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 = 0.0318

Normal bo'lmagan taqsimot, nayzali r = 0.0013

Faqat natijalarni ko'rsating > r = 0.0318

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 0.0524	Zaif ijobiy 0.0258	Zaif salbiy -0.0180	Zaif ijobiy 0.0949	Zaif ijobiy 0.0355	Zaif salbiy -0.0146	Zaif salbiy -0.1537
Answer 2	-	Zaif ijobiy 0.0175	Zaif salbiy -0.0058	Zaif salbiy -0.0387	Zaif ijobiy 0.0669	Zaif ijobiy 0.0494	Zaif ijobiy 0.0116	Zaif salbiy -0.0969
Answer 3	-	Zaif salbiy -0.0035	Zaif salbiy -0.0091	Zaif salbiy -0.0441	Zaif salbiy -0.0435	Zaif ijobiy 0.0477	Zaif ijobiy 0.0747	Zaif salbiy -0.0199
Answer 4	-	Zaif ijobiy 0.0412	Zaif ijobiy 0.0255	Zaif salbiy -0.0229	Zaif ijobiy 0.0192	Zaif ijobiy 0.0353	Zaif ijobiy 0.0246	Zaif salbiy -0.0990
Answer 5	-	Zaif ijobiy 0.0227	Zaif ijobiy 0.1271	Zaif ijobiy 0.0109	Zaif ijobiy 0.0770	Zaif salbiy -0.0005	Zaif salbiy -0.0175	Zaif salbiy -0.1774
Answer 6	-	Zaif salbiy -0.0055	Zaif ijobiy 0.0042	Zaif salbiy -0.0622	Zaif salbiy -0.0080	Zaif ijobiy 0.0249	Zaif ijobiy 0.0863	Zaif salbiy -0.0354
Answer 7	-	Zaif ijobiy 0.0084	Zaif ijobiy 0.0331	Zaif salbiy -0.0656	Zaif salbiy -0.0297	Zaif ijobiy 0.0523	Zaif ijobiy 0.0696	Zaif salbiy -0.0522
Answer 8	-	Zaif ijobiy 0.0629	Zaif ijobiy 0.0710	Zaif salbiy -0.0267	Zaif ijobiy 0.0130	Zaif ijobiy 0.0379	Zaif ijobiy 0.0184	Zaif salbiy -0.1339
Answer 9	-	Zaif ijobiy 0.0711	Zaif ijobiy 0.1602	Zaif ijobiy 0.0072	Zaif ijobiy 0.0643	Zaif salbiy -0.0106	Zaif salbiy -0.0484	Zaif salbiy -0.1819
Answer 10	-	Zaif ijobiy 0.0740	Zaif ijobiy 0.0656	Zaif salbiy -0.0150	Zaif ijobiy 0.0292	Zaif ijobiy 0.0321	Zaif salbiy -0.0123	Zaif salbiy -0.1359
Answer 11	-	Zaif ijobiy 0.0629	Zaif ijobiy 0.0524	Zaif salbiy -0.0098	Zaif ijobiy 0.0104	Zaif ijobiy 0.0253	Zaif ijobiy 0.0247	Zaif salbiy -0.1270
Answer 12	-	Zaif ijobiy 0.0433	Zaif ijobiy 0.0921	Zaif salbiy -0.0338	Zaif ijobiy 0.0335	Zaif ijobiy 0.0331	Zaif ijobiy 0.0257	Zaif salbiy -0.1540
Answer 13	-	Zaif ijobiy 0.0687	Zaif ijobiy 0.0957	Zaif salbiy -0.0396	Zaif ijobiy 0.0304	Zaif ijobiy 0.0408	Zaif ijobiy 0.0151	Zaif salbiy -0.1630
Answer 14	-	Zaif ijobiy 0.0781	Zaif ijobiy 0.0884	Zaif salbiy -0.0003	Zaif salbiy -0.0096	Zaif ijobiy 0.0050	Zaif ijobiy 0.0138	Zaif salbiy -0.1228
Answer 15	-	Zaif ijobiy 0.0539	Zaif ijobiy 0.1269	Zaif salbiy -0.0339	Zaif ijobiy 0.0148	Zaif salbiy -0.0172	Zaif ijobiy 0.0237	Zaif salbiy -0.1160
Answer 16	-	Zaif ijobiy 0.0690	Zaif ijobiy 0.0248	Zaif salbiy -0.0372	Zaif salbiy -0.0385	Zaif ijobiy 0.0703	Zaif ijobiy 0.0205	Zaif salbiy -0.0792

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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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