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) اقدامات شرکت ها در رابطه با پرسنل در ماه گذشته (بله / خیر)

2) اقدامات شرکت ها در رابطه با پرسنل در ماه گذشته (واقعیت در٪)

3) ترس

4) بزرگترین مشکلات پیش روی کشور من

5) رهبران خوب هنگام ساختن تیم های موفق از چه خصوصیات و توانایی هایی استفاده می کنند؟

6) گوگل. عواملی که بر اثربخشی تیم تأثیر می گذارد

7) اولویت های اصلی افراد متقاضی کار

8) چه چیزی رئیس را به یک رهبر بزرگ تبدیل می کند؟

9) چه چیزی باعث موفقیت افراد در کار می شود؟

10) آیا شما آماده دریافت دستمزد کمتری برای کار از راه دور هستید؟

11) آیا سن گرایی وجود دارد؟

12) سن گرایی در حرفه

13) سن گرایی در زندگی

14) علل سن گرایی

15) دلایلی که مردم تسلیم می شوند (توسط آنا ویتال)

16) اعتماد (#WVS)

17) بررسی خوشبختی آکسفورد

18) سلامت روانی

19) جالب ترین فرصت بعدی شما کجا خواهد بود؟

20) در این هفته چه کاری انجام خواهید داد تا از سلامت روانی خود مراقبت کنید؟

21) من زندگی می کنم در مورد گذشته ، حال یا آینده ام

22) شایسته سالاری

23) هوش مصنوعی و پایان تمدن

24) چرا مردم به تعویق می افتند؟

25) تفاوت جنسیتی در ایجاد اعتماد به نفس (IFD Allensbach)

26) ارزیابی فرهنگ Xing.com

27) پنج اختلال عملکرد یک تیم پاتریک لنسیونی

28) همدلی است ...

29) چه چیزی برای متخصصان فناوری اطلاعات در انتخاب پیشنهاد شغلی ضروری است؟

30) چرا مردم در برابر تغییر مقاومت می کنند (توسط Siobhán Mchale)

31) چگونه احساسات خود را تنظیم می کنید؟ (توسط Nawal Mustafa M.A.)

32) 21 مهارتی که برای همیشه به شما می پردازد (توسط ارمیا Teo / 赵汉昇)

33) آزادی واقعی ...

34) 12 راه برای ایجاد اعتماد با دیگران (توسط جاستین رایت)

35) ویژگی های یک کارمند با استعداد (توسط موسسه مدیریت استعداد)

36) 10 کلید برای ایجاد انگیزه در تیم خود

37) جبر وجدان (نویسنده ولادیمیر لوفور)

38) سه احتمال متمایز آینده (توسط دکتر کلر دبلیو گریوز)

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.

ترس

نمودار همبستگی

VUCA

مقدار بحرانی ضریب همبستگی

توزیع عادی ، توسط ویلیام سیلی گوست (دانشجو) r = 0.0335

توزیع غیر عادی ، توسط Spearman r = 0.0014

فقط نتایج را نشان می دهد > r = 0.0335

توزیع	غیر عادی	غیر عادی	غیر عادی	طبیعی	طبیعی	طبیعی	طبیعی	طبیعی
تمام س questions الات تمام س questions الات بزرگترین ترس من این است
بزرگترین ترس من این است
Answer 1	-	مثبت ضعیف 0.0521	مثبت ضعیف 0.0294	منفی ضعیف -0.0147	مثبت ضعیف 0.0885	مثبت ضعیف 0.0316	منفی ضعیف -0.0110	منفی ضعیف -0.1513
Answer 2	-	مثبت ضعیف 0.0213	مثبت ضعیف 0.0013	منفی ضعیف -0.0432	مثبت ضعیف 0.0618	مثبت ضعیف 0.0453	مثبت ضعیف 0.0103	منفی ضعیف -0.0918
Answer 3	-	منفی ضعیف -0.0042	منفی ضعیف -0.0116	منفی ضعیف -0.0406	منفی ضعیف -0.0477	مثبت ضعیف 0.0487	مثبت ضعیف 0.0767	منفی ضعیف -0.0191
Answer 4	-	مثبت ضعیف 0.0421	مثبت ضعیف 0.0350	منفی ضعیف -0.0115	مثبت ضعیف 0.0112	مثبت ضعیف 0.0307	مثبت ضعیف 0.0175	منفی ضعیف -0.0980
Answer 5	-	مثبت ضعیف 0.0288	مثبت ضعیف 0.1272	مثبت ضعیف 0.0146	مثبت ضعیف 0.0697	مثبت ضعیف 0.0037	منفی ضعیف -0.0215	منفی ضعیف -0.1746
Answer 6	-	منفی ضعیف -0.0001	مثبت ضعیف 0.0042	منفی ضعیف -0.0607	منفی ضعیف -0.0115	مثبت ضعیف 0.0231	مثبت ضعیف 0.0826	منفی ضعیف -0.0309
Answer 7	-	مثبت ضعیف 0.0117	مثبت ضعیف 0.0372	منفی ضعیف -0.0653	منفی ضعیف -0.0283	مثبت ضعیف 0.0495	مثبت ضعیف 0.0626	منفی ضعیف -0.0505
Answer 8	-	مثبت ضعیف 0.0658	مثبت ضعیف 0.0830	منفی ضعیف -0.0310	مثبت ضعیف 0.0139	مثبت ضعیف 0.0334	مثبت ضعیف 0.0134	منفی ضعیف -0.1322
Answer 9	-	مثبت ضعیف 0.0660	مثبت ضعیف 0.1658	مثبت ضعیف 0.0051	مثبت ضعیف 0.0691	منفی ضعیف -0.0093	منفی ضعیف -0.0498	منفی ضعیف -0.1820
Answer 10	-	مثبت ضعیف 0.0758	مثبت ضعیف 0.0724	منفی ضعیف -0.0173	مثبت ضعیف 0.0236	مثبت ضعیف 0.0312	منفی ضعیف -0.0115	منفی ضعیف -0.1263
Answer 11	-	مثبت ضعیف 0.0577	مثبت ضعیف 0.0544	منفی ضعیف -0.0075	مثبت ضعیف 0.0082	مثبت ضعیف 0.0185	مثبت ضعیف 0.0293	منفی ضعیف -0.1190
Answer 12	-	مثبت ضعیف 0.0376	مثبت ضعیف 0.1007	منفی ضعیف -0.0342	مثبت ضعیف 0.0296	مثبت ضعیف 0.0273	مثبت ضعیف 0.0341	منفی ضعیف -0.1500
Answer 13	-	مثبت ضعیف 0.0627	مثبت ضعیف 0.1017	منفی ضعیف -0.0443	مثبت ضعیف 0.0248	مثبت ضعیف 0.0434	مثبت ضعیف 0.0189	منفی ضعیف -0.1576
Answer 14	-	مثبت ضعیف 0.0732	مثبت ضعیف 0.1036	مثبت ضعیف 0.0048	منفی ضعیف -0.0105	منفی ضعیف -0.0039	مثبت ضعیف 0.0041	منفی ضعیف -0.1157
Answer 15	-	مثبت ضعیف 0.0539	مثبت ضعیف 0.1381	منفی ضعیف -0.0424	مثبت ضعیف 0.0163	منفی ضعیف -0.0147	مثبت ضعیف 0.0216	منفی ضعیف -0.1173
Answer 16	-	مثبت ضعیف 0.0590	مثبت ضعیف 0.0274	منفی ضعیف -0.0375	منفی ضعیف -0.0429	مثبت ضعیف 0.0687	مثبت ضعیف 0.0253	منفی ضعیف -0.0698

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

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

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

2023.10.13

والری

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