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) Accións das empresas en relación co persoal no último mes (si / non)

2) Accións de empresas en relación ao persoal no último mes (feito en%)

3) Medos

4) Maiores problemas aos que se enfronta o meu país

5) Que calidades e habilidades usan os bos líderes á hora de construír equipos de éxito?

6) Google. Factores que afectan á eficacia do equipo

7) As principais prioridades dos demandantes de emprego

8) Que fai dun xefe un gran líder?

9) Que fai que a xente teña éxito no traballo?

10) ¿Estás preparado para recibir menos pagos para traballar de forma remota?

11) Existe o idade?

12) Idade na carreira

13) Idade na vida

14) Causas do idade

15) Razóns polas que a xente renuncia (de Anna Vital)

16) Confía (#WVS)

17) Enquisa de felicidade de Oxford

18) Benestar psicolóxico

19) Onde sería a túa próxima oportunidade máis emocionante?

20) Que farás esta semana para coidar a túa saúde mental?

21) Vivo pensando no meu pasado, presente ou futuro

22) Meritocracia

23) Intelixencia artificial e o final da civilización

24) Por que a xente se procrastina?

25) Diferenza de xénero na construción de autoconfianza (IFD Allensbach)

26) Xing.com Avaliación da cultura

27) As cinco disfuncións dun equipo de Patrick Lencioni

28) A empatía é ...

29) Que é esencial para os especialistas en TI na elección dunha oferta de traballo?

30) Por que a xente se resiste ao cambio (de Siobhán McHale)

31) Como regulas as túas emocións? (de Nawal Mustafa M.A.)

32) 21 habilidades que che pagan para sempre (de Jeremiah Teo / 赵汉昇)

33) A liberdade real é ...

34) 12 xeitos de crear confianza cos demais (de Justin Wright)

35) Características dun empregado de talento (por Talent Management Institute)

36) 10 claves para motivar ao teu equipo

37) Álxebra da conciencia (por Vladimir Lefebvre)

38) Tres posibilidades distintas do futuro (pola doutora 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.

Medos

Charts Correlación

VUCA

O valor crítico do coeficiente de correlación

Distribución normal, de William Sealy Gosset (estudante) r = 0.0329

Distribución non normal, por Spearman r = 0.0013

Mostrar só resultados > r = 0.0329

Distribución	Non normal	Non normal	Non normal	Normal	Normal	Normal	Normal	Normal
Todas as preguntas Todas as preguntas O meu maior medo é
O meu maior medo é
Answer 1	-	Débil positivo 0.0566	Débil positivo 0.0332	Débil negativo -0.0170	Débil positivo 0.0912	Débil positivo 0.0308	Débil negativo -0.0153	Débil negativo -0.1537
Answer 2	-	Débil positivo 0.0223	Débil positivo 0.0011	Débil negativo -0.0442	Débil positivo 0.0639	Débil positivo 0.0464	Débil positivo 0.0120	Débil negativo -0.0960
Answer 3	-	Débil negativo -0.0031	Débil negativo -0.0104	Débil negativo -0.0407	Débil negativo -0.0463	Débil positivo 0.0475	Débil positivo 0.0779	Débil negativo -0.0213
Answer 4	-	Débil positivo 0.0437	Débil positivo 0.0357	Débil negativo -0.0197	Débil positivo 0.0161	Débil positivo 0.0311	Débil positivo 0.0187	Débil negativo -0.0987
Answer 5	-	Débil positivo 0.0296	Débil positivo 0.1300	Débil positivo 0.0124	Débil positivo 0.0749	Débil positivo 0.0014	Débil negativo -0.0231	Débil negativo -0.1771
Answer 6	-	Débil negativo -0.0008	Débil positivo 0.0090	Débil negativo -0.0613	Débil negativo -0.0070	Débil positivo 0.0196	Débil positivo 0.0803	Débil negativo -0.0321
Answer 7	-	Débil positivo 0.0118	Débil positivo 0.0401	Débil negativo -0.0693	Débil negativo -0.0246	Débil positivo 0.0471	Débil positivo 0.0623	Débil negativo -0.0505
Answer 8	-	Débil positivo 0.0697	Débil positivo 0.0875	Débil negativo -0.0316	Débil positivo 0.0155	Débil positivo 0.0346	Débil positivo 0.0098	Débil negativo -0.1373
Answer 9	-	Débil positivo 0.0679	Débil positivo 0.1707	Débil positivo 0.0105	Débil positivo 0.0676	Débil negativo -0.0138	Débil negativo -0.0545	Débil negativo -0.1821
Answer 10	-	Débil positivo 0.0793	Débil positivo 0.0772	Débil negativo -0.0208	Débil positivo 0.0242	Débil positivo 0.0343	Débil negativo -0.0152	Débil negativo -0.1300
Answer 11	-	Débil positivo 0.0590	Débil positivo 0.0559	Débil negativo -0.0071	Débil positivo 0.0082	Débil positivo 0.0205	Débil positivo 0.0266	Débil negativo -0.1213
Answer 12	-	Débil positivo 0.0405	Débil positivo 0.1050	Débil negativo -0.0363	Débil positivo 0.0361	Débil positivo 0.0253	Débil positivo 0.0277	Débil negativo -0.1522
Answer 13	-	Débil positivo 0.0655	Débil positivo 0.1056	Débil negativo -0.0439	Débil positivo 0.0270	Débil positivo 0.0417	Débil positivo 0.0152	Débil negativo -0.1601
Answer 14	-	Débil positivo 0.0728	Débil positivo 0.1049	Débil negativo -0.0002	Débil negativo -0.0088	Débil negativo -0.0007	Débil positivo 0.0061	Débil negativo -0.1187
Answer 15	-	Débil positivo 0.0561	Débil positivo 0.1378	Débil negativo -0.0415	Débil positivo 0.0178	Débil negativo -0.0162	Débil positivo 0.0194	Débil negativo -0.1176
Answer 16	-	Débil positivo 0.0606	Débil positivo 0.0308	Débil negativo -0.0348	Débil negativo -0.0421	Débil positivo 0.0642	Débil positivo 0.0250	Débil negativo -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

Valerii Kosenko

Propietario do produto SaaS SDTEST®

Valerii licenciouse como pedagogo social-psicólogo en 1993 e desde entón aplicou os seus coñecementos na xestión de proxectos.
Valerii obtivo un máster e a cualificación de director de proxectos e programas en 2013. Durante o seu programa de máster, familiarizouse con Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) e Spiral Dynamics.
Valerii é o autor de explorar a incerteza do V.U.C.A. concepto utilizando Spiral Dynamics e estatísticas matemáticas en psicoloxía, e 38 enquisas internacionais.

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