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 = 0.0353

Dáileadh Neamh -Ghnáth, le Spearman r = 0.0014

Taispeáin torthaí amháin > r = 0.0353

Imdháileadh	Neamhghnách	Gnáth-	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 0.0297	Dearfach lag 0.0298	Diúltach lag -0.0106	Dearfach lag 0.0970	Dearfach lag 0.0325	Diúltach lag -0.0019	Diúltach lag -0.1558
Answer 2	-	Dearfach lag 0.0188	Dearfach lag 0.0076	Diúltach lag -0.0360	Dearfach lag 0.0711	Dearfach lag 0.0387	Dearfach lag 0.0082	Diúltach lag -0.1011
Answer 3	-	Dearfach lag 0.0026	Diúltach lag -0.0170	Diúltach lag -0.0443	Diúltach lag -0.0458	Dearfach lag 0.0547	Dearfach lag 0.0808	Diúltach lag -0.0270
Answer 4	-	Dearfach lag 0.0332	Dearfach lag 0.0285	Diúltach lag -0.0006	Dearfach lag 0.0155	Dearfach lag 0.0276	Dearfach lag 0.0105	Diúltach lag -0.0917
Answer 5	-	Dearfach lag 0.0122	Dearfach lag 0.1193	Dearfach lag 0.0095	Dearfach lag 0.0721	Dearfach lag 0.0057	Diúltach lag -0.0083	Diúltach lag -0.1687
Answer 6	-	Dearfach lag 0.0044	Dearfach lag 0.0005	Diúltach lag -0.0582	Diúltach lag -0.0004	Dearfach lag 0.0210	Dearfach lag 0.0830	Diúltach lag -0.0418
Answer 7	-	Dearfach lag 0.0242	Dearfach lag 0.0368	Diúltach lag -0.0521	Diúltach lag -0.0234	Dearfach lag 0.0403	Dearfach lag 0.0568	Diúltach lag -0.0597
Answer 8	-	Dearfach lag 0.0707	Dearfach lag 0.0781	Diúltach lag -0.0244	Dearfach lag 0.0140	Dearfach lag 0.0303	Dearfach lag 0.0137	Diúltach lag -0.1334
Answer 9	-	Dearfach lag 0.0564	Dearfach lag 0.1531	Dearfach lag 0.0127	Dearfach lag 0.0769	Diúltach lag -0.0136	Diúltach lag -0.0495	Diúltach lag -0.1752
Answer 10	-	Dearfach lag 0.0711	Dearfach lag 0.0700	Diúltach lag -0.0127	Dearfach lag 0.0246	Dearfach lag 0.0363	Diúltach lag -0.0156	Diúltach lag -0.1273
Answer 11	-	Dearfach lag 0.0542	Dearfach lag 0.0488	Dearfach lag 0.0086	Dearfach lag 0.0078	Dearfach lag 0.0162	Dearfach lag 0.0315	Diúltach lag -0.1248
Answer 12	-	Dearfach lag 0.0281	Dearfach lag 0.0929	Diúltach lag -0.0325	Dearfach lag 0.0361	Dearfach lag 0.0276	Dearfach lag 0.0365	Diúltach lag -0.1482
Answer 13	-	Dearfach lag 0.0643	Dearfach lag 0.0916	Diúltach lag -0.0418	Dearfach lag 0.0237	Dearfach lag 0.0425	Dearfach lag 0.0239	Diúltach lag -0.1558
Answer 14	-	Dearfach lag 0.0697	Dearfach lag 0.1017	Dearfach lag 0.0149	Diúltach lag -0.0062	Diúltach lag -0.0087	Diúltach lag -0.0002	Diúltach lag -0.1161
Answer 15	-	Dearfach lag 0.0603	Dearfach lag 0.1299	Diúltach lag -0.0379	Dearfach lag 0.0163	Diúltach lag -0.0091	Dearfach lag 0.0164	Diúltach lag -0.1204
Answer 16	-	Dearfach lag 0.0691	Dearfach lag 0.0221	Diúltach lag -0.0305	Diúltach lag -0.0515	Dearfach lag 0.0750	Dearfach lag 0.0187	Diúltach lag -0.0696

Easpórtáil go MS Excel

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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.
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