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 = 0.033

غير معمولي تقسيم، سپيرمن طرفان r = 0.0013

صرف نتيجا ڏيکاريو > r = 0.033

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 0.0536	ڪمزور مثبت 0.0297	ڪمزور منفي -0.0174	ڪمزور مثبت 0.0910	ڪمزور مثبت 0.0303	ڪمزور منفي -0.0114	ڪمزور منفي -0.1522
Answer 2	-	ڪمزور مثبت 0.0197	ڪمزور منفي -0.0002	ڪمزور منفي -0.0449	ڪمزور مثبت 0.0661	ڪمزور مثبت 0.0446	ڪمزور مثبت 0.0121	ڪمزور منفي -0.0926
Answer 3	-	ڪمزور منفي -0.0055	ڪمزور منفي -0.0120	ڪمزور منفي -0.0413	ڪمزور منفي -0.0450	ڪمزور مثبت 0.0473	ڪمزور مثبت 0.0789	ڪمزور منفي -0.0205
Answer 4	-	ڪمزور مثبت 0.0427	ڪمزور مثبت 0.0339	ڪمزور منفي -0.0192	ڪمزور مثبت 0.0153	ڪمزور مثبت 0.0305	ڪمزور مثبت 0.0210	ڪمزور منفي -0.0983
Answer 5	-	ڪمزور مثبت 0.0252	ڪمزور مثبت 0.1256	ڪمزور مثبت 0.0135	ڪمزور مثبت 0.0733	ڪمزور منفي -0.0016	ڪمزور منفي -0.0198	ڪمزور منفي -0.1742
Answer 6	-	ڪمزور منفي -0.0024	ڪمزور مثبت 0.0078	ڪمزور منفي -0.0633	ڪمزور منفي -0.0069	ڪمزور مثبت 0.0198	ڪمزور مثبت 0.0835	ڪمزور منفي -0.0330
Answer 7	-	ڪمزور مثبت 0.0112	ڪمزور مثبت 0.0375	ڪمزور منفي -0.0688	ڪمزور منفي -0.0225	ڪمزور مثبت 0.0471	ڪمزور مثبت 0.0647	ڪمزور منفي -0.0528
Answer 8	-	ڪمزور مثبت 0.0698	ڪمزور مثبت 0.0830	ڪمزور منفي -0.0314	ڪمزور مثبت 0.0137	ڪمزور مثبت 0.0350	ڪمزور مثبت 0.0144	ڪمزور منفي -0.1376
Answer 9	-	ڪمزور مثبت 0.0644	ڪمزور مثبت 0.1664	ڪمزور مثبت 0.0083	ڪمزور مثبت 0.0702	ڪمزور منفي -0.0136	ڪمزور منفي -0.0517	ڪمزور منفي -0.1830
Answer 10	-	ڪمزور مثبت 0.0760	ڪمزور مثبت 0.0738	ڪمزور منفي -0.0199	ڪمزور مثبت 0.0242	ڪمزور مثبت 0.0319	ڪمزور منفي -0.0149	ڪمزور منفي -0.1320
Answer 11	-	ڪمزور مثبت 0.0580	ڪمزور مثبت 0.0514	ڪمزور منفي -0.0111	ڪمزور مثبت 0.0076	ڪمزور مثبت 0.0206	ڪمزور مثبت 0.0318	ڪمزور منفي -0.1213
Answer 12	-	ڪمزور مثبت 0.0367	ڪمزور مثبت 0.1023	ڪمزور منفي -0.0355	ڪمزور مثبت 0.0359	ڪمزور مثبت 0.0245	ڪمزور مثبت 0.0286	ڪمزور منفي -0.1524
Answer 13	-	ڪمزور مثبت 0.0619	ڪمزور مثبت 0.1049	ڪمزور منفي -0.0451	ڪمزور مثبت 0.0281	ڪمزور مثبت 0.0412	ڪمزور مثبت 0.0173	ڪمزور منفي -0.1609
Answer 14	-	ڪمزور مثبت 0.0707	ڪمزور مثبت 0.1011	ڪمزور مثبت 7.75E-5	ڪمزور منفي -0.0083	ڪمزور منفي -0.0012	ڪمزور مثبت 0.0083	ڪمزور منفي -0.1182
Answer 15	-	ڪمزور مثبت 0.0549	ڪمزور مثبت 0.1358	ڪمزور منفي -0.0409	ڪمزور مثبت 0.0176	ڪمزور منفي -0.0163	ڪمزور مثبت 0.0208	ڪمزور منفي -0.1180
Answer 16	-	ڪمزور مثبت 0.0582	ڪمزور مثبت 0.0259	ڪمزور منفي -0.0395	ڪمزور منفي -0.0403	ڪمزور مثبت 0.0652	ڪمزور مثبت 0.0283	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

مصنوعات جي مالڪ ساس پالتو پروجيڪٽ SDSTST®

وليري 1993 ۾ سماجي پيڊ اوگولوججسٽ- نفسيات جي ماهر طور قابليت ڪئي ۽ منصوبي جي انتظام ۾ پنهنجو علم لاڳو ڪيو ويو آهي.
وليري ماسٽر جي ڊگري حاصل ڪئي ۽ پروجيڪٽ ۽ پروگرام جو مئنيجر ايسٽمينٽ قابليت حاصل ڪئي. هن جي ماسٽر جي پروگرام دوران، هو پروفيسرز گيٽس جيوٽس اسٽرلينٽ فئڪٽڪز سان واقف ٿي ويو.
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