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 0.0559	Svakt positivt 0.0315	Svakt negativt -0.0170	Svakt positivt 0.0920	Svakt positivt 0.0294	Svakt negativt -0.0124	Svakt negativt -0.1539
Answer 2	-	Svakt positivt 0.0229	Svakt negativt -0.0002	Svakt negativt -0.0448	Svakt positivt 0.0636	Svakt positivt 0.0445	Svakt positivt 0.0134	Svakt negativt -0.0939
Answer 3	-	Svakt negativt -0.0032	Svakt negativt -0.0121	Svakt negativt -0.0416	Svakt negativt -0.0462	Svakt positivt 0.0466	Svakt positivt 0.0788	Svakt negativt -0.0195
Answer 4	-	Svakt positivt 0.0438	Svakt positivt 0.0348	Svakt negativt -0.0195	Svakt positivt 0.0153	Svakt positivt 0.0300	Svakt positivt 0.0207	Svakt negativt -0.0980
Answer 5	-	Svakt positivt 0.0304	Svakt positivt 0.1282	Svakt positivt 0.0135	Svakt positivt 0.0734	Svakt negativt -0.0013	Svakt negativt -0.0200	Svakt negativt -0.1757
Answer 6	-	Svakt negativt -0.0002	Svakt positivt 0.0082	Svakt negativt -0.0627	Svakt negativt -0.0083	Svakt positivt 0.0193	Svakt positivt 0.0831	Svakt negativt -0.0315
Answer 7	-	Svakt positivt 0.0126	Svakt positivt 0.0381	Svakt negativt -0.0687	Svakt negativt -0.0243	Svakt positivt 0.0469	Svakt positivt 0.0642	Svakt negativt -0.0515
Answer 8	-	Svakt positivt 0.0698	Svakt positivt 0.0848	Svakt negativt -0.0327	Svakt positivt 0.0148	Svakt positivt 0.0345	Svakt positivt 0.0134	Svakt negativt -0.1365
Answer 9	-	Svakt positivt 0.0668	Svakt positivt 0.1676	Svakt positivt 0.0083	Svakt positivt 0.0693	Svakt negativt -0.0131	Svakt negativt -0.0516	Svakt negativt -0.1818
Answer 10	-	Svakt positivt 0.0782	Svakt positivt 0.0753	Svakt negativt -0.0204	Svakt positivt 0.0247	Svakt positivt 0.0342	Svakt negativt -0.0131	Svakt negativt -0.1304
Answer 11	-	Svakt positivt 0.0578	Svakt positivt 0.0532	Svakt negativt -0.0096	Svakt positivt 0.0087	Svakt positivt 0.0195	Svakt positivt 0.0311	Svakt negativt -0.1196
Answer 12	-	Svakt positivt 0.0390	Svakt positivt 0.1037	Svakt negativt -0.0358	Svakt positivt 0.0358	Svakt positivt 0.0250	Svakt positivt 0.0299	Svakt negativt -0.1520
Answer 13	-	Svakt positivt 0.0644	Svakt positivt 0.1048	Svakt negativt -0.0448	Svakt positivt 0.0268	Svakt positivt 0.0417	Svakt positivt 0.0178	Svakt negativt -0.1600
Answer 14	-	Svakt positivt 0.0712	Svakt positivt 0.1021	Svakt negativt -0.0007	Svakt negativt -0.0088	Svakt negativt -0.0011	Svakt positivt 0.0088	Svakt negativt -0.1169
Answer 15	-	Svakt positivt 0.0557	Svakt positivt 0.1365	Svakt negativt -0.0423	Svakt positivt 0.0177	Svakt negativt -0.0162	Svakt positivt 0.0224	Svakt negativt -0.1179
Answer 16	-	Svakt positivt 0.0591	Svakt positivt 0.0273	Svakt negativt -0.0386	Svakt negativt -0.0400	Svakt positivt 0.0653	Svakt positivt 0.0284	Svakt negativt -0.0708

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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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