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) សកម្មភាពរបស់ក្រុមហ៊ុនទាក់ទងនឹងបុគ្គលិកនៅខែមុន (មែន / ទេ)

2) សកម្មភាពរបស់ក្រុមហ៊ុនទាក់ទងនឹងបុគ្គលិកនៅខែមុន (ការពិតក្នុង%)

3) ការភ័យខ្លាច

4) បញ្ហាធំបំផុតដែលប្រទេសខ្ញុំកំពុងប្រឈមមុខ

5) តើគុណភាពនិងសមត្ថភាពអ្វីខ្លះដែលអ្នកដឹកនាំល្អប្រើនៅពេលសាងសង់ក្រុមជោគជ័យ?

6) Google ។ កត្តាដែលជះឥទ្ធិពលដល់ក្រុមអ្នកមានប្រសិទ្ធិភាព

7) អាទិភាពសំខាន់ៗរបស់អ្នកស្វែងរកការងារ

8) តើអ្វីដែលធ្វើឱ្យថៅកែក្លាយជាមេដឹកនាំដ៏អស្ចារ្យម្នាក់?

9) តើអ្វីដែលធ្វើឱ្យមនុស្សទទួលបានជោគជ័យនៅកន្លែងធ្វើការ?

10) តើអ្នកត្រៀមខ្លួនទទួលបានប្រាក់ឈ្នួលតិចដើម្បីធ្វើការពីចម្ងាយទេ?

11) តើមានអាយុប៉ុន្មាន?

12) អាយុក្នុងអាជីព

13) អាយុក្នុងជីវិត

14) មូលហេតុនៃអាយុ

15) ហេតុផលដែលធ្វើឱ្យមនុស្សបោះបង់ចោល (ដោយអាណាវីតាល់)

16) តុកចិត្ដ (#WVS)

17) ការស្ទង់មតិសុភមង្គល Oxford

18) សុខុមាលភាពផ្លូវចិត្ត

19) តើឱកាសដ៏រំភើបបំផុតបន្ទាប់របស់អ្នកនៅឯណា?

20) តើអ្នកនឹងធ្វើអ្វីនៅសប្តាហ៍នេះដើម្បីថែរក្សាសុខភាពផ្លូវចិត្តរបស់អ្នក?

21) ខ្ញុំរស់នៅគិតអំពីអតីតកាលបច្ចុប្បន្នបច្ចុប្បន្នបច្ចុប្បន្ន

22) ការអយសដៃ

23) បញ្ញាសិប្បនិម្មិតនិងចុងបញ្ចប់នៃអារ្យធម៌

24) ហេតុអ្វីបានជាមនុស្សពន្យារកំណើត?

25) ភាពខុសគ្នានៃយេនឌ័រក្នុងការកសាងទំនុកចិត្តលើខ្លួនឯង (IFD Allensbach)

26) ការវាយតម្លៃវប្បធម៌ Xing.com

27) ការធ្វើចរាចរណ៍ទាំង 5 របស់ក្រុម ចំនួន 5 នាក់របស់ក្រុម "

28) ការយល់ចិត្តគឺ ...

29) តើអ្វីដែលចាំបាច់សម្រាប់អ្នកឯកទេសខាងព័ត៌មានវិទ្យាក្នុងការជ្រើសរើសការផ្តល់ការងារ?

30) ហេតុអ្វីបានជាមនុស្សទប់ទល់នឹងការផ្លាស់ប្តូរ (ដោយSiobhán Mchale)

31) តើអ្នកអាចគ្រប់គ្រងអារម្មណ៍របស់អ្នកយ៉ាងដូចម្តេច? (ដោយ Nawal Mustafa M.A. )

32) 21 ជំនាញដែលបង់លុយអ្នកជារៀងរហូត (ដោយយេរេមា Teo / 赵汉昇)

33) សេរីភាពពិតប្រាកដគឺ ...

34) វិធី 12 យ៉ាងដើម្បីពង្រឹងការទុកចិត្តជាមួយអ្នកដទៃ (ដោយចាស្ទីនរ៉ាយ)

35) លក្ខណៈពិសេសរបស់និយោជិកដែលមានទេពកោសល្យ (ដោយវិទ្យាស្ថានគ្រប់គ្រងទេពកោសល្យ)

36) គន្លឹះ 10 យ៉ាងដើម្បីជំរុញក្រុមរបស់អ្នក

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.

ការភ័យខ្លាច

តារាង ការជាប់ទាក់ទងគ្នា

VUCA

តម្លៃសំខាន់នៃមេគុណសហសម្ព័ន្ធនេះ

ការចែកចាយធម្មតាដោយវីលៀមស៊ាលីស្សាស (និស្សិត) r = 0.0353

ការចែកចាយមិនមែនធម្មតាដោយ Spearman r = 0.0014

បង្ហាញតែលទ្ធផលប៉ុណ្ណោះ > r = 0.0353

ការចេក	មិនមែនធម្មតាទេ	ដេលធម្ផតា	មិនមែនធម្មតាទេ	ដេលធម្ផតា	ដេលធម្ផតា	ដេលធម្ផតា	ដេលធម្ផតា	ដេលធម្ផតា
សំណួរទាំងអស់ សំណួរទាំងអស់ ការភ័យខ្លាចដ៏អស្ចារ្យបំផុតរបស់ខ្ញុំគឺ
ការភ័យខ្លាចដ៏អស្ចារ្យបំផុតរបស់ខ្ញុំគឺ
Answer 1	-	ខ្សោយវិជ្ជមាន 0.0297	ខ្សោយវិជ្ជមាន 0.0298	ខ្សោយអវិជ្ជមាន -0.0106	ខ្សោយវិជ្ជមាន 0.0970	ខ្សោយវិជ្ជមាន 0.0325	ខ្សោយអវិជ្ជមាន -0.0019	ខ្សោយអវិជ្ជមាន -0.1558
Answer 2	-	ខ្សោយវិជ្ជមាន 0.0188	ខ្សោយវិជ្ជមាន 0.0076	ខ្សោយអវិជ្ជមាន -0.0360	ខ្សោយវិជ្ជមាន 0.0711	ខ្សោយវិជ្ជមាន 0.0387	ខ្សោយវិជ្ជមាន 0.0082	ខ្សោយអវិជ្ជមាន -0.1011
Answer 3	-	ខ្សោយវិជ្ជមាន 0.0026	ខ្សោយអវិជ្ជមាន -0.0170	ខ្សោយអវិជ្ជមាន -0.0443	ខ្សោយអវិជ្ជមាន -0.0458	ខ្សោយវិជ្ជមាន 0.0547	ខ្សោយវិជ្ជមាន 0.0808	ខ្សោយអវិជ្ជមាន -0.0270
Answer 4	-	ខ្សោយវិជ្ជមាន 0.0332	ខ្សោយវិជ្ជមាន 0.0285	ខ្សោយអវិជ្ជមាន -0.0006	ខ្សោយវិជ្ជមាន 0.0155	ខ្សោយវិជ្ជមាន 0.0276	ខ្សោយវិជ្ជមាន 0.0105	ខ្សោយអវិជ្ជមាន -0.0917
Answer 5	-	ខ្សោយវិជ្ជមាន 0.0122	ខ្សោយវិជ្ជមាន 0.1193	ខ្សោយវិជ្ជមាន 0.0095	ខ្សោយវិជ្ជមាន 0.0721	ខ្សោយវិជ្ជមាន 0.0057	ខ្សោយអវិជ្ជមាន -0.0083	ខ្សោយអវិជ្ជមាន -0.1687
Answer 6	-	ខ្សោយវិជ្ជមាន 0.0044	ខ្សោយវិជ្ជមាន 0.0005	ខ្សោយអវិជ្ជមាន -0.0582	ខ្សោយអវិជ្ជមាន -0.0004	ខ្សោយវិជ្ជមាន 0.0210	ខ្សោយវិជ្ជមាន 0.0830	ខ្សោយអវិជ្ជមាន -0.0418
Answer 7	-	ខ្សោយវិជ្ជមាន 0.0242	ខ្សោយវិជ្ជមាន 0.0368	ខ្សោយអវិជ្ជមាន -0.0521	ខ្សោយអវិជ្ជមាន -0.0234	ខ្សោយវិជ្ជមាន 0.0403	ខ្សោយវិជ្ជមាន 0.0568	ខ្សោយអវិជ្ជមាន -0.0597
Answer 8	-	ខ្សោយវិជ្ជមាន 0.0707	ខ្សោយវិជ្ជមាន 0.0781	ខ្សោយអវិជ្ជមាន -0.0244	ខ្សោយវិជ្ជមាន 0.0140	ខ្សោយវិជ្ជមាន 0.0303	ខ្សោយវិជ្ជមាន 0.0137	ខ្សោយអវិជ្ជមាន -0.1334
Answer 9	-	ខ្សោយវិជ្ជមាន 0.0564	ខ្សោយវិជ្ជមាន 0.1531	ខ្សោយវិជ្ជមាន 0.0127	ខ្សោយវិជ្ជមាន 0.0769	ខ្សោយអវិជ្ជមាន -0.0136	ខ្សោយអវិជ្ជមាន -0.0495	ខ្សោយអវិជ្ជមាន -0.1752
Answer 10	-	ខ្សោយវិជ្ជមាន 0.0711	ខ្សោយវិជ្ជមាន 0.0700	ខ្សោយអវិជ្ជមាន -0.0127	ខ្សោយវិជ្ជមាន 0.0246	ខ្សោយវិជ្ជមាន 0.0363	ខ្សោយអវិជ្ជមាន -0.0156	ខ្សោយអវិជ្ជមាន -0.1273
Answer 11	-	ខ្សោយវិជ្ជមាន 0.0542	ខ្សោយវិជ្ជមាន 0.0488	ខ្សោយវិជ្ជមាន 0.0086	ខ្សោយវិជ្ជមាន 0.0078	ខ្សោយវិជ្ជមាន 0.0162	ខ្សោយវិជ្ជមាន 0.0315	ខ្សោយអវិជ្ជមាន -0.1248
Answer 12	-	ខ្សោយវិជ្ជមាន 0.0281	ខ្សោយវិជ្ជមាន 0.0929	ខ្សោយអវិជ្ជមាន -0.0325	ខ្សោយវិជ្ជមាន 0.0361	ខ្សោយវិជ្ជមាន 0.0276	ខ្សោយវិជ្ជមាន 0.0365	ខ្សោយអវិជ្ជមាន -0.1482
Answer 13	-	ខ្សោយវិជ្ជមាន 0.0643	ខ្សោយវិជ្ជមាន 0.0916	ខ្សោយអវិជ្ជមាន -0.0418	ខ្សោយវិជ្ជមាន 0.0237	ខ្សោយវិជ្ជមាន 0.0425	ខ្សោយវិជ្ជមាន 0.0239	ខ្សោយអវិជ្ជមាន -0.1558
Answer 14	-	ខ្សោយវិជ្ជមាន 0.0697	ខ្សោយវិជ្ជមាន 0.1017	ខ្សោយវិជ្ជមាន 0.0149	ខ្សោយអវិជ្ជមាន -0.0062	ខ្សោយអវិជ្ជមាន -0.0087	ខ្សោយអវិជ្ជមាន -0.0002	ខ្សោយអវិជ្ជមាន -0.1161
Answer 15	-	ខ្សោយវិជ្ជមាន 0.0603	ខ្សោយវិជ្ជមាន 0.1299	ខ្សោយអវិជ្ជមាន -0.0379	ខ្សោយវិជ្ជមាន 0.0163	ខ្សោយអវិជ្ជមាន -0.0091	ខ្សោយវិជ្ជមាន 0.0164	ខ្សោយអវិជ្ជមាន -0.1204
Answer 16	-	ខ្សោយវិជ្ជមាន 0.0691	ខ្សោយវិជ្ជមាន 0.0221	ខ្សោយអវិជ្ជមាន -0.0305	ខ្សោយអវិជ្ជមាន -0.0515	ខ្សោយវិជ្ជមាន 0.0750	ខ្សោយវិជ្ជមាន 0.0187	ខ្សោយអវិជ្ជមាន -0.0696

នាំចេញទៅជា MS Excel

មុខងារនេះនឹងមាននៅក្នុងការស្ទង់មតិ VUCA ផ្ទាល់ខ្លួនរបស់អ្នក។

យល់ព្រម

You can not only just create your poll in the ពន្ធ «អ្នករចនាម៉ូដស្ទង់មតិ V.U.C.A» (with a unique link and your logo) but also you can earn money by selling its results in the ពន្ធ «ហាងលក់ការស្ទង់មតិ», as already the authors of polls.

If you participated in VUCA polls, you can see your results and compare them with the overall polls results, which are constantly growing, in your personal account after purchasing ពន្ធ «របស់ខ្ញុំ SDT»

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

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

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

2023.10.13

valerii kesenko

ម្ចាស់ផលិតផលសារ៉ាសសាន់គម្រោងSDTEST®

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Valerii គឺជាអ្នកនិពន្ធនៃការស្វែងយល់ពីភាពមិនប្រាកដប្រជានៃ V.U.C.A. គំនិតដោយប្រើសក្ដានុពលនៃវង់និងស្ថិតិគណិតវិទ្យាផ្នែកចិត្តវិទ្យាមានជាង 20 នាក់។

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