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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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 = 0.033

Net normal Verdeelung, vum Spärman r = 0.0013

Weisen nëmme Resultater > r = 0.033

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

Produktbesëtzer Saas Pet Projekt SDTET®

D'Valerecht als eSIL Picogolog ass am Joer 1993 quissesch gemaach an huet mam Konsartagementsacissioun.
Den Valerii huet e Master gemaach an de Studien a Programm Manager Katitioun am 2013. Am Joer 2010. Wärend dem Minale säi Programm, gouf hien och PPM-Kontaphtsigainside (GPM, Gürtotto) a Sphmightside EadickTAp EightellaTMAp. Ve Cürfilung kritt d'Valeri
D'Valerii huet verschidde Wiral Dynamik Tester gemaach an huet säi Wëssen an d'Erfarung déi aktuell Versioun vu SDTEST unzepassen.
Valerii ass den Auteur fir d'Onsécherheet vun der V.u.c.a ze exploréieren. Konzept mat Spiral Dynamik a mathematesch Statistiken an der Psychologie, méi wéi 20 international Polls.

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