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) Ações das empresas em relação ao pessoal no último mês (sim / não)

2) Ações de empresas em relação ao pessoal no último mês (fato em%)

3) Medos

4) Maiores problemas enfrentados pelo meu país

5) Quais qualidades e habilidades os bons líderes usam ao criar equipes de sucesso?

6) Google. Fatores que afetam a eficácia da equipe

7) As principais prioridades dos candidatos a emprego

8) O que faz de um chefe um grande líder?

9) O que faz as pessoas bem -sucedidas no trabalho?

10) Você está pronto para receber menos pagamento para trabalhar remotamente?

11) O envelhecimento existe?

12) Envelhecimento na carreira

13) Envelhecimento na vida

14) Causas do envelhecimento

15) Razões pelas quais as pessoas desistem (de Anna Vital)

16) CONFIAR EM (#WVS)

17) Pesquisa de Felicidade de Oxford

18) Bem -estar psicológico

19) Onde seria sua próxima oportunidade mais emocionante?

20) O que você fará esta semana para cuidar de sua saúde mental?

21) Eu vivo pensando no meu passado, presente ou futuro

22) Meritocracia

23) Inteligência artificial e o fim da civilização

24) Por que as pessoas procrastinam?

25) Diferença de gênero na construção da autoconfiança (Ifd Allensbach)

26) Xing.com avaliação da cultura

27) Patrick Lencioni "As Cinco Disfunções de uma equipe"

28) Empatia é ...

29) O que é essencial para os especialistas em TI na escolha de uma oferta de emprego?

30) Por que as pessoas resistem à mudança (por Siobhán McHale)

31) Como você regular suas emoções? (Por Nawal Mustafa M.A.)

32) 21 Habilidades que pagam para sempre (por Jeremiah Teo / 赵汉昇)

33) A verdadeira liberdade é ...

34) 12 maneiras de construir confiança com outras pessoas (de Justin Wright)

35) Características de um funcionário talentoso (pelo Instituto de Gerenciamento de Talentos)

36) 10 chaves para motivar sua equipe

37) Álgebra da Consciência (por Vladimir Lefebvre)

38) Três possibilidades distintas do futuro (por Dra. 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.

Medos

charts Correlação

VUCA

O valor crítico do coeficiente de correlação

Distribuição normal, de William Sealy Gosset (aluno) r = 0.0331

Distribuição não normal, por Spearman r = 0.0013

Mostrar apenas resultados > r = 0.0331

Distribuição	Não normal	Não normal	Não normal	Normal	Normal	Normal	Normal	Normal
Todas as perguntas Todas as perguntas Meu maior medo é
Meu maior medo é
Answer 1	-	Fraco positivo 0.0562	Fraco positivo 0.0311	Negativo fraco -0.0164	Fraco positivo 0.0903	Fraco positivo 0.0301	Negativo fraco -0.0120	Negativo fraco -0.1534
Answer 2	-	Fraco positivo 0.0217	Fraco positivo 0.0011	Negativo fraco -0.0455	Fraco positivo 0.0660	Fraco positivo 0.0440	Fraco positivo 0.0117	Negativo fraco -0.0942
Answer 3	-	Negativo fraco -0.0034	Negativo fraco -0.0104	Negativo fraco -0.0419	Negativo fraco -0.0451	Fraco positivo 0.0462	Fraco positivo 0.0780	Negativo fraco -0.0204
Answer 4	-	Fraco positivo 0.0436	Fraco positivo 0.0362	Negativo fraco -0.0177	Fraco positivo 0.0150	Fraco positivo 0.0296	Fraco positivo 0.0189	Negativo fraco -0.0984
Answer 5	-	Fraco positivo 0.0298	Fraco positivo 0.1270	Fraco positivo 0.0133	Fraco positivo 0.0724	Negativo fraco -0.0002	Negativo fraco -0.0199	Negativo fraco -0.1742
Answer 6	-	Negativo fraco -0.0003	Fraco positivo 0.0089	Negativo fraco -0.0627	Negativo fraco -0.0074	Fraco positivo 0.0190	Fraco positivo 0.0825	Negativo fraco -0.0321
Answer 7	-	Fraco positivo 0.0123	Fraco positivo 0.0388	Negativo fraco -0.0684	Negativo fraco -0.0238	Fraco positivo 0.0468	Fraco positivo 0.0631	Negativo fraco -0.0517
Answer 8	-	Fraco positivo 0.0699	Fraco positivo 0.0857	Negativo fraco -0.0318	Fraco positivo 0.0150	Fraco positivo 0.0341	Fraco positivo 0.0125	Negativo fraco -0.1372
Answer 9	-	Fraco positivo 0.0666	Fraco positivo 0.1681	Fraco positivo 0.0094	Fraco positivo 0.0694	Negativo fraco -0.0131	Negativo fraco -0.0533	Negativo fraco -0.1815
Answer 10	-	Fraco positivo 0.0776	Fraco positivo 0.0744	Negativo fraco -0.0185	Fraco positivo 0.0224	Fraco positivo 0.0352	Negativo fraco -0.0135	Negativo fraco -0.1293
Answer 11	-	Fraco positivo 0.0585	Fraco positivo 0.0531	Negativo fraco -0.0094	Fraco positivo 0.0086	Fraco positivo 0.0195	Fraco positivo 0.0313	Negativo fraco -0.1200
Answer 12	-	Fraco positivo 0.0378	Fraco positivo 0.1030	Negativo fraco -0.0357	Fraco positivo 0.0350	Fraco positivo 0.0261	Fraco positivo 0.0297	Negativo fraco -0.1510
Answer 13	-	Fraco positivo 0.0642	Fraco positivo 0.1044	Negativo fraco -0.0454	Fraco positivo 0.0259	Fraco positivo 0.0424	Fraco positivo 0.0183	Negativo fraco -0.1595
Answer 14	-	Fraco positivo 0.0718	Fraco positivo 0.1034	Negativo fraco -0.0003	Negativo fraco -0.0085	Negativo fraco -0.0016	Fraco positivo 0.0074	Negativo fraco -0.1172
Answer 15	-	Fraco positivo 0.0550	Fraco positivo 0.1382	Negativo fraco -0.0418	Fraco positivo 0.0181	Negativo fraco -0.0163	Fraco positivo 0.0211	Negativo fraco -0.1183
Answer 16	-	Fraco positivo 0.0591	Fraco positivo 0.0276	Negativo fraco -0.0384	Negativo fraco -0.0397	Fraco positivo 0.0651	Fraco positivo 0.0280	Negativo fraco -0.0710

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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

Proprietário do produto SaaS Pet Project Sdtest®

Valerii foi qualificado como psicólogo social de pedagogo em 1993 e, desde então, aplicou seu conhecimento em gerenciamento de projetos.
Valerii obteve um mestrado e a qualificação do gerente do projeto e do programa em 2013. Durante o programa de mestrado, ele se familiarizou com o Roteiro do Projeto (GPM Deutsche Gesellschaft für projektmanagement e. V.) e dinâmica em espiral.
Valerii fez vários testes de dinâmica em espiral e usou seu conhecimento e experiência para adaptar a versão atual do SDTEST.
Valerii é o autor de explorar a incerteza do V.U.C.A. Conceito usando dinâmica espiral e estatística matemática em psicologia, mais de 20 pesquisas internacionais.

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