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) Nga mahi a nga kamupene e pa ana ki nga kaimahi i te marama kua hipa (ae / kaore)

2) Nga mahi a nga kamupene e pa ana ki nga kaimahi i te marama whakamutunga (meka i te%)

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14) Tuhinga o mua

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39) Nga Mahi ki te Hanga Whakawhirinaki Whaiaro Aueue (na Suren Samarchyan)

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.

Mataku

Ngā tūtohi Ine

VUCA

uara Critical o te whakarea te faatanoraa

Tohatoha noa, na William Sealy Gospes (akonga) r = 0.0318

Ko te tohatoha noa, na te taote r = 0.0013

Whakaatuhia anake nga hua > r = 0.0318

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

Kaipupuri Hua SaaS SDTEST®

I whai tohu a Valerii hei kai-whakaako-a-hinengaro i te tau 1993, a, mai i tera wa kua whakamahia e ia ona matauranga ki te whakahaere kaupapa.
I whiwhi a Valerii i te tohu Kaiwhakaako me te tohu kaiwhakahaere kaupapa me te kaupapa i te tau 2013. I te wa o te kaupapa a tona Kaiwhakaako, i mohio ia ki te Mahere Arataki Kaupapa (GPM Deutsche Gesellschaft für Projektmanagement e. V.) me Spiral Dynamics.
Ko Valerii te kaituhi o te tirotiro i te koretake o te V.U.C.A. ariā e whakamahi ana i te Spiral Dynamics me te tatauranga pāngarau i roto i te hinengaro hinengaro, me te 38 pooti o te ao.

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