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 = 0.0335

Kabo e tloaelehileng e sa tloaelehang, ka Spearman r = 0.0014

Bonts'a feela liphetho feela > r = 0.0335

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 0.0521	Fokolang positive 0.0294	Fokolang mpe -0.0147	Fokolang positive 0.0885	Fokolang positive 0.0316	Fokolang mpe -0.0110	Fokolang mpe -0.1513
Answer 2	-	Fokolang positive 0.0213	Fokolang positive 0.0013	Fokolang mpe -0.0432	Fokolang positive 0.0618	Fokolang positive 0.0453	Fokolang positive 0.0103	Fokolang mpe -0.0918
Answer 3	-	Fokolang mpe -0.0042	Fokolang mpe -0.0116	Fokolang mpe -0.0406	Fokolang mpe -0.0477	Fokolang positive 0.0487	Fokolang positive 0.0767	Fokolang mpe -0.0191
Answer 4	-	Fokolang positive 0.0421	Fokolang positive 0.0350	Fokolang mpe -0.0115	Fokolang positive 0.0112	Fokolang positive 0.0307	Fokolang positive 0.0175	Fokolang mpe -0.0980
Answer 5	-	Fokolang positive 0.0288	Fokolang positive 0.1272	Fokolang positive 0.0146	Fokolang positive 0.0697	Fokolang positive 0.0037	Fokolang mpe -0.0215	Fokolang mpe -0.1746
Answer 6	-	Fokolang mpe -0.0001	Fokolang positive 0.0042	Fokolang mpe -0.0607	Fokolang mpe -0.0115	Fokolang positive 0.0231	Fokolang positive 0.0826	Fokolang mpe -0.0309
Answer 7	-	Fokolang positive 0.0117	Fokolang positive 0.0372	Fokolang mpe -0.0653	Fokolang mpe -0.0283	Fokolang positive 0.0495	Fokolang positive 0.0626	Fokolang mpe -0.0505
Answer 8	-	Fokolang positive 0.0658	Fokolang positive 0.0830	Fokolang mpe -0.0310	Fokolang positive 0.0139	Fokolang positive 0.0334	Fokolang positive 0.0134	Fokolang mpe -0.1322
Answer 9	-	Fokolang positive 0.0660	Fokolang positive 0.1658	Fokolang positive 0.0051	Fokolang positive 0.0691	Fokolang mpe -0.0093	Fokolang mpe -0.0498	Fokolang mpe -0.1820
Answer 10	-	Fokolang positive 0.0758	Fokolang positive 0.0724	Fokolang mpe -0.0173	Fokolang positive 0.0236	Fokolang positive 0.0312	Fokolang mpe -0.0115	Fokolang mpe -0.1263
Answer 11	-	Fokolang positive 0.0577	Fokolang positive 0.0544	Fokolang mpe -0.0075	Fokolang positive 0.0082	Fokolang positive 0.0185	Fokolang positive 0.0293	Fokolang mpe -0.1190
Answer 12	-	Fokolang positive 0.0376	Fokolang positive 0.1007	Fokolang mpe -0.0342	Fokolang positive 0.0296	Fokolang positive 0.0273	Fokolang positive 0.0341	Fokolang mpe -0.1500
Answer 13	-	Fokolang positive 0.0627	Fokolang positive 0.1017	Fokolang mpe -0.0443	Fokolang positive 0.0248	Fokolang positive 0.0434	Fokolang positive 0.0189	Fokolang mpe -0.1576
Answer 14	-	Fokolang positive 0.0732	Fokolang positive 0.1036	Fokolang positive 0.0048	Fokolang mpe -0.0105	Fokolang mpe -0.0039	Fokolang positive 0.0041	Fokolang mpe -0.1157
Answer 15	-	Fokolang positive 0.0539	Fokolang positive 0.1381	Fokolang mpe -0.0424	Fokolang positive 0.0163	Fokolang mpe -0.0147	Fokolang positive 0.0216	Fokolang mpe -0.1173
Answer 16	-	Fokolang positive 0.0590	Fokolang positive 0.0274	Fokolang mpe -0.0375	Fokolang mpe -0.0429	Fokolang positive 0.0687	Fokolang positive 0.0253	Fokolang mpe -0.0698

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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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