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.

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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.

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Charts Korrelatioun

VUCA

Kritescher Wäert vun der Korrelatioun souguer gemaach

Normal Verdeelung, vum William Sighty Goesset (Student) r = 0.0318

Net normal Verdeelung, vum Spärman r = 0.0013

Weisen nëmme Resultater > r = 0.0318

Verdeelung	Net normal	Net normal	Net normal	Normelle	Normelle	Normelle	Normelle	Normelle
All Froen All Froen Meng gréissten Angscht ass
Meng gréissten Angscht ass
Answer 1	-	Schwaach positiv 0.0524	Schwaach positiv 0.0258	Schwaach negativ -0.0180	Schwaach positiv 0.0949	Schwaach positiv 0.0355	Schwaach negativ -0.0146	Schwaach negativ -0.1537
Answer 2	-	Schwaach positiv 0.0175	Schwaach negativ -0.0058	Schwaach negativ -0.0387	Schwaach positiv 0.0669	Schwaach positiv 0.0494	Schwaach positiv 0.0116	Schwaach negativ -0.0969
Answer 3	-	Schwaach negativ -0.0035	Schwaach negativ -0.0091	Schwaach negativ -0.0441	Schwaach negativ -0.0435	Schwaach positiv 0.0477	Schwaach positiv 0.0747	Schwaach negativ -0.0199
Answer 4	-	Schwaach positiv 0.0412	Schwaach positiv 0.0255	Schwaach negativ -0.0229	Schwaach positiv 0.0192	Schwaach positiv 0.0353	Schwaach positiv 0.0246	Schwaach negativ -0.0990
Answer 5	-	Schwaach positiv 0.0227	Schwaach positiv 0.1271	Schwaach positiv 0.0109	Schwaach positiv 0.0770	Schwaach negativ -0.0005	Schwaach negativ -0.0175	Schwaach negativ -0.1774
Answer 6	-	Schwaach negativ -0.0055	Schwaach positiv 0.0042	Schwaach negativ -0.0622	Schwaach negativ -0.0080	Schwaach positiv 0.0249	Schwaach positiv 0.0863	Schwaach negativ -0.0354
Answer 7	-	Schwaach positiv 0.0084	Schwaach positiv 0.0331	Schwaach negativ -0.0656	Schwaach negativ -0.0297	Schwaach positiv 0.0523	Schwaach positiv 0.0696	Schwaach negativ -0.0522
Answer 8	-	Schwaach positiv 0.0629	Schwaach positiv 0.0710	Schwaach negativ -0.0267	Schwaach positiv 0.0130	Schwaach positiv 0.0379	Schwaach positiv 0.0184	Schwaach negativ -0.1339
Answer 9	-	Schwaach positiv 0.0711	Schwaach positiv 0.1602	Schwaach positiv 0.0072	Schwaach positiv 0.0643	Schwaach negativ -0.0106	Schwaach negativ -0.0484	Schwaach negativ -0.1819
Answer 10	-	Schwaach positiv 0.0740	Schwaach positiv 0.0656	Schwaach negativ -0.0150	Schwaach positiv 0.0292	Schwaach positiv 0.0321	Schwaach negativ -0.0123	Schwaach negativ -0.1359
Answer 11	-	Schwaach positiv 0.0629	Schwaach positiv 0.0524	Schwaach negativ -0.0098	Schwaach positiv 0.0104	Schwaach positiv 0.0253	Schwaach positiv 0.0247	Schwaach negativ -0.1270
Answer 12	-	Schwaach positiv 0.0433	Schwaach positiv 0.0921	Schwaach negativ -0.0338	Schwaach positiv 0.0335	Schwaach positiv 0.0331	Schwaach positiv 0.0257	Schwaach negativ -0.1540
Answer 13	-	Schwaach positiv 0.0687	Schwaach positiv 0.0957	Schwaach negativ -0.0396	Schwaach positiv 0.0304	Schwaach positiv 0.0408	Schwaach positiv 0.0151	Schwaach negativ -0.1630
Answer 14	-	Schwaach positiv 0.0781	Schwaach positiv 0.0884	Schwaach negativ -0.0003	Schwaach negativ -0.0096	Schwaach positiv 0.0050	Schwaach positiv 0.0138	Schwaach negativ -0.1228
Answer 15	-	Schwaach positiv 0.0539	Schwaach positiv 0.1269	Schwaach negativ -0.0339	Schwaach positiv 0.0148	Schwaach negativ -0.0172	Schwaach positiv 0.0237	Schwaach negativ -0.1160
Answer 16	-	Schwaach positiv 0.0690	Schwaach positiv 0.0248	Schwaach negativ -0.0372	Schwaach negativ -0.0385	Schwaach positiv 0.0703	Schwaach positiv 0.0205	Schwaach negativ -0.0792

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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

Produit Besëtzer SaaS SDTEST®

De Valerii gouf 1993 als Sozialpädagog-Psycholog qualifizéiert an huet zënterhier säi Wëssen an der Projektmanagement applizéiert.
De Valerii krut e Masterstudium an d'Qualifikatioun vum Projet a Programmmanager am Joer 2013. Während sengem Masterprogramm huet hie sech mam Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) a Spiral Dynamics vertraut.
Valerii ass den Auteur fir d'Onsécherheet vun der V.U.C.A. Konzept mat Spiral Dynamik a mathematesch Statistiken an der Psychologie, an 38 international Ëmfroen.

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