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) Azzione di cumpagnie in relazione à u persunale in l'ultimu mese (Iè / No)

2) Azzione di cumpagnie in relazione à u persunale in l'ultimu mese (fattu in%)

3) Teme

4) I prublemi più grandi chì facenu u mo paese

5) Chì qualità è e capacità sò i boni dirigenti utilizanu quandu custruiscenu squadre di successu?

6) Google. Fattori chì impattu l'eventività di a squadra

7) E priorità principali di i cercatori di travagliu

8) Cosa face un capu un grande capu?

9) Chì face a ghjente riescita à u travagliu?

10) Sò pronti à riceve menu pagate per travaglià remotamente?

11) L'ugisimu esiste?

12) L'età in a carriera

13) Etisimu in a Vita

14) Cause di l'età

15) Motivi perchè a ghjente rende (da Anna Vital)

16) Fiducia (#WVS)

17) Sonda di felicità Oxford

18) Benessere psicologicu

19) Induva seria a vostra prossima opportunità più eccitante?

20) Chì farete sta settimana per guardà a vostra salute mentale?

21) Vivu pensendu à u mo passatu, presente o futuru

22) Meritocrazia

23) Intelligenza artificiale è a fine di a civiltà

24) Perchè a ghjente procrastinate?

25) Differenza di genere in custruisce a cunfidenza in sè stessu (ifd allensbach)

26) Xing.com Visualizazione di Cultura

27) Patrick Lenzi "i cinque disfunzioni di una squadra"

28) Empatia hè ...

29) Chì hè essenziale per i specialisti in scelta di un offerta di travagliu?

30) Perchè e persone chì resistenu u cambiamentu (da Siobhán mchale)

31) Cumu regulate e vostre emozioni? (da Nawal Mustafa m.a.)

32) 21 cumpetenze chì vi paganu per sempre (per jeremiah teo / 赵汉昇)

33) A libertà vera hè ...

34) 12 manere di custruisce fiducia cù l'altri (da Justin Wright)

35) Caratteristiche di un impiegatu di talentu (da istitutu di u talentu di u talentu)

36) 10 chjavi per motivà a vostra squadra

37) Algebra di a Cuscenza (di Vladimir Lefebvre)

38) Trè pussibulità distinte di u futuru (da Dr. Clare W. Graves)

39) Azioni per custruisce una fiducia in sè stessu (da 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.

Teme

ascolta Correlation

VUCA

Valore criticu di u coefficiente di correlazione

Distribuzione normale, da William Sealy Gosset (Studiente) r = 0.0318

Distribuzione non Normale, da Bearman r = 0.0013

Mostra solu risultati > r = 0.0318

Distribuzione	Non normale	Non normale	Non normale	Nurmale	Nurmale	Nurmale	Nurmale	Nurmale
Tutte e dumande Tutte e dumande A mo più grande paura hè
A mo più grande paura hè
Answer 1	-	Pusitivu debuli 0.0554	Pusitivu debuli 0.0283	Negativu debuli -0.0173	Pusitivu debuli 0.0940	Pusitivu debuli 0.0355	Negativu debuli -0.0157	Negativu debuli -0.1559
Answer 2	-	Pusitivu debuli 0.0194	Negativu debuli -0.0048	Negativu debuli -0.0394	Pusitivu debuli 0.0659	Pusitivu debuli 0.0490	Pusitivu debuli 0.0117	Negativu debuli -0.0981
Answer 3	-	Negativu debuli -0.0011	Negativu debuli -0.0085	Negativu debuli -0.0450	Negativu debuli -0.0440	Pusitivu debuli 0.0474	Pusitivu debuli 0.0740	Negativu debuli -0.0192
Answer 4	-	Pusitivu debuli 0.0427	Pusitivu debuli 0.0272	Negativu debuli -0.0230	Pusitivu debuli 0.0182	Pusitivu debuli 0.0351	Pusitivu debuli 0.0239	Negativu debuli -0.0995
Answer 5	-	Pusitivu debuli 0.0268	Pusitivu debuli 0.1299	Pusitivu debuli 0.0101	Pusitivu debuli 0.0772	Negativu debuli -0.0003	Negativu debuli -0.0182	Negativu debuli -0.1785
Answer 6	-	Negativu debuli -0.0028	Pusitivu debuli 0.0050	Negativu debuli -0.0621	Negativu debuli -0.0081	Pusitivu debuli 0.0241	Pusitivu debuli 0.0856	Negativu debuli -0.0347
Answer 7	-	Pusitivu debuli 0.0102	Pusitivu debuli 0.0340	Negativu debuli -0.0661	Negativu debuli -0.0304	Pusitivu debuli 0.0518	Pusitivu debuli 0.0687	Negativu debuli -0.0515
Answer 8	-	Pusitivu debuli 0.0632	Pusitivu debuli 0.0732	Negativu debuli -0.0275	Pusitivu debuli 0.0143	Pusitivu debuli 0.0371	Pusitivu debuli 0.0173	Negativu debuli -0.1337
Answer 9	-	Pusitivu debuli 0.0732	Pusitivu debuli 0.1619	Pusitivu debuli 0.0069	Pusitivu debuli 0.0644	Negativu debuli -0.0108	Negativu debuli -0.0489	Negativu debuli -0.1811
Answer 10	-	Pusitivu debuli 0.0756	Pusitivu debuli 0.0681	Negativu debuli -0.0139	Pusitivu debuli 0.0290	Pusitivu debuli 0.0341	Negativu debuli -0.0122	Negativu debuli -0.1343
Answer 11	-	Pusitivu debuli 0.0631	Pusitivu debuli 0.0536	Negativu debuli -0.0091	Pusitivu debuli 0.0113	Pusitivu debuli 0.0239	Pusitivu debuli 0.0247	Negativu debuli -0.1260
Answer 12	-	Pusitivu debuli 0.0442	Pusitivu debuli 0.0943	Negativu debuli -0.0340	Pusitivu debuli 0.0342	Pusitivu debuli 0.0335	Pusitivu debuli 0.0256	Negativu debuli -0.1535
Answer 13	-	Pusitivu debuli 0.0700	Pusitivu debuli 0.0962	Negativu debuli -0.0393	Pusitivu debuli 0.0295	Pusitivu debuli 0.0412	Pusitivu debuli 0.0147	Negativu debuli -0.1624
Answer 14	-	Pusitivu debuli 0.0783	Pusitivu debuli 0.0900	Negativu debuli -0.0019	Negativu debuli -0.0089	Pusitivu debuli 0.0043	Pusitivu debuli 0.0139	Negativu debuli -0.1221
Answer 15	-	Pusitivu debuli 0.0538	Pusitivu debuli 0.1282	Negativu debuli -0.0345	Pusitivu debuli 0.0152	Negativu debuli -0.0176	Pusitivu debuli 0.0237	Negativu debuli -0.1159
Answer 16	-	Pusitivu debuli 0.0699	Pusitivu debuli 0.0263	Negativu debuli -0.0371	Negativu debuli -0.0377	Pusitivu debuli 0.0699	Pusitivu debuli 0.0205	Negativu debuli -0.0788

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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

Pruprietariu di u produttu SaaS SDTEST®

Valerii hè statu qualificatu cum'è pedagogu suciale-psicologu in u 1993 è hà dapoi applicatu a so cunniscenza in a gestione di prughjetti.
Valerii hà ottenutu un diploma di Master è a qualificazione di u prughjettu è u prugramma manager in 2013. Durante u so prugramma di Master, hà familiarizatu cù Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) è Spiral Dynamics.
Valerii è l'autore di esplorare l'incertezza del V.U.C.A. cuncettu utilizendu Spiral Dynamics è statistiche matematiche in psiculugia, è 38 sondaggi internaziunali.

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