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) Acties van bedrijven met betrekking tot personeel in de afgelopen maand (ja / nee)

2) Acties van bedrijven in relatie tot personeel in de afgelopen maand (feit in%)

3) Angsten

4) Grootste problemen waarmee mijn land wordt geconfronteerd

5) Welke kwaliteiten en vaardigheden gebruiken goede leiders bij het bouwen van succesvolle teams?

6) Google. Factoren die invloed hebben op de effictiviteit van het team

7) De belangrijkste prioriteiten van werkzoekenden

8) Wat maakt een baas een geweldige leider?

9) Wat maakt mensen succesvol op het werk?

10) Ben je klaar om minder loon te ontvangen om op afstand te werken?

11) Bestaat Ageism?

12) Ageisme in carrière

13) Ageisme in het leven

14) Oorzaken van leeftijdsgebruik

15) Redenen waarom mensen opgeven (door Anna Vital)

16) VERTROUWEN (#WVS)

17) Oxford Happiness Survey

18) Geestelijk welzijn

19) Waar zou je volgende meest opwindende kans zijn?

20) Wat ga je deze week doen om voor je geestelijke gezondheid te zorgen?

21) Ik leef nadenken over mijn verleden, heden of toekomst

22) Meritocratie

23) Kunstmatige intelligentie en het einde van de beschaving

24) Waarom stellen mensen uit?

25) Genderverschil bij het opbouwen van zelfvertrouwen (IFD AllensBach)

26) Xing.com Cultuurbeoordeling

27) Patrick Lencioni's "De vijf disfuncties van een team"

28) Empathie is ...

29) Wat is essentieel voor IT -specialisten bij het kiezen van een vacature?

30) Waarom mensen zich verzetten tegen verandering (door Siobhán McHale)

31) Hoe reguleer je je emoties? (door Nawal Mustafa M.A.)

32) 21 vaardigheden die je voor altijd betalen (door Jeremiah Teo / 赵汉昇)

33) Echte vrijheid is ...

34) 12 manieren om vertrouwen bij anderen op te bouwen (door Justin Wright)

35) Kenmerken van een getalenteerde werknemer (door Talent Management Institute)

36) 10 sleutels om uw team te motiveren

37) Algebra van het geweten (door Vladimir Lefebvre)

38) Drie verschillende mogelijkheden van de toekomst (door Dr. Clare W. Graves)

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.

Angsten

Grafieken Correlatie

VUCA

Kritische waarde van de correlatiecoëfficiënt

Normale verdeling, door William Sealy Gosset (student) r = 0.033

Niet -normale verdeling, door Spearman r = 0.0013

Toon alleen resultaten > r = 0.033

Verdeling	Niet normaal	Niet normaal	Niet normaal	Normaal	Normaal	Normaal	Normaal	Normaal
Alle vragen Alle vragen Mijn grootste angst is
Mijn grootste angst is
Answer 1	-	Zwak positief 0.0569	Zwak positief 0.0313	Zwak negatief -0.0161	Zwak positief 0.0906	Zwak positief 0.0297	Zwak negatief -0.0118	Zwak negatief -0.1544
Answer 2	-	Zwak positief 0.0225	Zwak positief 0.0002	Zwak negatief -0.0450	Zwak positief 0.0644	Zwak positief 0.0442	Zwak positief 0.0128	Zwak negatief -0.0940
Answer 3	-	Zwak negatief -0.0030	Zwak negatief -0.0116	Zwak negatief -0.0411	Zwak negatief -0.0465	Zwak positief 0.0466	Zwak positief 0.0786	Zwak negatief -0.0200
Answer 4	-	Zwak positief 0.0440	Zwak positief 0.0354	Zwak negatief -0.0189	Zwak positief 0.0150	Zwak positief 0.0299	Zwak positief 0.0204	Zwak negatief -0.0986
Answer 5	-	Zwak positief 0.0309	Zwak positief 0.1278	Zwak positief 0.0137	Zwak positief 0.0728	Zwak negatief -0.0011	Zwak negatief -0.0195	Zwak negatief -0.1757
Answer 6	-	Zwak negatief -0.0001	Zwak positief 0.0086	Zwak negatief -0.0623	Zwak negatief -0.0085	Zwak positief 0.0193	Zwak positief 0.0829	Zwak negatief -0.0319
Answer 7	-	Zwak positief 0.0127	Zwak positief 0.0385	Zwak negatief -0.0683	Zwak negatief -0.0246	Zwak positief 0.0468	Zwak positief 0.0640	Zwak negatief -0.0519
Answer 8	-	Zwak positief 0.0700	Zwak positief 0.0853	Zwak negatief -0.0322	Zwak positief 0.0146	Zwak positief 0.0344	Zwak positief 0.0132	Zwak negatief -0.1370
Answer 9	-	Zwak positief 0.0670	Zwak positief 0.1680	Zwak positief 0.0087	Zwak positief 0.0692	Zwak negatief -0.0132	Zwak negatief -0.0518	Zwak negatief -0.1822
Answer 10	-	Zwak positief 0.0784	Zwak positief 0.0758	Zwak negatief -0.0199	Zwak positief 0.0245	Zwak positief 0.0342	Zwak negatief -0.0133	Zwak negatief -0.1308
Answer 11	-	Zwak positief 0.0586	Zwak positief 0.0528	Zwak negatief -0.0091	Zwak positief 0.0074	Zwak positief 0.0198	Zwak positief 0.0318	Zwak negatief -0.1198
Answer 12	-	Zwak positief 0.0392	Zwak positief 0.1042	Zwak negatief -0.0353	Zwak positief 0.0357	Zwak positief 0.0249	Zwak positief 0.0297	Zwak negatief -0.1526
Answer 13	-	Zwak positief 0.0646	Zwak positief 0.1052	Zwak negatief -0.0444	Zwak positief 0.0266	Zwak positief 0.0416	Zwak positief 0.0176	Zwak negatief -0.1605
Answer 14	-	Zwak positief 0.0714	Zwak positief 0.1026	Zwak negatief -0.0002	Zwak negatief -0.0090	Zwak negatief -0.0012	Zwak positief 0.0086	Zwak negatief -0.1174
Answer 15	-	Zwak positief 0.0558	Zwak positief 0.1369	Zwak negatief -0.0419	Zwak positief 0.0176	Zwak negatief -0.0163	Zwak positief 0.0222	Zwak negatief -0.1183
Answer 16	-	Zwak positief 0.0592	Zwak positief 0.0275	Zwak negatief -0.0384	Zwak negatief -0.0402	Zwak positief 0.0652	Zwak positief 0.0283	Zwak negatief -0.0710

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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

Producteigenaar SaaS Pet Project Sdtest®

Valerii was in 1993 gekwalificeerd als een sociale pedagoog-psycholoog en heeft sindsdien zijn kennis toegepast in projectmanagement.
Valerii behaalde een masterdiploma en de kwalificatie van het project- en programmabeheerder in 2013. Tijdens zijn masterprogramma raakte hij bekend met Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) en spiraalvormige dynamiek.
Valerii heeft verschillende spiraalvormige dynamiektests uitgevoerd en gebruikte zijn kennis en ervaring om de huidige versie van SDTest aan te passen.
Valerii is de auteur van het verkennen van de onzekerheid van de V.U.C.A. Concept met behulp van spiraalvormige dynamiek en wiskundige statistieken in de psychologie, meer dan 20 internationale peilingen.

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