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) 先月の人事に関する企業の行動（はい /いいえ）

2) 先月の職員に関連した企業の行動（％の場合）

3) 恐ろしい

4) 私の国が直面している最大の問題

5) 成功したチームを構築する際に、優れたリーダーがどのような資質と能力を使用していますか？

6) グーグル。チームの効率性に影響を与える要因

7) 求職者の主な優先事項

8) 何が上司を偉大なリーダーにしているのですか？

9) 何が人々を仕事で成功させるのですか？

10) リモートで仕事をするために少ない給料を受け取る準備はできていますか？

15) 人々があきらめる理由（アンナビタルによる）

16) 信頼 (#WVS)

17) オックスフォード幸福調査

18) 心理的幸福

19) あなたの次の最もエキサイティングな機会はどこにありますか？

20) あなたはあなたの精神的健康の世話をするために今週何をしますか？

21) 私は自分の過去、現在、または未来について考えて住んでいます

22) 功績

23) 人工知能と文明の終わり

24) なぜ人々は先延ばしになるのですか？

25) 自信の構築における性差（ifd allensbach）

26) xing.com文化評価

27) パトリック・レンシオーニの「チームの5つの機能不全」

28) 共感は...

29) ITスペシャリストが求人を選択するのに不可欠なことは何ですか？

30) 人々が変化に抵抗する理由（SiobhánMChaleによる）

31) 感情をどのように調節しますか？（Nawal Mustafa M.A.

32) あなたに永遠に支払う21スキル（エレミヤ・テオ /赵汉昇）

33) 本当の自由は...

34) 他の人との信頼を築くための12の方法（ジャスティンライトによる）

35) 才能のある従業員の特徴（Talent Management Instituteによる）

36) チームをやる気にさせるための10のキー

37) 良心の代数 (ウラジミール・ルフェーブル著)

38) 未来の 3 つの異なる可能性 (クレア W. グレイブス博士著)

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.

恐ろしい

チャート相関

VUCA

相関係数の臨界値

ウィリアム・シーリー・ゴセット（学生）による正規分布 r = 0.033

スピアマンによる非正規分布 r = 0.0013

結果のみを表示します > r = 0.033

分布	非正常	非正常	非正常	普通	普通	普通	普通	普通
すべての質問すべての質問私の最大の恐れは
私の最大の恐れは
Answer 1	-	弱いポジティブ 0.0558	弱いポジティブ 0.0313	弱いネガティブ -0.0163	弱いポジティブ 0.0916	弱いポジティブ 0.0302	弱いネガティブ -0.0128	弱いネガティブ -0.1543
Answer 2	-	弱いポジティブ 0.0228	弱いネガティブ -0.0008	弱いネガティブ -0.0444	弱いポジティブ 0.0633	弱いポジティブ 0.0452	弱いポジティブ 0.0131	弱いネガティブ -0.0941
Answer 3	-	弱いネガティブ -0.0029	弱いネガティブ -0.0120	弱いネガティブ -0.0413	弱いネガティブ -0.0466	弱いポジティブ 0.0471	弱いポジティブ 0.0784	弱いネガティブ -0.0197
Answer 4	-	弱いポジティブ 0.0438	弱いポジティブ 0.0343	弱いネガティブ -0.0203	弱いポジティブ 0.0152	弱いポジティブ 0.0311	弱いポジティブ 0.0204	弱いネガティブ -0.0978
Answer 5	-	弱いポジティブ 0.0305	弱いポジティブ 0.1279	弱いポジティブ 0.0130	弱いポジティブ 0.0732	弱いネガティブ -0.0002	弱いネガティブ -0.0204	弱いネガティブ -0.1756
Answer 6	-	弱いネガティブ -0.0007	弱いポジティブ 0.0076	弱いネガティブ -0.0634	弱いネガティブ -0.0077	弱いポジティブ 0.0195	弱いポジティブ 0.0833	弱いネガティブ -0.0310
Answer 7	-	弱いポジティブ 0.0120	弱いポジティブ 0.0377	弱いネガティブ -0.0696	弱いネガティブ -0.0237	弱いポジティブ 0.0472	弱いポジティブ 0.0644	弱いネガティブ -0.0512
Answer 8	-	弱いポジティブ 0.0699	弱いポジティブ 0.0852	弱いネガティブ -0.0331	弱いポジティブ 0.0147	弱いポジティブ 0.0347	弱いポジティブ 0.0132	弱いネガティブ -0.1366
Answer 9	-	弱いポジティブ 0.0670	弱いポジティブ 0.1684	弱いポジティブ 0.0088	弱いポジティブ 0.0687	弱いネガティブ -0.0130	弱いネガティブ -0.0520	弱いネガティブ -0.1823
Answer 10	-	弱いポジティブ 0.0781	弱いポジティブ 0.0752	弱いネガティブ -0.0216	弱いポジティブ 0.0249	弱いポジティブ 0.0349	弱いネガティブ -0.0132	弱いネガティブ -0.1300
Answer 11	-	弱いポジティブ 0.0580	弱いポジティブ 0.0526	弱いネガティブ -0.0095	弱いポジティブ 0.0083	弱いポジティブ 0.0204	弱いポジティブ 0.0307	弱いネガティブ -0.1196
Answer 12	-	弱いポジティブ 0.0391	弱いポジティブ 0.1039	弱いネガティブ -0.0361	弱いポジティブ 0.0357	弱いポジティブ 0.0256	弱いポジティブ 0.0295	弱いネガティブ -0.1522
Answer 13	-	弱いポジティブ 0.0647	弱いポジティブ 0.1042	弱いネガティブ -0.0439	弱いポジティブ 0.0261	弱いポジティブ 0.0425	弱いポジティブ 0.0173	弱いネガティブ -0.1602
Answer 14	-	弱いポジティブ 0.0713	弱いポジティブ 0.1028	弱いネガティブ -0.0008	弱いネガティブ -0.0090	弱いネガティブ -0.0006	弱いポジティブ 0.0084	弱いネガティブ -0.1173
Answer 15	-	弱いポジティブ 0.0556	弱いポジティブ 0.1363	弱いネガティブ -0.0433	弱いポジティブ 0.0179	弱いネガティブ -0.0155	弱いポジティブ 0.0223	弱いネガティブ -0.1176
Answer 16	-	弱いポジティブ 0.0592	弱いポジティブ 0.0270	弱いネガティブ -0.0386	弱いネガティブ -0.0401	弱いポジティブ 0.0657	弱いポジティブ 0.0282	弱いネガティブ -0.0708

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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

プロダクトオーナーSaaS PetProjectSdtest®

Valeriiは、1993年に社会教育教師の心理学者としての資格があり、その後、プロジェクト管理に関する知識を適用しています。
Valeriiは2013年に修士号とプロジェクトおよびプログラムマネージャーの資格を取得しました。修士課程のプログラムで、彼はプロジェクトロードマップ（GPM DeutscheGesellschaftFürProjektmanagemente。V。）とスパイラルダイナミクスに精通しました。
Valeriiはさまざまなスパイラルダイナミクステストを受け、彼の知識と経験を使用して、現在のバージョンのSDTestを適応させました。
Valeriiは、V.U.C.Aの不確実性を調査する著者です。精神学におけるスパイラルダイナミクスと数学統計を使用した概念、20を超える国際的な世論調査。

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