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 0.0567	Positif faible 0.0317	Négatif faible -0.0161	Positif faible 0.0910	Positif faible 0.0295	Négatif faible -0.0121	Négatif faible -0.1545
Answer 2	-	Positif faible 0.0228	Négatif faible -0.0002	Négatif faible -0.0450	Positif faible 0.0639	Positif faible 0.0444	Positif faible 0.0133	Négatif faible -0.0938
Answer 3	-	Négatif faible -0.0028	Négatif faible -0.0120	Négatif faible -0.0410	Négatif faible -0.0470	Positif faible 0.0467	Positif faible 0.0790	Négatif faible -0.0198
Answer 4	-	Positif faible 0.0443	Positif faible 0.0349	Négatif faible -0.0188	Positif faible 0.0144	Positif faible 0.0301	Positif faible 0.0209	Négatif faible -0.0984
Answer 5	-	Positif faible 0.0305	Positif faible 0.1282	Positif faible 0.0136	Positif faible 0.0734	Négatif faible -0.0013	Négatif faible -0.0200	Négatif faible -0.1758
Answer 6	-	Positif faible 8.40E-5	Positif faible 0.0083	Négatif faible -0.0622	Négatif faible -0.0089	Positif faible 0.0194	Positif faible 0.0832	Négatif faible -0.0318
Answer 7	-	Positif faible 0.0130	Positif faible 0.0382	Négatif faible -0.0683	Négatif faible -0.0250	Positif faible 0.0470	Positif faible 0.0644	Négatif faible -0.0518
Answer 8	-	Positif faible 0.0702	Positif faible 0.0849	Négatif faible -0.0322	Positif faible 0.0141	Positif faible 0.0345	Positif faible 0.0136	Négatif faible -0.1369
Answer 9	-	Positif faible 0.0672	Positif faible 0.1676	Positif faible 0.0087	Positif faible 0.0689	Négatif faible -0.0131	Négatif faible -0.0515	Négatif faible -0.1820
Answer 10	-	Positif faible 0.0786	Positif faible 0.0755	Négatif faible -0.0199	Positif faible 0.0241	Positif faible 0.0343	Négatif faible -0.0129	Négatif faible -0.1307
Answer 11	-	Positif faible 0.0582	Positif faible 0.0533	Négatif faible -0.0091	Positif faible 0.0080	Positif faible 0.0196	Positif faible 0.0313	Négatif faible -0.1199
Answer 12	-	Positif faible 0.0394	Positif faible 0.1038	Négatif faible -0.0353	Positif faible 0.0352	Positif faible 0.0251	Positif faible 0.0300	Négatif faible -0.1524
Answer 13	-	Positif faible 0.0648	Positif faible 0.1049	Négatif faible -0.0443	Positif faible 0.0262	Positif faible 0.0417	Positif faible 0.0179	Négatif faible -0.1604
Answer 14	-	Positif faible 0.0716	Positif faible 0.1022	Négatif faible -0.0002	Négatif faible -0.0094	Négatif faible -0.0010	Positif faible 0.0089	Négatif faible -0.1173
Answer 15	-	Positif faible 0.0560	Positif faible 0.1366	Négatif faible -0.0419	Positif faible 0.0172	Négatif faible -0.0161	Positif faible 0.0225	Négatif faible -0.1182
Answer 16	-	Positif faible 0.0593	Positif faible 0.0274	Négatif faible -0.0384	Négatif faible -0.0403	Positif faible 0.0653	Positif faible 0.0285	Négatif faible -0.0710

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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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