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:

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26) Uvavanyo lwenkcubeko ye Xing.com

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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.

Uloyiko

iitshati Ukuhlanganisa

VUCA

Ixabiso elibalulekileyo lomlinganiso wolungelelwaniso

Ukuhanjiswa okuqhelekileyo, nge-william gosset (umfundi) r = 0.0318

Ukusasazwa okuqhelekileyo, nge-spearman r = 0.0013

Bonisa iziphumo kuphela > r = 0.0318

Ukuhanjiswa	Ayiqhelekanga	Ayiqhelekanga	Ayiqhelekanga	Eqhelekileyo	Eqhelekileyo	Eqhelekileyo	Eqhelekileyo	Eqhelekileyo
Yonke imibuzo Yonke imibuzo Olona loyiko lwam lukhulu
Olona loyiko lwam lukhulu
Answer 1	-	HIV amandla 0.0548	HIV amandla 0.0285	Emibi amandla -0.0173	HIV amandla 0.0940	HIV amandla 0.0358	Emibi amandla -0.0156	Emibi amandla -0.1560
Answer 2	-	HIV amandla 0.0192	Emibi amandla -0.0048	Emibi amandla -0.0394	HIV amandla 0.0659	HIV amandla 0.0491	HIV amandla 0.0117	Emibi amandla -0.0981
Answer 3	-	Emibi amandla -0.0003	Emibi amandla -0.0088	Emibi amandla -0.0450	Emibi amandla -0.0440	HIV amandla 0.0471	HIV amandla 0.0739	Emibi amandla -0.0191
Answer 4	-	HIV amandla 0.0429	HIV amandla 0.0271	Emibi amandla -0.0230	HIV amandla 0.0182	HIV amandla 0.0351	HIV amandla 0.0239	Emibi amandla -0.0995
Answer 5	-	HIV amandla 0.0273	HIV amandla 0.1298	HIV amandla 0.0101	HIV amandla 0.0772	Emibi amandla -0.0006	Emibi amandla -0.0183	Emibi amandla -0.1784
Answer 6	-	Emibi amandla -0.0026	HIV amandla 0.0050	Emibi amandla -0.0621	Emibi amandla -0.0081	HIV amandla 0.0240	HIV amandla 0.0856	Emibi amandla -0.0346
Answer 7	-	HIV amandla 0.0105	HIV amandla 0.0339	Emibi amandla -0.0661	Emibi amandla -0.0304	HIV amandla 0.0517	HIV amandla 0.0686	Emibi amandla -0.0515
Answer 8	-	HIV amandla 0.0635	HIV amandla 0.0732	Emibi amandla -0.0275	HIV amandla 0.0143	HIV amandla 0.0370	HIV amandla 0.0172	Emibi amandla -0.1336
Answer 9	-	HIV amandla 0.0734	HIV amandla 0.1618	HIV amandla 0.0069	HIV amandla 0.0644	Emibi amandla -0.0109	Emibi amandla -0.0489	Emibi amandla -0.1811
Answer 10	-	HIV amandla 0.0764	HIV amandla 0.0679	Emibi amandla -0.0139	HIV amandla 0.0290	HIV amandla 0.0338	Emibi amandla -0.0123	Emibi amandla -0.1342
Answer 11	-	HIV amandla 0.0634	HIV amandla 0.0535	Emibi amandla -0.0091	HIV amandla 0.0113	HIV amandla 0.0238	HIV amandla 0.0247	Emibi amandla -0.1260
Answer 12	-	HIV amandla 0.0449	HIV amandla 0.0941	Emibi amandla -0.0341	HIV amandla 0.0342	HIV amandla 0.0332	HIV amandla 0.0255	Emibi amandla -0.1534
Answer 13	-	HIV amandla 0.0691	HIV amandla 0.0966	Emibi amandla -0.0393	HIV amandla 0.0295	HIV amandla 0.0417	HIV amandla 0.0148	Emibi amandla -0.1626
Answer 14	-	HIV amandla 0.0775	HIV amandla 0.0903	Emibi amandla -0.0019	Emibi amandla -0.0089	HIV amandla 0.0048	HIV amandla 0.0140	Emibi amandla -0.1223
Answer 15	-	HIV amandla 0.0544	HIV amandla 0.1280	Emibi amandla -0.0345	HIV amandla 0.0152	Emibi amandla -0.0178	HIV amandla 0.0236	Emibi amandla -0.1158
Answer 16	-	HIV amandla 0.0703	HIV amandla 0.0262	Emibi amandla -0.0371	Emibi amandla -0.0377	HIV amandla 0.0697	HIV amandla 0.0204	Emibi amandla -0.0788

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[1] https://twitter.com/wileyprof

[2] https://colinallen.dnsalias.org

[3] https://philpeople.org/profiles/colin-allen

2023.10.13

I-Valerii Kosenko

uMnini weMveliso i-SaaS SDTEST®

U-Valerii wayefaneleka njenge-social pedagogue-psychologist ngo-1993 kwaye ukususela ngoko uye wasebenzisa ulwazi lwakhe kulawulo lweprojekthi.
UValerii wafumana isidanga seMasters kunye neprojekthi kunye nesiqinisekiso somphathi weprogram ngo-2013. Ngexesha lenkqubo yakhe ye-Master, waqhelana neProjekthi yeNdlela yeNdlela (GPM Deutsche Gesellschaft für Projektmanagement e. V.) kunye ne-Spiral Dynamics.
UValerii ngumbhali wokuphonononga ukungaqiniseki kweV.U.C.A. Ingqiqo kusetyenziswa iSpiral Dynamics kunye nezibalo zezibalo kwipsychology, kunye ne-38 yokuvota kumazwe ngamazwe.

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