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 0.0536	کمزوری مثبت 0.0297	کمزوری منفي -0.0174	کمزوری مثبت 0.0910	کمزوری مثبت 0.0303	کمزوری منفي -0.0114	کمزوری منفي -0.1522
Answer 2	-	کمزوری مثبت 0.0194	کمزوری منفي -0.0004	کمزوری منفي -0.0449	کمزوری مثبت 0.0664	کمزوری مثبت 0.0447	کمزوری مثبت 0.0123	کمزوری منفي -0.0928
Answer 3	-	کمزوری منفي -0.0056	کمزوری منفي -0.0121	کمزوری منفي -0.0413	کمزوری منفي -0.0449	کمزوری مثبت 0.0473	کمزوری مثبت 0.0790	کمزوری منفي -0.0206
Answer 4	-	کمزوری مثبت 0.0425	کمزوری مثبت 0.0337	کمزوری منفي -0.0192	کمزوری مثبت 0.0154	کمزوری مثبت 0.0305	کمزوری مثبت 0.0211	کمزوری منفي -0.0984
Answer 5	-	کمزوری مثبت 0.0251	کمزوری مثبت 0.1256	کمزوری مثبت 0.0135	کمزوری مثبت 0.0733	کمزوری منفي -0.0016	کمزوری منفي -0.0197	کمزوری منفي -0.1742
Answer 6	-	کمزوری منفي -0.0026	کمزوری مثبت 0.0076	کمزوری منفي -0.0633	کمزوری منفي -0.0067	کمزوری مثبت 0.0199	کمزوری مثبت 0.0836	کمزوری منفي -0.0331
Answer 7	-	کمزوری مثبت 0.0109	کمزوری مثبت 0.0373	کمزوری منفي -0.0688	کمزوری منفي -0.0223	کمزوری مثبت 0.0472	کمزوری مثبت 0.0648	کمزوری منفي -0.0529
Answer 8	-	کمزوری مثبت 0.0696	کمزوری مثبت 0.0828	کمزوری منفي -0.0314	کمزوری مثبت 0.0139	کمزوری مثبت 0.0351	کمزوری مثبت 0.0146	کمزوری منفي -0.1377
Answer 9	-	کمزوری مثبت 0.0643	کمزوری مثبت 0.1662	کمزوری مثبت 0.0083	کمزوری مثبت 0.0704	کمزوری منفي -0.0135	کمزوری منفي -0.0516	کمزوری منفي -0.1831
Answer 10	-	کمزوری مثبت 0.0758	کمزوری مثبت 0.0736	کمزوری منفي -0.0199	کمزوری مثبت 0.0244	کمزوری مثبت 0.0320	کمزوری منفي -0.0147	کمزوری منفي -0.1321
Answer 11	-	کمزوری مثبت 0.0577	کمزوری مثبت 0.0512	کمزوری منفي -0.0111	کمزوری مثبت 0.0078	کمزوری مثبت 0.0207	کمزوری مثبت 0.0319	کمزوری منفي -0.1215
Answer 12	-	کمزوری مثبت 0.0365	کمزوری مثبت 0.1021	کمزوری منفي -0.0355	کمزوری مثبت 0.0361	کمزوری مثبت 0.0246	کمزوری مثبت 0.0288	کمزوری منفي -0.1525
Answer 13	-	کمزوری مثبت 0.0621	کمزوری مثبت 0.1051	کمزوری منفي -0.0451	کمزوری مثبت 0.0280	کمزوری مثبت 0.0411	کمزوری مثبت 0.0172	کمزوری منفي -0.1608
Answer 14	-	کمزوری مثبت 0.0710	کمزوری مثبت 0.1014	کمزوری مثبت 7.14E-5	کمزوری منفي -0.0086	کمزوری منفي -0.0013	کمزوری مثبت 0.0081	کمزوری منفي -0.1181
Answer 15	-	کمزوری مثبت 0.0547	کمزوری مثبت 0.1356	کمزوری منفي -0.0409	کمزوری مثبت 0.0177	کمزوری منفي -0.0162	کمزوری مثبت 0.0210	کمزوری منفي -0.1181
Answer 16	-	کمزوری مثبت 0.0581	کمزوری مثبت 0.0258	کمزوری منفي -0.0395	کمزوری منفي -0.0402	کمزوری مثبت 0.0653	کمزوری مثبت 0.0284	کمزوری منفي -0.0717

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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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