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 = 0.033

غیر نورمال توزیع، د سپرمان لخوا r = 0.0013

یوازې پایلې وښایاست > r = 0.033

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 0.0558	کمزوری مثبت 0.0311	کمزوری منفي -0.0169	کمزوری مثبت 0.0917	کمزوری مثبت 0.0304	کمزوری منفي -0.0128	کمزوری منفي -0.1541
Answer 2	-	کمزوری مثبت 0.0229	کمزوری منفي -0.0006	کمزوری منفي -0.0443	کمزوری مثبت 0.0632	کمزوری مثبت 0.0453	کمزوری مثبت 0.0130	کمزوری منفي -0.0942
Answer 3	-	کمزوری منفي -0.0032	کمزوری منفي -0.0122	کمزوری منفي -0.0413	کمزوری منفي -0.0464	کمزوری مثبت 0.0469	کمزوری مثبت 0.0786	کمزوری منفي -0.0196
Answer 4	-	کمزوری مثبت 0.0437	کمزوری مثبت 0.0345	کمزوری منفي -0.0196	کمزوری مثبت 0.0152	کمزوری مثبت 0.0307	کمزوری مثبت 0.0204	کمزوری منفي -0.0981
Answer 5	-	کمزوری مثبت 0.0303	کمزوری مثبت 0.1280	کمزوری مثبت 0.0134	کمزوری مثبت 0.0733	کمزوری منفي -0.0005	کمزوری منفي -0.0203	کمزوری منفي -0.1759
Answer 6	-	کمزوری منفي -0.0003	کمزوری مثبت 0.0082	کمزوری منفي -0.0630	کمزوری منفي -0.0082	کمزوری مثبت 0.0195	کمزوری مثبت 0.0830	کمزوری منفي -0.0315
Answer 7	-	کمزوری مثبت 0.0124	کمزوری مثبت 0.0382	کمزوری منفي -0.0694	کمزوری منفي -0.0241	کمزوری مثبت 0.0473	کمزوری مثبت 0.0641	کمزوری منفي -0.0514
Answer 8	-	کمزوری مثبت 0.0696	کمزوری مثبت 0.0850	کمزوری منفي -0.0333	کمزوری مثبت 0.0150	کمزوری مثبت 0.0346	کمزوری مثبت 0.0134	کمزوری منفي -0.1364
Answer 9	-	کمزوری مثبت 0.0667	کمزوری مثبت 0.1676	کمزوری مثبت 0.0077	کمزوری مثبت 0.0694	کمزوری منفي -0.0128	کمزوری منفي -0.0517	کمزوری منفي -0.1817
Answer 10	-	کمزوری مثبت 0.0780	کمزوری مثبت 0.0754	کمزوری منفي -0.0211	کمزوری مثبت 0.0249	کمزوری مثبت 0.0347	کمزوری منفي -0.0132	کمزوری منفي -0.1303
Answer 11	-	کمزوری مثبت 0.0579	کمزوری مثبت 0.0528	کمزوری منفي -0.0090	کمزوری مثبت 0.0083	کمزوری مثبت 0.0201	کمزوری مثبت 0.0308	کمزوری منفي -0.1198
Answer 12	-	کمزوری مثبت 0.0389	کمزوری مثبت 0.1036	کمزوری منفي -0.0362	کمزوری مثبت 0.0359	کمزوری مثبت 0.0255	کمزوری مثبت 0.0297	کمزوری منفي -0.1521
Answer 13	-	کمزوری مثبت 0.0645	کمزوری مثبت 0.1041	کمزوری منفي -0.0438	کمزوری مثبت 0.0262	کمزوری مثبت 0.0423	کمزوری مثبت 0.0174	کمزوری منفي -0.1603
Answer 14	-	کمزوری مثبت 0.0710	کمزوری مثبت 0.1022	کمزوری منفي -0.0015	کمزوری منفي -0.0085	کمزوری منفي -0.0006	کمزوری مثبت 0.0087	کمزوری منفي -0.1169
Answer 15	-	کمزوری مثبت 0.0555	کمزوری مثبت 0.1365	کمزوری منفي -0.0429	کمزوری مثبت 0.0179	کمزوری منفي -0.0158	کمزوری مثبت 0.0223	کمزوری منفي -0.1178
Answer 16	-	کمزوری مثبت 0.0591	کمزوری مثبت 0.0271	کمزوری منفي -0.0384	کمزوری منفي -0.0401	کمزوری مثبت 0.0655	کمزوری مثبت 0.0283	کمزوری منفي -0.0709

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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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د محصول مالک ساس پالتو پروژه SDTyst®

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