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) Hannelingen fan bedriuwen yn relaasje ta personiel yn 'e lêste moanne (ja / nee)

2) Hannelingen fan bedriuwen yn relaasje ta personiel yn 'e lêste moanne (feit yn%)

3) Fears

4) Grutste problemen nei myn lân

5) Hokker kwaliteiten en kapasiteiten brûke goede lieders by it bouwen fan suksesfolle teams?

6) Google. Faktoaren dy't ynfloed hawwe op it teamrefficpen

7) De wichtichste prioriteiten fan wurksykjenden

8) Wat makket in baas in geweldige lieder?

9) Wat makket minsken suksesfol op it wurk?

10) Binne jo ree om minder beteljen te ûntfangen om op ôfstân te wurkjen?

11) Bestiet se-leeftyd?

12) Ageism yn karriêre

13) Ageism yn it libben

14) Oarsaken fan Ageisme

15) RJOCHTEN WÊR BINNE BINNE JOU UP (troch Anna Vital)

16) FERTROUWE (#WVS)

17) Oxford Gelok Survey

18) Psychologyske wolwêzen

19) Wêr soe jo folgjende meast spannende kâns wêze?

20) Wat sille jo dizze wike dwaan om nei jo mentale sûnens te sjen?

21) Ik libje neitinke oer myn ferline, oanwêzich as takomst

22) Meritokrasy

23) Keunstmjittige yntelliginsje en it ein fan beskaving

24) Wêrom útstelle minsken?

25) Geslachtferskil yn it bouwen fan selsbetrouwen (IFD Allensbach)

26) Xing.com kultuer beoardieling

27) Patrick Lencioni's "De fiif dysfunksjes fan in team"

28) Empathy is ...

29) Wat is essensjeel foar it spesjalisten by it kiezen fan in baan oanbod?

30) Wêrom minsken wjerhâlde (troch Siobhán Mchale)

31) Hoe regelje jo jo emoasjes? (troch Nawal Mustafa M.A.)

32) 21 feardigens dy't jo betelje foar altyd (troch Jeremiah Teo / 赵汉昇)

33) Echte frijheid is ...

34) 12 manieren om fertrouwen te bouwen mei oaren (troch Justin Wright)

35) Karakteristiken fan in talintfolle wurknimmer (troch TALENT MANAGEMENT INSTITCH)

36) 10 toetsen om jo team te motivearjen

37) Algebra of Conscience (troch Vladimir Lefebvre)

38) Trije ûnderskate mooglikheden fan 'e takomst (troch 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.

Fears

Charts Korrelaasje

VUCA

Critical wearde fan de korrelaasje koëffisjint

Normale ferdieling, troch William Sealy Gosset (Student) r = 0.0329

Net normale ferdieling, troch Spearman r = 0.0013

Allinich resultaten sjen litte > r = 0.0329

Distribúsje	Net normaal	Net normaal	Net normaal	Normaal	Normaal	Normaal	Normaal	Normaal
Alle fragen Alle fragen Myn grutste eangst is
Myn grutste eangst is
Answer 1	-	Swak posityf 0.0566	Swak posityf 0.0332	Swak negatyf -0.0170	Swak posityf 0.0912	Swak posityf 0.0308	Swak negatyf -0.0153	Swak negatyf -0.1537
Answer 2	-	Swak posityf 0.0223	Swak posityf 0.0011	Swak negatyf -0.0442	Swak posityf 0.0639	Swak posityf 0.0464	Swak posityf 0.0120	Swak negatyf -0.0960
Answer 3	-	Swak negatyf -0.0031	Swak negatyf -0.0104	Swak negatyf -0.0407	Swak negatyf -0.0463	Swak posityf 0.0475	Swak posityf 0.0779	Swak negatyf -0.0213
Answer 4	-	Swak posityf 0.0437	Swak posityf 0.0357	Swak negatyf -0.0197	Swak posityf 0.0161	Swak posityf 0.0311	Swak posityf 0.0187	Swak negatyf -0.0987
Answer 5	-	Swak posityf 0.0296	Swak posityf 0.1300	Swak posityf 0.0124	Swak posityf 0.0749	Swak posityf 0.0014	Swak negatyf -0.0231	Swak negatyf -0.1771
Answer 6	-	Swak negatyf -0.0008	Swak posityf 0.0090	Swak negatyf -0.0613	Swak negatyf -0.0070	Swak posityf 0.0196	Swak posityf 0.0803	Swak negatyf -0.0321
Answer 7	-	Swak posityf 0.0118	Swak posityf 0.0401	Swak negatyf -0.0693	Swak negatyf -0.0246	Swak posityf 0.0471	Swak posityf 0.0623	Swak negatyf -0.0505
Answer 8	-	Swak posityf 0.0697	Swak posityf 0.0875	Swak negatyf -0.0316	Swak posityf 0.0155	Swak posityf 0.0346	Swak posityf 0.0098	Swak negatyf -0.1373
Answer 9	-	Swak posityf 0.0679	Swak posityf 0.1707	Swak posityf 0.0105	Swak posityf 0.0676	Swak negatyf -0.0138	Swak negatyf -0.0545	Swak negatyf -0.1821
Answer 10	-	Swak posityf 0.0793	Swak posityf 0.0772	Swak negatyf -0.0208	Swak posityf 0.0242	Swak posityf 0.0343	Swak negatyf -0.0152	Swak negatyf -0.1300
Answer 11	-	Swak posityf 0.0590	Swak posityf 0.0559	Swak negatyf -0.0071	Swak posityf 0.0082	Swak posityf 0.0205	Swak posityf 0.0266	Swak negatyf -0.1213
Answer 12	-	Swak posityf 0.0405	Swak posityf 0.1050	Swak negatyf -0.0363	Swak posityf 0.0361	Swak posityf 0.0253	Swak posityf 0.0277	Swak negatyf -0.1522
Answer 13	-	Swak posityf 0.0655	Swak posityf 0.1056	Swak negatyf -0.0439	Swak posityf 0.0270	Swak posityf 0.0417	Swak posityf 0.0152	Swak negatyf -0.1601
Answer 14	-	Swak posityf 0.0728	Swak posityf 0.1049	Swak negatyf -0.0002	Swak negatyf -0.0088	Swak negatyf -0.0007	Swak posityf 0.0061	Swak negatyf -0.1187
Answer 15	-	Swak posityf 0.0561	Swak posityf 0.1378	Swak negatyf -0.0415	Swak posityf 0.0178	Swak negatyf -0.0162	Swak posityf 0.0194	Swak negatyf -0.1176
Answer 16	-	Swak posityf 0.0606	Swak posityf 0.0308	Swak negatyf -0.0348	Swak negatyf -0.0421	Swak posityf 0.0642	Swak posityf 0.0250	Swak negatyf -0.0717

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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

Produkt Eigner SaaS SDTEST®

Valerii waard yn 1993 kwalifisearre as sosjaal pedagogysk psycholooch en hat syn kennis sûnt dy tiid tapast yn projektbehear.
Valerii helle in masterstitel en de kwalifikaasje projekt- en programmamanager yn 2013. Tidens syn masteroplieding kaam hy yn de kunde mei Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) en Spiral Dynamics.
Valerii is de skriuwer fan it ferkennen fan 'e ûnwissichheid fan' e V.U.C.A. konsept mei help fan Spiral Dynamics en wiskundige statistiken yn psychology, en 38 ynternasjonale polls.

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