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:

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

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

3) Eagla

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11) An bhfuil aoiseachas ann?

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38) Trí Fhéidearthacht ar Leith sa Todhchaí (leis an Dr. Clare W. Graves)

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 = 0.0331

Dáileadh Neamh -Ghnáth, le Spearman r = 0.0013

Taispeáin torthaí amháin > r = 0.0331

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 0.0562	Dearfach lag 0.0311	Diúltach lag -0.0164	Dearfach lag 0.0903	Dearfach lag 0.0301	Diúltach lag -0.0120	Diúltach lag -0.1534
Answer 2	-	Dearfach lag 0.0217	Dearfach lag 0.0011	Diúltach lag -0.0455	Dearfach lag 0.0660	Dearfach lag 0.0440	Dearfach lag 0.0117	Diúltach lag -0.0942
Answer 3	-	Diúltach lag -0.0034	Diúltach lag -0.0104	Diúltach lag -0.0419	Diúltach lag -0.0451	Dearfach lag 0.0462	Dearfach lag 0.0780	Diúltach lag -0.0204
Answer 4	-	Dearfach lag 0.0436	Dearfach lag 0.0362	Diúltach lag -0.0177	Dearfach lag 0.0150	Dearfach lag 0.0296	Dearfach lag 0.0189	Diúltach lag -0.0984
Answer 5	-	Dearfach lag 0.0298	Dearfach lag 0.1270	Dearfach lag 0.0133	Dearfach lag 0.0724	Diúltach lag -0.0002	Diúltach lag -0.0199	Diúltach lag -0.1742
Answer 6	-	Diúltach lag -0.0003	Dearfach lag 0.0089	Diúltach lag -0.0627	Diúltach lag -0.0074	Dearfach lag 0.0190	Dearfach lag 0.0825	Diúltach lag -0.0321
Answer 7	-	Dearfach lag 0.0123	Dearfach lag 0.0388	Diúltach lag -0.0684	Diúltach lag -0.0238	Dearfach lag 0.0468	Dearfach lag 0.0631	Diúltach lag -0.0517
Answer 8	-	Dearfach lag 0.0699	Dearfach lag 0.0857	Diúltach lag -0.0318	Dearfach lag 0.0150	Dearfach lag 0.0341	Dearfach lag 0.0125	Diúltach lag -0.1372
Answer 9	-	Dearfach lag 0.0666	Dearfach lag 0.1681	Dearfach lag 0.0094	Dearfach lag 0.0694	Diúltach lag -0.0131	Diúltach lag -0.0533	Diúltach lag -0.1815
Answer 10	-	Dearfach lag 0.0776	Dearfach lag 0.0744	Diúltach lag -0.0185	Dearfach lag 0.0224	Dearfach lag 0.0352	Diúltach lag -0.0135	Diúltach lag -0.1293
Answer 11	-	Dearfach lag 0.0585	Dearfach lag 0.0531	Diúltach lag -0.0094	Dearfach lag 0.0086	Dearfach lag 0.0195	Dearfach lag 0.0313	Diúltach lag -0.1200
Answer 12	-	Dearfach lag 0.0378	Dearfach lag 0.1030	Diúltach lag -0.0357	Dearfach lag 0.0350	Dearfach lag 0.0261	Dearfach lag 0.0297	Diúltach lag -0.1510
Answer 13	-	Dearfach lag 0.0642	Dearfach lag 0.1044	Diúltach lag -0.0454	Dearfach lag 0.0259	Dearfach lag 0.0424	Dearfach lag 0.0183	Diúltach lag -0.1595
Answer 14	-	Dearfach lag 0.0718	Dearfach lag 0.1034	Diúltach lag -0.0003	Diúltach lag -0.0085	Diúltach lag -0.0016	Dearfach lag 0.0074	Diúltach lag -0.1172
Answer 15	-	Dearfach lag 0.0550	Dearfach lag 0.1382	Diúltach lag -0.0418	Dearfach lag 0.0181	Diúltach lag -0.0163	Dearfach lag 0.0211	Diúltach lag -0.1183
Answer 16	-	Dearfach lag 0.0591	Dearfach lag 0.0276	Diúltach lag -0.0384	Diúltach lag -0.0397	Dearfach lag 0.0651	Dearfach lag 0.0280	Diúltach lag -0.0710

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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 an Táirge SaaS Pet Project Sdtest®

Bhí Valerii cáilithe mar shíceolaí oideolaíoch sóisialta i 1993 agus ó shin i leith chuir sé a chuid eolais i bhfeidhm i mbainistíocht tionscadail.
Fuair Valerii céim mháistreachta agus cáilíocht an tionscadail agus an bhainisteora cláir in 2013. Le linn a chláir mháistir, bhí sé eolach ar threochlár Project (GPM Deutsche Gesellschaft Für Projektmanagement e. V.) agus dinimic Spiral.
Ghlac Valerii tástálacha éagsúla dinimic bíseach agus d'úsáid sé a chuid eolais agus taithí chun an leagan reatha de SDTest a oiriúnú.
Is é Valerii údar iniúchadh a dhéanamh ar neamhchinnteacht an V.U.C.A. Coincheap ag baint úsáide as dinimic bíseach agus staitisticí matamaiticiúla i síceolaíocht, níos mó ná 20 vótaíocht idirnáisiúnta.

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