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) Zviito zvemakambani mune hukama nevashandi mumwedzi yekupedzisira (hongu / kwete)

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3) Kutya

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14) Zvinokonzeresa zera

15) Zvikonzero Nei Vanhu Vachikanda (neAnna Vakosha)

16) Kuvimba (#WVS)

17) Oxford Kubudirira Kuongorora

18) Psychological Wellbering

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20) Chii chaungaita vhiki ino kuti utarise hutano hwako hwepfungwa?

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22) Meritocracy

23) Kungwara kwehunyanzvi uye kuguma kwebudiriro

24) Sei vanhu vachimhanya?

25) Musiyano weGender Mukuvaka Kuzvivimba (IFD Allensbach)

26) Xing.com tsika yekuongorora

27) Patrick Lenicioni's "iyo shanu shanu dzechikwata"

28) Kunzwira tsitsi ...

29) Chii chakakosha kune iyo nyanzvi mukusarudza basa rekupa?

30) Nei vanhu vachiramba kuchinja (na Siobhán mchale)

31) Unotonga sei manzwiro ako? (NaNal Mustafa M.a.)

32) 21 Unyanzvi Unokubhadhara Nokusingaperi (naJeremia Teo / 赵汉昇)

33) Rusununguko chaidzo ...

34) Nzira mbiri dzekuvaka kuvimba nevamwe (neJustin Wright)

35) Hunhu hwemushandi ane tarenda (ne talent management Institute)

36) Mazano gumi ekukurudzira timu yako

37) Algebra yehana (yakanyorwa naVladimir Lefebvre)

38) Mikana mitatu Yakasiyana Yeramangwana (naDr. Clare W. Graves)

39) Zviito Zvekuvaka Kuzvivimba Kusingazununguki (naSuren 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.

Kutya

Charts Kuwirirana

VUCA

Critical kukosha kuwirirana coefficient

Zvakajairika kugoverwa, naWilliam Sealy Gosset (Mudzidzi) r = 0.0315

Isiri kugoverwa, nemapfumo r = 0.0013

Ratidza chete mhinduro > r = 0.0315

Kugovera	Zvisina kujairika	Zvisina kujairika	Zvisina kujairika	Zvakajairika	Zvakajairika	Zvakajairika	Zvakajairika	Zvakajairika
Mibvunzo yese Mibvunzo yese Kutya kwangu kukuru kuri
Kutya kwangu kukuru kuri
Answer 1	-	Vasina simba 0.0518	Vasina simba 0.0257	Kushaya simba -0.0203	Vasina simba 0.0942	Vasina simba 0.0391	Kushaya simba -0.0141	Kushaya simba -0.1546
Answer 2	-	Vasina simba 0.0178	Kushaya simba -0.0071	Kushaya simba -0.0376	Vasina simba 0.0631	Vasina simba 0.0501	Vasina simba 0.0133	Kushaya simba -0.0955
Answer 3	-	Kushaya simba -0.0025	Kushaya simba -0.0083	Kushaya simba -0.0456	Kushaya simba -0.0432	Vasina simba 0.0498	Vasina simba 0.0768	Kushaya simba -0.0241
Answer 4	-	Vasina simba 0.0428	Vasina simba 0.0297	Kushaya simba -0.0259	Vasina simba 0.0175	Vasina simba 0.0374	Vasina simba 0.0266	Kushaya simba -0.1027
Answer 5	-	Vasina simba 0.0228	Vasina simba 0.1240	Vasina simba 0.0115	Vasina simba 0.0735	Vasina simba 0.0010	Kushaya simba -0.0152	Kushaya simba -0.1755
Answer 6	-	Kushaya simba -0.0021	Vasina simba 0.0028	Kushaya simba -0.0619	Kushaya simba -0.0110	Vasina simba 0.0269	Vasina simba 0.0872	Kushaya simba -0.0366
Answer 7	-	Vasina simba 0.0107	Vasina simba 0.0313	Kushaya simba -0.0667	Kushaya simba -0.0310	Vasina simba 0.0538	Vasina simba 0.0715	Kushaya simba -0.0532
Answer 8	-	Vasina simba 0.0653	Vasina simba 0.0688	Kushaya simba -0.0267	Vasina simba 0.0117	Vasina simba 0.0398	Vasina simba 0.0185	Kushaya simba -0.1345
Answer 9	-	Vasina simba 0.0740	Vasina simba 0.1594	Vasina simba 0.0050	Vasina simba 0.0612	Kushaya simba -0.0067	Kushaya simba -0.0464	Kushaya simba -0.1836
Answer 10	-	Vasina simba 0.0754	Vasina simba 0.0624	Kushaya simba -0.0144	Vasina simba 0.0273	Vasina simba 0.0336	Kushaya simba -0.0107	Kushaya simba -0.1359
Answer 11	-	Vasina simba 0.0626	Vasina simba 0.0495	Kushaya simba -0.0084	Vasina simba 0.0094	Vasina simba 0.0277	Vasina simba 0.0251	Kushaya simba -0.1276
Answer 12	-	Vasina simba 0.0429	Vasina simba 0.0889	Kushaya simba -0.0323	Vasina simba 0.0317	Vasina simba 0.0350	Vasina simba 0.0265	Kushaya simba -0.1531
Answer 13	-	Vasina simba 0.0705	Vasina simba 0.0917	Kushaya simba -0.0384	Vasina simba 0.0287	Vasina simba 0.0437	Vasina simba 0.0151	Kushaya simba -0.1634
Answer 14	-	Vasina simba 0.0812	Vasina simba 0.0862	Kushaya simba -0.0035	Kushaya simba -0.0129	Vasina simba 0.0076	Vasina simba 0.0152	Kushaya simba -0.1208
Answer 15	-	Vasina simba 0.0555	Vasina simba 0.1235	Kushaya simba -0.0340	Vasina simba 0.0113	Kushaya simba -0.0139	Vasina simba 0.0261	Kushaya simba -0.1160
Answer 16	-	Vasina simba 0.0715	Vasina simba 0.0212	Kushaya simba -0.0388	Kushaya simba -0.0401	Vasina simba 0.0745	Vasina simba 0.0178	Kushaya simba -0.0772

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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

Muridzi weChigadzirwa SaaS SDTEST®

Valerii akakodzera sesocial pedagogue-psychologist muna 1993 uye kubvira ipapo akashandisa ruzivo rwake mukutungamira kweprojekiti.
Valerii akawana Master's degree uye chirongwa uye chirongwa chemaneja qualification muna 2013. Panguva yechirongwa chaTenzi wake, akazoziva Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) uye Spiral Dynamics.
Valerii ndiye munyori wekuongorora kusavimbika kweV.U.C.A. pfungwa inoshandisa Spiral Dynamics uye nhamba dzemasvomhu mune zvepfungwa, uye makumi matatu nemasere sarudzo dzepasi rose.

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