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) گذريل مهيني ۾ اهلڪارن جي حوالي سان ڪمپنين جا عمل (ها / نه)

2) گذريل مهيني ۾ اهلڪارن جي حوالي سان ڪمپنين جا ڪارناما (حقيقت٪ ۾)

3) خوفناڪ

4) منهنجي ملڪ کي منهن ڏيڻ وارا وڏا مسئلا

5) ڪامياب ٽيمون تعمير ڪرڻ وقت ڪهڙيون خوبيون ۽ صلاحيتون ۽ صلاحيتون استعمال ڪنديون آهن؟

6) گوگل. عنصر جيڪي ٽيم جي اثر تي اثر انداز ٿين ٿا

7) نوڪري ڳوليندڙن جا بنيادي ترجيحات

8) باس کي هڪ عظيم اڳواڻ ڇا ٺاهيندو آهي؟

9) ماڻهن کي ڪم تي ڪامياب ڇا بڻائي ٿو؟

10) ڇا توهان دور دراز ڪم ڪرڻ لاء گهٽ ادائيگي حاصل ڪرڻ لاء تيار آهيو؟

11) ڇا ايجنسزم موجود آهي؟

12) ڪيريئر ۾ ايجنٽ

13) عمر ۾ عمر

14) عمر جو سبب

15) ماڻهن کي ڇو ڇڏي ڏيو (انا جي اهم)

16) ڀروسو (#WVS)

17) آڪسفورڊ خوشي سروي

18) نفسياتي خوشحالي

19) توهان جو ايندڙ دلچسپ موقعو ڪٿي هوندو؟

20) توهان پنهنجي ذهني صحت جو خيال رکڻ لاء هن هفتي ڇا ڪندا؟

21) مان پنهنجي ماضي، موجوده يا مستقبل بابت سوچيندي رهندو آهيان

22) ميريڪريسي

23) مصنوعي ذهانت ۽ تهذيب جو خاتمو

24) ماڻهو ڇو طنز ڪندا آهن؟

25) خود اعتمادي جي تعمير ۾ صنف جو فرق (IFD يڪينبچ)

26) Xing.com ثقافت جو جائزو

27) پيٽرڪ لينسڪيسي جو "هڪ ٽيم جي پنج ڊفيڪشن"

28) ايمانداري آهي ...

29) نوڪري جي آڇ چونڊڻ ۾ ان لاء ڇا ضروري آهي؟

30) ماڻهو ڇو تبديلي جي مزاحمت ڪن ٿا (سيوبي مچلي ذريعي)

31) توهان پنهنجي جذبات کي ڪيئن منظم ڪيو؟ (نالالما ايم اي ايف اي ايم پاران)

32) 21 صلاحيتون جيڪي توهان کي هميشه لاء ادا ڪنديون آهن (جريميا ٽيو / 赵汉昇 طرفان)

33) حقيقي آزادي آهي ...

34) ٻين سان اعتماد پيدا ڪرڻ جا 12 طريقا (جسٽن رائيٽ ذريعي)

35) هڪ باصلاحيت ملازم جي خاصيتون (ٽيلنٽ مينيجمينٽ انسٽيٽيوٽ طرفان)

36) توهان جي ٽيم کي متحرڪ ڪرڻ لاء 10 ڪيچ

37) ضمير جو الجبرا (ولاديمير ليفيبري طرفان)

38) مستقبل جا ٽي الڳ امڪان (ڊاڪٽر ڪليئر ڊبليو قبرز پاران)

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.

خوفناڪ

چارٽس باهمي

VUCA

رابطي واري گنجائش جي نازڪ قدر

عام تقسيم، وليم سامونڊي گيسس (شاگرد) طرفان r = 0.0329

غير معمولي تقسيم، سپيرمن طرفان r = 0.0013

صرف نتيجا ڏيکاريو > r = 0.0329

تقسيم	غير عام نمبر	غير عام نمبر	غير عام نمبر	جنرل-- عام	جنرل-- عام	جنرل-- عام	جنرل-- عام	جنرل-- عام
سڀ سوال سڀ سوال منهنجو سڀ کان وڏو خوف آهي
منهنجو سڀ کان وڏو خوف آهي
Answer 1	-	ڪمزور مثبت 0.0566	ڪمزور مثبت 0.0332	ڪمزور منفي -0.0170	ڪمزور مثبت 0.0912	ڪمزور مثبت 0.0308	ڪمزور منفي -0.0153	ڪمزور منفي -0.1537
Answer 2	-	ڪمزور مثبت 0.0223	ڪمزور مثبت 0.0011	ڪمزور منفي -0.0442	ڪمزور مثبت 0.0639	ڪمزور مثبت 0.0464	ڪمزور مثبت 0.0120	ڪمزور منفي -0.0960
Answer 3	-	ڪمزور منفي -0.0031	ڪمزور منفي -0.0104	ڪمزور منفي -0.0407	ڪمزور منفي -0.0463	ڪمزور مثبت 0.0475	ڪمزور مثبت 0.0779	ڪمزور منفي -0.0213
Answer 4	-	ڪمزور مثبت 0.0437	ڪمزور مثبت 0.0357	ڪمزور منفي -0.0197	ڪمزور مثبت 0.0161	ڪمزور مثبت 0.0311	ڪمزور مثبت 0.0187	ڪمزور منفي -0.0987
Answer 5	-	ڪمزور مثبت 0.0296	ڪمزور مثبت 0.1300	ڪمزور مثبت 0.0124	ڪمزور مثبت 0.0749	ڪمزور مثبت 0.0014	ڪمزور منفي -0.0231	ڪمزور منفي -0.1771
Answer 6	-	ڪمزور منفي -0.0008	ڪمزور مثبت 0.0090	ڪمزور منفي -0.0613	ڪمزور منفي -0.0070	ڪمزور مثبت 0.0196	ڪمزور مثبت 0.0803	ڪمزور منفي -0.0321
Answer 7	-	ڪمزور مثبت 0.0118	ڪمزور مثبت 0.0401	ڪمزور منفي -0.0693	ڪمزور منفي -0.0246	ڪمزور مثبت 0.0471	ڪمزور مثبت 0.0623	ڪمزور منفي -0.0505
Answer 8	-	ڪمزور مثبت 0.0697	ڪمزور مثبت 0.0875	ڪمزور منفي -0.0316	ڪمزور مثبت 0.0155	ڪمزور مثبت 0.0346	ڪمزور مثبت 0.0098	ڪمزور منفي -0.1373
Answer 9	-	ڪمزور مثبت 0.0679	ڪمزور مثبت 0.1707	ڪمزور مثبت 0.0105	ڪمزور مثبت 0.0676	ڪمزور منفي -0.0138	ڪمزور منفي -0.0545	ڪمزور منفي -0.1821
Answer 10	-	ڪمزور مثبت 0.0793	ڪمزور مثبت 0.0772	ڪمزور منفي -0.0208	ڪمزور مثبت 0.0242	ڪمزور مثبت 0.0343	ڪمزور منفي -0.0152	ڪمزور منفي -0.1300
Answer 11	-	ڪمزور مثبت 0.0590	ڪمزور مثبت 0.0559	ڪمزور منفي -0.0071	ڪمزور مثبت 0.0082	ڪمزور مثبت 0.0205	ڪمزور مثبت 0.0266	ڪمزور منفي -0.1213
Answer 12	-	ڪمزور مثبت 0.0405	ڪمزور مثبت 0.1050	ڪمزور منفي -0.0363	ڪمزور مثبت 0.0361	ڪمزور مثبت 0.0253	ڪمزور مثبت 0.0277	ڪمزور منفي -0.1522
Answer 13	-	ڪمزور مثبت 0.0655	ڪمزور مثبت 0.1056	ڪمزور منفي -0.0439	ڪمزور مثبت 0.0270	ڪمزور مثبت 0.0417	ڪمزور مثبت 0.0152	ڪمزور منفي -0.1601
Answer 14	-	ڪمزور مثبت 0.0728	ڪمزور مثبت 0.1049	ڪمزور منفي -0.0002	ڪمزور منفي -0.0088	ڪمزور منفي -0.0007	ڪمزور مثبت 0.0061	ڪمزور منفي -0.1187
Answer 15	-	ڪمزور مثبت 0.0561	ڪمزور مثبت 0.1378	ڪمزور منفي -0.0415	ڪمزور مثبت 0.0178	ڪمزور منفي -0.0162	ڪمزور مثبت 0.0194	ڪمزور منفي -0.1176
Answer 16	-	ڪمزور مثبت 0.0606	ڪمزور مثبت 0.0308	ڪمزور منفي -0.0348	ڪمزور منفي -0.0421	ڪمزور مثبت 0.0642	ڪمزور مثبت 0.0250	ڪمزور 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

ويلري ڪوکوڪو

پيداوار جو مالڪ SaaS SDTEST®

والري 1993 ۾ هڪ سماجي تدريسي-ماهر نفسيات جي حيثيت سان قابليت حاصل ڪئي هئي ۽ ان کان پوء هن پنهنجي علم کي پروجيڪٽ مينيجمينٽ ۾ لاڳو ڪيو آهي.
والريئي 2013 ۾ ماسٽر جي ڊگري حاصل ڪئي ۽ پروجيڪٽ ۽ پروگرام مئنيجر جي قابليت حاصل ڪئي. پنهنجي ماسٽر پروگرام دوران، هو پروجيڪٽ روڊ ميپ (GPM Deutsche Gesellschaft für Projektmanagement e. V.) ۽ اسپيرل ڊائنامڪس کان واقف ٿيو.
والري V.U.C.A جي غير يقيني صورتحال کي ڳولڻ جو ليکڪ آهي. تصور استعمال ڪندي سرپل ڊائنامڪس ۽ رياضياتي انگ اکر نفسيات ۾، ۽ 38 بين الاقوامي پول.

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