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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7) Awọn pataki akọkọ ti awọn ti n wa ni iṣẹ

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9) Kini o mu ki eniyan ṣaṣeyọri ni ibi iṣẹ?

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11) Ṣe ọjọ-ori wa?

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26) Xing.com asa igbelewọn

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

28) Ifoju jẹ ...

29) Kini o ṣe pataki fun awọn alamọja ni yiyan ipese iṣẹ?

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32) Awọn ọgbọn 21 ti o sanwo fun ọ lailai (nipasẹ Jeremiah Teo / 赵汉昇)

33) Ominira gidi ni ...

34) Awọn ọna 12 lati kọ igbẹkẹle pẹlu awọn miiran (nipasẹ Justin Winght)

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36) 10 awọn bọtini lati rubọ ẹgbẹ rẹ

37) Algebra ti Ẹri (nipasẹ Vladimir Lefebvre)

38) Awọn aye Iyatọ Meta ti Ọjọ iwaju (nipasẹ Dokita Clare W. Graves)

39) Awọn iṣe lati Kọ Igbekele Ara-ẹni ti ko le mì (nipasẹ 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.

Ibẹru

shatti Ibamu

VUCA

Lominu ni iye ti awọn ibamu olùsọdipúpọ

Pinpin deede, nipasẹ William Searin (ọmọ ile-iwe) r = 0.0317

Pinpin deede, nipasẹ Spearman r = 0.0013

Fihan awọn abajade nikan > r = 0.0317

Pinpin	Ti kii ṣe deede	Ti kii ṣe deede	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 0.0520	Alailagbara 0.0258	Alailagbara odi -0.0186	Alailagbara 0.0947	Alailagbara 0.0383	Alailagbara odi -0.0166	Alailagbara odi -0.1540
Answer 2	-	Alailagbara 0.0179	Alailagbara odi -0.0060	Alailagbara odi -0.0379	Alailagbara 0.0660	Alailagbara 0.0504	Alailagbara 0.0106	Alailagbara odi -0.0970
Answer 3	-	Alailagbara odi -0.0024	Alailagbara odi -0.0096	Alailagbara odi -0.0439	Alailagbara odi -0.0442	Alailagbara 0.0486	Alailagbara 0.0756	Alailagbara odi -0.0218
Answer 4	-	Alailagbara 0.0433	Alailagbara 0.0269	Alailagbara odi -0.0231	Alailagbara 0.0160	Alailagbara 0.0371	Alailagbara 0.0233	Alailagbara odi -0.0988
Answer 5	-	Alailagbara 0.0232	Alailagbara 0.1266	Alailagbara 0.0122	Alailagbara 0.0749	Alailagbara 0.0006	Alailagbara odi -0.0173	Alailagbara odi -0.1776
Answer 6	-	Alailagbara odi -0.0041	Alailagbara 0.0042	Alailagbara odi -0.0608	Alailagbara odi -0.0091	Alailagbara 0.0260	Alailagbara 0.0852	Alailagbara odi -0.0367
Answer 7	-	Alailagbara 0.0096	Alailagbara 0.0333	Alailagbara odi -0.0653	Alailagbara odi -0.0297	Alailagbara 0.0522	Alailagbara 0.0691	Alailagbara odi -0.0532
Answer 8	-	Alailagbara 0.0647	Alailagbara 0.0706	Alailagbara odi -0.0253	Alailagbara 0.0118	Alailagbara 0.0395	Alailagbara 0.0163	Alailagbara odi -0.1346
Answer 9	-	Alailagbara 0.0730	Alailagbara 0.1589	Alailagbara 0.0065	Alailagbara 0.0619	Alailagbara odi -0.0062	Alailagbara odi -0.0490	Alailagbara odi -0.1830
Answer 10	-	Alailagbara 0.0749	Alailagbara 0.0644	Alailagbara odi -0.0138	Alailagbara 0.0278	Alailagbara 0.0341	Alailagbara odi -0.0140	Alailagbara odi -0.1358
Answer 11	-	Alailagbara 0.0633	Alailagbara 0.0513	Alailagbara odi -0.0084	Alailagbara 0.0091	Alailagbara 0.0274	Alailagbara 0.0235	Alailagbara odi -0.1274
Answer 12	-	Alailagbara 0.0437	Alailagbara 0.0926	Alailagbara odi -0.0319	Alailagbara 0.0307	Alailagbara 0.0332	Alailagbara 0.0254	Alailagbara odi -0.1532
Answer 13	-	Alailagbara 0.0707	Alailagbara 0.0946	Alailagbara odi -0.0386	Alailagbara 0.0281	Alailagbara 0.0433	Alailagbara 0.0143	Alailagbara odi -0.1638
Answer 14	-	Alailagbara 0.0804	Alailagbara 0.0893	Alailagbara odi -0.0016	Alailagbara odi -0.0118	Alailagbara 0.0064	Alailagbara 0.0128	Alailagbara odi -0.1222
Answer 15	-	Alailagbara 0.0545	Alailagbara 0.1260	Alailagbara odi -0.0328	Alailagbara 0.0121	Alailagbara odi -0.0152	Alailagbara 0.0235	Alailagbara odi -0.1157
Answer 16	-	Alailagbara 0.0725	Alailagbara 0.0230	Alailagbara odi -0.0371	Alailagbara odi -0.0407	Alailagbara 0.0733	Alailagbara 0.0163	Alailagbara odi -0.0776

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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 Olohun SaaS SDTEST®

Valerii jẹ oṣiṣẹ bi alamọdaju-ọrọ-apọju-ọrọ awujọ ni ọdun 1993 ati pe lati igba naa o ti lo imọ rẹ ni iṣakoso iṣẹ akanṣe.
Valerii gba alefa Titunto si ati iṣẹ akanṣe ati afijẹẹri oluṣakoso eto ni ọdun 2013. Lakoko eto Titunto rẹ, o faramọ pẹlu Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) ati Spiral Dynamics.
Valerii ni onkọwe ti ṣawari aidaniloju ti V.U.C.A. ero nipa lilo Ajija dainamiki ati mathematiki statistiki ni oroinuokan, ati 38 okeere idibo.

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