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.

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Here are reports of polls which SDTEST^® makes:

1) Gníomhartha cuideachtaí maidir le pearsanra le mí anuas (tá / níl)

2) Gníomhartha cuideachtaí maidir le pearsanra le mí an mhí dheiridh (fírinne i%)

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37) Ailgéabar coinsiasa le Vladimir Lefebvre

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39) Gníomhartha chun Féinmhuinín Dochreidte a Thógáil (le 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.

Eagla

Charts Comhghaoil

VUCA

Luach criticiúil an chomhéifeacht comhghaoil

Dáileadh Gnáth, le William Sealy Gosset (Mac Léinn) r = 0.0318

Dáileadh Neamh -Ghnáth, le Spearman r = 0.0013

Taispeáin torthaí amháin > r = 0.0318

Imdháileadh	Neamhghnách	Neamhghnách	Neamhghnách	Gnáth-	Gnáth-	Gnáth-	Gnáth-	Gnáth-
Gach ceist Gach ceist Is é an t-eagla is mó atá agam ná
Is é an t-eagla is mó atá agam ná
Answer 1	-	Dearfach lag 0.0524	Dearfach lag 0.0258	Diúltach lag -0.0180	Dearfach lag 0.0949	Dearfach lag 0.0355	Diúltach lag -0.0146	Diúltach lag -0.1537
Answer 2	-	Dearfach lag 0.0175	Diúltach lag -0.0058	Diúltach lag -0.0387	Dearfach lag 0.0669	Dearfach lag 0.0494	Dearfach lag 0.0116	Diúltach lag -0.0969
Answer 3	-	Diúltach lag -0.0035	Diúltach lag -0.0091	Diúltach lag -0.0441	Diúltach lag -0.0435	Dearfach lag 0.0477	Dearfach lag 0.0747	Diúltach lag -0.0199
Answer 4	-	Dearfach lag 0.0412	Dearfach lag 0.0255	Diúltach lag -0.0229	Dearfach lag 0.0192	Dearfach lag 0.0353	Dearfach lag 0.0246	Diúltach lag -0.0990
Answer 5	-	Dearfach lag 0.0227	Dearfach lag 0.1271	Dearfach lag 0.0109	Dearfach lag 0.0770	Diúltach lag -0.0005	Diúltach lag -0.0175	Diúltach lag -0.1774
Answer 6	-	Diúltach lag -0.0055	Dearfach lag 0.0042	Diúltach lag -0.0622	Diúltach lag -0.0080	Dearfach lag 0.0249	Dearfach lag 0.0863	Diúltach lag -0.0354
Answer 7	-	Dearfach lag 0.0084	Dearfach lag 0.0331	Diúltach lag -0.0656	Diúltach lag -0.0297	Dearfach lag 0.0523	Dearfach lag 0.0696	Diúltach lag -0.0522
Answer 8	-	Dearfach lag 0.0629	Dearfach lag 0.0710	Diúltach lag -0.0267	Dearfach lag 0.0130	Dearfach lag 0.0379	Dearfach lag 0.0184	Diúltach lag -0.1339
Answer 9	-	Dearfach lag 0.0711	Dearfach lag 0.1602	Dearfach lag 0.0072	Dearfach lag 0.0643	Diúltach lag -0.0106	Diúltach lag -0.0484	Diúltach lag -0.1819
Answer 10	-	Dearfach lag 0.0740	Dearfach lag 0.0656	Diúltach lag -0.0150	Dearfach lag 0.0292	Dearfach lag 0.0321	Diúltach lag -0.0123	Diúltach lag -0.1359
Answer 11	-	Dearfach lag 0.0629	Dearfach lag 0.0524	Diúltach lag -0.0098	Dearfach lag 0.0104	Dearfach lag 0.0253	Dearfach lag 0.0247	Diúltach lag -0.1270
Answer 12	-	Dearfach lag 0.0433	Dearfach lag 0.0921	Diúltach lag -0.0338	Dearfach lag 0.0335	Dearfach lag 0.0331	Dearfach lag 0.0257	Diúltach lag -0.1540
Answer 13	-	Dearfach lag 0.0687	Dearfach lag 0.0957	Diúltach lag -0.0396	Dearfach lag 0.0304	Dearfach lag 0.0408	Dearfach lag 0.0151	Diúltach lag -0.1630
Answer 14	-	Dearfach lag 0.0781	Dearfach lag 0.0884	Diúltach lag -0.0003	Diúltach lag -0.0096	Dearfach lag 0.0050	Dearfach lag 0.0138	Diúltach lag -0.1228
Answer 15	-	Dearfach lag 0.0539	Dearfach lag 0.1269	Diúltach lag -0.0339	Dearfach lag 0.0148	Diúltach lag -0.0172	Dearfach lag 0.0237	Diúltach lag -0.1160
Answer 16	-	Dearfach lag 0.0690	Dearfach lag 0.0248	Diúltach lag -0.0372	Diúltach lag -0.0385	Dearfach lag 0.0703	Dearfach lag 0.0205	Diúltach lag -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

Úinéir Táirge SaaS SDTEST®

Cáilíodh Valerii mar oideolaí-síceolaí sóisialta i 1993 agus tá a chuid eolais i mbainistíocht tionscadal curtha i bhfeidhm aige ó shin.
Ghnóthaigh Valerii céim Mháistreachta agus cáilíocht an bhainisteora tionscadail agus clár in 2013. Le linn a chláir Mháistreachta, chuir sé aithne ar Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) agus Spiral Dynamics.
Is é Valerii an t-údar a rinne iniúchadh ar éiginnteacht an V.U.C.A. coincheap ag baint úsáide as Dinimic Bíseach agus staitisticí matamaitice sa tsíceolaíocht, agus 38 vótaíocht idirnáisiúnta.

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