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) Acțiuni ale companiilor în raport cu personalul din ultima lună (da / nu)

2) Acțiuni ale companiilor în legătură cu personalul din ultima lună (fapt în%)

3) Temerile

4) Cele mai mari probleme cu care se confruntă țara mea

5) Ce calități și abilități folosesc liderii buni atunci când construiesc echipe de succes?

6) Google. Factori care afectează eficiența echipei

7) Principalele priorități ale solicitanților de locuri de muncă

8) Ce face un șef un mare lider?

9) Ce îi face pe oameni să aibă succes la serviciu?

10) Sunteți gata să primiți mai puțin salariu pentru a lucra de la distanță?

11) Există ageismul?

12) Ageismul în carieră

13) Ageismul în viață

14) Cauzele ageismului

15) Motivele pentru care oamenii renunță (de Anna Vital)

16) ÎNCREDERE (#WVS)

17) Oxford Happiness Survey

18) Bunăstarea psihologică

19) Unde ar fi următoarea ta cea mai interesantă oportunitate?

20) Ce vei face săptămâna aceasta pentru a avea grijă de sănătatea ta mentală?

21) Trăiesc gândindu -mă la trecutul, prezentul meu sau viitorul

22) Meritocrație

23) Inteligența artificială și sfârșitul civilizației

24) De ce se amânează oamenii?

25) Diferența de gen în construirea încrederii în sine (IFD Allensbach)

26) Xing.com Evaluarea culturii

27) „Cele cinci disfuncții ale unei echipe” ale lui Patrick Lencioni

28) Empatia este ...

29) Ce este esențial pentru specialiștii IT în alegerea unei oferte de muncă?

30) De ce oamenii rezistă schimbărilor (de Siobhán McHale)

31) Cum îți reglementezi emoțiile? (de Nawal Mustafa M.A.)

32) 21 Abilități care vă plătesc pentru totdeauna (de Jeremiah Teo / 赵汉昇)

33) Libertatea reală este ...

34) 12 moduri de a construi încredere cu ceilalți (de Justin Wright)

35) Caracteristicile unui angajat talentat (de către Institutul de Management Talent)

36) 10 taste pentru motivarea echipei tale

37) Algebra conștiinței (de Vladimir Lefebvre)

38) Trei posibilități distincte ale viitorului (de 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.

Temerile

Grafice Corelație

VUCA

Valoarea critică a coeficientului de corelație

Distribuție normală, de William Sealy Gosset (student) r = 0.033

Distribuție non -normală, de Spearman r = 0.0013

Arată doar rezultatele > r = 0.033

Distribuție	Non normal	Non normal	Non normal	Normal	Normal	Normal	Normal	Normal
Toate întrebările Toate întrebările Cea mai mare frica mea este
Cea mai mare frica mea este
Answer 1	-	Slab pozitiv 0.0559	Slab pozitiv 0.0314	Negativ slab -0.0163	Slab pozitiv 0.0915	Slab pozitiv 0.0303	Negativ slab -0.0129	Negativ slab -0.1543
Answer 2	-	Slab pozitiv 0.0229	Negativ slab -0.0007	Negativ slab -0.0444	Slab pozitiv 0.0633	Slab pozitiv 0.0453	Slab pozitiv 0.0130	Negativ slab -0.0941
Answer 3	-	Negativ slab -0.0032	Negativ slab -0.0122	Negativ slab -0.0413	Negativ slab -0.0464	Slab pozitiv 0.0469	Slab pozitiv 0.0786	Negativ slab -0.0196
Answer 4	-	Slab pozitiv 0.0435	Slab pozitiv 0.0340	Negativ slab -0.0203	Slab pozitiv 0.0155	Slab pozitiv 0.0309	Slab pozitiv 0.0206	Negativ slab -0.0977
Answer 5	-	Slab pozitiv 0.0302	Slab pozitiv 0.1276	Slab pozitiv 0.0130	Slab pozitiv 0.0735	Negativ slab -0.0004	Negativ slab -0.0202	Negativ slab -0.1756
Answer 6	-	Negativ slab -0.0004	Slab pozitiv 0.0079	Negativ slab -0.0634	Negativ slab -0.0080	Slab pozitiv 0.0197	Slab pozitiv 0.0831	Negativ slab -0.0311
Answer 7	-	Slab pozitiv 0.0124	Slab pozitiv 0.0380	Negativ slab -0.0696	Negativ slab -0.0240	Slab pozitiv 0.0474	Slab pozitiv 0.0642	Negativ slab -0.0513
Answer 8	-	Slab pozitiv 0.0697	Slab pozitiv 0.0850	Negativ slab -0.0331	Slab pozitiv 0.0149	Slab pozitiv 0.0345	Slab pozitiv 0.0134	Negativ slab -0.1365
Answer 9	-	Slab pozitiv 0.0669	Slab pozitiv 0.1682	Slab pozitiv 0.0088	Slab pozitiv 0.0689	Negativ slab -0.0131	Negativ slab -0.0519	Negativ slab -0.1822
Answer 10	-	Slab pozitiv 0.0779	Slab pozitiv 0.0750	Negativ slab -0.0216	Slab pozitiv 0.0251	Slab pozitiv 0.0348	Negativ slab -0.0131	Negativ slab -0.1299
Answer 11	-	Slab pozitiv 0.0578	Slab pozitiv 0.0524	Negativ slab -0.0095	Slab pozitiv 0.0085	Slab pozitiv 0.0203	Slab pozitiv 0.0309	Negativ slab -0.1195
Answer 12	-	Slab pozitiv 0.0389	Slab pozitiv 0.1037	Negativ slab -0.0361	Slab pozitiv 0.0359	Slab pozitiv 0.0255	Slab pozitiv 0.0297	Negativ slab -0.1521
Answer 13	-	Slab pozitiv 0.0645	Slab pozitiv 0.1040	Negativ slab -0.0439	Slab pozitiv 0.0263	Slab pozitiv 0.0423	Slab pozitiv 0.0174	Negativ slab -0.1601
Answer 14	-	Slab pozitiv 0.0711	Slab pozitiv 0.1026	Negativ slab -0.0008	Negativ slab -0.0088	Negativ slab -0.0008	Slab pozitiv 0.0086	Negativ slab -0.1172
Answer 15	-	Slab pozitiv 0.0554	Slab pozitiv 0.1362	Negativ slab -0.0434	Slab pozitiv 0.0181	Negativ slab -0.0157	Slab pozitiv 0.0224	Negativ slab -0.1175
Answer 16	-	Slab pozitiv 0.0590	Slab pozitiv 0.0269	Negativ slab -0.0386	Negativ slab -0.0400	Slab pozitiv 0.0656	Slab pozitiv 0.0283	Negativ slab -0.0707

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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

Proprietar de produse SaaS Pet Project SDTest®

Valerii a fost calificat ca pedagog-psiholog pe pedagog social în 1993 și de atunci și-a aplicat cunoștințele în managementul de proiect.
Valerii a obținut o diplomă de master și calificarea managerului de proiect și program în 2013. În timpul programului său de master, s -a familiarizat cu foaia de parcurs a proiectului (GPM Deutsche Gesellschaft Für ProjektManagement e. V.) și dinamica spirală.
Valerii a făcut diverse teste de dinamică în spirală și și -a folosit cunoștințele și experiența pentru a adapta versiunea actuală a SDTest.
Valerii este autorul explorării incertitudinii V.U.C.A. Conceptul folosind dinamica spirală și statisticile matematice în psihologie, mai mult de 20 de sondaje internaționale.

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