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) Actions des entreprises en relation avec le personnel au cours du dernier mois (oui / non)

2) Actions d'entreprises relatives au personnel au cours du dernier mois (en% en%)

3) Peurs

4) Les plus gros problèmes auxquels sont confrontés mon pays

5) Quelles qualités et capacités les bons leaders utilisent-ils lors de la création d'équipes réussies?

6) Google. Facteurs qui ont un impact sur l'efficacité de l'équipe

7) Les principales priorités des demandeurs d'emploi

8) Qu'est-ce qui fait d'un patron un grand leader?

9) Qu'est-ce qui fait que les gens réussissent au travail?

10) Êtes-vous prêt à recevoir moins de salaire pour travailler à distance?

11) L'âgisme existe-t-il?

12) L'âge en carrière

13) L'âge dans la vie

14) Causes de l'âgisme

15) Raisons pour lesquelles les gens abandonnent (par Anna Vital)

16) CONFIANCE (#WVS)

17) Enquête sur le bonheur d'Oxford

18) Bien-être psychologique

19) Où serait votre prochaine opportunité la plus excitante?

20) Que ferez-vous cette semaine pour prendre soin de votre santé mentale?

21) Je vis en pensant à mon passé, à mon présent ou à mon avenir

22) Méritocratie

23) Intelligence artificielle et fin de la civilisation

24) Pourquoi les gens tergiversent-ils?

25) Différence entre les sexes dans la construction de la confiance en soi (IFD Allensbach)

26) Xing.com Évaluation de la culture

27) Les cinq dysfonctionnements d'une équipe de Patrick Lencioni "de Patrick Lencioni"

28) L'empathie est ...

29) Qu'est-ce qui est essentiel pour les spécialistes informatiques dans le choix d'une offre d'emploi?

30) Pourquoi les gens résistent au changement (par Siobhán McHale)

31) Comment régulez-vous vos émotions? (Par Nawal Mustafa M.A.)

32) 21 compétences qui vous paient pour toujours (par Jeremiah Teo / 赵汉昇)

33) La vraie liberté est ...

34) 12 façons de renforcer la confiance avec les autres (par Justin Wright)

35) Caractéristiques d'un employé talentueux (par Talent Management Institute)

36) 10 clés pour motiver votre équipe

37) Algèbre de la conscience (par Vladimir Lefebvre)

38) Trois possibilités distinctes pour l'avenir (par 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.

Peurs

Graphiques Corrélation

VUCA

La valeur critique du coefficient de corrélation

Distribution normale, par William Sealy Gosset (étudiant) r = 0.033

Distribution non normale, par Spearman r = 0.0013

Afficher uniquement les résultats > r = 0.033

Distribution	Non normal	Non normal	Non normal	Normal	Normal	Normal	Normal	Normal
Toutes les questions Toutes les questions Ma plus grande peur est
Ma plus grande peur est
Answer 1	-	Positif faible 0.0558	Positif faible 0.0311	Négatif faible -0.0169	Positif faible 0.0917	Positif faible 0.0304	Négatif faible -0.0128	Négatif faible -0.1541
Answer 2	-	Positif faible 0.0229	Négatif faible -0.0006	Négatif faible -0.0443	Positif faible 0.0632	Positif faible 0.0453	Positif faible 0.0130	Négatif faible -0.0942
Answer 3	-	Négatif faible -0.0032	Négatif faible -0.0122	Négatif faible -0.0413	Négatif faible -0.0464	Positif faible 0.0469	Positif faible 0.0786	Négatif faible -0.0196
Answer 4	-	Positif faible 0.0437	Positif faible 0.0345	Négatif faible -0.0196	Positif faible 0.0152	Positif faible 0.0307	Positif faible 0.0204	Négatif faible -0.0981
Answer 5	-	Positif faible 0.0303	Positif faible 0.1280	Positif faible 0.0134	Positif faible 0.0733	Négatif faible -0.0005	Négatif faible -0.0203	Négatif faible -0.1759
Answer 6	-	Négatif faible -0.0003	Positif faible 0.0082	Négatif faible -0.0630	Négatif faible -0.0082	Positif faible 0.0195	Positif faible 0.0830	Négatif faible -0.0315
Answer 7	-	Positif faible 0.0124	Positif faible 0.0382	Négatif faible -0.0694	Négatif faible -0.0241	Positif faible 0.0473	Positif faible 0.0641	Négatif faible -0.0514
Answer 8	-	Positif faible 0.0696	Positif faible 0.0850	Négatif faible -0.0333	Positif faible 0.0150	Positif faible 0.0346	Positif faible 0.0134	Négatif faible -0.1364
Answer 9	-	Positif faible 0.0667	Positif faible 0.1676	Positif faible 0.0077	Positif faible 0.0694	Négatif faible -0.0128	Négatif faible -0.0517	Négatif faible -0.1817
Answer 10	-	Positif faible 0.0780	Positif faible 0.0754	Négatif faible -0.0211	Positif faible 0.0249	Positif faible 0.0347	Négatif faible -0.0132	Négatif faible -0.1303
Answer 11	-	Positif faible 0.0579	Positif faible 0.0528	Négatif faible -0.0090	Positif faible 0.0083	Positif faible 0.0201	Positif faible 0.0308	Négatif faible -0.1198
Answer 12	-	Positif faible 0.0389	Positif faible 0.1036	Négatif faible -0.0362	Positif faible 0.0359	Positif faible 0.0255	Positif faible 0.0297	Négatif faible -0.1521
Answer 13	-	Positif faible 0.0645	Positif faible 0.1041	Négatif faible -0.0438	Positif faible 0.0262	Positif faible 0.0423	Positif faible 0.0174	Négatif faible -0.1603
Answer 14	-	Positif faible 0.0710	Positif faible 0.1022	Négatif faible -0.0015	Négatif faible -0.0085	Négatif faible -0.0006	Positif faible 0.0087	Négatif faible -0.1169
Answer 15	-	Positif faible 0.0555	Positif faible 0.1365	Négatif faible -0.0429	Positif faible 0.0179	Négatif faible -0.0158	Positif faible 0.0223	Négatif faible -0.1178
Answer 16	-	Positif faible 0.0591	Positif faible 0.0271	Négatif faible -0.0384	Négatif faible -0.0401	Positif faible 0.0655	Positif faible 0.0283	Négatif faible -0.0709

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D'accord

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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

Propriétaire de produit SaaS Pet Project SDTEST®

Valerii était qualifié en tant que pédagogue social en 1993 et a depuis appliqué ses connaissances en gestion de projet.
Valerii a obtenu une maîtrise et la qualification du projet et des gestionnaires de programme en 2013. Au cours de son programme de maîtrise, il s'est familiarisé avec la feuille de route du projet (GPM Deutsche Gesellschaft Für Projektmanagement e. V.) et Spiral Dynamics.
Valerii a passé divers tests de dynamique en spirale et a utilisé ses connaissances et son expérience pour adapter la version actuelle de SDTest.
Valerii est l'auteur de l'exploration de l'incertitude du V.U.C.A. Concept utilisant la dynamique en spirale et les statistiques mathématiques en psychologie, plus de 20 sondages internationaux.

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