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) Agoj de kompanioj rilate al dungitaro en la lasta monato (jes / ne)

2) Agoj de kompanioj rilate al dungitaro en la lasta monato (fakto en%)

3) Timoj

4) Plej grandaj problemoj alfrontantaj mian landon

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6) Google. Faktoroj, kiuj influas teaman efikecon

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11) Ĉu ageismo ekzistas?

12) Ageismo en kariero

13) Ageismo en la vivo

14) Kaŭzoj de Ageismo

15) Kialoj Kial Homoj Rezignas (De Anna Vital)

16) Fidu (#WVS)

17) Oksforda Feliĉa Enketo

18) Psikologia bonstato

19) Kie estus via sekva plej ekscita okazo?

20) Kion vi faros ĉi -semajne por prizorgi vian mensan sanon?

21) Mi vivas pensante pri mia pasinteco, nuno aŭ estonteco

22) Meritokratio

23) Artefarita inteligenteco kaj la fino de civilizo

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33) Vera libereco estas ...

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38) Tri Distingaj Eblecoj de la Estonteco (de Dr. Clare W. Graves)

39) Agoj por Konstrui Neŝanceleblan Memfidon (de Suren Samarchyan)

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.

Timoj

furorlistoKorelacio

VUCA

Korelacia Tipo	Lineara (Pearson) Lineara (Pearson) Ne-linia (Lancisto)
Kritika valoro de la korelacio	Normala distribuo, de William Sealy Gosset (studento) Normala distribuo, de William Sealy Gosset (studento) Ne normala distribuo, de Spearman	Montri nur rezultojn > r = 0.0306

Distribuo	Ne normala	Ne normala	Ne normala	Normala	Normala	Normala	Normala	Normala
Ĉiuj demandoj Ĉiuj demandoj Mia plej granda timo estas
Mia plej granda timo estas
Answer 1	-	Malforta pozitiva 0.0513	Malforta pozitiva 0.0238	Malforta negativo -0.0213	Malforta pozitiva 0.0979	Malforta pozitiva 0.0385	Malforta negativo -0.0150	Malforta negativo -0.1537
Answer 2	-	Malforta pozitiva 0.0217	Malforta negativo -0.0020	Malforta negativo -0.0366	Malforta pozitiva 0.0594	Malforta pozitiva 0.0489	Malforta pozitiva 0.0103	Malforta negativo -0.0964
Answer 3	-	Malforta negativo -0.0015	Malforta negativo -0.0008	Malforta negativo -0.0430	Malforta negativo -0.0402	Malforta pozitiva 0.0438	Malforta pozitiva 0.0726	Malforta negativo -0.0251
Answer 4	-	Malforta pozitiva 0.0456	Malforta pozitiva 0.0323	Malforta negativo -0.0224	Malforta pozitiva 0.0167	Malforta pozitiva 0.0395	Malforta pozitiva 0.0183	Malforta negativo -0.1034
Answer 5	-	Malforta pozitiva 0.0239	Malforta pozitiva 0.1264	Malforta pozitiva 0.0096	Malforta pozitiva 0.0801	Malforta pozitiva 0.0005	Malforta negativo -0.0171	Malforta negativo -0.1782
Answer 6	-	Malforta pozitiva 0.0066	Malforta pozitiva 0.0146	Malforta negativo -0.0615	Malforta negativo -0.0115	Malforta pozitiva 0.0184	Malforta pozitiva 0.0831	Malforta negativo -0.0378
Answer 7	-	Malforta pozitiva 0.0117	Malforta pozitiva 0.0389	Malforta negativo -0.0627	Malforta negativo -0.0340	Malforta pozitiva 0.0475	Malforta pozitiva 0.0679	Malforta negativo -0.0511
Answer 8	-	Malforta pozitiva 0.0656	Malforta pozitiva 0.0807	Malforta negativo -0.0253	Malforta pozitiva 0.0087	Malforta pozitiva 0.0389	Malforta pozitiva 0.0139	Malforta negativo -0.1367
Answer 9	-	Malforta pozitiva 0.0781	Malforta pozitiva 0.1621	Malforta pozitiva 0.0038	Malforta pozitiva 0.0602	Malforta negativo -0.0067	Malforta negativo -0.0514	Malforta negativo -0.1805
Answer 10	-	Malforta pozitiva 0.0806	Malforta pozitiva 0.0630	Malforta negativo -0.0134	Malforta pozitiva 0.0210	Malforta pozitiva 0.0375	Malforta negativo -0.0091	Malforta negativo -0.1329
Answer 11	-	Malforta pozitiva 0.0653	Malforta pozitiva 0.0563	Malforta negativo -0.0078	Malforta pozitiva 0.0101	Malforta pozitiva 0.0267	Malforta pozitiva 0.0180	Malforta negativo -0.1268
Answer 12	-	Malforta pozitiva 0.0416	Malforta pozitiva 0.0966	Malforta negativo -0.0310	Malforta pozitiva 0.0333	Malforta pozitiva 0.0297	Malforta pozitiva 0.0220	Malforta negativo -0.1490
Answer 13	-	Malforta pozitiva 0.0718	Malforta pozitiva 0.0955	Malforta negativo -0.0363	Malforta pozitiva 0.0282	Malforta pozitiva 0.0385	Malforta pozitiva 0.0110	Malforta negativo -0.1588
Answer 14	-	Malforta pozitiva 0.0888	Malforta pozitiva 0.0922	Malforta negativo -0.0035	Malforta negativo -0.0157	Malforta pozitiva 0.0058	Malforta pozitiva 0.0069	Malforta negativo -0.1181
Answer 15	-	Malforta pozitiva 0.0589	Malforta pozitiva 0.1241	Malforta negativo -0.0303	Malforta pozitiva 0.0109	Malforta negativo -0.0182	Malforta pozitiva 0.0246	Malforta negativo -0.1170
Answer 16	-	Malforta pozitiva 0.0713	Malforta pozitiva 0.0247	Malforta negativo -0.0338	Malforta negativo -0.0428	Malforta pozitiva 0.0703	Malforta pozitiva 0.0124	Malforta negativo -0.0706

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

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

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

2023.10.13

FearpersonqualitiesprojectorganizationalstructureRACIresponsibilitymatrixCritical ChainProject Managementfocus factorJiraempathyleadersbossGermanyChinaPolicyUkraineRussiawarvolatilityuncertaintycomplexityambiguityVUCArelocatejobproblemcountryreasongive upobjectivekeyresultmathematicalpsychologyMBTIHR metricsstandardDEIcorrelationriskscoringmodelGame TheoryPrisoner's Dilemma

Valerii Kosenko

Produktposedanto SaaS SDTEST®

Valerii estis kvalifikita kiel socia pedagogo-psikologo en 1993 kaj poste aplikis sian scion en projektadministrado.
Valerii akiris magistron kaj la projekto- kaj programmanaĝertaŭgecon en 2013. Dum lia majstra programo, li iĝis konata kun Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) kaj Spiral Dynamics.
Valerii estas la verkinto de esplorado de la necerteco de la V.U.C.A. koncepto uzante Spiral Dynamics kaj matematikan statistikon en psikologio, kaj 38 internaciajn balotenketojn.

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