0089	Алсыз терс -0.0627	Алсыз терс -0.0074	Алсыз позитив 0.0190	Алсыз позитив 0.0825	Алсыз терс -0.0321
Answer 7	-	Алсыз позитив 0.0123	Алсыз позитив 0.0388	Алсыз терс -0.0684	Алсыз терс -0.0238	Алсыз позитив 0.0468	Алсыз позитив 0.0631	Алсыз терс -0.0517
Answer 8	-	Алсыз позитив 0.0699	Алсыз позитив 0.0857	Алсыз терс -0.0318	Алсыз позитив 0.0150	Алсыз позитив 0.0341	Алсыз позитив 0.0125	Алсыз терс -0.1372
Answer 9	-	Алсыз позитив 0.0666	Алсыз позитив 0.1681	Алсыз позитив 0.0094	Алсыз позитив 0.0694	Алсыз терс -0.0131	Алсыз терс -0.0533	Алсыз терс -0.1815
Answer 10	-	Алсыз позитив 0.0776	Алсыз позитив 0.0744	Алсыз терс -0.0185	Алсыз позитив 0.0224	Алсыз позитив 0.0352	Алсыз терс -0.0135	Алсыз терс -0.1293
Answer 11	-	Алсыз позитив 0.0585	Алсыз позитив 0.0531	Алсыз терс -0.0094	Алсыз позитив 0.0086	Алсыз позитив 0.0195	Алсыз позитив 0.0313	Алсыз терс -0.1200
Answer 12	-	Алсыз позитив 0.0378	Алсыз позитив 0.1030	Алсыз терс -0.0357	Алсыз позитив 0.0350	Алсыз позитив 0.0261	Алсыз позитив 0.0297	Алсыз терс -0.1510
Answer 13	-	Алсыз позитив 0.0642	Алсыз позитив 0.1044	Алсыз терс -0.0454	Алсыз позитив 0.0259	Алсыз позитив 0.0424	Алсыз позитив 0.0183	Алсыз терс -0.1595
Answer 14	-	Алсыз позитив 0.0718	Алсыз позитив 0.1034	Алсыз терс -0.0003	Алсыз терс -0.0085	Алсыз терс -0.0016	Алсыз позитив 0.0074	Алсыз терс -0.1172
Answer 15	-	Алсыз позитив 0.0550	Алсыз позитив 0.1382	Алсыз терс -0.0418	Алсыз позитив 0.0181	Алсыз терс -0.0163	Алсыз позитив 0.0211	Алсыз терс -0.1183
Answer 16	-	Алсыз позитив 0.0591	Алсыз позитив 0.0276	Алсыз терс -0.0384	Алсыз терс -0.0397	Алсыз позитив 0.0651	Алсыз позитив 0.0280	Алсыз терс -0.0710

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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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