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 0.0562	Nõrk positiivne 0.0311	Nõrk negatiivne -0.0164	Nõrk positiivne 0.0903	Nõrk positiivne 0.0301	Nõrk negatiivne -0.0120	Nõrk negatiivne -0.1534
Answer 2	-	Nõrk positiivne 0.0217	Nõrk positiivne 0.0011	Nõrk negatiivne -0.0455	Nõrk positiivne 0.0660	Nõrk positiivne 0.0440	Nõrk positiivne 0.0117	Nõrk negatiivne -0.0942
Answer 3	-	Nõrk negatiivne -0.0034	Nõrk negatiivne -0.0104	Nõrk negatiivne -0.0419	Nõrk negatiivne -0.0451	Nõrk positiivne 0.0462	Nõrk positiivne 0.0780	Nõrk negatiivne -0.0204
Answer 4	-	Nõrk positiivne 0.0436	Nõrk positiivne 0.0362	Nõrk negatiivne -0.0177	Nõrk positiivne 0.0150	Nõrk positiivne 0.0296	Nõrk positiivne 0.0189	Nõrk negatiivne -0.0984
Answer 5	-	Nõrk positiivne 0.0298	Nõrk positiivne 0.1270	Nõrk positiivne 0.0133	Nõrk positiivne 0.0724	Nõrk negatiivne -0.0002	Nõrk negatiivne -0.0199	Nõrk negatiivne -0.1742
Answer 6	-	Nõrk negatiivne -0.0003	Nõrk positiivne 0.0089	Nõrk negatiivne -0.0627	Nõrk negatiivne -0.0074	Nõrk positiivne 0.0190	Nõrk positiivne 0.0825	Nõrk negatiivne -0.0321
Answer 7	-	Nõrk positiivne 0.0123	Nõrk positiivne 0.0388	Nõrk negatiivne -0.0684	Nõrk negatiivne -0.0238	Nõrk positiivne 0.0468	Nõrk positiivne 0.0631	Nõrk negatiivne -0.0517
Answer 8	-	Nõrk positiivne 0.0699	Nõrk positiivne 0.0857	Nõrk negatiivne -0.0318	Nõrk positiivne 0.0150	Nõrk positiivne 0.0341	Nõrk positiivne 0.0125	Nõrk negatiivne -0.1372
Answer 9	-	Nõrk positiivne 0.0666	Nõrk positiivne 0.1681	Nõrk positiivne 0.0094	Nõrk positiivne 0.0694	Nõrk negatiivne -0.0131	Nõrk negatiivne -0.0533	Nõrk negatiivne -0.1815
Answer 10	-	Nõrk positiivne 0.0776	Nõrk positiivne 0.0744	Nõrk negatiivne -0.0185	Nõrk positiivne 0.0224	Nõrk positiivne 0.0352	Nõrk negatiivne -0.0135	Nõrk negatiivne -0.1293
Answer 11	-	Nõrk positiivne 0.0585	Nõrk positiivne 0.0531	Nõrk negatiivne -0.0094	Nõrk positiivne 0.0086	Nõrk positiivne 0.0195	Nõrk positiivne 0.0313	Nõrk negatiivne -0.1200
Answer 12	-	Nõrk positiivne 0.0378	Nõrk positiivne 0.1030	Nõrk negatiivne -0.0357	Nõrk positiivne 0.0350	Nõrk positiivne 0.0261	Nõrk positiivne 0.0297	Nõrk negatiivne -0.1510
Answer 13	-	Nõrk positiivne 0.0642	Nõrk positiivne 0.1044	Nõrk negatiivne -0.0454	Nõrk positiivne 0.0259	Nõrk positiivne 0.0424	Nõrk positiivne 0.0183	Nõrk negatiivne -0.1595
Answer 14	-	Nõrk positiivne 0.0718	Nõrk positiivne 0.1034	Nõrk negatiivne -0.0003	Nõrk negatiivne -0.0085	Nõrk negatiivne -0.0016	Nõrk positiivne 0.0074	Nõrk negatiivne -0.1172
Answer 15	-	Nõrk positiivne 0.0550	Nõrk positiivne 0.1382	Nõrk negatiivne -0.0418	Nõrk positiivne 0.0181	Nõrk negatiivne -0.0163	Nõrk positiivne 0.0211	Nõrk negatiivne -0.1183
Answer 16	-	Nõrk positiivne 0.0591	Nõrk positiivne 0.0276	Nõrk negatiivne -0.0384	Nõrk negatiivne -0.0397	Nõrk positiivne 0.0651	Nõrk positiivne 0.0280	Nõrk negatiivne -0.0710

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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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