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) Acciones de las empresas en relación con el personal en el último mes (sí / no)

2) Acciones de las empresas en relación con el personal en el último mes (hecho en%)

3) Miedo

4) Mayores problemas que enfrentan mi país

5) ¿Qué cualidades y habilidades usan los buenos líderes al construir equipos exitosos?

6) Google. Factores que afectan la eficacia del equipo

7) Las principales prioridades de los solicitantes de empleo

8) ¿Qué hace que un jefe sea un gran líder?

9) ¿Qué hace que las personas tengan éxito en el trabajo?

10) ¿Estás listo para recibir menos pago para trabajar de forma remota?

11) ¿Existe el ageismo?

12) Ageismo en la carrera

13) Ageismo en la vida

14) Causas del ageismo

15) Razones por las cuales la gente se rinde (por Anna Vital)

16) CONFIANZA (#WVS)

17) Encuesta de felicidad de Oxford

18) Bienestar psicológico

19) ¿Dónde estaría su próxima oportunidad más emocionante?

20) ¿Qué harás esta semana para cuidar tu salud mental?

21) Vivo pensando en mi pasado, presente o futuro

22) Meritocracia

23) Inteligencia artificial y el fin de la civilización

24) ¿Por qué la gente postergue?

25) Diferencia de género en la construcción de confianza en sí mismo (IFD Allensbach)

26) Xing.com evaluación de la cultura

27) Las cinco disfunciones de un equipo de Patrick Lencioni de un equipo "

28) La empatía es ...

29) ¿Qué es esencial para los especialistas en TI al elegir una oferta de trabajo?

30) Por qué la gente resiste el cambio (por Siobhán McHale)

31) ¿Cómo regulas tus emociones? (por Nawal Mustafa M.A.)

32) 21 habilidades que te pagan para siempre (por Jeremiah Teo / 赵汉昇)

33) La verdadera libertad es ...

34) 12 formas de generar confianza con los demás (por Justin Wright)

35) Características de un empleado talentoso (por Talent Management Institute)

36) 10 claves para motivar a tu equipo

37) Álgebra de la conciencia (por Vladimir Lefebvre)

38) Tres posibilidades distintas del futuro (por la Dra. 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.

Miedo

Gráficos Correlación

VUCA

Valor crítico del coeficiente de correlación

Distribución normal, por William Sealy Gosset (estudiante) r = 0.033

Distribución no normal, por Spearman r = 0.0013

Mostrar solo resultados > r = 0.033

Distribución	No normal	No normal	No normal	Normal	Normal	Normal	Normal	Normal
Todas las preguntas Todas las preguntas Mi mayor miedo es
Mi mayor miedo es
Answer 1	-	Débil positivo 0.0532	Débil positivo 0.0292	Débil negativo -0.0175	Débil positivo 0.0919	Débil positivo 0.0301	Débil negativo -0.0114	Débil negativo -0.1523
Answer 2	-	Débil positivo 0.0208	Débil negativo -0.0014	Débil negativo -0.0431	Débil positivo 0.0641	Débil positivo 0.0449	Débil positivo 0.0130	Débil negativo -0.0931
Answer 3	-	Débil negativo -0.0053	Débil negativo -0.0130	Débil negativo -0.0406	Débil negativo -0.0456	Débil positivo 0.0474	Débil positivo 0.0793	Débil negativo -0.0204
Answer 4	-	Débil positivo 0.0427	Débil positivo 0.0328	Débil negativo -0.0200	Débil positivo 0.0158	Débil positivo 0.0306	Débil positivo 0.0217	Débil negativo -0.0980
Answer 5	-	Débil positivo 0.0255	Débil positivo 0.1255	Débil positivo 0.0143	Débil positivo 0.0732	Débil negativo -0.0019	Débil negativo -0.0196	Débil negativo -0.1747
Answer 6	-	Débil negativo -0.0027	Débil positivo 0.0074	Débil negativo -0.0629	Débil negativo -0.0074	Débil positivo 0.0199	Débil positivo 0.0835	Débil negativo -0.0324
Answer 7	-	Débil positivo 0.0110	Débil positivo 0.0371	Débil negativo -0.0688	Débil negativo -0.0227	Débil positivo 0.0471	Débil positivo 0.0650	Débil negativo -0.0523
Answer 8	-	Débil positivo 0.0693	Débil positivo 0.0825	Débil negativo -0.0321	Débil positivo 0.0139	Débil positivo 0.0351	Débil positivo 0.0147	Débil negativo -0.1369
Answer 9	-	Débil positivo 0.0643	Débil positivo 0.1659	Débil positivo 0.0082	Débil positivo 0.0699	Débil negativo -0.0136	Débil negativo -0.0513	Débil negativo -0.1826
Answer 10	-	Débil positivo 0.0760	Débil positivo 0.0730	Débil negativo -0.0219	Débil positivo 0.0254	Débil positivo 0.0318	Débil negativo -0.0138	Débil negativo -0.1318
Answer 11	-	Débil positivo 0.0571	Débil positivo 0.0514	Débil negativo -0.0099	Débil positivo 0.0077	Débil positivo 0.0206	Débil positivo 0.0308	Débil negativo -0.1211
Answer 12	-	Débil positivo 0.0373	Débil positivo 0.1013	Débil negativo -0.0357	Débil positivo 0.0357	Débil positivo 0.0243	Débil positivo 0.0296	Débil negativo -0.1524
Answer 13	-	Débil positivo 0.0621	Débil positivo 0.1036	Débil negativo -0.0438	Débil positivo 0.0273	Débil positivo 0.0414	Débil positivo 0.0176	Débil negativo -0.1608
Answer 14	-	Débil positivo 0.0703	Débil positivo 0.1007	Débil positivo 9.54E-5	Débil negativo -0.0088	Débil negativo -0.0011	Débil positivo 0.0084	Débil negativo -0.1174
Answer 15	-	Débil positivo 0.0554	Débil positivo 0.1349	Débil negativo -0.0418	Débil positivo 0.0179	Débil negativo -0.0165	Débil positivo 0.0219	Débil negativo -0.1181
Answer 16	-	Débil positivo 0.0581	Débil positivo 0.0255	Débil negativo -0.0388	Débil negativo -0.0407	Débil positivo 0.0654	Débil positivo 0.0283	Débil negativo -0.0714

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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 del producto Saas Pet Project Sdtest®

Valerii fue calificado como psicólogo de pedagogo social en 1993 y desde entonces ha aplicado su conocimiento en la gestión de proyectos.
Valerii obtuvo una maestría y la calificación del gerente del proyecto y del programa en 2013. Durante su programa de maestría, se familiarizó con Project Roadmap (GPM Deutsche Gesellschaft Für Projektmanagement e. V.) y dinámica espiral.
Valerii realizó varias pruebas de dinámica en espiral y utilizó su conocimiento y experiencia para adaptar la versión actual de SDTest.
Valerii es el autor de explorar la incertidumbre del V.U.C.A. Concepto utilizando la dinámica espiral y las estadísticas matemáticas en psicología, más de 20 encuestas internacionales.

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