Namai/Dienoraštis/Mathematical Psychology

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) Įmonės veiksmai, susiję su personalu per pastarąjį mėnesį (taip / ne)

2) Įmonių veiksmai, susiję su personalo per pastarąjį mėnesį (tai)

3) Baimė

4) Didžiausios mano šalies problemos

5) Kokias savybes ir sugebėjimus geri lyderiai naudoja kurdami sėkmingas komandas?

6) Google. Veiksniai, darantys įtaką komandos efektyvumui

7) Pagrindiniai darbo ieškančių asmenų prioritetai

8) Kas daro viršininką puikiu lyderiu?

9) Kas daro žmones sėkmingus darbe?

10) Ar esate pasirengęs gauti mažiau mokėjimo už darbą nuotoliniu būdu?

11) Ar egzistuoja ageizmas?

12) Ageizmas karjeroje

13) Ageizmas gyvenime

14) Ageizmo priežastys

15) Priežastys, kodėl žmonės atsisako (pateikė Anna Vital)

16) Pasitikėjimas (#WVS)

17) Oksfordo laimės apklausa

18) Psichologinė gerovė

19) Kur būtų kita jūsų įdomiausia galimybė?

20) Ką darysite šią savaitę, kad prižiūrėtumėte savo psichinę sveikatą?

21) Aš gyvenu galvodamas apie savo praeitį, dabartį ar ateitį

22) Meritokratija

23) Dirbtinis intelektas ir civilizacijos pabaiga

24) Kodėl žmonės vilkinasi?

25) Lyčių skirtumas kuriant pasitikėjimą savimi (IFD Allensbach)

26) Xing.com kultūros vertinimas

27) Patricko Lencioni „Penki komandos disfunkcijos“

28) Empatija yra ...

29) Kas yra būtina IT specialistams renkantis darbo pasiūlymą?

30) Kodėl žmonės priešinasi pokyčiams (pateikė Siobhán McHale)

31) Kaip reguliuojate savo emocijas? (Autorius: Nawal Mustafa M.A.)

32) 21 įgūdžiai, kurie jums moka amžinai (pateikė Jeremiah Teo / 赵汉昇)

33) Tikra laisvė yra ...

34) 12 būdų, kaip sukurti pasitikėjimą su kitais (pateikė Justinas Wrightas)

35) Talentingo darbuotojo savybės (talentų valdymo institutas)

36) 10 raktų, kaip motyvuoti savo komandą

37) Sąžinės algebra (Vladimir Lefebvre)

38) Trys išskirtinės ateities galimybės (dr. Clare W. Graves)

39) Veiksmai, skirti ugdyti nepajudinamą pasitikėjimą savimi (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.

Baimė

Grafikai Koreliacija

VUCA

Kritinė reikšmė koreliacijos koeficientas

Normalus platinimas, pateikė William Sealy Gosset (studentas) r = 0.0318

Ne normalus pasiskirstymas, autorius Spearman r = 0.0013

Rodyti tik rezultatus > r = 0.0318

Paskirstymas	Ne normalu	Ne normalu	Ne normalu	Normalus	Normalus	Normalus	Normalus	Normalus
Visi klausimai Visi klausimai Mano didžiausia baimė yra
Mano didžiausia baimė yra
Answer 1	-	Silpnas teigiamas 0.0548	Silpnas teigiamas 0.0285	Silpnas neigiamas -0.0173	Silpnas teigiamas 0.0940	Silpnas teigiamas 0.0358	Silpnas neigiamas -0.0156	Silpnas neigiamas -0.1560
Answer 2	-	Silpnas teigiamas 0.0192	Silpnas neigiamas -0.0048	Silpnas neigiamas -0.0394	Silpnas teigiamas 0.0659	Silpnas teigiamas 0.0491	Silpnas teigiamas 0.0117	Silpnas neigiamas -0.0981
Answer 3	-	Silpnas neigiamas -0.0003	Silpnas neigiamas -0.0088	Silpnas neigiamas -0.0450	Silpnas neigiamas -0.0440	Silpnas teigiamas 0.0471	Silpnas teigiamas 0.0739	Silpnas neigiamas -0.0191
Answer 4	-	Silpnas teigiamas 0.0429	Silpnas teigiamas 0.0271	Silpnas neigiamas -0.0230	Silpnas teigiamas 0.0182	Silpnas teigiamas 0.0351	Silpnas teigiamas 0.0239	Silpnas neigiamas -0.0995
Answer 5	-	Silpnas teigiamas 0.0273	Silpnas teigiamas 0.1298	Silpnas teigiamas 0.0101	Silpnas teigiamas 0.0772	Silpnas neigiamas -0.0006	Silpnas neigiamas -0.0183	Silpnas neigiamas -0.1784
Answer 6	-	Silpnas neigiamas -0.0026	Silpnas teigiamas 0.0050	Silpnas neigiamas -0.0621	Silpnas neigiamas -0.0081	Silpnas teigiamas 0.0240	Silpnas teigiamas 0.0856	Silpnas neigiamas -0.0346
Answer 7	-	Silpnas teigiamas 0.0105	Silpnas teigiamas 0.0339	Silpnas neigiamas -0.0661	Silpnas neigiamas -0.0304	Silpnas teigiamas 0.0517	Silpnas teigiamas 0.0686	Silpnas neigiamas -0.0515
Answer 8	-	Silpnas teigiamas 0.0635	Silpnas teigiamas 0.0732	Silpnas neigiamas -0.0275	Silpnas teigiamas 0.0143	Silpnas teigiamas 0.0370	Silpnas teigiamas 0.0172	Silpnas neigiamas -0.1336
Answer 9	-	Silpnas teigiamas 0.0734	Silpnas teigiamas 0.1618	Silpnas teigiamas 0.0069	Silpnas teigiamas 0.0644	Silpnas neigiamas -0.0109	Silpnas neigiamas -0.0489	Silpnas neigiamas -0.1811
Answer 10	-	Silpnas teigiamas 0.0764	Silpnas teigiamas 0.0679	Silpnas neigiamas -0.0139	Silpnas teigiamas 0.0290	Silpnas teigiamas 0.0338	Silpnas neigiamas -0.0123	Silpnas neigiamas -0.1342
Answer 11	-	Silpnas teigiamas 0.0634	Silpnas teigiamas 0.0535	Silpnas neigiamas -0.0091	Silpnas teigiamas 0.0113	Silpnas teigiamas 0.0238	Silpnas teigiamas 0.0247	Silpnas neigiamas -0.1260
Answer 12	-	Silpnas teigiamas 0.0449	Silpnas teigiamas 0.0941	Silpnas neigiamas -0.0341	Silpnas teigiamas 0.0342	Silpnas teigiamas 0.0332	Silpnas teigiamas 0.0255	Silpnas neigiamas -0.1534
Answer 13	-	Silpnas teigiamas 0.0691	Silpnas teigiamas 0.0966	Silpnas neigiamas -0.0393	Silpnas teigiamas 0.0295	Silpnas teigiamas 0.0417	Silpnas teigiamas 0.0148	Silpnas neigiamas -0.1626
Answer 14	-	Silpnas teigiamas 0.0775	Silpnas teigiamas 0.0903	Silpnas neigiamas -0.0019	Silpnas neigiamas -0.0089	Silpnas teigiamas 0.0048	Silpnas teigiamas 0.0140	Silpnas neigiamas -0.1223
Answer 15	-	Silpnas teigiamas 0.0544	Silpnas teigiamas 0.1280	Silpnas neigiamas -0.0345	Silpnas teigiamas 0.0152	Silpnas neigiamas -0.0178	Silpnas teigiamas 0.0236	Silpnas neigiamas -0.1158
Answer 16	-	Silpnas teigiamas 0.0703	Silpnas teigiamas 0.0262	Silpnas neigiamas -0.0371	Silpnas neigiamas -0.0377	Silpnas teigiamas 0.0697	Silpnas teigiamas 0.0204	Silpnas neigiamas -0.0788

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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

Produkto savininkas SaaS SDTEST®

1993 metais Valerii įgijo socialinio pedagogo-psichologo kvalifikaciją ir nuo tada savo žinias pritaikė projektų valdyme.
2013 m. Valerii įgijo magistro laipsnį ir projektų bei programų vadovo kvalifikaciją. Magistrantūros studijų metu susipažino su Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) ir Spiral Dynamics.
Valerii yra V.U.C.A. netikrumo tyrinėjimo autorius. koncepcija, naudojant spiralinę dinamiką ir matematinę statistiką psichologijoje, ir 38 tarptautinės apklausos.

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