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) Tindakan syarikat berhubung dengan kakitangan pada bulan lalu (ya / tidak)

2) Tindakan syarikat berhubung dengan kakitangan pada bulan lepas (fakta dalam%)

3) Ketakutan

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11) Adakah umur wujud?

12) Ageism dalam kerjaya

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14) Punca umur

15) Sebab Mengapa Orang Menyerah (oleh Anna Vital)

16) Kepercayaan (#WVS)

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18) Kesejahteraan psikologi

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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 = 0.0318

Pengedaran tidak normal, oleh Spearman r = 0.0013

Tunjukkan hanya hasil > r = 0.0318

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

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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