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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26) Xing.com asa igbelewọn

27) Patrick Levension ká "awọn dysfocnu marun ti ẹgbẹ kan"

28) Ifoju jẹ ...

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30) Kilode ti awọn eniyan tako iyipada (nipasẹ Siobhán MChale)

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36) 10 awọn bọtini lati rubọ ẹgbẹ rẹ

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.

Ibẹru

shatti Ibamu

VUCA

Lominu ni iye ti awọn ibamu olùsọdipúpọ

Pinpin deede, nipasẹ William Searin (ọmọ ile-iwe) r = 0.0353

Pinpin deede, nipasẹ Spearman r = 0.0014

Fihan awọn abajade nikan > r = 0.0353

Pinpin	Ti kii ṣe deede	Deedee	Ti kii ṣe deede	Deedee	Deedee	Deedee	Deedee	Deedee
Gbogbo awọn ibeere Gbogbo awọn ibeere Ibẹru nla mi jẹ
Ibẹru nla mi jẹ
Answer 1	-	Alailagbara 0.0297	Alailagbara 0.0298	Alailagbara odi -0.0106	Alailagbara 0.0970	Alailagbara 0.0325	Alailagbara odi -0.0019	Alailagbara odi -0.1558
Answer 2	-	Alailagbara 0.0188	Alailagbara 0.0076	Alailagbara odi -0.0360	Alailagbara 0.0711	Alailagbara 0.0387	Alailagbara 0.0082	Alailagbara odi -0.1011
Answer 3	-	Alailagbara 0.0026	Alailagbara odi -0.0170	Alailagbara odi -0.0443	Alailagbara odi -0.0458	Alailagbara 0.0547	Alailagbara 0.0808	Alailagbara odi -0.0270
Answer 4	-	Alailagbara 0.0332	Alailagbara 0.0285	Alailagbara odi -0.0006	Alailagbara 0.0155	Alailagbara 0.0276	Alailagbara 0.0105	Alailagbara odi -0.0917
Answer 5	-	Alailagbara 0.0122	Alailagbara 0.1193	Alailagbara 0.0095	Alailagbara 0.0721	Alailagbara 0.0057	Alailagbara odi -0.0083	Alailagbara odi -0.1687
Answer 6	-	Alailagbara 0.0044	Alailagbara 0.0005	Alailagbara odi -0.0582	Alailagbara odi -0.0004	Alailagbara 0.0210	Alailagbara 0.0830	Alailagbara odi -0.0418
Answer 7	-	Alailagbara 0.0242	Alailagbara 0.0368	Alailagbara odi -0.0521	Alailagbara odi -0.0234	Alailagbara 0.0403	Alailagbara 0.0568	Alailagbara odi -0.0597
Answer 8	-	Alailagbara 0.0707	Alailagbara 0.0781	Alailagbara odi -0.0244	Alailagbara 0.0140	Alailagbara 0.0303	Alailagbara 0.0137	Alailagbara odi -0.1334
Answer 9	-	Alailagbara 0.0564	Alailagbara 0.1531	Alailagbara 0.0127	Alailagbara 0.0769	Alailagbara odi -0.0136	Alailagbara odi -0.0495	Alailagbara odi -0.1752
Answer 10	-	Alailagbara 0.0711	Alailagbara 0.0700	Alailagbara odi -0.0127	Alailagbara 0.0246	Alailagbara 0.0363	Alailagbara odi -0.0156	Alailagbara odi -0.1273
Answer 11	-	Alailagbara 0.0542	Alailagbara 0.0488	Alailagbara 0.0086	Alailagbara 0.0078	Alailagbara 0.0162	Alailagbara 0.0315	Alailagbara odi -0.1248
Answer 12	-	Alailagbara 0.0281	Alailagbara 0.0929	Alailagbara odi -0.0325	Alailagbara 0.0361	Alailagbara 0.0276	Alailagbara 0.0365	Alailagbara odi -0.1482
Answer 13	-	Alailagbara 0.0643	Alailagbara 0.0916	Alailagbara odi -0.0418	Alailagbara 0.0237	Alailagbara 0.0425	Alailagbara 0.0239	Alailagbara odi -0.1558
Answer 14	-	Alailagbara 0.0697	Alailagbara 0.1017	Alailagbara 0.0149	Alailagbara odi -0.0062	Alailagbara odi -0.0087	Alailagbara odi -0.0002	Alailagbara odi -0.1161
Answer 15	-	Alailagbara 0.0603	Alailagbara 0.1299	Alailagbara odi -0.0379	Alailagbara 0.0163	Alailagbara odi -0.0091	Alailagbara 0.0164	Alailagbara odi -0.1204
Answer 16	-	Alailagbara 0.0691	Alailagbara 0.0221	Alailagbara odi -0.0305	Alailagbara odi -0.0515	Alailagbara 0.0750	Alailagbara 0.0187	Alailagbara odi -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

Valeriii Kosenko

Ọja Sus Pet Project Sdtest®

A ṣe oṣiṣẹ Valerii gẹgẹbi onimọ-jinlẹ ti o jẹ aṣoju-ọrọ ti o jẹ aṣoju ọdun 1993 ati pe o ti lo imo rẹ ni iṣakoso iṣẹ akanṣe.
Valerii gba ìyí ti oluwa rẹ ati iṣẹ akanṣe ati ilana ilana eto eto ni ọdun 2013. Lakoko eto oluwa rẹ, o jẹ ipinya ti agbekale (GPM Rutscherschaft Für ProjekThatamencationscramentamencationscramentamencation
Valerii mu ọpọlọpọ awọn idanwo awọn idanwo shanics ati lo imoye rẹ ati iriri lati mu ẹya ti isiyi ṣe deede.
Valerii ni onkọwe ti ṣawari aidaniloju ti V.u.c.i. Erongba nipa lilo awọn agbara ajira ati awọn iṣiro iṣiro iṣiro ni ọpọlọ, diẹ ẹ sii ju 20 ibo ibo kariaye.

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