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^®

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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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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 0.0526	Dearfach lag 0.0260	Diúltach lag -0.0183	Dearfach lag 0.0946	Dearfach lag 0.0358	Diúltach lag -0.0143	Diúltach lag -0.1540
Answer 2	-	Dearfach lag 0.0175	Diúltach lag -0.0058	Diúltach lag -0.0388	Dearfach lag 0.0668	Dearfach lag 0.0496	Dearfach lag 0.0117	Diúltach lag -0.0970
Answer 3	-	Diúltach lag -0.0035	Diúltach lag -0.0091	Diúltach lag -0.0441	Diúltach lag -0.0435	Dearfach lag 0.0478	Dearfach lag 0.0747	Diúltach lag -0.0200
Answer 4	-	Dearfach lag 0.0414	Dearfach lag 0.0257	Diúltach lag -0.0232	Dearfach lag 0.0188	Dearfach lag 0.0356	Dearfach lag 0.0249	Diúltach lag -0.0993
Answer 5	-	Dearfach lag 0.0226	Dearfach lag 0.1270	Dearfach lag 0.0111	Dearfach lag 0.0773	Diúltach lag -0.0008	Diúltach lag -0.0177	Diúltach lag -0.1772
Answer 6	-	Diúltach lag -0.0057	Dearfach lag 0.0040	Diúltach lag -0.0620	Diúltach lag -0.0076	Dearfach lag 0.0246	Dearfach lag 0.0860	Diúltach lag -0.0351
Answer 7	-	Dearfach lag 0.0082	Dearfach lag 0.0329	Diúltach lag -0.0653	Diúltach lag -0.0294	Dearfach lag 0.0519	Dearfach lag 0.0693	Diúltach lag -0.0520
Answer 8	-	Dearfach lag 0.0627	Dearfach lag 0.0709	Diúltach lag -0.0265	Dearfach lag 0.0134	Dearfach lag 0.0376	Dearfach lag 0.0181	Diúltach lag -0.1337
Answer 9	-	Dearfach lag 0.0710	Dearfach lag 0.1600	Dearfach lag 0.0074	Dearfach lag 0.0646	Diúltach lag -0.0109	Diúltach lag -0.0487	Diúltach lag -0.1817
Answer 10	-	Dearfach lag 0.0739	Dearfach lag 0.0654	Diúltach lag -0.0147	Dearfach lag 0.0296	Dearfach lag 0.0318	Diúltach lag -0.0126	Diúltach lag -0.1357
Answer 11	-	Dearfach lag 0.0627	Dearfach lag 0.0522	Diúltach lag -0.0096	Dearfach lag 0.0108	Dearfach lag 0.0250	Dearfach lag 0.0244	Diúltach lag -0.1268
Answer 12	-	Dearfach lag 0.0431	Dearfach lag 0.0920	Diúltach lag -0.0336	Dearfach lag 0.0339	Dearfach lag 0.0327	Dearfach lag 0.0254	Diúltach lag -0.1537
Answer 13	-	Dearfach lag 0.0685	Dearfach lag 0.0956	Diúltach lag -0.0394	Dearfach lag 0.0308	Dearfach lag 0.0405	Dearfach lag 0.0148	Diúltach lag -0.1628
Answer 14	-	Dearfach lag 0.0779	Dearfach lag 0.0883	Diúltach lag -0.0001	Diúltach lag -0.0092	Dearfach lag 0.0046	Dearfach lag 0.0135	Diúltach lag -0.1225
Answer 15	-	Dearfach lag 0.0537	Dearfach lag 0.1267	Diúltach lag -0.0337	Dearfach lag 0.0152	Diúltach lag -0.0175	Dearfach lag 0.0234	Diúltach lag -0.1158
Answer 16	-	Dearfach lag 0.0689	Dearfach lag 0.0247	Diúltach lag -0.0371	Diúltach lag -0.0383	Dearfach lag 0.0702	Dearfach lag 0.0203	Diúltach lag -0.0791

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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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