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)

39) Acțiuni pentru a construi o încredere în sine de neclintit (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.

Temerile

Grafice Corelație

VUCA

Valoarea critică a coeficientului de corelație

Distribuție normală, de William Sealy Gosset (student) r = 0.0324

Distribuție non -normală, de Spearman r = 0.0013

Arată doar rezultatele > r = 0.0324

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 0.0503	Slab pozitiv 0.0309	Negativ slab -0.0174	Slab pozitiv 0.0937	Slab pozitiv 0.0365	Negativ slab -0.0154	Negativ slab -0.1558
Answer 2	-	Slab pozitiv 0.0169	Slab pozitiv 0.0001	Negativ slab -0.0435	Slab pozitiv 0.0641	Slab pozitiv 0.0484	Slab pozitiv 0.0154	Negativ slab -0.0966
Answer 3	-	Negativ slab -0.0045	Negativ slab -0.0113	Negativ slab -0.0467	Negativ slab -0.0441	Slab pozitiv 0.0511	Slab pozitiv 0.0788	Negativ slab -0.0221
Answer 4	-	Slab pozitiv 0.0414	Slab pozitiv 0.0275	Negativ slab -0.0208	Slab pozitiv 0.0176	Slab pozitiv 0.0325	Slab pozitiv 0.0248	Negativ slab -0.0985
Answer 5	-	Slab pozitiv 0.0238	Slab pozitiv 0.1308	Slab pozitiv 0.0098	Slab pozitiv 0.0800	Slab pozitiv 0.0007	Negativ slab -0.0233	Negativ slab -0.1792
Answer 6	-	Negativ slab -0.0077	Slab pozitiv 0.0094	Negativ slab -0.0669	Negativ slab -0.0067	Slab pozitiv 0.0237	Slab pozitiv 0.0848	Negativ slab -0.0330
Answer 7	-	Slab pozitiv 0.0100	Slab pozitiv 0.0390	Negativ slab -0.0728	Negativ slab -0.0271	Slab pozitiv 0.0514	Slab pozitiv 0.0677	Negativ slab -0.0520
Answer 8	-	Slab pozitiv 0.0669	Slab pozitiv 0.0815	Negativ slab -0.0332	Slab pozitiv 0.0155	Slab pozitiv 0.0363	Slab pozitiv 0.0153	Negativ slab -0.1368
Answer 9	-	Slab pozitiv 0.0676	Slab pozitiv 0.1663	Slab pozitiv 0.0050	Slab pozitiv 0.0658	Negativ slab -0.0118	Negativ slab -0.0516	Negativ slab -0.1795
Answer 10	-	Slab pozitiv 0.0776	Slab pozitiv 0.0726	Negativ slab -0.0239	Slab pozitiv 0.0275	Slab pozitiv 0.0311	Negativ slab -0.0118	Negativ slab -0.1336
Answer 11	-	Slab pozitiv 0.0607	Slab pozitiv 0.0569	Negativ slab -0.0087	Slab pozitiv 0.0088	Slab pozitiv 0.0215	Slab pozitiv 0.0240	Negativ slab -0.1245
Answer 12	-	Slab pozitiv 0.0399	Slab pozitiv 0.0995	Negativ slab -0.0395	Slab pozitiv 0.0367	Slab pozitiv 0.0318	Slab pozitiv 0.0242	Negativ slab -0.1529
Answer 13	-	Slab pozitiv 0.0650	Slab pozitiv 0.1015	Negativ slab -0.0438	Slab pozitiv 0.0288	Slab pozitiv 0.0433	Slab pozitiv 0.0156	Negativ slab -0.1629
Answer 14	-	Slab pozitiv 0.0710	Slab pozitiv 0.0986	Negativ slab -0.0019	Negativ slab -0.0063	Slab pozitiv 0.0036	Slab pozitiv 0.0089	Negativ slab -0.1222
Answer 15	-	Slab pozitiv 0.0538	Slab pozitiv 0.1350	Negativ slab -0.0374	Slab pozitiv 0.0189	Negativ slab -0.0179	Slab pozitiv 0.0200	Negativ slab -0.1182
Answer 16	-	Slab pozitiv 0.0645	Slab pozitiv 0.0283	Negativ slab -0.0360	Negativ slab -0.0431	Slab pozitiv 0.0652	Slab pozitiv 0.0244	Negativ slab -0.0743

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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 produs SaaS SDTEST®

Valerii a fost calificat ca pedagog social-psiholog în 1993 și de atunci și-a aplicat cunoștințele în managementul proiectelor.
Valerii a obținut o diplomă de master și calificarea de manager de proiect și program în 2013. În timpul programului său de master, s-a familiarizat cu Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) și Spiral Dynamics.
Valerii este autorul explorării incertitudinii V.U.C.A. concept folosind Spiral Dynamics și statistici matematice în psihologie și 38 de sondaje internaționale.

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