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:

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2) Izenzo zeenkampani ngokunxulumene nabasebenzi kwinyanga ephelileyo (inyani kwi%)

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10) Ngaba ukulungele ukufumana umvuzo omncinci ukusebenza kude?

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24) Kutheni le nto abantu behlazela?

25) Umahluko wesini ekwakheni ukuzithemba (i-Allensbach)

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32) 21 Izakhono ezikuhlawula ngonaphakade (nguYeremiya Teo / 赵汉昇)

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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.

Uloyiko

iitshati Ukuhlanganisa

VUCA

Ixabiso elibalulekileyo lomlinganiso wolungelelwaniso

Ukuhanjiswa okuqhelekileyo, nge-william gosset (umfundi) r = 0.0335

Ukusasazwa okuqhelekileyo, nge-spearman r = 0.0014

Bonisa iziphumo kuphela > r = 0.0335

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 0.0521	HIV amandla 0.0294	Emibi amandla -0.0147	HIV amandla 0.0885	HIV amandla 0.0316	Emibi amandla -0.0110	Emibi amandla -0.1513
Answer 2	-	HIV amandla 0.0213	HIV amandla 0.0013	Emibi amandla -0.0432	HIV amandla 0.0618	HIV amandla 0.0453	HIV amandla 0.0103	Emibi amandla -0.0918
Answer 3	-	Emibi amandla -0.0042	Emibi amandla -0.0116	Emibi amandla -0.0406	Emibi amandla -0.0477	HIV amandla 0.0487	HIV amandla 0.0767	Emibi amandla -0.0191
Answer 4	-	HIV amandla 0.0421	HIV amandla 0.0350	Emibi amandla -0.0115	HIV amandla 0.0112	HIV amandla 0.0307	HIV amandla 0.0175	Emibi amandla -0.0980
Answer 5	-	HIV amandla 0.0288	HIV amandla 0.1272	HIV amandla 0.0146	HIV amandla 0.0697	HIV amandla 0.0037	Emibi amandla -0.0215	Emibi amandla -0.1746
Answer 6	-	Emibi amandla -0.0001	HIV amandla 0.0042	Emibi amandla -0.0607	Emibi amandla -0.0115	HIV amandla 0.0231	HIV amandla 0.0826	Emibi amandla -0.0309
Answer 7	-	HIV amandla 0.0117	HIV amandla 0.0372	Emibi amandla -0.0653	Emibi amandla -0.0283	HIV amandla 0.0495	HIV amandla 0.0626	Emibi amandla -0.0505
Answer 8	-	HIV amandla 0.0658	HIV amandla 0.0830	Emibi amandla -0.0310	HIV amandla 0.0139	HIV amandla 0.0334	HIV amandla 0.0134	Emibi amandla -0.1322
Answer 9	-	HIV amandla 0.0660	HIV amandla 0.1658	HIV amandla 0.0051	HIV amandla 0.0691	Emibi amandla -0.0093	Emibi amandla -0.0498	Emibi amandla -0.1820
Answer 10	-	HIV amandla 0.0758	HIV amandla 0.0724	Emibi amandla -0.0173	HIV amandla 0.0236	HIV amandla 0.0312	Emibi amandla -0.0115	Emibi amandla -0.1263
Answer 11	-	HIV amandla 0.0577	HIV amandla 0.0544	Emibi amandla -0.0075	HIV amandla 0.0082	HIV amandla 0.0185	HIV amandla 0.0293	Emibi amandla -0.1190
Answer 12	-	HIV amandla 0.0376	HIV amandla 0.1007	Emibi amandla -0.0342	HIV amandla 0.0296	HIV amandla 0.0273	HIV amandla 0.0341	Emibi amandla -0.1500
Answer 13	-	HIV amandla 0.0627	HIV amandla 0.1017	Emibi amandla -0.0443	HIV amandla 0.0248	HIV amandla 0.0434	HIV amandla 0.0189	Emibi amandla -0.1576
Answer 14	-	HIV amandla 0.0732	HIV amandla 0.1036	HIV amandla 0.0048	Emibi amandla -0.0105	Emibi amandla -0.0039	HIV amandla 0.0041	Emibi amandla -0.1157
Answer 15	-	HIV amandla 0.0539	HIV amandla 0.1381	Emibi amandla -0.0424	HIV amandla 0.0163	Emibi amandla -0.0147	HIV amandla 0.0216	Emibi amandla -0.1173
Answer 16	-	HIV amandla 0.0590	HIV amandla 0.0274	Emibi amandla -0.0375	Emibi amandla -0.0429	HIV amandla 0.0687	HIV amandla 0.0253	Emibi amandla -0.0698

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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

Imveliso ye-Saas ye-SDTEst®

UValerii wakufanelekela njenge-Pedagogue-Psychologitha ngo-1993 kwaye ukusebenzise ulwazi lwakhe kulawulo lweprojekthi.
I-Valerii ifumene isidanga se-Master kunye neProjekthi yeProjekthi kunye neNkqubo yeNkqubo yeNkqubo ngo-2013. Ngexesha lenkqubo yenkosi yakhe, waqhelana neProtsep yeProjek ye-E. V.
UValerii wathatha iimvavanyo ezahlukeneyo ze-spimics kwaye wasebenzisa ulwazi kunye namava akhe ukuhlengahlengisa uhlobo lwangoku lwe-SDTEst.
UValerii ngumbhali wokuphonononga ukungaqiniseki kweV.U.C.C.C.C.C.A. Umxholo usebenzisa i-spirals synamics nakwiinkcukacha-manani zemathematics kwi-Psychologlogy, ngaphezulu kwe-20 yamazwe aphesheya.

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