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)

39) غير متزلزل خود اعتمادي پيدا ڪرڻ لاءِ عمل (جي سرن سمارچيان)

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.

خوفناڪ

چارٽس باهمي

VUCA

رابطي واري گنجائش جي نازڪ قدر

عام تقسيم، وليم سامونڊي گيسس (شاگرد) طرفان r = 0.0317

غير معمولي تقسيم، سپيرمن طرفان r = 0.0013

صرف نتيجا ڏيکاريو > r = 0.0317

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

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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