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.

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Here are reports of polls which SDTEST^® makes:

1) ئالدىنقى ئايدىكى خادىملارغا مۇناسىۋەتلىك شىركەتلەرنىڭ ھەرىكىتى (ھەئە / ياق)

2) شىركەتلەرنىڭ ئالدىنقى ئايدىكى خادىملارغا مۇناسىۋەتلىك ھەرىكەتلىرى (%/)

3) قورقۇنچ

4) دۆلىتىمگە دۇچ كەلگەن ئەڭ چوڭ مەسىلىلەر

5) مۇۋەپپەقىيەت قازانغان كوماندا بەرگەندە قانداق سۈپەت ۋە ئىقتىدارلارنى ئىشلىتىۋاتىدۇ?

6) Google. كوماندىنىڭ ئۈنۈمسىزلىقىغا تەسىر كۆرسىتىدىغان ئامىللار

7) خىزمەت ئىزدىگۈچىلەرنىڭ ئاساسلىق مۇھىملىقى

8) خوجايىننى ئۇلۇغ رەھبەر قىلىدىغان نەرسە نېمە?

9) كىشىلەرنى خىزمەتتە نېمىگە ئايلاندۇرىدۇ?

10) يىراقتىن ئىشلەش ئۈچۈن ئازراق پۇل تاپشۇرۇۋېلىش تەييارمۇ?

15) كىشىلەرنىڭ ۋاز كېچىشىدىكى سەۋەبلەر (ئاننا ئىنتايىن مۇھىم)

16) ئىشەنچ (#WVS)

17) ئوكسفورد خۇشاللىق تەكشۈرۈشى

18) پىسخىكىلىق يېقىشلىق

19) كېيىنكى كىشىنى ئەڭ ھاياجانلاندۇرىدىغان پۇرسىتىڭىز بولىدۇ?

20) بۇ ھەپتە سىزنىڭ روھىي ساغلاملىقىڭىزغا قاراش ئۈچۈن بۇ ھەپتە نېمە قىلىسىز?

21) مەن ئۆتمۈشۈم, ھازىرقى ياكى كەلگۈسىمنى ئويلايمەن

22) مۇتاگات

23) سۈنئىي ئىدراك ۋە مەدەنىيەت ئاخىرلاشقان

24) كىشىلەر نېمىشقا كېچىكتۈرىدۇ?

25) ئۆز-ئۆزىگە بولغان ئىشەنچنى ئاشۇرۇشتىكى جىنس پەرقى (IFD ALD ALDSBCH)

26) Xing.com مەدەنىيەتنى باھالاش

27) Patrick lencioni نىڭ «بىر گۇرۇپپىنىڭ بەش خىل ئۇسۇلى»

28) ھېسداشلىق قىلىش ...

29) خىزمەت تەكلىپىنى تاللاشتا مۇتەخەسسىسلەر ئۈچۈن قايسىسى مۇھىم?

30) كىشىلەر نېمىشقا ئۆزگىرىشكە قارشى تۇرىدۇ (siobhn mchale)

31) ھېسسىياتىڭىزنى قانداق تەڭشىدىڭىز? (ناۋال مۇستاپا m.a.)

32) 21-نومۇرلۇق سىزگە مەڭگۈ پۇل تۆلەيدىغان 21 ماھارەت

33) ھەقىقىي ئەركىنلىك ...

34) باشقىلار بىلەن بولغان ئىشەنچنى ئاشۇرۇشنىڭ 12 خىل ئۇسۇلى (جاستىننىڭ قورالى)

35) تالانتلىق خىزمەتچىنىڭ ئالاھىدىلىكى (ئىختىساسلىقلارنى باشقۇرۇش ئورنى)

36) گۇرۇپپىڭىزنى قوزغىتىش ئۈچۈن 10 كۇنۇپكا

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.

قورقۇنچ

جەدۋەل مۇناسىۋەتلىك

VUCA

مۇناسىۋەتلىك كوئېففىتسېنتى ھالقىلىق قىممىتى

نورمال تەقسىملەش, ۋىليام دېڭىز قىرغىقىدا (ئوقۇغۇچى) r = 0.0353

نەيزە بىلەن نورمال تەقسىمات ئەمەس r = 0.0014

پەقەت نەتىجىلەرنى كۆرسەت > r = 0.0353

تەقسىملەش	نورمال ئەمەس	نورمال	نورمال ئەمەس	نورمال	نورمال	نورمال	نورمال	نورمال
بارلىق سوئاللار بارلىق سوئاللار مېنىڭ ئەڭ قورقىدىغىنىم
مېنىڭ ئەڭ قورقىدىغىنىم
Answer 1	-	ئاجىز مۇسبەت 0.0297	ئاجىز مۇسبەت 0.0298	ئاجىز مەنپىي -0.0106	ئاجىز مۇسبەت 0.0970	ئاجىز مۇسبەت 0.0325	ئاجىز مەنپىي -0.0019	ئاجىز مەنپىي -0.1558
Answer 2	-	ئاجىز مۇسبەت 0.0188	ئاجىز مۇسبەت 0.0076	ئاجىز مەنپىي -0.0360	ئاجىز مۇسبەت 0.0711	ئاجىز مۇسبەت 0.0387	ئاجىز مۇسبەت 0.0082	ئاجىز مەنپىي -0.1011
Answer 3	-	ئاجىز مۇسبەت 0.0026	ئاجىز مەنپىي -0.0170	ئاجىز مەنپىي -0.0443	ئاجىز مەنپىي -0.0458	ئاجىز مۇسبەت 0.0547	ئاجىز مۇسبەت 0.0808	ئاجىز مەنپىي -0.0270
Answer 4	-	ئاجىز مۇسبەت 0.0332	ئاجىز مۇسبەت 0.0285	ئاجىز مەنپىي -0.0006	ئاجىز مۇسبەت 0.0155	ئاجىز مۇسبەت 0.0276	ئاجىز مۇسبەت 0.0105	ئاجىز مەنپىي -0.0917
Answer 5	-	ئاجىز مۇسبەت 0.0122	ئاجىز مۇسبەت 0.1193	ئاجىز مۇسبەت 0.0095	ئاجىز مۇسبەت 0.0721	ئاجىز مۇسبەت 0.0057	ئاجىز مەنپىي -0.0083	ئاجىز مەنپىي -0.1687
Answer 6	-	ئاجىز مۇسبەت 0.0044	ئاجىز مۇسبەت 0.0005	ئاجىز مەنپىي -0.0582	ئاجىز مەنپىي -0.0004	ئاجىز مۇسبەت 0.0210	ئاجىز مۇسبەت 0.0830	ئاجىز مەنپىي -0.0418
Answer 7	-	ئاجىز مۇسبەت 0.0242	ئاجىز مۇسبەت 0.0368	ئاجىز مەنپىي -0.0521	ئاجىز مەنپىي -0.0234	ئاجىز مۇسبەت 0.0403	ئاجىز مۇسبەت 0.0568	ئاجىز مەنپىي -0.0597
Answer 8	-	ئاجىز مۇسبەت 0.0707	ئاجىز مۇسبەت 0.0781	ئاجىز مەنپىي -0.0244	ئاجىز مۇسبەت 0.0140	ئاجىز مۇسبەت 0.0303	ئاجىز مۇسبەت 0.0137	ئاجىز مەنپىي -0.1334
Answer 9	-	ئاجىز مۇسبەت 0.0564	ئاجىز مۇسبەت 0.1531	ئاجىز مۇسبەت 0.0127	ئاجىز مۇسبەت 0.0769	ئاجىز مەنپىي -0.0136	ئاجىز مەنپىي -0.0495	ئاجىز مەنپىي -0.1752
Answer 10	-	ئاجىز مۇسبەت 0.0711	ئاجىز مۇسبەت 0.0700	ئاجىز مەنپىي -0.0127	ئاجىز مۇسبەت 0.0246	ئاجىز مۇسبەت 0.0363	ئاجىز مەنپىي -0.0156	ئاجىز مەنپىي -0.1273
Answer 11	-	ئاجىز مۇسبەت 0.0542	ئاجىز مۇسبەت 0.0488	ئاجىز مۇسبەت 0.0086	ئاجىز مۇسبەت 0.0078	ئاجىز مۇسبەت 0.0162	ئاجىز مۇسبەت 0.0315	ئاجىز مەنپىي -0.1248
Answer 12	-	ئاجىز مۇسبەت 0.0281	ئاجىز مۇسبەت 0.0929	ئاجىز مەنپىي -0.0325	ئاجىز مۇسبەت 0.0361	ئاجىز مۇسبەت 0.0276	ئاجىز مۇسبەت 0.0365	ئاجىز مەنپىي -0.1482
Answer 13	-	ئاجىز مۇسبەت 0.0643	ئاجىز مۇسبەت 0.0916	ئاجىز مەنپىي -0.0418	ئاجىز مۇسبەت 0.0237	ئاجىز مۇسبەت 0.0425	ئاجىز مۇسبەت 0.0239	ئاجىز مەنپىي -0.1558
Answer 14	-	ئاجىز مۇسبەت 0.0697	ئاجىز مۇسبەت 0.1017	ئاجىز مۇسبەت 0.0149	ئاجىز مەنپىي -0.0062	ئاجىز مەنپىي -0.0087	ئاجىز مەنپىي -0.0002	ئاجىز مەنپىي -0.1161
Answer 15	-	ئاجىز مۇسبەت 0.0603	ئاجىز مۇسبەت 0.1299	ئاجىز مەنپىي -0.0379	ئاجىز مۇسبەت 0.0163	ئاجىز مەنپىي -0.0091	ئاجىز مۇسبەت 0.0164	ئاجىز مەنپىي -0.1204
Answer 16	-	ئاجىز مۇسبەت 0.0691	ئاجىز مۇسبەت 0.0221	ئاجىز مەنپىي -0.0305	ئاجىز مەنپىي -0.0515	ئاجىز مۇسبەت 0.0750	ئاجىز مۇسبەت 0.0187	ئاجىز مەنپىي -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

ۋالېرىي كوسېنكو

مەھسۇلات ئىگىسى سائا ئەرمەك ھايۋانلار تۈرى SDIST®

ۋالرىي 1993-يىلى ئىجتىمائىي زەھەرلىك پىسخىكا دوختۇرى بولۇپ, شۇنىڭدىن كېيىن ئۇنىڭ تۈر باشقۇرۇشىغا ئىلتىماس قىلغان.
Valiii دانىۋى ئۇنۋانىغا ئېرىشكەن, ئۇ خوجايىننىڭ تەرەققىي قىلىشىدا تۈر ۋە پروگراممىنىڭ سالاھىيىتىگە ئىنتىلىدىغان بولۇپ, تۈر يول خەرىتىسى (GPM Disutsche Gejeclashicatemation e. V.) ۋە ئايلانما ھەرىكەتلەندۈرگۈچ كۈچ.
ۋالېرىي شىتات ھەرىكەتلەندۈرگۈچ كۈچ كوماندىسىنى ئېلىپ, ئۇنىڭ بىلىمى ۋە تەجرىبىسىنى ئىشلەتكەن.
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