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) O'tgan oyda xodimlarning xodimlariga nisbatan harakatlari (ha / yo'q)

2) O'tgan oyda kompaniyalarning xodimlariga nisbatan harakatlari (%%)

3) Qo'rquv

4) Mening mamlakatimga eng katta muammolar

5) Muvaffaqiyatli jamoalarni qurishda yaxshi rahbarlar qanday fazilatlar va qobiliyatlardan foydalanishadi?

6) Google. Jamoa samaradorligiga ta'sir qiladigan omillar

7) Ish qidiruvchilar uchun asosiy ustuvorliklari

8) Bossning buyuk rahbarni nimada qilyapti?

9) Odamlarni ishda nimaga olib ketadi?

10) Siz masofadan ishlash uchun kamroq to'lovni olishga tayyormisiz?

11) Yoshlik mavjudmi?

12) Faoliyatdagi yoshizm

13) Hayotdagi yoshlik

14) Yoshlik sabablari

15) Odamlar nima uchun taslim bo'lishining sabablari (Anna Vital)

16) Ishonch (#WVS)

17) Oksford Baxt so'rovi

18) Psixologik farovonlik

19) Sizning keyingi eng hayajonli imkoniyatingiz qayerda bo'ladi?

20) Bu hafta sizning ruhiy salomatligingizga qarash uchun nima qilasiz?

21) Men o'tmishim, hozirgi yoki kelajak haqida o'ylayman

22) Meritokratiya

23) Sun'iy aql va tsivilizatsiya oxiri

24) Nega odamlar prokuraturada?

25) O'ziga bo'lgan ishonchni qurishda gender farq (IFD AlliesBAch)

26) Xing.com Kadriyatni baholash

27) Patrik Lensisioni "jamoaning beshta disfampti"

28) Xafa - bu ...

29) Ish taklifini tanlashda mutaxassislar uchun nima kerak?

30) Nima uchun odamlar o'zgarishga qarshi turadilar (Siobhan Mheale tomonidan)

31) Sizning his-tuyg'ularingizni qanday tartibga solyapsiz? (Navol Mustafo M.A.)

32) Sizga abadiy pul to'laydigan 21 ta ko'nikma (Eremiyo Te赵汉昇)

33) Haqiqiy erkinlik ...

34) Boshqalarga ishonchni rivojlantirishning 12 usuli (Justin Rayt tomonidan)

35) Iqtidorli xodimning xususiyatlari (iste'dod instituti tomonidan)

36) Jamoangizni qo'zg'atadigan 10 ta tugmalar

37) Vijdon algebrasi (Vladimir Lefebr tomonidan)

38) Kelajakning uchta aniq imkoniyatlari (doktor Kler U. Graves tomonidan)

39) O'z-o'ziga ishonchni mustahkamlash bo'yicha harakatlar (Suren Samarchyan)

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.

Qo'rquv

Grafikalar Korelasyon

VUCA

Korrelyatsiya koeffitsientining kritik qiymati

Oddiy tarqatish, Uilyam dengizi goset (Talaba) r = 0.0317

Normal bo'lmagan taqsimot, nayzali r = 0.0013

Faqat natijalarni ko'rsating > r = 0.0317

Taqsimlash	Normal bo'lmagan	Normal bo'lmagan	Normal bo'lmagan	Normal	Normal	Normal	Normal	Normal
Barcha savollar Barcha savollar Mening eng katta qo'rquvim
Mening eng katta qo'rquvim
Answer 1	-	Zaif ijobiy 0.0540	Zaif ijobiy 0.0288	Zaif salbiy -0.0178	Zaif ijobiy 0.0946	Zaif ijobiy 0.0383	Zaif salbiy -0.0180	Zaif salbiy -0.1561
Answer 2	-	Zaif ijobiy 0.0198	Zaif salbiy -0.0049	Zaif salbiy -0.0389	Zaif ijobiy 0.0652	Zaif ijobiy 0.0497	Zaif ijobiy 0.0103	Zaif salbiy -0.0978
Answer 3	-	Zaif salbiy -0.0003	Zaif salbiy -0.0082	Zaif salbiy -0.0451	Zaif salbiy -0.0442	Zaif ijobiy 0.0484	Zaif ijobiy 0.0743	Zaif salbiy -0.0207
Answer 4	-	Zaif ijobiy 0.0437	Zaif ijobiy 0.0290	Zaif salbiy -0.0235	Zaif ijobiy 0.0160	Zaif ijobiy 0.0370	Zaif ijobiy 0.0223	Zaif salbiy -0.0992
Answer 5	-	Zaif ijobiy 0.0274	Zaif ijobiy 0.1292	Zaif ijobiy 0.0110	Zaif ijobiy 0.0748	Zaif ijobiy 0.0010	Zaif salbiy -0.0175	Zaif salbiy -0.1786
Answer 6	-	Zaif salbiy -0.0017	Zaif ijobiy 0.0059	Zaif salbiy -0.0609	Zaif salbiy -0.0092	Zaif ijobiy 0.0254	Zaif ijobiy 0.0845	Zaif salbiy -0.0363
Answer 7	-	Zaif ijobiy 0.0111	Zaif ijobiy 0.0349	Zaif salbiy -0.0659	Zaif salbiy -0.0303	Zaif ijobiy 0.0520	Zaif ijobiy 0.0687	Zaif salbiy -0.0532
Answer 8	-	Zaif ijobiy 0.0655	Zaif ijobiy 0.0730	Zaif salbiy -0.0260	Zaif ijobiy 0.0126	Zaif ijobiy 0.0386	Zaif ijobiy 0.0154	Zaif salbiy -0.1344
Answer 9	-	Zaif ijobiy 0.0757	Zaif ijobiy 0.1606	Zaif ijobiy 0.0062	Zaif ijobiy 0.0614	Zaif salbiy -0.0064	Zaif salbiy -0.0492	Zaif salbiy -0.1821
Answer 10	-	Zaif ijobiy 0.0763	Zaif ijobiy 0.0671	Zaif salbiy -0.0129	Zaif ijobiy 0.0273	Zaif ijobiy 0.0364	Zaif salbiy -0.0130	Zaif salbiy -0.1347
Answer 11	-	Zaif ijobiy 0.0633	Zaif ijobiy 0.0527	Zaif salbiy -0.0080	Zaif ijobiy 0.0098	Zaif ijobiy 0.0264	Zaif ijobiy 0.0242	Zaif salbiy -0.1269
Answer 12	-	Zaif ijobiy 0.0448	Zaif ijobiy 0.0944	Zaif salbiy -0.0323	Zaif ijobiy 0.0310	Zaif ijobiy 0.0341	Zaif ijobiy 0.0261	Zaif salbiy -0.1532
Answer 13	-	Zaif ijobiy 0.0723	Zaif ijobiy 0.0947	Zaif salbiy -0.0385	Zaif ijobiy 0.0267	Zaif ijobiy 0.0442	Zaif ijobiy 0.0146	Zaif salbiy -0.1636
Answer 14	-	Zaif ijobiy 0.0819	Zaif ijobiy 0.0899	Zaif salbiy -0.0035	Zaif salbiy -0.0120	Zaif ijobiy 0.0060	Zaif ijobiy 0.0136	Zaif salbiy -0.1212
Answer 15	-	Zaif ijobiy 0.0548	Zaif ijobiy 0.1267	Zaif salbiy -0.0338	Zaif ijobiy 0.0121	Zaif salbiy -0.0153	Zaif ijobiy 0.0243	Zaif salbiy -0.1155
Answer 16	-	Zaif ijobiy 0.0731	Zaif ijobiy 0.0243	Zaif salbiy -0.0375	Zaif salbiy -0.0397	Zaif ijobiy 0.0729	Zaif ijobiy 0.0170	Zaif salbiy -0.0774

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[1] https://twitter.com/wileyprof

[2] https://colinallen.dnsalias.org

[3] https://philpeople.org/profiles/colin-allen

2023.10.13

Valerii Kosenko

Mahsulot egasi SaaS SDTEST®

Valeriy 1993 yilda ijtimoiy pedagog-psixolog malakasiga ega bo'lgan va shundan beri o'z bilimlarini loyihalarni boshqarishda qo'llagan.
Valeriy 2013-yilda magistrlik darajasini va loyiha va dastur menejeri malakasini oldi. Magistrlik dasturi davomida u Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) va Spiral Dynamics bilan tanishdi.
Valeriy V.U.C.A.ning noaniqligini o'rganish muallifi. psixologiyada Spiral dinamikasi va matematik statistikadan foydalangan holda kontseptsiya va 38 ta xalqaro so'rov.

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