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 = 0.0335

Distribuição não normal, por Spearman r = 0.0014

Mostrar apenas resultados > r = 0.0335

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

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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