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 = 0.0335

Mitte normaalne jaotus, autor Spearman r = 0.0014

Näidata ainult tulemusi > r = 0.0335

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 0.0521	Nõrk positiivne 0.0294	Nõrk negatiivne -0.0147	Nõrk positiivne 0.0885	Nõrk positiivne 0.0316	Nõrk negatiivne -0.0110	Nõrk negatiivne -0.1513
Answer 2	-	Nõrk positiivne 0.0213	Nõrk positiivne 0.0013	Nõrk negatiivne -0.0432	Nõrk positiivne 0.0618	Nõrk positiivne 0.0453	Nõrk positiivne 0.0103	Nõrk negatiivne -0.0918
Answer 3	-	Nõrk negatiivne -0.0042	Nõrk negatiivne -0.0116	Nõrk negatiivne -0.0406	Nõrk negatiivne -0.0477	Nõrk positiivne 0.0487	Nõrk positiivne 0.0767	Nõrk negatiivne -0.0191
Answer 4	-	Nõrk positiivne 0.0421	Nõrk positiivne 0.0350	Nõrk negatiivne -0.0115	Nõrk positiivne 0.0112	Nõrk positiivne 0.0307	Nõrk positiivne 0.0175	Nõrk negatiivne -0.0980
Answer 5	-	Nõrk positiivne 0.0288	Nõrk positiivne 0.1272	Nõrk positiivne 0.0146	Nõrk positiivne 0.0697	Nõrk positiivne 0.0037	Nõrk negatiivne -0.0215	Nõrk negatiivne -0.1746
Answer 6	-	Nõrk negatiivne -0.0001	Nõrk positiivne 0.0042	Nõrk negatiivne -0.0607	Nõrk negatiivne -0.0115	Nõrk positiivne 0.0231	Nõrk positiivne 0.0826	Nõrk negatiivne -0.0309
Answer 7	-	Nõrk positiivne 0.0117	Nõrk positiivne 0.0372	Nõrk negatiivne -0.0653	Nõrk negatiivne -0.0283	Nõrk positiivne 0.0495	Nõrk positiivne 0.0626	Nõrk negatiivne -0.0505
Answer 8	-	Nõrk positiivne 0.0658	Nõrk positiivne 0.0830	Nõrk negatiivne -0.0310	Nõrk positiivne 0.0139	Nõrk positiivne 0.0334	Nõrk positiivne 0.0134	Nõrk negatiivne -0.1322
Answer 9	-	Nõrk positiivne 0.0660	Nõrk positiivne 0.1658	Nõrk positiivne 0.0051	Nõrk positiivne 0.0691	Nõrk negatiivne -0.0093	Nõrk negatiivne -0.0498	Nõrk negatiivne -0.1820
Answer 10	-	Nõrk positiivne 0.0758	Nõrk positiivne 0.0724	Nõrk negatiivne -0.0173	Nõrk positiivne 0.0236	Nõrk positiivne 0.0312	Nõrk negatiivne -0.0115	Nõrk negatiivne -0.1263
Answer 11	-	Nõrk positiivne 0.0577	Nõrk positiivne 0.0544	Nõrk negatiivne -0.0075	Nõrk positiivne 0.0082	Nõrk positiivne 0.0185	Nõrk positiivne 0.0293	Nõrk negatiivne -0.1190
Answer 12	-	Nõrk positiivne 0.0376	Nõrk positiivne 0.1007	Nõrk negatiivne -0.0342	Nõrk positiivne 0.0296	Nõrk positiivne 0.0273	Nõrk positiivne 0.0341	Nõrk negatiivne -0.1500
Answer 13	-	Nõrk positiivne 0.0627	Nõrk positiivne 0.1017	Nõrk negatiivne -0.0443	Nõrk positiivne 0.0248	Nõrk positiivne 0.0434	Nõrk positiivne 0.0189	Nõrk negatiivne -0.1576
Answer 14	-	Nõrk positiivne 0.0732	Nõrk positiivne 0.1036	Nõrk positiivne 0.0048	Nõrk negatiivne -0.0105	Nõrk negatiivne -0.0039	Nõrk positiivne 0.0041	Nõrk negatiivne -0.1157
Answer 15	-	Nõrk positiivne 0.0539	Nõrk positiivne 0.1381	Nõrk negatiivne -0.0424	Nõrk positiivne 0.0163	Nõrk negatiivne -0.0147	Nõrk positiivne 0.0216	Nõrk negatiivne -0.1173
Answer 16	-	Nõrk positiivne 0.0590	Nõrk positiivne 0.0274	Nõrk negatiivne -0.0375	Nõrk negatiivne -0.0429	Nõrk positiivne 0.0687	Nõrk positiivne 0.0253	Nõrk negatiivne -0.0698

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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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