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 = 0.033

Distribuzione non normale, di Spearman r = 0.0013

Mostra solo risultati > r = 0.033

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 0.0532	Debole positivo 0.0292	Debole negativo -0.0175	Debole positivo 0.0919	Debole positivo 0.0301	Debole negativo -0.0114	Debole negativo -0.1523
Answer 2	-	Debole positivo 0.0208	Debole negativo -0.0014	Debole negativo -0.0431	Debole positivo 0.0641	Debole positivo 0.0449	Debole positivo 0.0130	Debole negativo -0.0931
Answer 3	-	Debole negativo -0.0053	Debole negativo -0.0130	Debole negativo -0.0406	Debole negativo -0.0456	Debole positivo 0.0474	Debole positivo 0.0793	Debole negativo -0.0204
Answer 4	-	Debole positivo 0.0427	Debole positivo 0.0328	Debole negativo -0.0200	Debole positivo 0.0158	Debole positivo 0.0306	Debole positivo 0.0217	Debole negativo -0.0980
Answer 5	-	Debole positivo 0.0255	Debole positivo 0.1255	Debole positivo 0.0143	Debole positivo 0.0732	Debole negativo -0.0019	Debole negativo -0.0196	Debole negativo -0.1747
Answer 6	-	Debole negativo -0.0027	Debole positivo 0.0074	Debole negativo -0.0629	Debole negativo -0.0074	Debole positivo 0.0199	Debole positivo 0.0835	Debole negativo -0.0324
Answer 7	-	Debole positivo 0.0110	Debole positivo 0.0371	Debole negativo -0.0688	Debole negativo -0.0227	Debole positivo 0.0471	Debole positivo 0.0650	Debole negativo -0.0523
Answer 8	-	Debole positivo 0.0693	Debole positivo 0.0825	Debole negativo -0.0321	Debole positivo 0.0139	Debole positivo 0.0351	Debole positivo 0.0147	Debole negativo -0.1369
Answer 9	-	Debole positivo 0.0643	Debole positivo 0.1659	Debole positivo 0.0082	Debole positivo 0.0699	Debole negativo -0.0136	Debole negativo -0.0513	Debole negativo -0.1826
Answer 10	-	Debole positivo 0.0760	Debole positivo 0.0730	Debole negativo -0.0219	Debole positivo 0.0254	Debole positivo 0.0318	Debole negativo -0.0138	Debole negativo -0.1318
Answer 11	-	Debole positivo 0.0571	Debole positivo 0.0514	Debole negativo -0.0099	Debole positivo 0.0077	Debole positivo 0.0206	Debole positivo 0.0308	Debole negativo -0.1211
Answer 12	-	Debole positivo 0.0373	Debole positivo 0.1013	Debole negativo -0.0357	Debole positivo 0.0357	Debole positivo 0.0243	Debole positivo 0.0296	Debole negativo -0.1524
Answer 13	-	Debole positivo 0.0621	Debole positivo 0.1036	Debole negativo -0.0438	Debole positivo 0.0273	Debole positivo 0.0414	Debole positivo 0.0176	Debole negativo -0.1608
Answer 14	-	Debole positivo 0.0703	Debole positivo 0.1007	Debole positivo 9.54E-5	Debole negativo -0.0088	Debole negativo -0.0011	Debole positivo 0.0084	Debole negativo -0.1174
Answer 15	-	Debole positivo 0.0554	Debole positivo 0.1349	Debole negativo -0.0418	Debole positivo 0.0179	Debole negativo -0.0165	Debole positivo 0.0219	Debole negativo -0.1181
Answer 16	-	Debole positivo 0.0581	Debole positivo 0.0255	Debole negativo -0.0388	Debole negativo -0.0407	Debole positivo 0.0654	Debole positivo 0.0283	Debole negativo -0.0714

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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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