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 = 0.0322

Ne normalus pasiskirstymas, autorius Spearman r = 0.0013

Rodyti tik rezultatus > r = 0.0322

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 0.0509	Silpnas teigiamas 0.0353	Silpnas neigiamas -0.0167	Silpnas teigiamas 0.0940	Silpnas teigiamas 0.0349	Silpnas neigiamas -0.0183	Silpnas neigiamas -0.1554
Answer 2	-	Silpnas teigiamas 0.0194	Silpnas teigiamas 0.0016	Silpnas neigiamas -0.0408	Silpnas teigiamas 0.0642	Silpnas teigiamas 0.0454	Silpnas teigiamas 0.0126	Silpnas neigiamas -0.0968
Answer 3	-	Silpnas neigiamas -0.0015	Silpnas neigiamas -0.0086	Silpnas neigiamas -0.0466	Silpnas neigiamas -0.0457	Silpnas teigiamas 0.0478	Silpnas teigiamas 0.0754	Silpnas neigiamas -0.0172
Answer 4	-	Silpnas teigiamas 0.0408	Silpnas teigiamas 0.0320	Silpnas neigiamas -0.0223	Silpnas teigiamas 0.0187	Silpnas teigiamas 0.0301	Silpnas teigiamas 0.0224	Silpnas neigiamas -0.0965
Answer 5	-	Silpnas teigiamas 0.0297	Silpnas teigiamas 0.1339	Silpnas teigiamas 0.0088	Silpnas teigiamas 0.0792	Silpnas neigiamas -0.0007	Silpnas neigiamas -0.0227	Silpnas neigiamas -0.1792
Answer 6	-	Silpnas neigiamas -0.0035	Silpnas teigiamas 0.0113	Silpnas neigiamas -0.0659	Silpnas neigiamas -0.0085	Silpnas teigiamas 0.0205	Silpnas teigiamas 0.0842	Silpnas neigiamas -0.0303
Answer 7	-	Silpnas teigiamas 0.0119	Silpnas teigiamas 0.0427	Silpnas neigiamas -0.0709	Silpnas neigiamas -0.0287	Silpnas teigiamas 0.0477	Silpnas teigiamas 0.0655	Silpnas neigiamas -0.0496
Answer 8	-	Silpnas teigiamas 0.0639	Silpnas teigiamas 0.0832	Silpnas neigiamas -0.0292	Silpnas teigiamas 0.0150	Silpnas teigiamas 0.0348	Silpnas teigiamas 0.0132	Silpnas neigiamas -0.1343
Answer 9	-	Silpnas teigiamas 0.0681	Silpnas teigiamas 0.1696	Silpnas teigiamas 0.0047	Silpnas teigiamas 0.0669	Silpnas neigiamas -0.0144	Silpnas neigiamas -0.0506	Silpnas neigiamas -0.1780
Answer 10	-	Silpnas teigiamas 0.0770	Silpnas teigiamas 0.0736	Silpnas neigiamas -0.0207	Silpnas teigiamas 0.0263	Silpnas teigiamas 0.0315	Silpnas neigiamas -0.0105	Silpnas neigiamas -0.1289
Answer 11	-	Silpnas teigiamas 0.0621	Silpnas teigiamas 0.0594	Silpnas neigiamas -0.0051	Silpnas teigiamas 0.0080	Silpnas teigiamas 0.0176	Silpnas teigiamas 0.0238	Silpnas neigiamas -0.1225
Answer 12	-	Silpnas teigiamas 0.0424	Silpnas teigiamas 0.1016	Silpnas neigiamas -0.0350	Silpnas teigiamas 0.0354	Silpnas teigiamas 0.0304	Silpnas teigiamas 0.0239	Silpnas neigiamas -0.1526
Answer 13	-	Silpnas teigiamas 0.0680	Silpnas teigiamas 0.1023	Silpnas neigiamas -0.0379	Silpnas teigiamas 0.0271	Silpnas teigiamas 0.0404	Silpnas teigiamas 0.0140	Silpnas neigiamas -0.1620
Answer 14	-	Silpnas teigiamas 0.0725	Silpnas teigiamas 0.0997	Silpnas neigiamas -0.0033	Silpnas neigiamas -0.0064	Silpnas teigiamas 0.0023	Silpnas teigiamas 0.0114	Silpnas neigiamas -0.1216
Answer 15	-	Silpnas teigiamas 0.0549	Silpnas teigiamas 0.1346	Silpnas neigiamas -0.0341	Silpnas teigiamas 0.0170	Silpnas neigiamas -0.0195	Silpnas teigiamas 0.0208	Silpnas neigiamas -0.1180
Answer 16	-	Silpnas teigiamas 0.0666	Silpnas teigiamas 0.0287	Silpnas neigiamas -0.0339	Silpnas neigiamas -0.0426	Silpnas teigiamas 0.0647	Silpnas teigiamas 0.0251	Silpnas neigiamas -0.0746

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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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