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 = 0.033

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

Bonts'a feela liphetho feela > r = 0.033

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 0.0536	Fokolang positive 0.0297	Fokolang mpe -0.0174	Fokolang positive 0.0910	Fokolang positive 0.0303	Fokolang mpe -0.0114	Fokolang mpe -0.1522
Answer 2	-	Fokolang positive 0.0197	Fokolang mpe -0.0002	Fokolang mpe -0.0449	Fokolang positive 0.0661	Fokolang positive 0.0446	Fokolang positive 0.0121	Fokolang mpe -0.0926
Answer 3	-	Fokolang mpe -0.0055	Fokolang mpe -0.0120	Fokolang mpe -0.0413	Fokolang mpe -0.0450	Fokolang positive 0.0473	Fokolang positive 0.0789	Fokolang mpe -0.0205
Answer 4	-	Fokolang positive 0.0427	Fokolang positive 0.0339	Fokolang mpe -0.0192	Fokolang positive 0.0153	Fokolang positive 0.0305	Fokolang positive 0.0210	Fokolang mpe -0.0983
Answer 5	-	Fokolang positive 0.0252	Fokolang positive 0.1256	Fokolang positive 0.0135	Fokolang positive 0.0733	Fokolang mpe -0.0016	Fokolang mpe -0.0198	Fokolang mpe -0.1742
Answer 6	-	Fokolang mpe -0.0024	Fokolang positive 0.0078	Fokolang mpe -0.0633	Fokolang mpe -0.0069	Fokolang positive 0.0198	Fokolang positive 0.0835	Fokolang mpe -0.0330
Answer 7	-	Fokolang positive 0.0112	Fokolang positive 0.0375	Fokolang mpe -0.0688	Fokolang mpe -0.0225	Fokolang positive 0.0471	Fokolang positive 0.0647	Fokolang mpe -0.0528
Answer 8	-	Fokolang positive 0.0698	Fokolang positive 0.0830	Fokolang mpe -0.0314	Fokolang positive 0.0137	Fokolang positive 0.0350	Fokolang positive 0.0144	Fokolang mpe -0.1376
Answer 9	-	Fokolang positive 0.0644	Fokolang positive 0.1664	Fokolang positive 0.0083	Fokolang positive 0.0702	Fokolang mpe -0.0136	Fokolang mpe -0.0517	Fokolang mpe -0.1830
Answer 10	-	Fokolang positive 0.0760	Fokolang positive 0.0738	Fokolang mpe -0.0199	Fokolang positive 0.0242	Fokolang positive 0.0319	Fokolang mpe -0.0149	Fokolang mpe -0.1320
Answer 11	-	Fokolang positive 0.0580	Fokolang positive 0.0514	Fokolang mpe -0.0111	Fokolang positive 0.0076	Fokolang positive 0.0206	Fokolang positive 0.0318	Fokolang mpe -0.1213
Answer 12	-	Fokolang positive 0.0367	Fokolang positive 0.1023	Fokolang mpe -0.0355	Fokolang positive 0.0359	Fokolang positive 0.0245	Fokolang positive 0.0286	Fokolang mpe -0.1524
Answer 13	-	Fokolang positive 0.0619	Fokolang positive 0.1049	Fokolang mpe -0.0451	Fokolang positive 0.0281	Fokolang positive 0.0412	Fokolang positive 0.0173	Fokolang mpe -0.1609
Answer 14	-	Fokolang positive 0.0707	Fokolang positive 0.1011	Fokolang positive 7.75E-5	Fokolang mpe -0.0083	Fokolang mpe -0.0012	Fokolang positive 0.0083	Fokolang mpe -0.1182
Answer 15	-	Fokolang positive 0.0549	Fokolang positive 0.1358	Fokolang mpe -0.0409	Fokolang positive 0.0176	Fokolang mpe -0.0163	Fokolang positive 0.0208	Fokolang mpe -0.1180
Answer 16	-	Fokolang positive 0.0582	Fokolang positive 0.0259	Fokolang mpe -0.0395	Fokolang mpe -0.0403	Fokolang positive 0.0652	Fokolang positive 0.0283	Fokolang mpe -0.0717

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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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