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) Fihetsiketsehana orinasa mifandraika amin'ny mpiasam-panjakana amin'ny volana farany (eny / tsia)

2) Fihetsiketsehana orinasa mifandraika amin'ny mpiasam-panjakana amin'ny volana lasa (zava-misy ao%)

3) Tahotra

4) Olana lehibe indrindra atrehin'ny fireneko

5) Inona no toetra sy fahaiza-manao ampiasain'ny mpitarika tsara rehefa manorina ekipa mahomby?

6) Google. Ireo antony izay misy fiantraikany amin'ny fananana ekipa

7) Ny laharam-pahamehan'ny mpitady asa

8) Inona no mahatonga ny tompon'andraikitra ho mpitarika lehibe?

9) Inona no mahatonga ny olona hahomby amin'ny asa?

10) Vonona ve ianao handray karama kely kokoa hiasa lavitra?

11) Misy ny fiantrana ve?

12) AgeM amin'ny sehatry ny asa

13) Ageism amin'ny fiainana

14) Antony ny fiandohan-tena

15) Ny antony mahatonga ny olona ho kivy (nataon'i Anna Vital)

16) fahatokiana (#WVS)

17) Fanadihadiana momba ny Oxford

18) Ny fahasalamana ara-tsaina

19) Aiza ny fotoana mety hampientam-po anao indrindra?

20) Inona no hataonao amin'ity herinandro ity hikarakara ny fahasalamanao ara-tsaina?

21) Miaina mieritreritra ny lasa, ankehitriny na ho avy aho

22) Meritocokracy

23) Ny faharanitan-tsaina voajanahary sy ny fiafaran'ny sivilizasiona

24) Nahoana ny olona no mangataka?

25) Fahasamihafana ny lahy sy ny vavy amin'ny fananganana fahatokisan-tena (IFD allensbach)

26) Xing. Fandinihana ny kolontsaina

27) Patrick Lencioni's "The DysFunctions an'ny ekipa"

28) Ny fiaraha-miory dia ...

29) Inona no tena ilaina amin'ny manam-pahaizana manokana amin'ny fisafidianana ny tolotra amin'ny asa?

30) Maninona ny olona no manohitra ny fanovana (avy amin'i Siobhán Mchale)

31) Ahoana no fomba handraisanao ny fihetseham-ponao? (nataon'i Nawal Mustafa M.a.)

32) Fahaiza-manao 21 izay mandoa anao mandrakizay (nataon'i Jeremia Teo / 赵汉昇)

33) Ny tena fahafahana dia ...

34) Fomba 12 hananganana fahatokisana amin'ny hafa (nataon'i Justin Wright)

35) Toetran'ny mpiasa manan-talenta (avy amin'ny andrim-pitantanana talenta)

36) 10 Fanalahidy hanosika ny ekipanao

37) Algebra of conscience (nataon'i Vladimir Lefebvre)

38) Fahafahana telo miavaka amin'ny ho avy (nataon'i Dr. Clare W. Graves)

39) Hetsika hananganana fahatokisan-tena tsy azo hozongozonina (nataon'i 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.

Tahotra

tabilaoFifandraisany

VUCA

Critical lanjan'ny ny fifandraisany coefficient

Fizarana ara-dalàna, nataon'i William Sealy Gosset (mpianatra) r = 0.0315

Fizarana tsy mahazatra, avy amin'ny Spearman r = 0.0013

Asehoy ihany ny valiny > r = 0.0315

fizarana	Non normal	Non normal	Non normal	ara-dalàna	ara-dalàna	ara-dalàna	ara-dalàna	ara-dalàna
Ny fanontaniana rehetra Ny fanontaniana rehetra Ny tahotra lehibe indrindra ananako dia
Ny tahotra lehibe indrindra ananako dia
Answer 1	-	Malemy tsara 0.0548	Malemy tsara 0.0273	Malemy ratsy -0.0187	Malemy tsara 0.0929	Malemy tsara 0.0386	Malemy ratsy -0.0156	Malemy ratsy -0.1555
Answer 2	-	Malemy tsara 0.0176	Malemy ratsy -0.0078	Malemy ratsy -0.0391	Malemy tsara 0.0636	Malemy tsara 0.0505	Malemy tsara 0.0131	Malemy ratsy -0.0956
Answer 3	-	Malemy ratsy -0.0007	Malemy ratsy -0.0092	Malemy ratsy -0.0470	Malemy ratsy -0.0433	Malemy tsara 0.0499	Malemy tsara 0.0756	Malemy ratsy -0.0216
Answer 4	-	Malemy tsara 0.0457	Malemy tsara 0.0323	Malemy ratsy -0.0260	Malemy tsara 0.0164	Malemy tsara 0.0371	Malemy tsara 0.0262	Malemy ratsy -0.1045
Answer 5	-	Malemy tsara 0.0262	Malemy tsara 0.1265	Malemy tsara 0.0101	Malemy tsara 0.0745	Malemy tsara 0.0006	Malemy ratsy -0.0155	Malemy ratsy -0.1761
Answer 6	-	Malemy tsara 0.0006	Malemy tsara 0.0050	Malemy ratsy -0.0626	Malemy ratsy -0.0111	Malemy tsara 0.0260	Malemy tsara 0.0848	Malemy ratsy -0.0351
Answer 7	-	Malemy tsara 0.0123	Malemy tsara 0.0322	Malemy ratsy -0.0680	Malemy ratsy -0.0316	Malemy tsara 0.0538	Malemy tsara 0.0698	Malemy ratsy -0.0520
Answer 8	-	Malemy tsara 0.0659	Malemy tsara 0.0710	Malemy ratsy -0.0280	Malemy tsara 0.0129	Malemy tsara 0.0390	Malemy tsara 0.0170	Malemy ratsy -0.1339
Answer 9	-	Malemy tsara 0.0774	Malemy tsara 0.1609	Malemy tsara 0.0053	Malemy tsara 0.0600	Malemy ratsy -0.0068	Malemy ratsy -0.0488	Malemy ratsy -0.1816
Answer 10	-	Malemy tsara 0.0766	Malemy tsara 0.0633	Malemy ratsy -0.0121	Malemy tsara 0.0264	Malemy tsara 0.0354	Malemy ratsy -0.0101	Malemy ratsy -0.1334
Answer 11	-	Malemy tsara 0.0633	Malemy tsara 0.0514	Malemy ratsy -0.0086	Malemy tsara 0.0095	Malemy tsara 0.0276	Malemy tsara 0.0252	Malemy ratsy -0.1273
Answer 12	-	Malemy tsara 0.0434	Malemy tsara 0.0910	Malemy ratsy -0.0333	Malemy tsara 0.0327	Malemy tsara 0.0360	Malemy tsara 0.0268	Malemy ratsy -0.1534
Answer 13	-	Malemy tsara 0.0714	Malemy tsara 0.0922	Malemy ratsy -0.0385	Malemy tsara 0.0279	Malemy tsara 0.0445	Malemy tsara 0.0159	Malemy ratsy -0.1639
Answer 14	-	Malemy tsara 0.0820	Malemy tsara 0.0880	Malemy ratsy -0.0054	Malemy ratsy -0.0122	Malemy tsara 0.0070	Malemy tsara 0.0156	Malemy ratsy -0.1209
Answer 15	-	Malemy tsara 0.0554	Malemy tsara 0.1237	Malemy ratsy -0.0348	Malemy tsara 0.0113	Malemy ratsy -0.0143	Malemy tsara 0.0274	Malemy ratsy -0.1160
Answer 16	-	Malemy tsara 0.0716	Malemy tsara 0.0217	Malemy ratsy -0.0386	Malemy ratsy -0.0393	Malemy tsara 0.0742	Malemy tsara 0.0184	Malemy ratsy -0.0763

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[1] https://twitter.com/wileyprof

[2] https://colinallen.dnsalias.org

[3] https://philpeople.org/profiles/colin-allen

2023.10.13

FearpersonqualitiesprojectorganizationalstructureRACIresponsibilitymatrixCritical ChainProject Managementfocus factorJiraempathyleadersbossGermanyChinaPolicyUkraineRussiawarvolatilityuncertaintycomplexityambiguityVUCArelocatejobproblemcountryreasongive upobjectivekeyresultmathematicalpsychologyMBTIHR metricsstandardDEIcorrelationriskscoringmodelGame TheoryPrisoner's Dilemma

Valerii Kosenko

Tompon'ny vokatra SaaS SDTEST®

Valerii dia nahafeno fepetra ho pedagogy-psychologist sosialy tamin'ny 1993 ary nanomboka nampihatra ny fahalalany tamin'ny fitantanana tetikasa.
Valerii dia nahazo mari-pahaizana Master sy ny mari-pahaizana momba ny tetikasa ary ny programa amin'ny 2013. Nandritra ny fandaharam-pampianarana Master dia nanjary nahafantatra ny Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) sy ny Spiral Dynamics izy.
Valerii no mpanoratra ny fikarohana ny tsy fahatokisana ny V.U.C.A. hevitra mampiasa Spiral Dynamics sy statistika matematika amin'ny psikolojia, ary fitsapan-kevitra iraisam-pirenena 38.

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