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) Ettevõtete toimingud seoses personaliga viimasel kuul (jah / ei)

2) Ettevõtete tegevus seoses personali poolt viimase kuu jooksul (fakt%)

3) Kartma

4) Minu riigi suurimad probleemid

5) Milliseid omadusi ja võimeid kasutavad head juhid edukate meeskondade ehitamisel?

6) Google. Meeskonna efektiivsust mõjutavad tegurid

7) Tööotsijate peamised prioriteedid

8) Mis teeb ülemusest suurepärase juhi?

9) Mis teeb inimesed tööl edukaks?

10) Kas olete valmis eemalt töötamise eest vähem palka saama?

11) Kas ageism on olemas?

12) Ageism karjääris

13) Ageism elus

14) Ageismi põhjused

15) Põhjused, miks inimesed loobuvad (autor Anna Vital)

16) Usaldus (#WVS)

17) Oxfordi õnneuuring

18) Psühholoogiline heaolu

19) Kus oleks teie järgmine põnevam võimalus?

20) Mida teete sel nädalal oma vaimse tervise eest hoolitsemiseks?

21) Ma elan oma mineviku, oleviku või tuleviku peale

22) Meritokraatia

23) Tehisintellekt ja tsivilisatsiooni lõpp

24) Miks inimesed viivitavad?

25) Sooline erinevus enesekindluse loomisel (IFD Allensbach)

26) Xing.com kultuuri hindamine

27) Patrick Lencioni "meeskonna viis düsfunktsiooni"

28) Empaatia on ...

29) Mis on IT -spetsialistide jaoks hädavajalik tööpakkumise valimisel?

30) Miks inimesed muutustele vastu seisavad (autor Siobhán McHale)

31) Kuidas oma emotsioone reguleerida? (Autor: Nawal Mustafa M.A.)

32) 21 oskust, mis maksavad teile igavesti (autor Jeremiah Teo / 赵汉昇)

33) Tõeline vabadus on ...

34) 12 viisi teistega usalduse loomiseks (autor Justin Wright)

35) Andeka töötaja omadused (talentide juhtimise instituudi poolt)

36) 10 võtit oma meeskonna motiveerimiseks

37) Südametunnistuse algebra (Vladimir Lefebvre)

38) Kolm erinevat tulevikuvõimalust (autor. dr Clare W. Graves)

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.

Kartma

Äritegevus Korrelatsioon

VUCA

Kriitiline väärtus korrelatsioonikordaja

Normaalne jaotus, autor William Sealy Gosset (õpilane) r = 0.0331

Mitte normaalne jaotus, autor Spearman r = 0.0013

Näidata ainult tulemusi > r = 0.0331

Jaotus	Mitte normaalne	Mitte normaalne	Mitte normaalne	Normaalne	Normaalne	Normaalne	Normaalne	Normaalne
Kõik küsimused Kõik küsimused Minu suurim hirm on
Minu suurim hirm on
Answer 1	-	Nõrk positiivne 0.0563	Nõrk positiivne 0.0317	Nõrk negatiivne -0.0161	Nõrk positiivne 0.0907	Nõrk positiivne 0.0298	Nõrk negatiivne -0.0126	Nõrk negatiivne -0.1537
Answer 2	-	Nõrk positiivne 0.0216	Nõrk positiivne 0.0002	Nõrk negatiivne -0.0458	Nõrk positiivne 0.0654	Nõrk positiivne 0.0445	Nõrk positiivne 0.0124	Nõrk negatiivne -0.0937
Answer 3	-	Nõrk negatiivne -0.0035	Nõrk negatiivne -0.0111	Nõrk negatiivne -0.0421	Nõrk negatiivne -0.0456	Nõrk positiivne 0.0466	Nõrk positiivne 0.0786	Nõrk negatiivne -0.0201
Answer 4	-	Nõrk positiivne 0.0435	Nõrk positiivne 0.0353	Nõrk negatiivne -0.0181	Nõrk positiivne 0.0145	Nõrk positiivne 0.0301	Nõrk positiivne 0.0197	Nõrk negatiivne -0.0979
Answer 5	-	Nõrk positiivne 0.0299	Nõrk positiivne 0.1279	Nõrk positiivne 0.0136	Nõrk positiivne 0.0730	Nõrk negatiivne -0.0007	Nõrk negatiivne -0.0207	Nõrk negatiivne -0.1746
Answer 6	-	Nõrk negatiivne -0.0004	Nõrk positiivne 0.0082	Nõrk negatiivne -0.0629	Nõrk negatiivne -0.0078	Nõrk positiivne 0.0193	Nõrk positiivne 0.0830	Nõrk negatiivne -0.0318
Answer 7	-	Nõrk positiivne 0.0122	Nõrk positiivne 0.0381	Nõrk negatiivne -0.0686	Nõrk negatiivne -0.0242	Nõrk positiivne 0.0471	Nõrk positiivne 0.0636	Nõrk negatiivne -0.0513
Answer 8	-	Nõrk positiivne 0.0698	Nõrk positiivne 0.0849	Nõrk negatiivne -0.0321	Nõrk positiivne 0.0146	Nõrk positiivne 0.0345	Nõrk positiivne 0.0130	Nõrk negatiivne -0.1368
Answer 9	-	Nõrk positiivne 0.0665	Nõrk positiivne 0.1674	Nõrk positiivne 0.0092	Nõrk positiivne 0.0691	Nõrk negatiivne -0.0128	Nõrk negatiivne -0.0528	Nõrk negatiivne -0.1812
Answer 10	-	Nõrk positiivne 0.0778	Nõrk positiivne 0.0755	Nõrk negatiivne -0.0180	Nõrk positiivne 0.0231	Nõrk positiivne 0.0346	Nõrk negatiivne -0.0146	Nõrk negatiivne -0.1298
Answer 11	-	Nõrk positiivne 0.0584	Nõrk positiivne 0.0524	Nõrk negatiivne -0.0096	Nõrk positiivne 0.0081	Nõrk positiivne 0.0199	Nõrk positiivne 0.0318	Nõrk negatiivne -0.1197
Answer 12	-	Nõrk positiivne 0.0380	Nõrk positiivne 0.1042	Nõrk negatiivne -0.0352	Nõrk positiivne 0.0357	Nõrk positiivne 0.0254	Nõrk positiivne 0.0286	Nõrk negatiivne -0.1515
Answer 13	-	Nõrk positiivne 0.0644	Nõrk positiivne 0.1057	Nõrk negatiivne -0.0448	Nõrk positiivne 0.0268	Nõrk positiivne 0.0416	Nõrk positiivne 0.0169	Nõrk negatiivne -0.1600
Answer 14	-	Nõrk positiivne 0.0717	Nõrk positiivne 0.1026	Nõrk negatiivne -0.0006	Nõrk negatiivne -0.0089	Nõrk negatiivne -0.0012	Nõrk positiivne 0.0080	Nõrk negatiivne -0.1168
Answer 15	-	Nõrk positiivne 0.0549	Nõrk positiivne 0.1375	Nõrk negatiivne -0.0420	Nõrk positiivne 0.0178	Nõrk negatiivne -0.0160	Nõrk positiivne 0.0216	Nõrk negatiivne -0.1180
Answer 16	-	Nõrk positiivne 0.0591	Nõrk positiivne 0.0273	Nõrk negatiivne -0.0386	Nõrk negatiivne -0.0399	Nõrk positiivne 0.0653	Nõrk positiivne 0.0282	Nõrk negatiivne -0.0708

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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

Tooteomanik Saas PET -projekt SDTEST®

Valerii kvalifitseerus 1993. aastal sotsiaalse pedagoogi psühholoogiks ja on sellest ajast alates oma teadmisi projektijuhtimisel rakendanud.
Valerii omandas magistrikraadi ning projekti- ja programmijuhi kvalifikatsiooni 2013. aastal. Magistriprogrammi ajal sai ta tuttavaks projekti teekaardiga (GPM Deutsche Gesellschaft für projektmanagement e. V.) ja spiraaldünaamikaga.
Valerii tegi mitmesuguseid spiraalse dünaamika teste ja kasutas oma teadmisi ja kogemusi SDTesti praeguse versiooni kohandamiseks.
Valerii on V.U.C.A. ebakindluse uurimise autor. Mõiste, mis kasutab spiraalset dünaamikat ja matemaatilist statistikat psühholoogias, enam kui 20 rahvusvahelist küsitlust.

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