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)

2) Zviito zvemakambani mune hukama nevashandi mumwedzi yekupedzisira (chokwadi mu%)

3) Kutya

4) Matambudziko makuru akatarisana nenyika yangu

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6) Google. Zvinhu zvinokanganisa timu inowedzera

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8) Chii chinoita mutongi mukuru mutungamiri mukuru?

9) Chii chinoita kuti vanhu vabudirire pabasa?

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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?

21) Ini ndinorarama kufunga nezve yangu yapfuura, iripo kana ramangwana

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 = 0.0322

Isiri kugoverwa, nemapfumo r = 0.0013

Ratidza chete mhinduro > r = 0.0322

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 0.0482	Vasina simba 0.0333	Kushaya simba -0.0178	Vasina simba 0.0944	Vasina simba 0.0354	Kushaya simba -0.0171	Kushaya simba -0.1538
Answer 2	-	Vasina simba 0.0174	Vasina simba 0.0011	Kushaya simba -0.0402	Vasina simba 0.0648	Vasina simba 0.0458	Vasina simba 0.0125	Kushaya simba -0.0960
Answer 3	-	Kushaya simba -0.0041	Kushaya simba -0.0091	Kushaya simba -0.0457	Kushaya simba -0.0452	Vasina simba 0.0480	Vasina simba 0.0760	Kushaya simba -0.0179
Answer 4	-	Vasina simba 0.0395	Vasina simba 0.0308	Kushaya simba -0.0225	Vasina simba 0.0193	Vasina simba 0.0305	Vasina simba 0.0233	Kushaya simba -0.0963
Answer 5	-	Vasina simba 0.0251	Vasina simba 0.1311	Vasina simba 0.0097	Vasina simba 0.0793	Kushaya simba -0.0013	Kushaya simba -0.0223	Kushaya simba -0.1782
Answer 6	-	Kushaya simba -0.0063	Vasina simba 0.0106	Kushaya simba -0.0658	Kushaya simba -0.0081	Vasina simba 0.0208	Vasina simba 0.0844	Kushaya simba -0.0308
Answer 7	-	Vasina simba 0.0102	Vasina simba 0.0417	Kushaya simba -0.0701	Kushaya simba -0.0279	Vasina simba 0.0479	Vasina simba 0.0660	Kushaya simba -0.0502
Answer 8	-	Vasina simba 0.0636	Vasina simba 0.0810	Kushaya simba -0.0282	Vasina simba 0.0139	Vasina simba 0.0352	Vasina simba 0.0140	Kushaya simba -0.1346
Answer 9	-	Vasina simba 0.0657	Vasina simba 0.1683	Vasina simba 0.0050	Vasina simba 0.0671	Kushaya simba -0.0147	Kushaya simba -0.0505	Kushaya simba -0.1789
Answer 10	-	Vasina simba 0.0751	Vasina simba 0.0714	Kushaya simba -0.0215	Vasina simba 0.0267	Vasina simba 0.0290	Kushaya simba -0.0113	Kushaya simba -0.1304
Answer 11	-	Vasina simba 0.0615	Vasina simba 0.0584	Kushaya simba -0.0058	Vasina simba 0.0074	Vasina simba 0.0185	Vasina simba 0.0234	Kushaya simba -0.1234
Answer 12	-	Vasina simba 0.0410	Vasina simba 0.0994	Kushaya simba -0.0346	Vasina simba 0.0348	Vasina simba 0.0296	Vasina simba 0.0233	Kushaya simba -0.1529
Answer 13	-	Vasina simba 0.0660	Vasina simba 0.1017	Kushaya simba -0.0382	Vasina simba 0.0281	Vasina simba 0.0398	Vasina simba 0.0139	Kushaya simba -0.1626
Answer 14	-	Vasina simba 0.0718	Vasina simba 0.0982	Kushaya simba -0.0017	Kushaya simba -0.0070	Vasina simba 0.0024	Vasina simba 0.0108	Kushaya simba -0.1221
Answer 15	-	Vasina simba 0.0549	Vasina simba 0.1333	Kushaya simba -0.0333	Vasina simba 0.0169	Kushaya simba -0.0197	Vasina simba 0.0204	Kushaya simba -0.1180
Answer 16	-	Vasina simba 0.0657	Vasina simba 0.0273	Kushaya simba -0.0343	Kushaya simba -0.0433	Vasina simba 0.0646	Vasina simba 0.0246	Kushaya simba -0.0750

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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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