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) Azioni delle società in relazione al personale nell'ultimo mese (sì / no)

2) Azioni delle aziende in relazione al personale nell'ultimo mese (fatto in%)

3) Paure

4) Maggiori problemi che affrontano il mio paese

5) Quali qualità e abilità utilizzano buoni leader quando si costruiscono squadre di successo?

6) Google. Fattori che incidono sull'efficatività della squadra

7) Le principali priorità delle persone in cerca di lavoro

8) Cosa rende un capo un grande leader?

9) Cosa rende le persone di successo sul lavoro?

10) Sei pronto a ricevere meno paga per lavorare in remoto?

11) Esiste l'età?

12) Ageismo in carriera

13) Ageismo nella vita

14) Cause di età

15) Motivi per cui le persone si arrendono (di Anna Vital)

16) FIDUCIA (#WVS)

17) Oxford Happiness Survey

18) Benessere psicologico

19) Dove sarebbe la tua prossima opportunità più eccitante?

20) Cosa farai questa settimana per occuparti della tua salute mentale?

21) Vivo a pensare al mio passato, presente o futuro

22) Meritocrazia

23) Intelligenza artificiale e fine della civiltà

24) Perché le persone procrastinano?

25) Differenza di genere nella costruzione della fiducia in se stessi (IFD Allensbach)

26) Xing.com VALUTAZIONE CULTURA

27) Le cinque disfunzioni di una squadra di Patrick Lencioni

28) L'empatia è ...

29) Cosa è essenziale per gli specialisti IT nella scelta di un'offerta di lavoro?

30) Perché le persone resistono al cambiamento (di Siobhán McHale)

31) Come regolano le tue emozioni? (di Nawal Mustafa M.A.)

32) 21 abilità che ti pagano per sempre (di Jeremiah Teo / 赵汉昇)

33) La vera libertà è ...

34) 12 modi per costruire la fiducia con gli altri (di Justin Wright)

35) Caratteristiche di un dipendente di talento (del Talent Management Institute)

36) 10 chiavi per motivare la tua squadra

37) Algebra della coscienza (di Vladimir Lefebvre)

38) Tre distinte possibilità del futuro (della Dott.ssa 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.

Paure

Grafici Correlazione

VUCA

Valore critico del coefficiente di correlazione

Distribuzione normale, di William Sealy Gosset (Studente) r = 0.0335

Distribuzione non normale, di Spearman r = 0.0014

Mostra solo risultati > r = 0.0335

Distribuzione	Non normale	Non normale	Non normale	Normale	Normale	Normale	Normale	Normale
Tutte le domande Tutte le domande La mia più grande paura è
La mia più grande paura è
Answer 1	-	Debole positivo 0.0521	Debole positivo 0.0294	Debole negativo -0.0147	Debole positivo 0.0885	Debole positivo 0.0316	Debole negativo -0.0110	Debole negativo -0.1513
Answer 2	-	Debole positivo 0.0213	Debole positivo 0.0013	Debole negativo -0.0432	Debole positivo 0.0618	Debole positivo 0.0453	Debole positivo 0.0103	Debole negativo -0.0918
Answer 3	-	Debole negativo -0.0042	Debole negativo -0.0116	Debole negativo -0.0406	Debole negativo -0.0477	Debole positivo 0.0487	Debole positivo 0.0767	Debole negativo -0.0191
Answer 4	-	Debole positivo 0.0421	Debole positivo 0.0350	Debole negativo -0.0115	Debole positivo 0.0112	Debole positivo 0.0307	Debole positivo 0.0175	Debole negativo -0.0980
Answer 5	-	Debole positivo 0.0288	Debole positivo 0.1272	Debole positivo 0.0146	Debole positivo 0.0697	Debole positivo 0.0037	Debole negativo -0.0215	Debole negativo -0.1746
Answer 6	-	Debole negativo -0.0001	Debole positivo 0.0042	Debole negativo -0.0607	Debole negativo -0.0115	Debole positivo 0.0231	Debole positivo 0.0826	Debole negativo -0.0309
Answer 7	-	Debole positivo 0.0117	Debole positivo 0.0372	Debole negativo -0.0653	Debole negativo -0.0283	Debole positivo 0.0495	Debole positivo 0.0626	Debole negativo -0.0505
Answer 8	-	Debole positivo 0.0658	Debole positivo 0.0830	Debole negativo -0.0310	Debole positivo 0.0139	Debole positivo 0.0334	Debole positivo 0.0134	Debole negativo -0.1322
Answer 9	-	Debole positivo 0.0660	Debole positivo 0.1658	Debole positivo 0.0051	Debole positivo 0.0691	Debole negativo -0.0093	Debole negativo -0.0498	Debole negativo -0.1820
Answer 10	-	Debole positivo 0.0758	Debole positivo 0.0724	Debole negativo -0.0173	Debole positivo 0.0236	Debole positivo 0.0312	Debole negativo -0.0115	Debole negativo -0.1263
Answer 11	-	Debole positivo 0.0577	Debole positivo 0.0544	Debole negativo -0.0075	Debole positivo 0.0082	Debole positivo 0.0185	Debole positivo 0.0293	Debole negativo -0.1190
Answer 12	-	Debole positivo 0.0376	Debole positivo 0.1007	Debole negativo -0.0342	Debole positivo 0.0296	Debole positivo 0.0273	Debole positivo 0.0341	Debole negativo -0.1500
Answer 13	-	Debole positivo 0.0627	Debole positivo 0.1017	Debole negativo -0.0443	Debole positivo 0.0248	Debole positivo 0.0434	Debole positivo 0.0189	Debole negativo -0.1576
Answer 14	-	Debole positivo 0.0732	Debole positivo 0.1036	Debole positivo 0.0048	Debole negativo -0.0105	Debole negativo -0.0039	Debole positivo 0.0041	Debole negativo -0.1157
Answer 15	-	Debole positivo 0.0539	Debole positivo 0.1381	Debole negativo -0.0424	Debole positivo 0.0163	Debole negativo -0.0147	Debole positivo 0.0216	Debole negativo -0.1173
Answer 16	-	Debole positivo 0.0590	Debole positivo 0.0274	Debole negativo -0.0375	Debole negativo -0.0429	Debole positivo 0.0687	Debole positivo 0.0253	Debole negativo -0.0698

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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

Product Owner SaaS Pet Project Sdtest®

Valerii è stato qualificato come social pedagogo-psicologo nel 1993 e da allora ha applicato le sue conoscenze nella gestione del progetto.
Valerii ha conseguito una laurea in Master e la qualifica del Progetto e del Programma nel 2013. Durante il programma del suo Master, ha acquisito familiarità con il progetto Roadmap (GPM Deutsche Gesellschaft Für Projektmanagement e. V.) e Spiral Dynamics.
Valerii ha fatto vari test di dinamica a spirale e ha usato la sua conoscenza ed esperienza per adattare la versione attuale di SDTest.
Valerii è l'autore di esplorare l'incertezza del V.U.C.A. Concetto usando le dinamiche a spirale e le statistiche matematiche in psicologia, più di 20 sondaggi internazionali.

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