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) Virksomheders handlinger i relation til personale i den sidste måned (ja / nej)

2) Handlinger af virksomheder i forhold til personale i den sidste måned (faktum i%)

3) Frygt.

4) Største problemer står overfor mit land

5) Hvilke kvaliteter og evner bruger gode ledere, når de bygger succesrige hold?

6) Google. Faktorer, der påvirker teamets effektiv

7) De vigtigste prioriteter for jobsøgende

8) Hvad gør en chef til en stor leder?

9) Hvad gør folk succesrige på arbejdet?

10) Er du klar til at modtage mindre løn for at arbejde eksternt?

11) Eksisterer ageisme?

12) Alderisme i karriere

13) Alderisme i livet

14) Årsager til alder

15) Årsager til, at folk giver op (af Anna Vital)

16) TILLID (#WVS)

17) Oxford Happiness Survey

18) Psykologisk velvære

19) Hvor ville være din næste mest spændende mulighed?

20) Hvad vil du gøre i denne uge for at passe på din mentale sundhed?

21) Jeg lever og tænker på min fortid, nutid eller fremtid

22) Meritokrati

23) Kunstig intelligens og civilisationens afslutning

24) Hvorfor udsætter folk?

25) Kønsforskel i opbygning af selvtillid (IFD Allensbach)

26) Xing.com kulturvurdering

27) Patrick Lencionis "de fem dysfunktioner af et hold"

28) Empati er ...

29) Hvad er vigtigt for IT -specialister i at vælge et jobtilbud?

30) Hvorfor folk modstår forandring (af Siobhán McHale)

31) Hvordan regulerer du dine følelser? (af Nawal Mustafa M.A.)

32) 21 færdigheder, der betaler dig for evigt (af Jeremiah Teo / 赵汉昇)

33) Rigtig frihed er ...

34) 12 måder at opbygge tillid hos andre (af Justin Wright)

35) Karakteristika for en talentfuld medarbejder (af Talent Management Institute)

36) 10 nøgler til at motivere dit team

37) Samvittighedens algebra (af Vladimir Lefebvre)

38) Fremtidens tre distinkte muligheder (af 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.

Frygt.

Diagrammer Korrelation

VUCA

Kritisk værdi af korrelationskoefficienten

Normal distribution af William Sealy Gosset (studerende) r = 0.0329

Ikke normal distribution af Spearman r = 0.0013

Vis kun resultater > r = 0.0329

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

Produktejer SaaS SDTEST®

Valerii blev uddannet socialpædagog-psykolog i 1993 og har siden anvendt sin viden i projektledelse.
Valerii opnåede en kandidatgrad og projekt- og programlederkvalifikationen i 2013. I løbet af sin kandidatuddannelse blev han fortrolig med Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) og Spiral Dynamics.
Valerii er forfatteren til at udforske usikkerheden i V.U.C.A. koncept ved hjælp af Spiral Dynamics og matematisk statistik i psykologi, og 38 internationale meningsmålinger.

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