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)

39) د غیر متزلزل ځان باور رامینځته کولو لپاره کړنې (د سورین سمارچین لخوا)

40)

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 = 0.0324

غیر نورمال توزیع، د سپرمان لخوا r = 0.0013

یوازې پایلې وښایاست > r = 0.0324

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 0.0530	کمزوری مثبت 0.0328	کمزوری منفي -0.0162	کمزوری مثبت 0.0934	کمزوری مثبت 0.0360	کمزوری منفي -0.0164	کمزوری منفي -0.1574
Answer 2	-	کمزوری مثبت 0.0190	کمزوری مثبت 0.0008	کمزوری منفي -0.0443	کمزوری مثبت 0.0635	کمزوری مثبت 0.0480	کمزوری مثبت 0.0156	کمزوری منفي -0.0974
Answer 3	-	کمزوری منفي -0.0021	کمزوری منفي -0.0105	کمزوری منفي -0.0475	کمزوری منفي -0.0446	کمزوری مثبت 0.0508	کمزوری مثبت 0.0783	کمزوری منفي -0.0212
Answer 4	-	کمزوری مثبت 0.0426	کمزوری مثبت 0.0288	کمزوری منفي -0.0204	کمزوری مثبت 0.0171	کمزوری مثبت 0.0321	کمزوری مثبت 0.0239	کمزوری منفي -0.0985
Answer 5	-	کمزوری مثبت 0.0284	کمزوری مثبت 0.1335	کمزوری مثبت 0.0089	کمزوری مثبت 0.0802	کمزوری مثبت 0.0014	کمزوری منفي -0.0237	کمزوری منفي -0.1801
Answer 6	-	کمزوری منفي -0.0050	کمزوری مثبت 0.0102	کمزوری منفي -0.0670	کمزوری منفي -0.0071	کمزوری مثبت 0.0234	کمزوری مثبت 0.0846	کمزوری منفي -0.0323
Answer 7	-	کمزوری مثبت 0.0117	کمزوری مثبت 0.0402	کمزوری منفي -0.0735	کمزوری منفي -0.0279	کمزوری مثبت 0.0512	کمزوری مثبت 0.0674	کمزوری منفي -0.0511
Answer 8	-	کمزوری مثبت 0.0673	کمزوری مثبت 0.0838	کمزوری منفي -0.0343	کمزوری مثبت 0.0168	کمزوری مثبت 0.0357	کمزوری مثبت 0.0144	کمزوری منفي -0.1363
Answer 9	-	کمزوری مثبت 0.0699	کمزوری مثبت 0.1677	کمزوری مثبت 0.0047	کمزوری مثبت 0.0657	کمزوری منفي -0.0114	کمزوری منفي -0.0516	کمزوری منفي -0.1785
Answer 10	-	کمزوری مثبت 0.0795	کمزوری مثبت 0.0748	کمزوری منفي -0.0230	کمزوری مثبت 0.0272	کمزوری مثبت 0.0336	کمزوری منفي -0.0109	کمزوری منفي -0.1320
Answer 11	-	کمزوری مثبت 0.0613	کمزوری مثبت 0.0581	کمزوری منفي -0.0079	کمزوری مثبت 0.0096	کمزوری مثبت 0.0206	کمزوری مثبت 0.0245	کمزوری منفي -0.1233
Answer 12	-	کمزوری مثبت 0.0413	کمزوری مثبت 0.1017	کمزوری منفي -0.0399	کمزوری مثبت 0.0373	کمزوری مثبت 0.0327	کمزوری مثبت 0.0246	کمزوری منفي -0.1524
Answer 13	-	کمزوری مثبت 0.0668	کمزوری مثبت 0.1021	کمزوری منفي -0.0435	کمزوری مثبت 0.0280	کمزوری مثبت 0.0439	کمزوری مثبت 0.0157	کمزوری منفي -0.1620
Answer 14	-	کمزوری مثبت 0.0717	کمزوری مثبت 0.1001	کمزوری منفي -0.0034	کمزوری منفي -0.0056	کمزوری مثبت 0.0037	کمزوری مثبت 0.0095	کمزوری منفي -0.1215
Answer 15	-	کمزوری مثبت 0.0536	کمزوری مثبت 0.1365	کمزوری منفي -0.0384	کمزوری مثبت 0.0190	کمزوری منفي -0.0178	کمزوری مثبت 0.0204	کمزوری منفي -0.1181
Answer 16	-	کمزوری مثبت 0.0655	کمزوری مثبت 0.0299	کمزوری منفي -0.0356	کمزوری منفي -0.0424	کمزوری مثبت 0.0653	کمزوری مثبت 0.0249	کمزوری منفي -0.0738

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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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