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) Aksies van maatskappye in verhouding tot personeel die afgelope maand (ja / nee)

2) Aksies van maatskappye met betrekking tot personeel in die laaste maand (feit in%)

3) Vrese

4) Grootste probleme wat my land in die gesig staar

5) Watter eienskappe en vermoëns gebruik goeie leiers as hulle suksesvolle spanne bou?

6) Google. Faktore wat die effektiwiteit van die span beïnvloed

7) Die belangrikste prioriteite van werksoekers

8) Wat maak 'n baas 'n wonderlike leier?

9) Wat maak mense suksesvol by die werk?

10) Is u gereed om minder betaal te ontvang om op afstand te werk?

11) Bestaan ouderdomsisme?

12) Ouderdom in loopbaan

13) Ouderdom in die lewe

14) Oorsake van ouderdomsisme

15) Redes waarom mense opgee (deur Anna Vital)

16) VERTROUE (#WVS)

17) Oxford Happiness Survey

18) Sielkundige welstand

19) Waar sou u volgende mees opwindende geleentheid wees?

20) Wat sal u hierdie week doen om na u geestesgesondheid om te sien?

21) Ek leef nadink oor my verlede, hede of toekoms

22) Meritokrasie

23) Kunsmatige intelligensie en die einde van die beskawing

24) Waarom stel mense uit?

25) Geslagsverskil in die bou van selfvertroue (IFD Allensbach)

26) Xing.com -kultuurassessering

27) Patrick Lencioni se "The Five Disfunctions of a Team"

28) Empatie is ...

29) Wat is noodsaaklik vir IT -spesialiste om 'n werkaanbod te kies?

30) Waarom mense weerstand bied teen verandering (deur Siobhán McHale)

31) Hoe reguleer u u emosies? (deur Nawal Mustafa M.A.)

32) 21 Vaardighede wat u vir ewig betaal (deur Jeremiah Teo / 赵汉昇)

33) Regte vryheid is ...

34) 12 maniere om vertroue met ander op te bou (deur Justin Wright)

35) Eienskappe van 'n talentvolle werknemer (deur Talent Management Institute)

36) 10 sleutels om u span te motiveer

37) Algebra van die gewete (deur Vladimir Lefebvre)

38) Drie duidelike moontlikhede van die toekoms (deur Dr. Clare W. Graves)

39) Aksies om onwrikbare selfvertroue te bou (deur 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.

Vrese

KaarteKorrelasie

VUCA

Kritieke waarde van die korrelasiekoëffisiënt

Normale verspreiding, deur William Sealy Gosset (student) r = 0.0312

Nie normale verspreiding, deur Spearman r = 0.0013

Toon slegs resultate > r = 0.0312

Verspreiding	Nie normaal nie	Nie normaal nie	Nie normaal nie	Normaal	Normaal	Normaal	Normaal	Normaal
Alle vrae Alle vrae My grootste vrees is
My grootste vrees is
Answer 1	-	Swak positief 0.0545	Swak positief 0.0259	Swak negatief -0.0190	Swak positief 0.0954	Swak positief 0.0405	Swak negatief -0.0166	Swak negatief -0.1575
Answer 2	-	Swak positief 0.0187	Swak negatief -0.0050	Swak negatief -0.0404	Swak positief 0.0633	Swak positief 0.0517	Swak positief 0.0122	Swak negatief -0.0973
Answer 3	-	Swak negatief -0.0022	Swak negatief -0.0057	Swak negatief -0.0443	Swak negatief -0.0400	Swak positief 0.0486	Swak positief 0.0744	Swak negatief -0.0262
Answer 4	-	Swak positief 0.0450	Swak positief 0.0334	Swak negatief -0.0271	Swak positief 0.0156	Swak positief 0.0418	Swak positief 0.0243	Swak negatief -0.1059
Answer 5	-	Swak positief 0.0234	Swak positief 0.1269	Swak positief 0.0107	Swak positief 0.0761	Swak positief 0.0006	Swak negatief -0.0158	Swak negatief -0.1763
Answer 6	-	Swak positief 0.0003	Swak positief 0.0052	Swak negatief -0.0607	Swak negatief -0.0078	Swak positief 0.0238	Swak positief 0.0840	Swak negatief -0.0368
Answer 7	-	Swak positief 0.0112	Swak positief 0.0332	Swak negatief -0.0633	Swak negatief -0.0307	Swak positief 0.0510	Swak positief 0.0683	Swak negatief -0.0528
Answer 8	-	Swak positief 0.0647	Swak positief 0.0710	Swak negatief -0.0247	Swak positief 0.0105	Swak positief 0.0412	Swak positief 0.0155	Swak negatief -0.1345
Answer 9	-	Swak positief 0.0771	Swak positief 0.1596	Swak positief 0.0070	Swak positief 0.0609	Swak negatief -0.0045	Swak negatief -0.0525	Swak negatief -0.1822
Answer 10	-	Swak positief 0.0775	Swak positief 0.0619	Swak negatief -0.0121	Swak positief 0.0225	Swak positief 0.0383	Swak negatief -0.0105	Swak negatief -0.1318
Answer 11	-	Swak positief 0.0626	Swak positief 0.0521	Swak negatief -0.0074	Swak positief 0.0089	Swak positief 0.0300	Swak positief 0.0213	Swak negatief -0.1269
Answer 12	-	Swak positief 0.0415	Swak positief 0.0927	Swak negatief -0.0316	Swak positief 0.0336	Swak positief 0.0344	Swak positief 0.0250	Swak negatief -0.1528
Answer 13	-	Swak positief 0.0711	Swak positief 0.0935	Swak negatief -0.0370	Swak positief 0.0278	Swak positief 0.0446	Swak positief 0.0120	Swak negatief -0.1630
Answer 14	-	Swak positief 0.0826	Swak positief 0.0875	Swak negatief -0.0011	Swak negatief -0.0136	Swak positief 0.0081	Swak positief 0.0121	Swak negatief -0.1213
Answer 15	-	Swak positief 0.0578	Swak positief 0.1220	Swak negatief -0.0316	Swak positief 0.0083	Swak negatief -0.0127	Swak positief 0.0245	Swak negatief -0.1153
Answer 16	-	Swak positief 0.0716	Swak positief 0.0208	Swak negatief -0.0371	Swak negatief -0.0408	Swak positief 0.0751	Swak positief 0.0157	Swak negatief -0.0743

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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

Produk Eienaar SaaS SDTEST®

Valerii is in 1993 as 'n sosiale pedagoog-sielkundige gekwalifiseer en het sedertdien sy kennis in projekbestuur toegepas.
Valerii het 'n Meestersgraad en die projek- en programbestuurderkwalifikasie verwerf in 2013. Tydens sy Meesterprogram het hy vertroud geraak met Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) en Spiral Dynamics.
Valerii is die skrywer van die verkenning van die onsekerheid van die V.U.C.A. konsep met behulp van Spiraaldinamika en wiskundige statistieke in sielkunde, en 38 internasionale peilings.

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