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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13) Ognsm ni igbesi aye

14) Awọn okunfa ti ọjọ ori

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16) Igbẹkẹle (#WVS)

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18) Ooye imọ-ara

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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?

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

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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)

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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 = 0.0325

Pinpin deede, nipasẹ Spearman r = 0.0013

Fihan awọn abajade nikan > r = 0.0325

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 0.0511	Alailagbara 0.0305	Alailagbara odi -0.0167	Alailagbara 0.0956	Alailagbara 0.0356	Alailagbara odi -0.0171	Alailagbara odi -0.1563
Answer 2	-	Alailagbara 0.0186	Alailagbara 0.0002	Alailagbara odi -0.0427	Alailagbara 0.0659	Alailagbara 0.0465	Alailagbara 0.0117	Alailagbara odi -0.0953
Answer 3	-	Alailagbara odi -0.0035	Alailagbara odi -0.0106	Alailagbara odi -0.0474	Alailagbara odi -0.0442	Alailagbara 0.0507	Alailagbara 0.0778	Alailagbara odi -0.0209
Answer 4	-	Alailagbara 0.0418	Alailagbara 0.0263	Alailagbara odi -0.0219	Alailagbara 0.0173	Alailagbara 0.0339	Alailagbara 0.0227	Alailagbara odi -0.0963
Answer 5	-	Alailagbara 0.0220	Alailagbara 0.1301	Alailagbara 0.0095	Alailagbara 0.0790	Alailagbara 0.0025	Alailagbara odi -0.0228	Alailagbara odi -0.1788
Answer 6	-	Alailagbara odi -0.0060	Alailagbara 0.0110	Alailagbara odi -0.0683	Alailagbara odi -0.0056	Alailagbara 0.0219	Alailagbara 0.0843	Alailagbara odi -0.0326
Answer 7	-	Alailagbara 0.0116	Alailagbara 0.0402	Alailagbara odi -0.0739	Alailagbara odi -0.0261	Alailagbara 0.0496	Alailagbara 0.0668	Alailagbara odi -0.0511
Answer 8	-	Alailagbara 0.0682	Alailagbara 0.0830	Alailagbara odi -0.0345	Alailagbara 0.0168	Alailagbara 0.0372	Alailagbara 0.0136	Alailagbara odi -0.1383
Answer 9	-	Alailagbara 0.0696	Alailagbara 0.1671	Alailagbara 0.0048	Alailagbara 0.0664	Alailagbara odi -0.0115	Alailagbara odi -0.0537	Alailagbara odi -0.1806
Answer 10	-	Alailagbara 0.0787	Alailagbara 0.0733	Alailagbara odi -0.0240	Alailagbara 0.0278	Alailagbara 0.0335	Alailagbara odi -0.0155	Alailagbara odi -0.1343
Answer 11	-	Alailagbara 0.0623	Alailagbara 0.0577	Alailagbara odi -0.0100	Alailagbara 0.0095	Alailagbara 0.0232	Alailagbara 0.0215	Alailagbara odi -0.1253
Answer 12	-	Alailagbara 0.0390	Alailagbara 0.1012	Alailagbara odi -0.0414	Alailagbara 0.0360	Alailagbara 0.0321	Alailagbara 0.0262	Alailagbara odi -0.1533
Answer 13	-	Alailagbara 0.0648	Alailagbara 0.1027	Alailagbara odi -0.0448	Alailagbara 0.0295	Alailagbara 0.0464	Alailagbara 0.0148	Alailagbara odi -0.1656
Answer 14	-	Alailagbara 0.0700	Alailagbara 0.0992	Alailagbara odi -0.0021	Alailagbara odi -0.0071	Alailagbara 0.0054	Alailagbara 0.0075	Alailagbara odi -0.1216
Answer 15	-	Alailagbara 0.0537	Alailagbara 0.1341	Alailagbara odi -0.0385	Alailagbara 0.0208	Alailagbara odi -0.0172	Alailagbara 0.0172	Alailagbara odi -0.1170
Answer 16	-	Alailagbara 0.0659	Alailagbara 0.0306	Alailagbara odi -0.0383	Alailagbara odi -0.0413	Alailagbara 0.0666	Alailagbara 0.0220	Alailagbara odi -0.0760

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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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