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) 지난 달 직원과 관련하여 회사의 행동 (예 / 아니오)

2) 지난 달의 인원과 관련하여 회사의 행동 (사실 %)

3) 두려움

4) 우리나라가 직면 한 가장 큰 문제

5) 성공적인 팀을 구성 할 때 훌륭한 리더는 어떤 자질과 능력을 사용합니까?

6) Google. 팀 효율성에 영향을 미치는 요인

7) 구직자의 주요 우선 순위

8) 상사를 위대한 지도자로 만드는 이유는 무엇입니까?

9) 사람들이 직장에서 성공하게 만드는 이유는 무엇입니까?

10) 원격으로 일할 수있는 임금을 적게받을 준비가 되셨습니까?

15) 사람들이 포기하는 이유 (Anna Vital)

16) 신뢰하다 (#WVS)

17) 옥스포드 행복 설문 조사

18) 심리적 안녕

19) 다음으로 가장 흥미 진진한 기회는 어디에 있습니까?

20) 이번 주에 정신 건강을 돌보기 위해 무엇을 하시겠습니까?

21) 나는 내 과거, 현재 또는 미래에 대해 생각하고 산다

22) 메리 토크 라시

23) 인공 지능과 문명의 끝

24) 사람들은 왜 미루는가?

25) 자신감 구축의 성별 차이 (IFD Allensbach)

26) Xing.com 문화 평가

27) Patrick Lencioni의 "팀의 5 가지 기능 장애"

28) 공감은 ...

29) IT 전문가가 구인 제안을 선택하는 데 필수적인 점은 무엇입니까?

30) 사람들이 변화에 저항하는 이유 (Siobhán McHale)

31) 감정을 어떻게 조절합니까? (Nawal Mustafa M.A.)

32) 영원히 당신에게 지불하는 21 기술 (예레미야 테오 / 赵汉昇)

33) 진정한 자유는 ...

34) 다른 사람과의 신뢰를 구축하는 12 가지 방법 (저스틴 라이트)

35) 재능있는 직원의 특성 (Talent Management Institute의)

36) 팀 동기를 부여하는 10 개의 열쇠

37) 양심 대수학(블라디미르 르페브르 저)

38) 미래의 세 가지 뚜렷한 가능성(Clare W. Graves 박사 저)

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.

두려움

차트 상관 관계

VUCA

상관 계수의 임계 값

William Sealy Gosset (학생)의 정규 분포 r = 0.0335

Spearman에 의한 비 정규 분포 r = 0.0014

결과 만 보여줍니다 > r = 0.0335

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

제품 소유자 Saas Pet Project SDTest®

Valerii는 1993 년에 사회 교육학 심리학자로 자격을 얻었으며 이후 프로젝트 관리에 대한 지식을 적용했습니다.
Valerii는 2013 년 석사 학위 및 프로젝트 및 프로그램 관리자 자격을 취득했습니다. 그의 석사 프로그램에서 그는 Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) 및 나선형 역학에 익숙해졌습니다.
Valerii는 다양한 나선 역학 테스트를 수행했으며 그의 지식과 경험을 사용하여 현재 버전의 SDTest를 조정했습니다.
Valerii는 V.U.C.A.의 불확실성을 탐구하는 저자입니다. 심리학에서 나선형 역학 및 수학적 통계를 사용한 개념, 20 개 이상의 국제 여론 조사.

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