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

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 = 0.0353

غیر معمولی تقسیم ، اسپیئر مین کے ذریعہ r = 0.0014

صرف نتائج دکھائیں > r = 0.0353

تقسیم	غیر معمول	عام	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 0.0297	کمزور مثبت 0.0298	کمزور منفی -0.0106	کمزور مثبت 0.0970	کمزور مثبت 0.0325	کمزور منفی -0.0019	کمزور منفی -0.1558
Answer 2	-	کمزور مثبت 0.0188	کمزور مثبت 0.0076	کمزور منفی -0.0360	کمزور مثبت 0.0711	کمزور مثبت 0.0387	کمزور مثبت 0.0082	کمزور منفی -0.1011
Answer 3	-	کمزور مثبت 0.0026	کمزور منفی -0.0170	کمزور منفی -0.0443	کمزور منفی -0.0458	کمزور مثبت 0.0547	کمزور مثبت 0.0808	کمزور منفی -0.0270
Answer 4	-	کمزور مثبت 0.0332	کمزور مثبت 0.0285	کمزور منفی -0.0006	کمزور مثبت 0.0155	کمزور مثبت 0.0276	کمزور مثبت 0.0105	کمزور منفی -0.0917
Answer 5	-	کمزور مثبت 0.0122	کمزور مثبت 0.1193	کمزور مثبت 0.0095	کمزور مثبت 0.0721	کمزور مثبت 0.0057	کمزور منفی -0.0083	کمزور منفی -0.1687
Answer 6	-	کمزور مثبت 0.0044	کمزور مثبت 0.0005	کمزور منفی -0.0582	کمزور منفی -0.0004	کمزور مثبت 0.0210	کمزور مثبت 0.0830	کمزور منفی -0.0418
Answer 7	-	کمزور مثبت 0.0242	کمزور مثبت 0.0368	کمزور منفی -0.0521	کمزور منفی -0.0234	کمزور مثبت 0.0403	کمزور مثبت 0.0568	کمزور منفی -0.0597
Answer 8	-	کمزور مثبت 0.0707	کمزور مثبت 0.0781	کمزور منفی -0.0244	کمزور مثبت 0.0140	کمزور مثبت 0.0303	کمزور مثبت 0.0137	کمزور منفی -0.1334
Answer 9	-	کمزور مثبت 0.0564	کمزور مثبت 0.1531	کمزور مثبت 0.0127	کمزور مثبت 0.0769	کمزور منفی -0.0136	کمزور منفی -0.0495	کمزور منفی -0.1752
Answer 10	-	کمزور مثبت 0.0711	کمزور مثبت 0.0700	کمزور منفی -0.0127	کمزور مثبت 0.0246	کمزور مثبت 0.0363	کمزور منفی -0.0156	کمزور منفی -0.1273
Answer 11	-	کمزور مثبت 0.0542	کمزور مثبت 0.0488	کمزور مثبت 0.0086	کمزور مثبت 0.0078	کمزور مثبت 0.0162	کمزور مثبت 0.0315	کمزور منفی -0.1248
Answer 12	-	کمزور مثبت 0.0281	کمزور مثبت 0.0929	کمزور منفی -0.0325	کمزور مثبت 0.0361	کمزور مثبت 0.0276	کمزور مثبت 0.0365	کمزور منفی -0.1482
Answer 13	-	کمزور مثبت 0.0643	کمزور مثبت 0.0916	کمزور منفی -0.0418	کمزور مثبت 0.0237	کمزور مثبت 0.0425	کمزور مثبت 0.0239	کمزور منفی -0.1558
Answer 14	-	کمزور مثبت 0.0697	کمزور مثبت 0.1017	کمزور مثبت 0.0149	کمزور منفی -0.0062	کمزور منفی -0.0087	کمزور منفی -0.0002	کمزور منفی -0.1161
Answer 15	-	کمزور مثبت 0.0603	کمزور مثبت 0.1299	کمزور منفی -0.0379	کمزور مثبت 0.0163	کمزور منفی -0.0091	کمزور مثبت 0.0164	کمزور منفی -0.1204
Answer 16	-	کمزور مثبت 0.0691	کمزور مثبت 0.0221	کمزور منفی -0.0305	کمزور منفی -0.0515	کمزور مثبت 0.0750	کمزور مثبت 0.0187	کمزور منفی -0.0696

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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 کے مالک ساس پیٹ پروجیکٹ SDTEST®

ویلری 1993 میں ایک سماجی تعلیمی تعلیم کے ماہر کی حیثیت سے اہل تھا اور اس کے بعد سے اس نے اپنے علم کو پروجیکٹ مینجمنٹ میں لاگو کیا ہے۔
ویلری نے 2013 میں ماسٹر کی ڈگری اور پروجیکٹ اور پروگرام مینیجر کی قابلیت حاصل کی۔ اپنے ماسٹر کے پروگرام کے دوران ، وہ پروجیکٹ روڈ میپ (جی پی ایم ڈوئچے جیسیلشافٹ فر پروجیکٹ مینجمنٹ ای وی وی) اور سرپل حرکیات سے واقف ہوگئے۔
ویلری نے مختلف سرپل ڈائنامکس ٹیسٹ کیے اور اپنے علم اور تجربے کو ایس ڈی ٹیسٹ کے موجودہ ورژن کو اپنانے کے لئے استعمال کیا۔
ویلری V.U.C.A کی غیر یقینی صورتحال کی تلاش کے مصنف ہیں۔ نفسیات میں سرپل حرکیات اور ریاضی کے اعدادوشمار کا استعمال کرتے ہوئے تصور ، 20 سے زیادہ بین الاقوامی انتخابات۔

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