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 = 0.0322

Distribuzione non Normale, da Bearman r = 0.0013

Mostra solu risultati > r = 0.0322

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 0.0509	Pusitivu debuli 0.0353	Negativu debuli -0.0167	Pusitivu debuli 0.0940	Pusitivu debuli 0.0349	Negativu debuli -0.0183	Negativu debuli -0.1554
Answer 2	-	Pusitivu debuli 0.0194	Pusitivu debuli 0.0016	Negativu debuli -0.0408	Pusitivu debuli 0.0642	Pusitivu debuli 0.0454	Pusitivu debuli 0.0126	Negativu debuli -0.0968
Answer 3	-	Negativu debuli -0.0015	Negativu debuli -0.0086	Negativu debuli -0.0466	Negativu debuli -0.0457	Pusitivu debuli 0.0478	Pusitivu debuli 0.0754	Negativu debuli -0.0172
Answer 4	-	Pusitivu debuli 0.0408	Pusitivu debuli 0.0320	Negativu debuli -0.0223	Pusitivu debuli 0.0187	Pusitivu debuli 0.0301	Pusitivu debuli 0.0224	Negativu debuli -0.0965
Answer 5	-	Pusitivu debuli 0.0297	Pusitivu debuli 0.1339	Pusitivu debuli 0.0088	Pusitivu debuli 0.0792	Negativu debuli -0.0007	Negativu debuli -0.0227	Negativu debuli -0.1792
Answer 6	-	Negativu debuli -0.0035	Pusitivu debuli 0.0113	Negativu debuli -0.0659	Negativu debuli -0.0085	Pusitivu debuli 0.0205	Pusitivu debuli 0.0842	Negativu debuli -0.0303
Answer 7	-	Pusitivu debuli 0.0119	Pusitivu debuli 0.0427	Negativu debuli -0.0709	Negativu debuli -0.0287	Pusitivu debuli 0.0477	Pusitivu debuli 0.0655	Negativu debuli -0.0496
Answer 8	-	Pusitivu debuli 0.0639	Pusitivu debuli 0.0832	Negativu debuli -0.0292	Pusitivu debuli 0.0150	Pusitivu debuli 0.0348	Pusitivu debuli 0.0132	Negativu debuli -0.1343
Answer 9	-	Pusitivu debuli 0.0681	Pusitivu debuli 0.1696	Pusitivu debuli 0.0047	Pusitivu debuli 0.0669	Negativu debuli -0.0144	Negativu debuli -0.0506	Negativu debuli -0.1780
Answer 10	-	Pusitivu debuli 0.0770	Pusitivu debuli 0.0736	Negativu debuli -0.0207	Pusitivu debuli 0.0263	Pusitivu debuli 0.0315	Negativu debuli -0.0105	Negativu debuli -0.1289
Answer 11	-	Pusitivu debuli 0.0621	Pusitivu debuli 0.0594	Negativu debuli -0.0051	Pusitivu debuli 0.0080	Pusitivu debuli 0.0176	Pusitivu debuli 0.0238	Negativu debuli -0.1225
Answer 12	-	Pusitivu debuli 0.0424	Pusitivu debuli 0.1016	Negativu debuli -0.0350	Pusitivu debuli 0.0354	Pusitivu debuli 0.0304	Pusitivu debuli 0.0239	Negativu debuli -0.1526
Answer 13	-	Pusitivu debuli 0.0680	Pusitivu debuli 0.1023	Negativu debuli -0.0379	Pusitivu debuli 0.0271	Pusitivu debuli 0.0404	Pusitivu debuli 0.0140	Negativu debuli -0.1620
Answer 14	-	Pusitivu debuli 0.0725	Pusitivu debuli 0.0997	Negativu debuli -0.0033	Negativu debuli -0.0064	Pusitivu debuli 0.0023	Pusitivu debuli 0.0114	Negativu debuli -0.1216
Answer 15	-	Pusitivu debuli 0.0549	Pusitivu debuli 0.1346	Negativu debuli -0.0341	Pusitivu debuli 0.0170	Negativu debuli -0.0195	Pusitivu debuli 0.0208	Negativu debuli -0.1180
Answer 16	-	Pusitivu debuli 0.0666	Pusitivu debuli 0.0287	Negativu debuli -0.0339	Negativu debuli -0.0426	Pusitivu debuli 0.0647	Pusitivu debuli 0.0251	Negativu debuli -0.0746

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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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