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) Handlinger fra selskaper i forhold til personell den siste måneden (ja / nei)

2) Handlinger av selskaper i forhold til personell i den siste måneden (faktum i%)

3) Frykter

4) Største problemer som landet mitt står overfor

5) Hvilke egenskaper og evner bruker gode ledere når de bygger vellykkede team?

6) Google. Faktorer som påvirker teamet effektivitet

7) Hovedprioriteringene til jobbsøkere

8) Hva gjør en sjef til en stor leder?

9) Hva gjør folk til å lykkes på jobben?

10) Er du klar til å motta mindre lønn for å jobbe eksternt?

11) Eksisterer alderen?

12) Alderisme i karriere

13) Alderisme i livet

14) Årsaker til alderen

15) Årsaker til at folk gir opp (av Anna Vital)

16) TILLIT (#WVS)

17) Oxford Happiness Survey

18) Psykologisk velvære

19) Hvor ville være din neste mest spennende mulighet?

20) Hva vil du gjøre denne uken for å passe på din mentale helse?

21) Jeg lever og tenker på min fortid, nåtid eller fremtid

22) Meritokrati

23) Kunstig intelligens og slutten av sivilisasjonen

24) Hvorfor utsetter folk seg?

25) Kjønnsforskjell i å bygge selvtillit (IFD Allensbach)

26) Xing.com kulturvurdering

27) Patrick Lencionis "The Five Dysfunctions of a Team"

28) Empati er ...

29) Hva er viktig for IT -spesialister i å velge et jobbtilbud?

30) Hvorfor folk motstår endring (av Siobhán McHale)

31) Hvordan regulerer du følelsene dine? (av Nawal Mustafa M.A.)

32) 21 ferdigheter som betaler deg for alltid (av Jeremiah Teo / 赵汉昇)

33) Ekte frihet er ...

34) 12 måter å bygge tillit med andre (av Justin Wright)

35) Kjennetegn på en talentfull ansatt (av Talent Management Institute)

36) 10 nøkler til å motivere teamet ditt

37) Algebra of Conscience (av Vladimir Lefebvre)

38) Fremtidens tre distinkte muligheter (av Dr. Clare W. Graves)

39) Handlinger for å bygge urokkelig selvtillit (av Suren Samarchyan)

40)

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.

Frykter

diagrammer Sammenheng

VUCA

Kritiske verdi av korrelasjonskoeffisienten

Normal distribusjon, av William Sealy Gosset (student) r = 0.0318

Ikke normal distribusjon, av Spearman r = 0.0013

Vis bare resultater > r = 0.0318

Fordeling	Ikke normal	Ikke normal	Ikke normal	Vanlig	Vanlig	Vanlig	Vanlig	Vanlig
Alle spørsmål Alle spørsmål Min største frykt er
Min største frykt er
Answer 1	-	Svakt positivt 0.0548	Svakt positivt 0.0285	Svakt negativt -0.0173	Svakt positivt 0.0940	Svakt positivt 0.0358	Svakt negativt -0.0156	Svakt negativt -0.1560
Answer 2	-	Svakt positivt 0.0192	Svakt negativt -0.0048	Svakt negativt -0.0394	Svakt positivt 0.0659	Svakt positivt 0.0491	Svakt positivt 0.0117	Svakt negativt -0.0981
Answer 3	-	Svakt negativt -0.0003	Svakt negativt -0.0088	Svakt negativt -0.0450	Svakt negativt -0.0440	Svakt positivt 0.0471	Svakt positivt 0.0739	Svakt negativt -0.0191
Answer 4	-	Svakt positivt 0.0429	Svakt positivt 0.0271	Svakt negativt -0.0230	Svakt positivt 0.0182	Svakt positivt 0.0351	Svakt positivt 0.0239	Svakt negativt -0.0995
Answer 5	-	Svakt positivt 0.0273	Svakt positivt 0.1298	Svakt positivt 0.0101	Svakt positivt 0.0772	Svakt negativt -0.0006	Svakt negativt -0.0183	Svakt negativt -0.1784
Answer 6	-	Svakt negativt -0.0026	Svakt positivt 0.0050	Svakt negativt -0.0621	Svakt negativt -0.0081	Svakt positivt 0.0240	Svakt positivt 0.0856	Svakt negativt -0.0346
Answer 7	-	Svakt positivt 0.0105	Svakt positivt 0.0339	Svakt negativt -0.0661	Svakt negativt -0.0304	Svakt positivt 0.0517	Svakt positivt 0.0686	Svakt negativt -0.0515
Answer 8	-	Svakt positivt 0.0635	Svakt positivt 0.0732	Svakt negativt -0.0275	Svakt positivt 0.0143	Svakt positivt 0.0370	Svakt positivt 0.0172	Svakt negativt -0.1336
Answer 9	-	Svakt positivt 0.0734	Svakt positivt 0.1618	Svakt positivt 0.0069	Svakt positivt 0.0644	Svakt negativt -0.0109	Svakt negativt -0.0489	Svakt negativt -0.1811
Answer 10	-	Svakt positivt 0.0764	Svakt positivt 0.0679	Svakt negativt -0.0139	Svakt positivt 0.0290	Svakt positivt 0.0338	Svakt negativt -0.0123	Svakt negativt -0.1342
Answer 11	-	Svakt positivt 0.0634	Svakt positivt 0.0535	Svakt negativt -0.0091	Svakt positivt 0.0113	Svakt positivt 0.0238	Svakt positivt 0.0247	Svakt negativt -0.1260
Answer 12	-	Svakt positivt 0.0449	Svakt positivt 0.0941	Svakt negativt -0.0341	Svakt positivt 0.0342	Svakt positivt 0.0332	Svakt positivt 0.0255	Svakt negativt -0.1534
Answer 13	-	Svakt positivt 0.0691	Svakt positivt 0.0966	Svakt negativt -0.0393	Svakt positivt 0.0295	Svakt positivt 0.0417	Svakt positivt 0.0148	Svakt negativt -0.1626
Answer 14	-	Svakt positivt 0.0775	Svakt positivt 0.0903	Svakt negativt -0.0019	Svakt negativt -0.0089	Svakt positivt 0.0048	Svakt positivt 0.0140	Svakt negativt -0.1223
Answer 15	-	Svakt positivt 0.0544	Svakt positivt 0.1280	Svakt negativt -0.0345	Svakt positivt 0.0152	Svakt negativt -0.0178	Svakt positivt 0.0236	Svakt negativt -0.1158
Answer 16	-	Svakt positivt 0.0703	Svakt positivt 0.0262	Svakt negativt -0.0371	Svakt negativt -0.0377	Svakt positivt 0.0697	Svakt positivt 0.0204	Svakt negativt -0.0788

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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

Produkteier SaaS SDTEST®

Valerii ble utdannet sosialpedagog-psykolog i 1993 og har siden brukt sin kunnskap innen prosjektledelse.
Valerii oppnådde en Mastergrad og prosjekt- og programlederkvalifikasjonen i 2013. I løpet av masterstudiet ble han kjent med Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) og Spiral Dynamics.
Valerii er forfatteren av å utforske usikkerheten til V.U.C.A. konsept ved hjelp av Spiral Dynamics og matematisk statistikk i psykologi, og 38 internasjonale meningsmålinger.

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