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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9) He aha te mea e angitu ai te tangata ki te mahi?

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36) 10 taviri hei akiaki i to roopu

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 = 0.0353

Ko te tohatoha noa, na te taote r = 0.0014

Whakaatuhia anake nga hua > r = 0.0353

Whakaratonga	Kore noa	Tonu	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 0.0297	Pai ngoikore 0.0298	Negative ngoikore -0.0106	Pai ngoikore 0.0970	Pai ngoikore 0.0325	Negative ngoikore -0.0019	Negative ngoikore -0.1558
Answer 2	-	Pai ngoikore 0.0188	Pai ngoikore 0.0076	Negative ngoikore -0.0360	Pai ngoikore 0.0711	Pai ngoikore 0.0387	Pai ngoikore 0.0082	Negative ngoikore -0.1011
Answer 3	-	Pai ngoikore 0.0026	Negative ngoikore -0.0170	Negative ngoikore -0.0443	Negative ngoikore -0.0458	Pai ngoikore 0.0547	Pai ngoikore 0.0808	Negative ngoikore -0.0270
Answer 4	-	Pai ngoikore 0.0332	Pai ngoikore 0.0285	Negative ngoikore -0.0006	Pai ngoikore 0.0155	Pai ngoikore 0.0276	Pai ngoikore 0.0105	Negative ngoikore -0.0917
Answer 5	-	Pai ngoikore 0.0122	Pai ngoikore 0.1193	Pai ngoikore 0.0095	Pai ngoikore 0.0721	Pai ngoikore 0.0057	Negative ngoikore -0.0083	Negative ngoikore -0.1687
Answer 6	-	Pai ngoikore 0.0044	Pai ngoikore 0.0005	Negative ngoikore -0.0582	Negative ngoikore -0.0004	Pai ngoikore 0.0210	Pai ngoikore 0.0830	Negative ngoikore -0.0418
Answer 7	-	Pai ngoikore 0.0242	Pai ngoikore 0.0368	Negative ngoikore -0.0521	Negative ngoikore -0.0234	Pai ngoikore 0.0403	Pai ngoikore 0.0568	Negative ngoikore -0.0597
Answer 8	-	Pai ngoikore 0.0707	Pai ngoikore 0.0781	Negative ngoikore -0.0244	Pai ngoikore 0.0140	Pai ngoikore 0.0303	Pai ngoikore 0.0137	Negative ngoikore -0.1334
Answer 9	-	Pai ngoikore 0.0564	Pai ngoikore 0.1531	Pai ngoikore 0.0127	Pai ngoikore 0.0769	Negative ngoikore -0.0136	Negative ngoikore -0.0495	Negative ngoikore -0.1752
Answer 10	-	Pai ngoikore 0.0711	Pai ngoikore 0.0700	Negative ngoikore -0.0127	Pai ngoikore 0.0246	Pai ngoikore 0.0363	Negative ngoikore -0.0156	Negative ngoikore -0.1273
Answer 11	-	Pai ngoikore 0.0542	Pai ngoikore 0.0488	Pai ngoikore 0.0086	Pai ngoikore 0.0078	Pai ngoikore 0.0162	Pai ngoikore 0.0315	Negative ngoikore -0.1248
Answer 12	-	Pai ngoikore 0.0281	Pai ngoikore 0.0929	Negative ngoikore -0.0325	Pai ngoikore 0.0361	Pai ngoikore 0.0276	Pai ngoikore 0.0365	Negative ngoikore -0.1482
Answer 13	-	Pai ngoikore 0.0643	Pai ngoikore 0.0916	Negative ngoikore -0.0418	Pai ngoikore 0.0237	Pai ngoikore 0.0425	Pai ngoikore 0.0239	Negative ngoikore -0.1558
Answer 14	-	Pai ngoikore 0.0697	Pai ngoikore 0.1017	Pai ngoikore 0.0149	Negative ngoikore -0.0062	Negative ngoikore -0.0087	Negative ngoikore -0.0002	Negative ngoikore -0.1161
Answer 15	-	Pai ngoikore 0.0603	Pai ngoikore 0.1299	Negative ngoikore -0.0379	Pai ngoikore 0.0163	Negative ngoikore -0.0091	Pai ngoikore 0.0164	Negative ngoikore -0.1204
Answer 16	-	Pai ngoikore 0.0691	Pai ngoikore 0.0221	Negative ngoikore -0.0305	Negative ngoikore -0.0515	Pai ngoikore 0.0750	Pai ngoikore 0.0187	Negative ngoikore -0.0696

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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 Pet Project SDtest®

Ko Valerii te tohu he kaupapa hinengaro-hinengaro-a-iwi i te tau 1993, mai i te mea kua paahitia tona matauranga ki te whakahaere kaupapa.
I whiwhi a Valerii i te tohu a te rangatira me te kaupapa me te Kaiwhakahaere Kaupapa Kaupapa i te tau 2013. I te wa e mohio ana ia ki te kaupapa o tona rangatira (GPM deutsche geselschaft f.
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Ko Valeyi te kaituhi o te torotoro i te koretake o te V.U.C.A. Te ariā ma te whakamahi i nga hihiri a te spiro me nga tatauranga pāngarau i roto i te hinengaro hinengaro, neke atu i te 20 nga pooti o te ao.

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