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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: 

  1. 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? 
  2. How does the mathematical approach in mathematical psychology differ from other branches of psychology, like psychophysics and psychometrics? 
  3. 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:

  1. Advocating quantitative methods broadly. Mathematical psychology emerged partly to push psychology to embrace quantitative modeling and mathematics beyond basic statistics.
  2. Drawing from diverse mathematical tools. With greater training in mathematics, mathematical psychologists utilize more advanced and varied mathematical techniques like topology and differential geometry.
  3. Linking models and experiments. Mathematical psychologists emphasize tightly connecting experimental design and statistical analysis, with experiments created to test specific models.
  4. Favoring theoretical models. Mathematical psychology incorporates "pure" mathematical results and prefers analytic, hand-fitted models over data-driven computer models.
  5. 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)


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

mamlakat
til
-
Mail
Qayta hisoblamoq
Korrelyatsiya koeffitsientining kritik qiymati
Oddiy tarqatish, Uilyam dengizi goset (Talaba) r = 0.033
Oddiy tarqatish, Uilyam dengizi goset (Talaba) r = 0.033
Normal bo'lmagan taqsimot, nayzali r = 0.0013
TaqsimlashNormal
bo'lmagan
Normal
bo'lmagan
Normal
bo'lmagan
NormalNormalNormalNormalNormal
Barcha savollar
Barcha savollar
Mening eng katta qo'rquvim
Mening eng katta qo'rquvim
Answer 1-
Zaif ijobiy
0.0532
Zaif ijobiy
0.0292
Zaif salbiy
-0.0175
Zaif ijobiy
0.0919
Zaif ijobiy
0.0301
Zaif salbiy
-0.0114
Zaif salbiy
-0.1523
Answer 2-
Zaif ijobiy
0.0208
Zaif salbiy
-0.0014
Zaif salbiy
-0.0431
Zaif ijobiy
0.0641
Zaif ijobiy
0.0449
Zaif ijobiy
0.0130
Zaif salbiy
-0.0931
Answer 3-
Zaif salbiy
-0.0053
Zaif salbiy
-0.0130
Zaif salbiy
-0.0406
Zaif salbiy
-0.0456
Zaif ijobiy
0.0474
Zaif ijobiy
0.0793
Zaif salbiy
-0.0204
Answer 4-
Zaif ijobiy
0.0427
Zaif ijobiy
0.0328
Zaif salbiy
-0.0200
Zaif ijobiy
0.0158
Zaif ijobiy
0.0306
Zaif ijobiy
0.0217
Zaif salbiy
-0.0980
Answer 5-
Zaif ijobiy
0.0255
Zaif ijobiy
0.1255
Zaif ijobiy
0.0143
Zaif ijobiy
0.0732
Zaif salbiy
-0.0019
Zaif salbiy
-0.0196
Zaif salbiy
-0.1747
Answer 6-
Zaif salbiy
-0.0027
Zaif ijobiy
0.0074
Zaif salbiy
-0.0629
Zaif salbiy
-0.0074
Zaif ijobiy
0.0199
Zaif ijobiy
0.0835
Zaif salbiy
-0.0324
Answer 7-
Zaif ijobiy
0.0110
Zaif ijobiy
0.0371
Zaif salbiy
-0.0688
Zaif salbiy
-0.0227
Zaif ijobiy
0.0471
Zaif ijobiy
0.0650
Zaif salbiy
-0.0523
Answer 8-
Zaif ijobiy
0.0693
Zaif ijobiy
0.0825
Zaif salbiy
-0.0321
Zaif ijobiy
0.0139
Zaif ijobiy
0.0351
Zaif ijobiy
0.0147
Zaif salbiy
-0.1369
Answer 9-
Zaif ijobiy
0.0643
Zaif ijobiy
0.1659
Zaif ijobiy
0.0082
Zaif ijobiy
0.0699
Zaif salbiy
-0.0136
Zaif salbiy
-0.0513
Zaif salbiy
-0.1826
Answer 10-
Zaif ijobiy
0.0760
Zaif ijobiy
0.0730
Zaif salbiy
-0.0219
Zaif ijobiy
0.0254
Zaif ijobiy
0.0318
Zaif salbiy
-0.0138
Zaif salbiy
-0.1318
Answer 11-
Zaif ijobiy
0.0571
Zaif ijobiy
0.0514
Zaif salbiy
-0.0099
Zaif ijobiy
0.0077
Zaif ijobiy
0.0206
Zaif ijobiy
0.0308
Zaif salbiy
-0.1211
Answer 12-
Zaif ijobiy
0.0373
Zaif ijobiy
0.1013
Zaif salbiy
-0.0357
Zaif ijobiy
0.0357
Zaif ijobiy
0.0243
Zaif ijobiy
0.0296
Zaif salbiy
-0.1524
Answer 13-
Zaif ijobiy
0.0621
Zaif ijobiy
0.1036
Zaif salbiy
-0.0438
Zaif ijobiy
0.0273
Zaif ijobiy
0.0414
Zaif ijobiy
0.0176
Zaif salbiy
-0.1608
Answer 14-
Zaif ijobiy
0.0703
Zaif ijobiy
0.1007
Zaif ijobiy
9.54E-5
Zaif salbiy
-0.0088
Zaif salbiy
-0.0011
Zaif ijobiy
0.0084
Zaif salbiy
-0.1174
Answer 15-
Zaif ijobiy
0.0554
Zaif ijobiy
0.1349
Zaif salbiy
-0.0418
Zaif ijobiy
0.0179
Zaif salbiy
-0.0165
Zaif ijobiy
0.0219
Zaif salbiy
-0.1181
Answer 16-
Zaif ijobiy
0.0581
Zaif ijobiy
0.0255
Zaif salbiy
-0.0388
Zaif salbiy
-0.0407
Zaif ijobiy
0.0654
Zaif ijobiy
0.0283
Zaif salbiy
-0.0714


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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 Uy hayvonlari loyihasi SDTest®

Valerii 1993 yilda ijtimoiy pedagog-psixolog sifatida malaka oshirgan va shu sababli o'z bilimlarini Loyihani boshqarish bo'yicha bilimlarini qo'llagan.
2013 yilda Valerii magistratura va loyiha menejerlari magistraturasiga ega bo'ldi. Ustozining dasturi davomida u Loyiha RoadMap (Gesellsche Gesellschagt (Gesellschagent-ning (Gesellschagement (Gesellschagement (Gesellschagement (Gesellschagement) bilan tanishdi. V.) va spiral dinamikani tanishdi.
Valerii SPTHESTning joriy versiyasini moslashtirish uchun turli xil spiral dinamikani sinab ko'rdi va o'z bilimlari va tajribasidan foydalangan.
Valerii - V.U.C.A noaniqligini o'rganish muallifi. Psixologiya, 20 dan ortiq xalqaro so'rovlar bo'yicha spiral dinamikasi va matematik statistikadan foydalangan holda tushuncha.
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Salom! Sizdan so'rasam, siz allaqachon spiral dinamikani yaxshi bilasizmi?