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.

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

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3) Kartma

4) Minu riigi suurimad probleemid

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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

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23) Tehisintellekt ja tsivilisatsiooni lõpp

24) Miks inimesed viivitavad?

25) Sooline erinevus enesekindluse loomisel (IFD Allensbach)

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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)

39) Tegevused kõigutamatu enesekindluse loomiseks (autor 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.

Kartma

Äritegevus Korrelatsioon

VUCA

Kriitiline väärtus korrelatsioonikordaja

Normaalne jaotus, autor William Sealy Gosset (õpilane) r = 0.0318

Mitte normaalne jaotus, autor Spearman r = 0.0013

Näidata ainult tulemusi > r = 0.0318

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 0.0554	Nõrk positiivne 0.0283	Nõrk negatiivne -0.0173	Nõrk positiivne 0.0940	Nõrk positiivne 0.0355	Nõrk negatiivne -0.0157	Nõrk negatiivne -0.1559
Answer 2	-	Nõrk positiivne 0.0194	Nõrk negatiivne -0.0048	Nõrk negatiivne -0.0394	Nõrk positiivne 0.0659	Nõrk positiivne 0.0490	Nõrk positiivne 0.0117	Nõrk negatiivne -0.0981
Answer 3	-	Nõrk negatiivne -0.0011	Nõrk negatiivne -0.0085	Nõrk negatiivne -0.0450	Nõrk negatiivne -0.0440	Nõrk positiivne 0.0474	Nõrk positiivne 0.0740	Nõrk negatiivne -0.0192
Answer 4	-	Nõrk positiivne 0.0427	Nõrk positiivne 0.0272	Nõrk negatiivne -0.0230	Nõrk positiivne 0.0182	Nõrk positiivne 0.0351	Nõrk positiivne 0.0239	Nõrk negatiivne -0.0995
Answer 5	-	Nõrk positiivne 0.0268	Nõrk positiivne 0.1299	Nõrk positiivne 0.0101	Nõrk positiivne 0.0772	Nõrk negatiivne -0.0003	Nõrk negatiivne -0.0182	Nõrk negatiivne -0.1785
Answer 6	-	Nõrk negatiivne -0.0028	Nõrk positiivne 0.0050	Nõrk negatiivne -0.0621	Nõrk negatiivne -0.0081	Nõrk positiivne 0.0241	Nõrk positiivne 0.0856	Nõrk negatiivne -0.0347
Answer 7	-	Nõrk positiivne 0.0102	Nõrk positiivne 0.0340	Nõrk negatiivne -0.0661	Nõrk negatiivne -0.0304	Nõrk positiivne 0.0518	Nõrk positiivne 0.0687	Nõrk negatiivne -0.0515
Answer 8	-	Nõrk positiivne 0.0632	Nõrk positiivne 0.0732	Nõrk negatiivne -0.0275	Nõrk positiivne 0.0143	Nõrk positiivne 0.0371	Nõrk positiivne 0.0173	Nõrk negatiivne -0.1337
Answer 9	-	Nõrk positiivne 0.0732	Nõrk positiivne 0.1619	Nõrk positiivne 0.0069	Nõrk positiivne 0.0644	Nõrk negatiivne -0.0108	Nõrk negatiivne -0.0489	Nõrk negatiivne -0.1811
Answer 10	-	Nõrk positiivne 0.0756	Nõrk positiivne 0.0681	Nõrk negatiivne -0.0139	Nõrk positiivne 0.0290	Nõrk positiivne 0.0341	Nõrk negatiivne -0.0122	Nõrk negatiivne -0.1343
Answer 11	-	Nõrk positiivne 0.0631	Nõrk positiivne 0.0536	Nõrk negatiivne -0.0091	Nõrk positiivne 0.0113	Nõrk positiivne 0.0239	Nõrk positiivne 0.0247	Nõrk negatiivne -0.1260
Answer 12	-	Nõrk positiivne 0.0442	Nõrk positiivne 0.0943	Nõrk negatiivne -0.0340	Nõrk positiivne 0.0342	Nõrk positiivne 0.0335	Nõrk positiivne 0.0256	Nõrk negatiivne -0.1535
Answer 13	-	Nõrk positiivne 0.0700	Nõrk positiivne 0.0962	Nõrk negatiivne -0.0393	Nõrk positiivne 0.0295	Nõrk positiivne 0.0412	Nõrk positiivne 0.0147	Nõrk negatiivne -0.1624
Answer 14	-	Nõrk positiivne 0.0783	Nõrk positiivne 0.0900	Nõrk negatiivne -0.0019	Nõrk negatiivne -0.0089	Nõrk positiivne 0.0043	Nõrk positiivne 0.0139	Nõrk negatiivne -0.1221
Answer 15	-	Nõrk positiivne 0.0538	Nõrk positiivne 0.1282	Nõrk negatiivne -0.0345	Nõrk positiivne 0.0152	Nõrk negatiivne -0.0176	Nõrk positiivne 0.0237	Nõrk negatiivne -0.1159
Answer 16	-	Nõrk positiivne 0.0699	Nõrk positiivne 0.0263	Nõrk negatiivne -0.0371	Nõrk negatiivne -0.0377	Nõrk positiivne 0.0699	Nõrk positiivne 0.0205	Nõrk negatiivne -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

Tooteomanik SaaS SDTEST®

Valerii omandas sotsiaalpedagoog-psühholoogi kvalifikatsiooni 1993. aastal ning on seejärel oma teadmisi projektijuhtimises rakendanud.
Valerii omandas magistrikraadi ning projekti- ja programmijuhi kvalifikatsiooni 2013. aastal. Magistriõppe käigus tutvus ta projekti teekaardiga (GPM Deutsche Gesellschaft für Projektmanagement e. V.) ja spiraaldünaamikaga.
Valerii on V.U.C.A. ebakindluse uurimise autor. kontseptsioon, kasutades spiraaldünaamikat ja matemaatilist statistikat psühholoogias ning 38 rahvusvahelist küsitlust.

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