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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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 = 0.033

Dáileadh Neamh -Ghnáth, le Spearman r = 0.0013

Taispeáin torthaí amháin > r = 0.033

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 0.0532	Dearfach lag 0.0292	Diúltach lag -0.0175	Dearfach lag 0.0919	Dearfach lag 0.0301	Diúltach lag -0.0114	Diúltach lag -0.1523
Answer 2	-	Dearfach lag 0.0208	Diúltach lag -0.0014	Diúltach lag -0.0431	Dearfach lag 0.0641	Dearfach lag 0.0449	Dearfach lag 0.0130	Diúltach lag -0.0931
Answer 3	-	Diúltach lag -0.0053	Diúltach lag -0.0130	Diúltach lag -0.0406	Diúltach lag -0.0456	Dearfach lag 0.0474	Dearfach lag 0.0793	Diúltach lag -0.0204
Answer 4	-	Dearfach lag 0.0427	Dearfach lag 0.0328	Diúltach lag -0.0200	Dearfach lag 0.0158	Dearfach lag 0.0306	Dearfach lag 0.0217	Diúltach lag -0.0980
Answer 5	-	Dearfach lag 0.0255	Dearfach lag 0.1255	Dearfach lag 0.0143	Dearfach lag 0.0732	Diúltach lag -0.0019	Diúltach lag -0.0196	Diúltach lag -0.1747
Answer 6	-	Diúltach lag -0.0027	Dearfach lag 0.0074	Diúltach lag -0.0629	Diúltach lag -0.0074	Dearfach lag 0.0199	Dearfach lag 0.0835	Diúltach lag -0.0324
Answer 7	-	Dearfach lag 0.0110	Dearfach lag 0.0371	Diúltach lag -0.0688	Diúltach lag -0.0227	Dearfach lag 0.0471	Dearfach lag 0.0650	Diúltach lag -0.0523
Answer 8	-	Dearfach lag 0.0693	Dearfach lag 0.0825	Diúltach lag -0.0321	Dearfach lag 0.0139	Dearfach lag 0.0351	Dearfach lag 0.0147	Diúltach lag -0.1369
Answer 9	-	Dearfach lag 0.0643	Dearfach lag 0.1659	Dearfach lag 0.0082	Dearfach lag 0.0699	Diúltach lag -0.0136	Diúltach lag -0.0513	Diúltach lag -0.1826
Answer 10	-	Dearfach lag 0.0760	Dearfach lag 0.0730	Diúltach lag -0.0219	Dearfach lag 0.0254	Dearfach lag 0.0318	Diúltach lag -0.0138	Diúltach lag -0.1318
Answer 11	-	Dearfach lag 0.0571	Dearfach lag 0.0514	Diúltach lag -0.0099	Dearfach lag 0.0077	Dearfach lag 0.0206	Dearfach lag 0.0308	Diúltach lag -0.1211
Answer 12	-	Dearfach lag 0.0373	Dearfach lag 0.1013	Diúltach lag -0.0357	Dearfach lag 0.0357	Dearfach lag 0.0243	Dearfach lag 0.0296	Diúltach lag -0.1524
Answer 13	-	Dearfach lag 0.0621	Dearfach lag 0.1036	Diúltach lag -0.0438	Dearfach lag 0.0273	Dearfach lag 0.0414	Dearfach lag 0.0176	Diúltach lag -0.1608
Answer 14	-	Dearfach lag 0.0703	Dearfach lag 0.1007	Dearfach lag 9.54E-5	Diúltach lag -0.0088	Diúltach lag -0.0011	Dearfach lag 0.0084	Diúltach lag -0.1174
Answer 15	-	Dearfach lag 0.0554	Dearfach lag 0.1349	Diúltach lag -0.0418	Dearfach lag 0.0179	Diúltach lag -0.0165	Dearfach lag 0.0219	Diúltach lag -0.1181
Answer 16	-	Dearfach lag 0.0581	Dearfach lag 0.0255	Diúltach lag -0.0388	Diúltach lag -0.0407	Dearfach lag 0.0654	Dearfach lag 0.0283	Diúltach lag -0.0714

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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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