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) 上个月与人员有关的公司的行动（是 /否）

2) 公司在上个月内与人员有关的行动（事实为％）

3) 恐惧

4) 我国家面临的最大问题

5) 建立成功的团队时，好的领导者会使用哪些素质和能力？

10) 您准备好获得更少的薪水远程工作吗？

15) 人们放弃的原因（Anna Vital）

16) 相信 (#WVS)

17) 牛津幸福调查

18) 心理健康

19) 您的下一个最激动人心的机会将在哪里？

20) 您本周将做些什么来照顾您的心理健康？

21) 我生活在思考我的过去，现在或将来

22) 精英制

23) 人工智能和文明的终结

24) 人们为什么拖延？

25) 建立自信的性别差异（IFD Allensbach）

26) XING.COM文化评估

27) 帕特里克·林奇尼（Patrick Lencioni）的“团队的五个功能障碍”

28) 移情是...

29) IT专家选择工作机会的必不可少？

30) 为什么人们抵制变化（SiobhánMchale作者）

31) 您如何调节情绪？（由Nawal Mustafa M.A.）

32) 21个永远付给您的技能（由Jeremiah Teo /赵汉升）

33) 真正的自由是...

34) 与他人建立信任的12种方法（贾斯汀·赖特（Justin Wright））

35) 才华横溢的员工的特征（人才管理学院）

36) 激励团队的10个关键

37) 良心代数（弗拉基米尔·列斐伏尔）

38) 未来的三种不同的可能性（作者：Clare W. Graves 博士）

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.

恐惧

圖表相关性

VUCA

的相关系数的临界值

正态分布，威廉·西莉·格塞特（William Sealy Gosset）（学生） r = 0.0331

非正态分布，Spearman r = 0.0013

仅显示结果 > r = 0.0331

分配	非正常	非正常	非正常	普通的	普通的	普通的	普通的	普通的
所有问题所有问题我最大的恐惧是
我最大的恐惧是
Answer 1	-	弱阳性 0.0535	弱阳性 0.0288	弱负 -0.0174	弱阳性 0.0904	弱阳性 0.0307	弱负 -0.0109	弱负 -0.1518
Answer 2	-	弱阳性 0.0195	弱阳性 0.0002	弱负 -0.0444	弱阳性 0.0669	弱阳性 0.0443	弱阳性 0.0114	弱负 -0.0932
Answer 3	-	弱负 -0.0055	弱负 -0.0112	弱负 -0.0412	弱负 -0.0443	弱阳性 0.0469	弱阳性 0.0786	弱负 -0.0212
Answer 4	-	弱阳性 0.0426	弱阳性 0.0344	弱负 -0.0185	弱阳性 0.0156	弱阳性 0.0302	弱阳性 0.0199	弱负 -0.0984
Answer 5	-	弱阳性 0.0249	弱阳性 0.1242	弱阳性 0.0138	弱阳性 0.0722	弱负 -0.0009	弱负 -0.0194	弱负 -0.1732
Answer 6	-	弱负 -0.0026	弱阳性 0.0080	弱负 -0.0627	弱负 -0.0066	弱阳性 0.0196	弱阳性 0.0828	弱负 -0.0331
Answer 7	-	弱阳性 0.0109	弱阳性 0.0376	弱负 -0.0680	弱负 -0.0224	弱阳性 0.0471	弱阳性 0.0638	弱负 -0.0526
Answer 8	-	弱阳性 0.0696	弱阳性 0.0832	弱负 -0.0308	弱阳性 0.0140	弱阳性 0.0349	弱阳性 0.0136	弱负 -0.1377
Answer 9	-	弱阳性 0.0642	弱阳性 0.1662	弱阳性 0.0096	弱阳性 0.0698	弱负 -0.0135	弱负 -0.0531	弱负 -0.1825
Answer 10	-	弱阳性 0.0756	弱阳性 0.0718	弱负 -0.0196	弱阳性 0.0228	弱阳性 0.0329	弱负 -0.0144	弱负 -0.1308
Answer 11	-	弱阳性 0.0578	弱阳性 0.0516	弱负 -0.0105	弱阳性 0.0079	弱阳性 0.0205	弱阳性 0.0310	弱负 -0.1215
Answer 12	-	弱阳性 0.0363	弱阳性 0.1005	弱负 -0.0354	弱阳性 0.0348	弱阳性 0.0255	弱阳性 0.0295	弱负 -0.1514
Answer 13	-	弱阳性 0.0620	弱阳性 0.1036	弱负 -0.0456	弱阳性 0.0269	弱阳性 0.0420	弱阳性 0.0185	弱负 -0.1601
Answer 14	-	弱阳性 0.0710	弱阳性 0.1018	弱阳性 0.0009	弱负 -0.0087	弱负 -0.0015	弱阳性 0.0070	弱负 -0.1179
Answer 15	-	弱阳性 0.0548	弱阳性 0.1365	弱负 -0.0408	弱阳性 0.0182	弱负 -0.0166	弱阳性 0.0205	弱负 -0.1186
Answer 16	-	弱阳性 0.0581	弱阳性 0.0259	弱负 -0.0390	弱负 -0.0403	弱阳性 0.0652	弱阳性 0.0279	弱负 -0.0716

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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

产品所有者SaaS宠物项目SDTEST®

Valeri于1993年获得社会教育心理学家资格，并将其知识应用于项目管理。
Valeri于2013年获得硕士学位以及项目和项目经理资格。在硕士课程期间，他熟悉了项目路线图（GPM Deutsche Gesellschaft für Projektmanagement e.V.）和螺旋动力学。
Valeri参加了各种螺旋动力学测试，并利用他的知识和经验调整了当前版本的SDTEST。
Valeri在20多项国际民意调查中，利用螺旋动力学和心理学数理统计，探索了V.U.C.A.概念的不确定性。

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