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 = 0.0335

Ikke normal distribution af Spearman r = 0.0014

Vis kun resultater > r = 0.0335

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 0.0521	Svag positiv 0.0294	Svag negativ -0.0147	Svag positiv 0.0885	Svag positiv 0.0316	Svag negativ -0.0110	Svag negativ -0.1513
Answer 2	-	Svag positiv 0.0213	Svag positiv 0.0013	Svag negativ -0.0432	Svag positiv 0.0618	Svag positiv 0.0453	Svag positiv 0.0103	Svag negativ -0.0918
Answer 3	-	Svag negativ -0.0042	Svag negativ -0.0116	Svag negativ -0.0406	Svag negativ -0.0477	Svag positiv 0.0487	Svag positiv 0.0767	Svag negativ -0.0191
Answer 4	-	Svag positiv 0.0421	Svag positiv 0.0350	Svag negativ -0.0115	Svag positiv 0.0112	Svag positiv 0.0307	Svag positiv 0.0175	Svag negativ -0.0980
Answer 5	-	Svag positiv 0.0288	Svag positiv 0.1272	Svag positiv 0.0146	Svag positiv 0.0697	Svag positiv 0.0037	Svag negativ -0.0215	Svag negativ -0.1746
Answer 6	-	Svag negativ -0.0001	Svag positiv 0.0042	Svag negativ -0.0607	Svag negativ -0.0115	Svag positiv 0.0231	Svag positiv 0.0826	Svag negativ -0.0309
Answer 7	-	Svag positiv 0.0117	Svag positiv 0.0372	Svag negativ -0.0653	Svag negativ -0.0283	Svag positiv 0.0495	Svag positiv 0.0626	Svag negativ -0.0505
Answer 8	-	Svag positiv 0.0658	Svag positiv 0.0830	Svag negativ -0.0310	Svag positiv 0.0139	Svag positiv 0.0334	Svag positiv 0.0134	Svag negativ -0.1322
Answer 9	-	Svag positiv 0.0660	Svag positiv 0.1658	Svag positiv 0.0051	Svag positiv 0.0691	Svag negativ -0.0093	Svag negativ -0.0498	Svag negativ -0.1820
Answer 10	-	Svag positiv 0.0758	Svag positiv 0.0724	Svag negativ -0.0173	Svag positiv 0.0236	Svag positiv 0.0312	Svag negativ -0.0115	Svag negativ -0.1263
Answer 11	-	Svag positiv 0.0577	Svag positiv 0.0544	Svag negativ -0.0075	Svag positiv 0.0082	Svag positiv 0.0185	Svag positiv 0.0293	Svag negativ -0.1190
Answer 12	-	Svag positiv 0.0376	Svag positiv 0.1007	Svag negativ -0.0342	Svag positiv 0.0296	Svag positiv 0.0273	Svag positiv 0.0341	Svag negativ -0.1500
Answer 13	-	Svag positiv 0.0627	Svag positiv 0.1017	Svag negativ -0.0443	Svag positiv 0.0248	Svag positiv 0.0434	Svag positiv 0.0189	Svag negativ -0.1576
Answer 14	-	Svag positiv 0.0732	Svag positiv 0.1036	Svag positiv 0.0048	Svag negativ -0.0105	Svag negativ -0.0039	Svag positiv 0.0041	Svag negativ -0.1157
Answer 15	-	Svag positiv 0.0539	Svag positiv 0.1381	Svag negativ -0.0424	Svag positiv 0.0163	Svag negativ -0.0147	Svag positiv 0.0216	Svag negativ -0.1173
Answer 16	-	Svag positiv 0.0590	Svag positiv 0.0274	Svag negativ -0.0375	Svag negativ -0.0429	Svag positiv 0.0687	Svag positiv 0.0253	Svag negativ -0.0698

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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 Pet Project SDTest®

Valerii blev kvalificeret som social pædagoge-psykolog i 1993 og har siden anvendt sin viden inden for projektledelse.
Valerii opnåede en kandidatgrad og projekt- og programlederkvalifikationen i 2013. Under sin kandidatuddannelse blev han fortrolig med Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement E. V.) og spiraldynamik.
Valerii tog forskellige spiraldynamikforsøg og brugte sin viden og erfaring til at tilpasse den aktuelle version af SDTest.
Valerii er forfatteren af at udforske usikkerheden i V.U.C.A. Koncept ved hjælp af spiraldynamik og matematisk statistik inden for psykologi, mere end 20 internationale afstemninger.

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