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) په تیره میاشت کې د پرسونل په تړاو د شرکتونو عمل (هو / نه)

2) په تیره میاشت کې د پرسونل په تړاو د شرکتونو عمل (حقیقت په٪)

3) ویره

4) زما د هیواد په وړاندې ترټولو لوی مشکلات

5) کوم خصوصیات او وړتیاوې د بریالي ټیمونو جوړولو پر مهال ښه مشران کاروي؟

6) Google. فاکتورونه چې د ټیم EFFINT باندې تاثیر کوي

7) د دندو لټون کونکو اصلي لومړیتوبونه

8) کوم شی یو عالي مشر رامینځته کوي؟

9) څه خلک په کار کې بریالي کوي؟

10) ایا تاسو چمتو یاست چې د لرې ځای لپاره لږ معاش ترلاسه کړئ؟

11) ایا اتمال شتون لري؟

12) عظایف په مسلک کې

13) په ژوند کې اجتماعده

14) د عذاب لاملونه

15) لاملونه ولې خلک پریږدي (د انا حیاتي لخوا)

16) باور (#WVS)

17) د اکسفورډ خوښۍ سروې

18) رواني هوساینې

19) ستاسو راتلونکی په زړه پوری فرصت دی؟

20) تاسو به پدې اونۍ کې د خپل رواني روغتیا څارلو لپاره څه وکړئ؟

21) زه د خپل تیر، اوسني یا راتلونکي په اړه فکر کوم

22) متبادیکسیس

23) مصنوعي استخبارات او د تمدن پای

24) ولې خلک تراوسه اعلان کوي؟

25) د ځان باور په جوړولو کې د جنډر توپیر (که IFDINDINBCH)

26) د Xing.com کلتور ارزونه

27) پیټریک لنسي "د ټیم پنځه تخریبونه"

28) خواخوږي ده ...

29) د دندې وړاندیز غوره کولو کې د دې متخصصینو لپاره لازمي دي؟

30) ولې خلک د شعاع په وړاندې مقاومت کوي (د سیوبحین مچیل لخوا)

31) تاسو خپل احساسات څنګه تنظیم کوئ؟ (د نوال مصطفی م.

32) 21 مهارتونه چې تاسو ته د تل لپاره تادیه کوي (د Jeamiiah teo/ 赵汉昇)

33) ریښتینی ازادي ...

34) د نورو سره د باور جوړولو 12 لارې (په جسټین راویت)

35) د تکړه کارمند ځانګړتیاوې (د استعداد مدیریت انستیتوت)

36) ستاسو د ټیم هڅولو لپاره 10 کلي

37) د ضمیر الجبرا (د ولادیمیر لیفبویر لخوا)

38) د راتلونکي درې ځانګړي امکانات (د ډاکټر کلیر ډبلیو قبرز لخوا)

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.

ویره

چارتونه اړیکه

VUCA

د ارتباط ضريب مهمو ارزښت

نورمال ویش، د ولیم سمندري ګوسټ (زده کونکي) لخوا r = 0.0331

غیر نورمال توزیع، د سپرمان لخوا r = 0.0013

یوازې پایلې وښایاست > r = 0.0331

ویش	غیر نورمال	غیر نورمال	غیر نورمال	نورمال	نورمال	نورمال	نورمال	نورمال
ټولې پوښتنې ټولې پوښتنې زما ترټولو لوی ویره ده
زما ترټولو لوی ویره ده
Answer 1	-	کمزوری مثبت 0.0563	کمزوری مثبت 0.0317	کمزوری منفي -0.0161	کمزوری مثبت 0.0907	کمزوری مثبت 0.0298	کمزوری منفي -0.0126	کمزوری منفي -0.1537
Answer 2	-	کمزوری مثبت 0.0216	کمزوری مثبت 0.0002	کمزوری منفي -0.0458	کمزوری مثبت 0.0654	کمزوری مثبت 0.0445	کمزوری مثبت 0.0124	کمزوری منفي -0.0937
Answer 3	-	کمزوری منفي -0.0035	کمزوری منفي -0.0111	کمزوری منفي -0.0421	کمزوری منفي -0.0456	کمزوری مثبت 0.0466	کمزوری مثبت 0.0786	کمزوری منفي -0.0201
Answer 4	-	کمزوری مثبت 0.0435	کمزوری مثبت 0.0353	کمزوری منفي -0.0181	کمزوری مثبت 0.0145	کمزوری مثبت 0.0301	کمزوری مثبت 0.0197	کمزوری منفي -0.0979
Answer 5	-	کمزوری مثبت 0.0299	کمزوری مثبت 0.1279	کمزوری مثبت 0.0136	کمزوری مثبت 0.0730	کمزوری منفي -0.0007	کمزوری منفي -0.0207	کمزوری منفي -0.1746
Answer 6	-	کمزوری منفي -0.0004	کمزوری مثبت 0.0082	کمزوری منفي -0.0629	کمزوری منفي -0.0078	کمزوری مثبت 0.0193	کمزوری مثبت 0.0830	کمزوری منفي -0.0318
Answer 7	-	کمزوری مثبت 0.0122	کمزوری مثبت 0.0381	کمزوری منفي -0.0686	کمزوری منفي -0.0242	کمزوری مثبت 0.0471	کمزوری مثبت 0.0636	کمزوری منفي -0.0513
Answer 8	-	کمزوری مثبت 0.0698	کمزوری مثبت 0.0849	کمزوری منفي -0.0321	کمزوری مثبت 0.0146	کمزوری مثبت 0.0345	کمزوری مثبت 0.0130	کمزوری منفي -0.1368
Answer 9	-	کمزوری مثبت 0.0665	کمزوری مثبت 0.1674	کمزوری مثبت 0.0092	کمزوری مثبت 0.0691	کمزوری منفي -0.0128	کمزوری منفي -0.0528	کمزوری منفي -0.1812
Answer 10	-	کمزوری مثبت 0.0778	کمزوری مثبت 0.0755	کمزوری منفي -0.0180	کمزوری مثبت 0.0231	کمزوری مثبت 0.0346	کمزوری منفي -0.0146	کمزوری منفي -0.1298
Answer 11	-	کمزوری مثبت 0.0584	کمزوری مثبت 0.0524	کمزوری منفي -0.0096	کمزوری مثبت 0.0081	کمزوری مثبت 0.0199	کمزوری مثبت 0.0318	کمزوری منفي -0.1197
Answer 12	-	کمزوری مثبت 0.0380	کمزوری مثبت 0.1042	کمزوری منفي -0.0352	کمزوری مثبت 0.0357	کمزوری مثبت 0.0254	کمزوری مثبت 0.0286	کمزوری منفي -0.1515
Answer 13	-	کمزوری مثبت 0.0644	کمزوری مثبت 0.1057	کمزوری منفي -0.0448	کمزوری مثبت 0.0268	کمزوری مثبت 0.0416	کمزوری مثبت 0.0169	کمزوری منفي -0.1600
Answer 14	-	کمزوری مثبت 0.0717	کمزوری مثبت 0.1026	کمزوری منفي -0.0006	کمزوری منفي -0.0089	کمزوری منفي -0.0012	کمزوری مثبت 0.0080	کمزوری منفي -0.1168
Answer 15	-	کمزوری مثبت 0.0549	کمزوری مثبت 0.1375	کمزوری منفي -0.0420	کمزوری مثبت 0.0178	کمزوری منفي -0.0160	کمزوری مثبت 0.0216	کمزوری منفي -0.1180
Answer 16	-	کمزوری مثبت 0.0591	کمزوری مثبت 0.0273	کمزوری منفي -0.0386	کمزوری منفي -0.0399	کمزوری مثبت 0.0653	کمزوری مثبت 0.0282	کمزوری منفي -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

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