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

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 = 0.0353

Distribuzione non Normale, da Bearman r = 0.0014

Mostra solu risultati > r = 0.0353

Distribuzione	Non normale	Nurmale	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 0.0297	Pusitivu debuli 0.0298	Negativu debuli -0.0106	Pusitivu debuli 0.0970	Pusitivu debuli 0.0325	Negativu debuli -0.0019	Negativu debuli -0.1558
Answer 2	-	Pusitivu debuli 0.0188	Pusitivu debuli 0.0076	Negativu debuli -0.0360	Pusitivu debuli 0.0711	Pusitivu debuli 0.0387	Pusitivu debuli 0.0082	Negativu debuli -0.1011
Answer 3	-	Pusitivu debuli 0.0026	Negativu debuli -0.0170	Negativu debuli -0.0443	Negativu debuli -0.0458	Pusitivu debuli 0.0547	Pusitivu debuli 0.0808	Negativu debuli -0.0270
Answer 4	-	Pusitivu debuli 0.0332	Pusitivu debuli 0.0285	Negativu debuli -0.0006	Pusitivu debuli 0.0155	Pusitivu debuli 0.0276	Pusitivu debuli 0.0105	Negativu debuli -0.0917
Answer 5	-	Pusitivu debuli 0.0122	Pusitivu debuli 0.1193	Pusitivu debuli 0.0095	Pusitivu debuli 0.0721	Pusitivu debuli 0.0057	Negativu debuli -0.0083	Negativu debuli -0.1687
Answer 6	-	Pusitivu debuli 0.0044	Pusitivu debuli 0.0005	Negativu debuli -0.0582	Negativu debuli -0.0004	Pusitivu debuli 0.0210	Pusitivu debuli 0.0830	Negativu debuli -0.0418
Answer 7	-	Pusitivu debuli 0.0242	Pusitivu debuli 0.0368	Negativu debuli -0.0521	Negativu debuli -0.0234	Pusitivu debuli 0.0403	Pusitivu debuli 0.0568	Negativu debuli -0.0597
Answer 8	-	Pusitivu debuli 0.0707	Pusitivu debuli 0.0781	Negativu debuli -0.0244	Pusitivu debuli 0.0140	Pusitivu debuli 0.0303	Pusitivu debuli 0.0137	Negativu debuli -0.1334
Answer 9	-	Pusitivu debuli 0.0564	Pusitivu debuli 0.1531	Pusitivu debuli 0.0127	Pusitivu debuli 0.0769	Negativu debuli -0.0136	Negativu debuli -0.0495	Negativu debuli -0.1752
Answer 10	-	Pusitivu debuli 0.0711	Pusitivu debuli 0.0700	Negativu debuli -0.0127	Pusitivu debuli 0.0246	Pusitivu debuli 0.0363	Negativu debuli -0.0156	Negativu debuli -0.1273
Answer 11	-	Pusitivu debuli 0.0542	Pusitivu debuli 0.0488	Pusitivu debuli 0.0086	Pusitivu debuli 0.0078	Pusitivu debuli 0.0162	Pusitivu debuli 0.0315	Negativu debuli -0.1248
Answer 12	-	Pusitivu debuli 0.0281	Pusitivu debuli 0.0929	Negativu debuli -0.0325	Pusitivu debuli 0.0361	Pusitivu debuli 0.0276	Pusitivu debuli 0.0365	Negativu debuli -0.1482
Answer 13	-	Pusitivu debuli 0.0643	Pusitivu debuli 0.0916	Negativu debuli -0.0418	Pusitivu debuli 0.0237	Pusitivu debuli 0.0425	Pusitivu debuli 0.0239	Negativu debuli -0.1558
Answer 14	-	Pusitivu debuli 0.0697	Pusitivu debuli 0.1017	Pusitivu debuli 0.0149	Negativu debuli -0.0062	Negativu debuli -0.0087	Negativu debuli -0.0002	Negativu debuli -0.1161
Answer 15	-	Pusitivu debuli 0.0603	Pusitivu debuli 0.1299	Negativu debuli -0.0379	Pusitivu debuli 0.0163	Negativu debuli -0.0091	Pusitivu debuli 0.0164	Negativu debuli -0.1204
Answer 16	-	Pusitivu debuli 0.0691	Pusitivu debuli 0.0221	Negativu debuli -0.0305	Negativu debuli -0.0515	Pusitivu debuli 0.0750	Pusitivu debuli 0.0187	Negativu debuli -0.0696

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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

U pruprietariu di u produttu Saas Project prugettu SDTEST®

Valerii hè stata qualificata cum'è psicologu suciale in u 1993 è hà dapulu chì a so cunniscenza in a gestione di u prugettu.
Valerii ottenutu un masturatu è u prugettu è u prugettu di u spettore, diventò fami (GPM deutsche Roadmaft per T. V.) è Dì Spitchenje.
Valerii hà pigliatu parechji testi di dinaghjicati Superali è utilizonu a so cunniscenza è l'esperienza per adattà a versione attuale di Sdtest.
Valerii hè l'autore di spiegà l'incertezza di u v.u.c.a. cuncettu utilizendu statistiche spreal Dìmiche è statistiche matematiche in psicologia, più di 20 sondaghji internaziunali.

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