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 = 0.0335

スピアマンによる非正規分布 r = 0.0014

結果のみを表示します > r = 0.0335

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

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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