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:

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3) Ketakutan

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11) Adakah umur wujud?

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14) Punca umur

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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.

Ketakutan

carta Korelasi

VUCA

Nilai kritikal pekali korelasi

Pengagihan Normal, oleh William Sealy Gosset (Pelajar) r = 0.0325

Pengedaran tidak normal, oleh Spearman r = 0.0013

Tunjukkan hanya hasil > r = 0.0325

Pengedaran	Tidak normal	Tidak normal	Tidak normal	Biasa	Biasa	Biasa	Biasa	Biasa
Semua soalan Semua soalan Ketakutan terbesar saya adalah
Ketakutan terbesar saya adalah
Answer 1	-	Lemah positif 0.0511	Lemah positif 0.0305	Lemah negatif -0.0167	Lemah positif 0.0956	Lemah positif 0.0356	Lemah negatif -0.0171	Lemah negatif -0.1563
Answer 2	-	Lemah positif 0.0185	Lemah positif 0.0002	Lemah negatif -0.0427	Lemah positif 0.0659	Lemah positif 0.0466	Lemah positif 0.0116	Lemah negatif -0.0953
Answer 3	-	Lemah negatif -0.0035	Lemah negatif -0.0105	Lemah negatif -0.0474	Lemah negatif -0.0445	Lemah positif 0.0502	Lemah positif 0.0780	Lemah negatif -0.0205
Answer 4	-	Lemah positif 0.0418	Lemah positif 0.0264	Lemah negatif -0.0219	Lemah positif 0.0171	Lemah positif 0.0335	Lemah positif 0.0228	Lemah negatif -0.0960
Answer 5	-	Lemah positif 0.0221	Lemah positif 0.1302	Lemah positif 0.0095	Lemah positif 0.0787	Lemah positif 0.0020	Lemah negatif -0.0226	Lemah negatif -0.1783
Answer 6	-	Lemah negatif -0.0059	Lemah positif 0.0111	Lemah negatif -0.0683	Lemah negatif -0.0059	Lemah positif 0.0214	Lemah positif 0.0845	Lemah negatif -0.0322
Answer 7	-	Lemah positif 0.0117	Lemah positif 0.0403	Lemah negatif -0.0739	Lemah negatif -0.0263	Lemah positif 0.0491	Lemah positif 0.0669	Lemah negatif -0.0507
Answer 8	-	Lemah positif 0.0682	Lemah positif 0.0831	Lemah negatif -0.0345	Lemah positif 0.0165	Lemah positif 0.0366	Lemah positif 0.0138	Lemah negatif -0.1378
Answer 9	-	Lemah positif 0.0696	Lemah positif 0.1671	Lemah positif 0.0048	Lemah positif 0.0664	Lemah negatif -0.0114	Lemah negatif -0.0537	Lemah negatif -0.1806
Answer 10	-	Lemah positif 0.0787	Lemah positif 0.0733	Lemah negatif -0.0240	Lemah positif 0.0278	Lemah positif 0.0334	Lemah negatif -0.0155	Lemah negatif -0.1342
Answer 11	-	Lemah positif 0.0624	Lemah positif 0.0577	Lemah negatif -0.0100	Lemah positif 0.0094	Lemah positif 0.0231	Lemah positif 0.0215	Lemah negatif -0.1252
Answer 12	-	Lemah positif 0.0391	Lemah positif 0.1013	Lemah negatif -0.0414	Lemah positif 0.0357	Lemah positif 0.0316	Lemah positif 0.0263	Lemah negatif -0.1529
Answer 13	-	Lemah positif 0.0649	Lemah positif 0.1028	Lemah negatif -0.0448	Lemah positif 0.0291	Lemah positif 0.0458	Lemah positif 0.0150	Lemah negatif -0.1651
Answer 14	-	Lemah positif 0.0701	Lemah positif 0.0992	Lemah negatif -0.0021	Lemah negatif -0.0073	Lemah positif 0.0052	Lemah positif 0.0075	Lemah negatif -0.1214
Answer 15	-	Lemah positif 0.0538	Lemah positif 0.1341	Lemah negatif -0.0385	Lemah positif 0.0204	Lemah negatif -0.0178	Lemah positif 0.0174	Lemah negatif -0.1164
Answer 16	-	Lemah positif 0.0660	Lemah positif 0.0307	Lemah negatif -0.0383	Lemah negatif -0.0414	Lemah positif 0.0663	Lemah positif 0.0221	Lemah negatif -0.0758

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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

Pemilik Produk SaaS SDTEST®

Valerii telah layak sebagai pedagogue-psikologi sosial pada tahun 1993 dan sejak itu telah menggunakan pengetahuannya dalam pengurusan projek.
Valerii memperoleh ijazah Sarjana dan kelayakan pengurus projek dan program pada tahun 2013. Semasa program Sarjananya, beliau mengenali Pelan Hala Tuju Projek (GPM Deutsche Gesellschaft für Projektmanagement e. V.) dan Spiral Dynamics.
Valerii ialah pengarang meneroka ketidakpastian V.U.C.A. konsep menggunakan Spiral Dynamics dan statistik matematik dalam psikologi, dan 38 tinjauan antarabangsa.

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