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) Ketso tsa lik'hamphani tse mabapi le basebetsi khoeling ea ho qetela (e / che)

2) Ketso tsa lik'hamphani tse mabapi le basebetsi khoeling ea ho qetela (e 'nete ea%)

3) Tšabo

4) Mathata a maholo a tobaneng le naha ea ka

5) Ke litšoaneleho life le bokhoni bo botle ba sebelisang litšobotsi le bokhoni bofe bo sebelisang ha ho aha lihlopha tse atlehileng?

6) Google. Lintlha tse amang sehlopha se sebetsang le sehlopha

7) Lintho tse ka sehloohong tse tlang pele

8) Ke eng e etsang mookameli e motle?

9) Ke eng e etsang hore batho ba atlehe mosebetsing?

10) Na u se u loketse ho fumana moputso o fokolang hore o sebetse hole?

11) Na Agesomm e teng?

12) Agesomm ea mosebetsi

13) Agerimphe bophelong

14) Lisosa tsa Age

15) Mabaka a etsang hore batho ba inehele (ke Anna ba bohlokoa)

16) Tšepa (#WVS)

17) Tlhahlobo ea thabo ea Oxford

18) Bophelo bo botle ba kelello

19) Monyetla o latelang o ne o tla ba kae?

20) U tla etsa eng bekeng ena ho hlokomela bophelo ba hau ba kelello?

21) Ke phela ka ho nahana ka nako e fetileng, ea hona joale kapa ea bokamoso

22) Meritocracy

23) Bohlale ba maiketsetso le pheletso ea tsoelo-pele

24) Hobaneng ha batho ba lieha?

25) Phapang ea bong ho aha boitšepo (IFD Allensbach)

26) Xing.com Tlhahlobo ea setso

27) Patrick Lecioli's "ho bapala tse hlano tsa sehlopha"

28) Kutloelo-bohloko ke ...

29) Ke eng ea bohlokoa bakeng sa eona e ikhethang ha u khetha tlhahiso ea mosebetsi?

30) Hobaneng ha batho ba hana liphetoho (ke Siobhán Mchale)

31) U laola maikutlo a hau joang? (ke Nawal MealAFA M.A.)

32) 21 Tsebo e lefang ka ho sa feleng (ka Jeremia Teo / 赵汉昇)

33) Tokoloho ea 'nete ke ...

34) Mekhoa e 12 ea ho aha ts'epo ea ho ts'epa

35) Litšobotsi tsa mohiruoa ea nang le talenta (ka instant actite ea Talenta)

36) 10 Litsela tsa ho susumetsa sehlopha sa hau

37) Algebra ea Letsoalo (ea Vladimir Lefebvre)

38) Menyetla e meraro e Ikhethang ea Bokamoso (ka 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.

Tšabo

lichate Correlation

VUCA

Mahlonoko tseo ho leng bohlokoa ba Correlation coefficient

Kabo e tloaelehileng, ke William Searly Gosset (seithuti) r = 0.0331

Kabo e tloaelehileng e sa tloaelehang, ka Spearman r = 0.0013

Bonts'a feela liphetho feela > r = 0.0331

TLHOKOMELISO	Se seng se tloaelehileng	Se seng se tloaelehileng	Se seng se tloaelehileng	Tloaelehileng	Tloaelehileng	Tloaelehileng	Tloaelehileng	Tloaelehileng
Lipotso tsohle Lipotso tsohle Tšabo ea ka e kholo ke
Tšabo ea ka e kholo ke
Answer 1	-	Fokolang positive 0.0563	Fokolang positive 0.0317	Fokolang mpe -0.0161	Fokolang positive 0.0907	Fokolang positive 0.0298	Fokolang mpe -0.0126	Fokolang mpe -0.1537
Answer 2	-	Fokolang positive 0.0216	Fokolang positive 0.0002	Fokolang mpe -0.0458	Fokolang positive 0.0654	Fokolang positive 0.0445	Fokolang positive 0.0124	Fokolang mpe -0.0937
Answer 3	-	Fokolang mpe -0.0035	Fokolang mpe -0.0111	Fokolang mpe -0.0421	Fokolang mpe -0.0456	Fokolang positive 0.0466	Fokolang positive 0.0786	Fokolang mpe -0.0201
Answer 4	-	Fokolang positive 0.0435	Fokolang positive 0.0353	Fokolang mpe -0.0181	Fokolang positive 0.0145	Fokolang positive 0.0301	Fokolang positive 0.0197	Fokolang mpe -0.0979
Answer 5	-	Fokolang positive 0.0299	Fokolang positive 0.1279	Fokolang positive 0.0136	Fokolang positive 0.0730	Fokolang mpe -0.0007	Fokolang mpe -0.0207	Fokolang mpe -0.1746
Answer 6	-	Fokolang mpe -0.0004	Fokolang positive 0.0082	Fokolang mpe -0.0629	Fokolang mpe -0.0078	Fokolang positive 0.0193	Fokolang positive 0.0830	Fokolang mpe -0.0318
Answer 7	-	Fokolang positive 0.0122	Fokolang positive 0.0381	Fokolang mpe -0.0686	Fokolang mpe -0.0242	Fokolang positive 0.0471	Fokolang positive 0.0636	Fokolang mpe -0.0513
Answer 8	-	Fokolang positive 0.0698	Fokolang positive 0.0849	Fokolang mpe -0.0321	Fokolang positive 0.0146	Fokolang positive 0.0345	Fokolang positive 0.0130	Fokolang mpe -0.1368
Answer 9	-	Fokolang positive 0.0665	Fokolang positive 0.1674	Fokolang positive 0.0092	Fokolang positive 0.0691	Fokolang mpe -0.0128	Fokolang mpe -0.0528	Fokolang mpe -0.1812
Answer 10	-	Fokolang positive 0.0778	Fokolang positive 0.0755	Fokolang mpe -0.0180	Fokolang positive 0.0231	Fokolang positive 0.0346	Fokolang mpe -0.0146	Fokolang mpe -0.1298
Answer 11	-	Fokolang positive 0.0584	Fokolang positive 0.0524	Fokolang mpe -0.0096	Fokolang positive 0.0081	Fokolang positive 0.0199	Fokolang positive 0.0318	Fokolang mpe -0.1197
Answer 12	-	Fokolang positive 0.0380	Fokolang positive 0.1042	Fokolang mpe -0.0352	Fokolang positive 0.0357	Fokolang positive 0.0254	Fokolang positive 0.0286	Fokolang mpe -0.1515
Answer 13	-	Fokolang positive 0.0644	Fokolang positive 0.1057	Fokolang mpe -0.0448	Fokolang positive 0.0268	Fokolang positive 0.0416	Fokolang positive 0.0169	Fokolang mpe -0.1600
Answer 14	-	Fokolang positive 0.0717	Fokolang positive 0.1026	Fokolang mpe -0.0006	Fokolang mpe -0.0089	Fokolang mpe -0.0012	Fokolang positive 0.0080	Fokolang mpe -0.1168
Answer 15	-	Fokolang positive 0.0549	Fokolang positive 0.1375	Fokolang mpe -0.0420	Fokolang positive 0.0178	Fokolang mpe -0.0160	Fokolang positive 0.0216	Fokolang mpe -0.1180
Answer 16	-	Fokolang positive 0.0591	Fokolang positive 0.0273	Fokolang mpe -0.0386	Fokolang mpe -0.0399	Fokolang positive 0.0653	Fokolang positive 0.0282	Fokolang mpe -0.0708

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[1] https://twitter.com/wileyprof

[2] https://colinallen.dnsalias.org

[3] https://philpeople.org/profiles/colin-allen

2023.10.13

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