1 Mathematical Psychology
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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: 

  1. 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? 
  2. How does the mathematical approach in mathematical psychology differ from other branches of psychology, like psychophysics and psychometrics? 
  3. 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:

  1. Advocating quantitative methods broadly. Mathematical psychology emerged partly to push psychology to embrace quantitative modeling and mathematics beyond basic statistics.
  2. Drawing from diverse mathematical tools. With greater training in mathematics, mathematical psychologists utilize more advanced and varied mathematical techniques like topology and differential geometry.
  3. Linking models and experiments. Mathematical psychologists emphasize tightly connecting experimental design and statistical analysis, with experiments created to test specific models.
  4. Favoring theoretical models. Mathematical psychology incorporates "pure" mathematical results and prefers analytic, hand-fitted models over data-driven computer models.
  5. 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:


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2) Tindakan syarikat berhubung dengan kakitangan pada bulan lepas (fakta dalam%)

3) Ketakutan

4) Masalah terbesar yang dihadapi negara saya

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7) Keutamaan utama pencari kerja

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9) Apa yang membuat orang berjaya di tempat kerja?

10) Adakah anda bersedia untuk menerima bayaran yang kurang untuk bekerja dari jauh?

11) Adakah umur wujud?

12) Ageism dalam kerjaya

13) Umur dalam hidup

14) Punca umur

15) Sebab Mengapa Orang Menyerah (oleh Anna Vital)

16) Kepercayaan (#WVS)

17) Kajian Kebahagiaan Oxford

18) Kesejahteraan psikologi

19) Di manakah peluang paling menarik seterusnya?

20) Apa yang akan anda lakukan minggu ini untuk menjaga kesihatan mental anda?

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22) Meritokrasi

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26) Xing.com Penilaian Budaya

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33) Kebebasan sebenar adalah ...

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39) Tindakan untuk Membina Kepercayaan Diri yang Tidak Tergoyah (oleh Suren Samarchyan)

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.

Ketakutan

negara
bahasa
-
Mail
Mengira semula
Nilai kritikal pekali korelasi
Pengagihan Normal, oleh William Sealy Gosset (Pelajar) r = 0.0315
Pengagihan Normal, oleh William Sealy Gosset (Pelajar) r = 0.0315
Pengedaran tidak normal, oleh Spearman r = 0.0013
PengedaranTidak
normal
Tidak
normal
Tidak
normal
BiasaBiasaBiasaBiasaBiasa
Semua soalan
Semua soalan
Ketakutan terbesar saya adalah
Ketakutan terbesar saya adalah
Answer 1-
Lemah positif
0.0543
Lemah positif
0.0273
Lemah negatif
-0.0190
Lemah positif
0.0935
Lemah positif
0.0385
Lemah negatif
-0.0161
Lemah negatif
-0.1550
Answer 2-
Lemah positif
0.0175
Lemah negatif
-0.0076
Lemah negatif
-0.0388
Lemah positif
0.0638
Lemah positif
0.0496
Lemah positif
0.0135
Lemah negatif
-0.0956
Answer 3-
Lemah negatif
-0.0015
Lemah negatif
-0.0091
Lemah negatif
-0.0472
Lemah negatif
-0.0424
Lemah positif
0.0499
Lemah positif
0.0762
Lemah negatif
-0.0221
Answer 4-
Lemah positif
0.0450
Lemah positif
0.0322
Lemah negatif
-0.0266
Lemah positif
0.0171
Lemah positif
0.0375
Lemah positif
0.0257
Lemah negatif
-0.1041
Answer 5-
Lemah positif
0.0263
Lemah positif
0.1264
Lemah positif
0.0099
Lemah positif
0.0744
Lemah positif
0.0015
Lemah negatif
-0.0157
Lemah negatif
-0.1765
Answer 6-
Lemah positif
0.0007
Lemah positif
0.0049
Lemah negatif
-0.0626
Lemah negatif
-0.0111
Lemah positif
0.0263
Lemah positif
0.0853
Lemah negatif
-0.0360
Answer 7-
Lemah positif
0.0119
Lemah positif
0.0323
Lemah negatif
-0.0680
Lemah negatif
-0.0311
Lemah positif
0.0535
Lemah positif
0.0701
Lemah negatif
-0.0523
Answer 8-
Lemah positif
0.0653
Lemah positif
0.0710
Lemah negatif
-0.0284
Lemah positif
0.0134
Lemah positif
0.0393
Lemah positif
0.0167
Lemah negatif
-0.1337
Answer 9-
Lemah positif
0.0774
Lemah positif
0.1611
Lemah positif
0.0055
Lemah positif
0.0601
Lemah negatif
-0.0074
Lemah negatif
-0.0486
Lemah negatif
-0.1816
Answer 10-
Lemah positif
0.0763
Lemah positif
0.0633
Lemah negatif
-0.0124
Lemah positif
0.0267
Lemah positif
0.0355
Lemah negatif
-0.0106
Lemah negatif
-0.1330
Answer 11-
Lemah positif
0.0633
Lemah positif
0.0516
Lemah negatif
-0.0083
Lemah positif
0.0095
Lemah positif
0.0269
Lemah positif
0.0254
Lemah negatif
-0.1273
Answer 12-
Lemah positif
0.0435
Lemah positif
0.0911
Lemah negatif
-0.0333
Lemah positif
0.0326
Lemah positif
0.0356
Lemah positif
0.0264
Lemah negatif
-0.1527
Answer 13-
Lemah positif
0.0715
Lemah positif
0.0923
Lemah negatif
-0.0386
Lemah positif
0.0277
Lemah positif
0.0442
Lemah positif
0.0154
Lemah negatif
-0.1632
Answer 14-
Lemah positif
0.0816
Lemah positif
0.0879
Lemah negatif
-0.0058
Lemah negatif
-0.0120
Lemah positif
0.0073
Lemah positif
0.0149
Lemah negatif
-0.1202
Answer 15-
Lemah positif
0.0548
Lemah positif
0.1236
Lemah negatif
-0.0354
Lemah positif
0.0119
Lemah negatif
-0.0137
Lemah positif
0.0269
Lemah negatif
-0.1157
Answer 16-
Lemah positif
0.0714
Lemah positif
0.0218
Lemah negatif
-0.0386
Lemah negatif
-0.0390
Lemah positif
0.0742
Lemah positif
0.0186
Lemah negatif
-0.0766


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[1] https://twitter.com/wileyprof
[2] https://colinallen.dnsalias.org
[3] https://philpeople.org/profiles/colin-allen

2023.10.13
FearpersonqualitiesprojectorganizationalstructureRACIresponsibilitymatrixCritical ChainProject Managementfocus factorJiraempathyleadersbossGermanyChinaPolicyUkraineRussiawarvolatilityuncertaintycomplexityambiguityVUCArelocatejobproblemcountryreasongive upobjectivekeyresultmathematicalpsychologyMBTIHR metricsstandardDEIcorrelationriskscoringmodelGame TheoryPrisoner's Dilemma
Valerii Kosenko
Pemilik Produk SaaS SDTEST®

Valerii telah layak sebagai pedagogue-psikologi sosial pada tahun 1993 dan sejak itu telah menggunakan pengetahuannya dalam pengurusan projek.
Valerii memperoleh ijazah Sarjana dan kelayakan pengurus projek dan program pada tahun 2013. Semasa program Sarjananya, beliau mengenali Pelan Hala Tuju Projek (GPM Deutsche Gesellschaft für Projektmanagement e. V.) dan Spiral Dynamics.
Valerii ialah pengarang meneroka ketidakpastian V.U.C.A. konsep menggunakan Spiral Dynamics dan statistik matematik dalam psikologi, dan 38 tinjauan antarabangsa.
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