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) Accions de les empreses en relació amb el personal del darrer mes (sí / no)

2) Accions d'empreses en relació amb el personal en l'últim mes (fet en%)

3) Temors

4) Majors problemes que té el meu país

5) Quines qualitats i habilitats fan servir els bons líders a l’hora de construir equips d’èxit?

6) Google. Factors que afecten l’eficàcia de l’equip

7) Les principals prioritats dels sol·licitants d’ocupació

8) Què fa que un cap sigui un gran líder?

9) Què fa que la gent tingui èxit a la feina?

10) Esteu a punt per rebre menys pagaments per treballar de forma remota?

11) Existeix l’edatisme?

12) Ageisme a la carrera

13) Ageisme a la vida

14) Causes de l’edatisme

15) Raons per les quals la gent es rendeix (per Anna Vital)

16) Confiar (#WVS)

17) Enquesta de felicitat d'Oxford

18) Benestar psicològic

19) On seria la vostra propera oportunitat més emocionant?

20) Què fareu aquesta setmana per tenir cura de la vostra salut mental?

21) Visc pensant en el meu passat, present o futur

22) Meritocràcia

23) Intel·ligència artificial i el final de la civilització

24) Per què la gent es procrastina?

25) Diferència de gènere en la creació de confiança en si mateix (IFD Allensbach)

26) Xing.com Avaluació de la cultura

27) Les cinc disfuncions d'un equip de Patrick Lencioni

28) L’empatia és ...

29) Què és essencial per als especialistes informàtics per triar una oferta de treball?

30) Per què la gent resisteix al canvi (de Siobhán McHale)

31) Com reguleu les vostres emocions? (de Nawal Mustafa M.A.)

32) 21 Habilitats que us paguen per sempre (de Jeremiah Teo / 赵汉昇)

33) La veritable llibertat és ...

34) 12 maneres de crear confiança amb altres (de Justin Wright)

35) Característiques d’un empleat amb talent (de l’Institut de Gestió de Talent)

36) 10 claus per motivar el vostre equip

37) Àlgebra de la consciència (de Vladimir Lefebvre)

38) Three Distinct Possibilities of the Future (per la Dra. Clare W. Graves)

39) Accions per construir una autoconfiança inquebrantable (de 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.

Temors

gràfics Correlació

VUCA

Valor crític de el coeficient de correlació

Distribució normal, de William Sealy Gosset (estudiant) r = 0.0318

Distribució no normal, per Spearman r = 0.0013

Mostra només resultats > r = 0.0318

Distribució	No normal	No normal	No normal	Normal	Normal	Normal	Normal	Normal
Totes les preguntes Totes les preguntes El meu major temor és
El meu major temor és
Answer 1	-	Positiva feble 0.0546	Positiva feble 0.0291	Negativa feble -0.0174	Positiva feble 0.0940	Positiva feble 0.0348	Negativa feble -0.0152	Negativa feble -0.1554
Answer 2	-	Positiva feble 0.0189	Negativa feble -0.0048	Negativa feble -0.0401	Positiva feble 0.0658	Positiva feble 0.0496	Positiva feble 0.0122	Negativa feble -0.0981
Answer 3	-	Negativa feble -0.0017	Negativa feble -0.0085	Negativa feble -0.0455	Negativa feble -0.0447	Positiva feble 0.0486	Positiva feble 0.0747	Negativa feble -0.0193
Answer 4	-	Positiva feble 0.0419	Positiva feble 0.0279	Negativa feble -0.0240	Positiva feble 0.0179	Positiva feble 0.0357	Positiva feble 0.0245	Negativa feble -0.0993
Answer 5	-	Positiva feble 0.0268	Positiva feble 0.1300	Positiva feble 0.0098	Positiva feble 0.0766	Positiva feble 0.0004	Negativa feble -0.0175	Negativa feble -0.1790
Answer 6	-	Negativa feble -0.0033	Positiva feble 0.0054	Negativa feble -0.0629	Negativa feble -0.0092	Positiva feble 0.0253	Positiva feble 0.0867	Negativa feble -0.0350
Answer 7	-	Positiva feble 0.0099	Positiva feble 0.0345	Negativa feble -0.0669	Negativa feble -0.0312	Positiva feble 0.0528	Positiva feble 0.0697	Negativa feble -0.0520
Answer 8	-	Positiva feble 0.0632	Positiva feble 0.0735	Negativa feble -0.0283	Positiva feble 0.0143	Positiva feble 0.0377	Positiva feble 0.0180	Negativa feble -0.1342
Answer 9	-	Positiva feble 0.0731	Positiva feble 0.1624	Positiva feble 0.0060	Positiva feble 0.0639	Negativa feble -0.0102	Negativa feble -0.0481	Negativa feble -0.1814
Answer 10	-	Positiva feble 0.0749	Positiva feble 0.0681	Negativa feble -0.0133	Positiva feble 0.0285	Positiva feble 0.0335	Negativa feble -0.0110	Negativa feble -0.1340
Answer 11	-	Positiva feble 0.0624	Positiva feble 0.0537	Negativa feble -0.0091	Positiva feble 0.0106	Positiva feble 0.0239	Positiva feble 0.0260	Negativa feble -0.1260
Answer 12	-	Positiva feble 0.0438	Positiva feble 0.0947	Negativa feble -0.0347	Positiva feble 0.0335	Positiva feble 0.0341	Positiva feble 0.0267	Negativa feble -0.1538
Answer 13	-	Positiva feble 0.0705	Positiva feble 0.0964	Negativa feble -0.0397	Positiva feble 0.0294	Positiva feble 0.0421	Positiva feble 0.0149	Negativa feble -0.1635
Answer 14	-	Positiva feble 0.0787	Positiva feble 0.0912	Negativa feble -0.0031	Negativa feble -0.0091	Positiva feble 0.0050	Positiva feble 0.0143	Negativa feble -0.1230
Answer 15	-	Positiva feble 0.0535	Positiva feble 0.1285	Negativa feble -0.0352	Positiva feble 0.0145	Negativa feble -0.0166	Positiva feble 0.0246	Negativa feble -0.1163
Answer 16	-	Positiva feble 0.0698	Positiva feble 0.0267	Negativa feble -0.0375	Negativa feble -0.0378	Positiva feble 0.0701	Positiva feble 0.0209	Negativa feble -0.0793

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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

Product Owner SaaS SDTEST®

Valerii va ser titulat com a pedagog social-psicòleg l'any 1993 i des de llavors ha aplicat els seus coneixements en gestió de projectes.
Valerii va obtenir un màster i la qualificació de director de projectes i programes el 2013. Durant el seu programa de màster, es va familiaritzar amb Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) i Spiral Dynamics.
Valerii és l'autor d'explorar la incertesa del V.U.C.A. concepte utilitzant Spiral Dynamics i estadístiques matemàtiques en psicologia, i 38 enquestes internacionals.

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