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

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

Kaarte Korrelasie

VUCA

Kritieke waarde van die korrelasiekoëffisiënt

Normale verspreiding, deur William Sealy Gosset (student) r = 0.0353

Nie normale verspreiding, deur Spearman r = 0.0014

Toon slegs resultate > r = 0.0353

Verspreiding	Nie normaal nie	Normaal	Nie normaal nie	Normaal	Normaal	Normaal	Normaal	Normaal
Alle vrae Alle vrae My grootste vrees is
My grootste vrees is
Answer 1	-	Swak positief 0.0297	Swak positief 0.0298	Swak negatief -0.0106	Swak positief 0.0970	Swak positief 0.0325	Swak negatief -0.0019	Swak negatief -0.1558
Answer 2	-	Swak positief 0.0188	Swak positief 0.0076	Swak negatief -0.0360	Swak positief 0.0711	Swak positief 0.0387	Swak positief 0.0082	Swak negatief -0.1011
Answer 3	-	Swak positief 0.0026	Swak negatief -0.0170	Swak negatief -0.0443	Swak negatief -0.0458	Swak positief 0.0547	Swak positief 0.0808	Swak negatief -0.0270
Answer 4	-	Swak positief 0.0332	Swak positief 0.0285	Swak negatief -0.0006	Swak positief 0.0155	Swak positief 0.0276	Swak positief 0.0105	Swak negatief -0.0917
Answer 5	-	Swak positief 0.0122	Swak positief 0.1193	Swak positief 0.0095	Swak positief 0.0721	Swak positief 0.0057	Swak negatief -0.0083	Swak negatief -0.1687
Answer 6	-	Swak positief 0.0044	Swak positief 0.0005	Swak negatief -0.0582	Swak negatief -0.0004	Swak positief 0.0210	Swak positief 0.0830	Swak negatief -0.0418
Answer 7	-	Swak positief 0.0242	Swak positief 0.0368	Swak negatief -0.0521	Swak negatief -0.0234	Swak positief 0.0403	Swak positief 0.0568	Swak negatief -0.0597
Answer 8	-	Swak positief 0.0707	Swak positief 0.0781	Swak negatief -0.0244	Swak positief 0.0140	Swak positief 0.0303	Swak positief 0.0137	Swak negatief -0.1334
Answer 9	-	Swak positief 0.0564	Swak positief 0.1531	Swak positief 0.0127	Swak positief 0.0769	Swak negatief -0.0136	Swak negatief -0.0495	Swak negatief -0.1752
Answer 10	-	Swak positief 0.0711	Swak positief 0.0700	Swak negatief -0.0127	Swak positief 0.0246	Swak positief 0.0363	Swak negatief -0.0156	Swak negatief -0.1273
Answer 11	-	Swak positief 0.0542	Swak positief 0.0488	Swak positief 0.0086	Swak positief 0.0078	Swak positief 0.0162	Swak positief 0.0315	Swak negatief -0.1248
Answer 12	-	Swak positief 0.0281	Swak positief 0.0929	Swak negatief -0.0325	Swak positief 0.0361	Swak positief 0.0276	Swak positief 0.0365	Swak negatief -0.1482
Answer 13	-	Swak positief 0.0643	Swak positief 0.0916	Swak negatief -0.0418	Swak positief 0.0237	Swak positief 0.0425	Swak positief 0.0239	Swak negatief -0.1558
Answer 14	-	Swak positief 0.0697	Swak positief 0.1017	Swak positief 0.0149	Swak negatief -0.0062	Swak negatief -0.0087	Swak negatief -0.0002	Swak negatief -0.1161
Answer 15	-	Swak positief 0.0603	Swak positief 0.1299	Swak negatief -0.0379	Swak positief 0.0163	Swak negatief -0.0091	Swak positief 0.0164	Swak negatief -0.1204
Answer 16	-	Swak positief 0.0691	Swak positief 0.0221	Swak negatief -0.0305	Swak negatief -0.0515	Swak positief 0.0750	Swak positief 0.0187	Swak negatief -0.0696

Uitvoer na 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

Produk -eienaar SaaS Pet Project SdTest®

Valerii is in 1993 as 'n maatskaplike pedagoge-sielkundige gekwalifiseer en het sedertdien sy kennis in projekbestuur toegepas.
Valerii het in 2013 'n meestersgraad en die kwalifikasie van die projek- en programbestuurder verwerf. Tydens sy meestersprogram het hy vertroud geraak met Project Roadmap (GPM Deutsche Gesellschaft Für Projektmanagement e. V.) en Spiral Dynamics.
Valerii het verskillende spiraaldinamika -toetse afgelê en sy kennis en ervaring gebruik om die huidige weergawe van SDTest aan te pas.
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, meer as 20 internasionale peilings.

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