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)

39) Accións para construír unha autoconfianza inquebrantable (por Suren 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.

Medos

Charts Correlación

VUCA

O valor crítico do coeficiente de correlación

Distribución normal, de William Sealy Gosset (estudante) r = 0.0322

Distribución non normal, por Spearman r = 0.0013

Mostrar só resultados > r = 0.0322

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

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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