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) پچھلے مہینے میں اہلکاروں کے سلسلے میں کمپنیوں کے اقدامات (ہاں / نہیں)

2) گزشتہ مہینے میں اہلکاروں کے سلسلے میں کمپنیوں کے اعمال (حقیقت میں٪)

3) خوف

4) میرے ملک کو درپیش سب سے بڑی پریشانی

5) کامیاب ٹیموں کی تعمیر کے وقت اچھے قائدین کونسی خصوصیات اور صلاحیتوں کا استعمال کرتے ہیں؟

6) گوگل۔ عوامل جو ٹیم کی افادیت کو متاثر کرتے ہیں

7) ملازمت کے متلاشیوں کی بنیادی ترجیحات

8) کیا باس کو ایک عظیم قائد بناتا ہے؟

9) کیا کام میں لوگوں کو کامیاب بناتا ہے؟

10) کیا آپ دور سے کام کرنے کے لئے کم تنخواہ وصول کرنے کے لئے تیار ہیں؟

11) کیا عمر پسندی موجود ہے؟

12) کیریئر میں عمر ازم

13) زندگی میں عمر

14) عمر کی وجوہات

15) وجوہات کیوں لوگ ہار مانتے ہیں (بذریعہ انا اہم)

16) اعتماد (#WVS)

17) آکسفورڈ خوشی کا سروے

18) نفسیاتی تندرستی

19) آپ کا اگلا سب سے دلچسپ موقع کہاں ہوگا؟

20) اپنی ذہنی صحت کی دیکھ بھال کے لئے آپ اس ہفتے کیا کریں گے؟

21) میں اپنے ماضی ، حال یا مستقبل کے بارے میں سوچتا ہوں

22) میرٹوکریسی

23) مصنوعی ذہانت اور تہذیب کا خاتمہ

24) لوگ کیوں تاخیر کرتے ہیں؟

25) خود اعتمادی کی تعمیر میں صنفی فرق (IFD ایلنسباچ)

26) Xing.com ثقافت کی تشخیص

27) پیٹرک لینسیونی کی "ایک ٹیم کے پانچ dysfunctions"

28) ہمدردی ہے ...

29) ملازمت کی پیش کش کا انتخاب کرنے میں آئی ٹی ماہرین کے لئے کیا ضروری ہے؟

30) لوگ تبدیلی کے خلاف کیوں مزاحمت کرتے ہیں (بذریعہ سیوبن میک ہیل)

31) آپ اپنے جذبات کو کس طرح منظم کرتے ہیں؟ (بذریعہ نوال مصطفیٰ ایم اے)

32) 21 ہنر جو آپ کو ہمیشہ کے لئے ادائیگی کرتے ہیں (بذریعہ یرمیاہ تیو / 赵汉昇)

33) حقیقی آزادی ہے ...

34) دوسروں کے ساتھ اعتماد پیدا کرنے کے 12 طریقے (بذریعہ جسٹن رائٹ)

35) باصلاحیت ملازم کی خصوصیات (ٹیلنٹ مینجمنٹ انسٹی ٹیوٹ کے ذریعہ)

36) اپنی ٹیم کو حوصلہ افزائی کرنے کی 10 کلیدیں

37) ضمیر کا الجبرا (بذریعہ ولادیمیر لیفیبرے)

38) مستقبل کے تین امتیازی امکانات (بذریعہ ڈاکٹر کلیئر ڈبلیو گریوز)

39) غیر متزلزل خود اعتمادی پیدا کرنے کے اقدامات (بذریعہ سورین سمارچیان)

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.

خوف

چارٹس سہسنبند

VUCA

ارتباط گتانک کے اہم قدر

عام تقسیم ، بذریعہ ولیم سیلی گوسیٹ (طالب علم) r = 0.0317

غیر معمولی تقسیم ، اسپیئر مین کے ذریعہ r = 0.0013

صرف نتائج دکھائیں > r = 0.0317

تقسیم	غیر معمول	غیر معمول	غیر معمول	عام	عام	عام	عام	عام
تمام سوالات تمام سوالات میرا سب سے بڑا خوف ہے
میرا سب سے بڑا خوف ہے
Answer 1	-	کمزور مثبت 0.0537	کمزور مثبت 0.0288	کمزور منفی -0.0175	کمزور مثبت 0.0948	کمزور مثبت 0.0381	کمزور منفی -0.0178	کمزور منفی -0.1563
Answer 2	-	کمزور مثبت 0.0194	کمزور منفی -0.0048	کمزور منفی -0.0385	کمزور مثبت 0.0655	کمزور مثبت 0.0495	کمزور مثبت 0.0106	کمزور منفی -0.0982
Answer 3	-	کمزور منفی -0.0001	کمزور منفی -0.0084	کمزور منفی -0.0449	کمزور منفی -0.0445	کمزور مثبت 0.0485	کمزور مثبت 0.0742	کمزور منفی -0.0207
Answer 4	-	کمزور مثبت 0.0433	کمزور مثبت 0.0291	کمزور منفی -0.0232	کمزور مثبت 0.0163	کمزور مثبت 0.0367	کمزور مثبت 0.0226	کمزور منفی -0.0996
Answer 5	-	کمزور مثبت 0.0277	کمزور مثبت 0.1291	کمزور مثبت 0.0108	کمزور مثبت 0.0745	کمزور مثبت 0.0012	کمزور منفی -0.0177	کمزور منفی -0.1783
Answer 6	-	کمزور منفی -0.0015	کمزور مثبت 0.0058	کمزور منفی -0.0607	کمزور منفی -0.0094	کمزور مثبت 0.0255	کمزور مثبت 0.0844	کمزور منفی -0.0363
Answer 7	-	کمزور مثبت 0.0113	کمزور مثبت 0.0348	کمزور منفی -0.0657	کمزور منفی -0.0305	کمزور مثبت 0.0521	کمزور مثبت 0.0686	کمزور منفی -0.0532
Answer 8	-	کمزور مثبت 0.0657	کمزور مثبت 0.0728	کمزور منفی -0.0255	کمزور مثبت 0.0124	کمزور مثبت 0.0386	کمزور مثبت 0.0153	کمزور منفی -0.1345
Answer 9	-	کمزور مثبت 0.0757	کمزور مثبت 0.1605	کمزور مثبت 0.0066	کمزور مثبت 0.0612	کمزور منفی -0.0063	کمزور منفی -0.0492	کمزور منفی -0.1822
Answer 10	-	کمزور مثبت 0.0764	کمزور مثبت 0.0669	کمزور منفی -0.0124	کمزور مثبت 0.0271	کمزور مثبت 0.0365	کمزور منفی -0.0130	کمزور منفی -0.1348
Answer 11	-	کمزور مثبت 0.0634	کمزور مثبت 0.0526	کمزور منفی -0.0075	کمزور مثبت 0.0096	کمزور مثبت 0.0264	کمزور مثبت 0.0242	کمزور منفی -0.1270
Answer 12	-	کمزور مثبت 0.0450	کمزور مثبت 0.0944	کمزور منفی -0.0323	کمزور مثبت 0.0307	کمزور مثبت 0.0343	کمزور مثبت 0.0260	کمزور منفی -0.1530
Answer 13	-	کمزور مثبت 0.0725	کمزور مثبت 0.0947	کمزور منفی -0.0389	کمزور مثبت 0.0265	کمزور مثبت 0.0443	کمزور مثبت 0.0144	کمزور منفی -0.1631
Answer 14	-	کمزور مثبت 0.0820	کمزور مثبت 0.0897	کمزور منفی -0.0030	کمزور منفی -0.0122	کمزور مثبت 0.0060	کمزور مثبت 0.0135	کمزور منفی -0.1213
Answer 15	-	کمزور مثبت 0.0549	کمزور مثبت 0.1265	کمزور منفی -0.0334	کمزور مثبت 0.0119	کمزور منفی -0.0153	کمزور مثبت 0.0242	کمزور منفی -0.1157
Answer 16	-	کمزور مثبت 0.0732	کمزور مثبت 0.0242	کمزور منفی -0.0373	کمزور منفی -0.0398	کمزور مثبت 0.0729	کمزور مثبت 0.0169	کمزور منفی -0.0774

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[1] https://twitter.com/wileyprof

[2] https://colinallen.dnsalias.org

[3] https://philpeople.org/profiles/colin-allen

2023.10.13

ویلری کوسنکو

پروڈکٹ کا مالک SaaS SDTEST®

ویلیری 1993 میں ایک سماجی ماہر نفسیات کے طور پر اہل ہوئے تھے اور اس کے بعد سے وہ پروجیکٹ مینجمنٹ میں اپنے علم کا اطلاق کرتے ہیں۔
ویلری نے 2013 میں ماسٹر کی ڈگری اور پروجیکٹ اور پروگرام مینیجر کی اہلیت حاصل کی۔ اپنے ماسٹرز پروگرام کے دوران، وہ پروجیکٹ روڈ میپ (GPM Deutsche Gesellschaft für Projektmanagement e. V.) اور Spiral Dynamics سے واقف ہوئے۔
ویلیری V.U.C.A کی غیر یقینی صورتحال کو تلاش کرنے کے مصنف ہیں۔ نفسیات میں اسپائرل ڈائنامکس اور ریاضی کے اعدادوشمار کا استعمال کرتے ہوئے تصور، اور 38 بین الاقوامی پول۔

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