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)

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 = 0.033

Ikke normal distribusjon, av Spearman r = 0.0013

Vis bare resultater > r = 0.033

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

Produkteier SaaS Pet Project SDTEST®

Valerii ble kvalifisert som sosial pedagog-psykolog i 1993 og har siden brukt sin kunnskap i prosjektledelse.
Valerii oppnådde en mastergrad og prosjekt- og programlederkvalifisering i 2013. Under masterprogrammet ble han kjent med Project Roadmap (GPM Deutsche Gesellschaft Für ProjektManagement e. V.) og spiraltynamikk.
Valerii tok forskjellige spiraltynamikkprøver og brukte sin kunnskap og erfaring til å tilpasse den nåværende versjonen av SDTEST.
Valerii er forfatteren av å utforske usikkerheten til V.U.C.A. Konsept ved bruk av spiraltynamikk og matematisk statistikk i psykologi, mer enn 20 internasjonale meningsmålinger.

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