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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:


1) Tumindak perusahaan sing ana gandhengane karo personel ing wulan kepungkur (ya / ora)

2) Tumindak perusahaan sing ana hubungane karo personel ing wulan kepungkur (kasunyatan ing%)

3) Wedi

4) Masalah paling gedhe sing madhep negaraku

5) Apa kuwalitas lan kabisan nindakake pimpinan sing apik nalika mbangun tim sukses?

6) Google. Faktor sing duwe pengaruh efak

7) Prioritas utama sing golek

8) Apa sing dadi pimpinan sing apik?

9) Apa sing ndadekake wong sukses ing kerja?

10) Apa sampeyan siap nampa mbayar sing kurang kanggo nyambut gawe?

11) Apa eganisme ana?

12) Ageisme ing karir

13) Ageism Ing Urip

14) Nimbulaké agama

15) Alasan Napa Wong Nyerah (dening Anna Vital)

16) Kapercayan (#WVS)

17) Survey rasa seneng Oxford

18) Kesejahteraan psikologis

19) Ing endi sampeyan bakal dadi kesempatan paling apik sampeyan?

20) Apa sing bakal ditindakake minggu iki kanggo njaga kesehatan mental sampeyan?

21) Aku urip mikir babagan kepungkur, saiki utawa masa depan

22) Meritokrasi

23) Intelijen buatan lan pungkasan peradaban

24) Napa wong sing nompo?

25) Bedane Gender ing Bangunan Kapercayan Dhiri (IFD ALLENSBACH)

26) Xing.com Taksiran Budaya

27) Patrick Lencioni "The Lima Dysfunctions tim"

28) Empathy iku ...

29) Apa sing penting kanggo milih penawaran proyek?

30) Napa wong nolak ganti (dening siobhán Mchale)

31) Kepiye carane ngatur emosi? (dening Nawal Mustafa M.A.)

32) 21 katrampilan sing mbayar sampeyan ing salawas-lawase (dening Yeremia Too / 赵汉昇)

33) Kabebasan nyata yaiku ...

34) 12 cara kanggo mbangun kapercayan karo wong liya (dening Justin Wright)

35) Karakteristik karyawan sing duwe bakat (dening Institut Manajemen Talent)

36) 10 tombol kanggo motivasi tim sampeyan

37) Algebra of Conscience (dening Vladimir Lefebvre)

38) Telung Kemungkinan Beda ing Masa Depan (dening Dr. Clare W. Graves)


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.

Wedi

Negara
Language
-
Mail
Ngeculke
Nilai kritis koefisien gathukane
Distribusi normal, dening William Sefery Gosset (siswa) r = 0.0331
Distribusi normal, dening William Sefery Gosset (siswa) r = 0.0331
Distribusi Non Non, dening Spearman r = 0.0014
DistribusiOra
normal
Ora
normal
Ora
normal
NormalNormalNormalNormalNormal
Kabeh pitakon
Kabeh pitakon
Wedi paling gedhe yaiku
Wedi paling gedhe yaiku
Answer 1-
Positif ringkih
0.0536
Positif ringkih
0.0287
Negatif lemah
-0.0176
Positif ringkih
0.0902
Positif ringkih
0.0311
Negatif lemah
-0.0122
Negatif lemah
-0.1507
Answer 2-
Positif ringkih
0.0195
Negatif lemah
-0.0003
Negatif lemah
-0.0428
Positif ringkih
0.0663
Positif ringkih
0.0454
Positif ringkih
0.0101
Negatif lemah
-0.0934
Answer 3-
Negatif lemah
-0.0058
Negatif lemah
-0.0113
Negatif lemah
-0.0406
Negatif lemah
-0.0443
Positif ringkih
0.0473
Positif ringkih
0.0786
Negatif lemah
-0.0220
Answer 4-
Positif ringkih
0.0432
Positif ringkih
0.0335
Negatif lemah
-0.0169
Positif ringkih
0.0146
Positif ringkih
0.0308
Positif ringkih
0.0184
Negatif lemah
-0.0981
Answer 5-
Positif ringkih
0.0250
Positif ringkih
0.1247
Positif ringkih
0.0131
Positif ringkih
0.0719
Positif ringkih
0.0008
Negatif lemah
-0.0201
Negatif lemah
-0.1738
Answer 6-
Negatif lemah
-0.0034
Positif ringkih
0.0079
Negatif lemah
-0.0629
Negatif lemah
-0.0061
Positif ringkih
0.0202
Positif ringkih
0.0826
Negatif lemah
-0.0334
Answer 7-
Positif ringkih
0.0108
Positif ringkih
0.0381
Negatif lemah
-0.0683
Negatif lemah
-0.0233
Positif ringkih
0.0480
Positif ringkih
0.0635
Negatif lemah
-0.0527
Answer 8-
Positif ringkih
0.0694
Positif ringkih
0.0833
Negatif lemah
-0.0312
Positif ringkih
0.0143
Positif ringkih
0.0355
Positif ringkih
0.0131
Negatif lemah
-0.1380
Answer 9-
Positif ringkih
0.0629
Positif ringkih
0.1661
Positif ringkih
0.0092
Positif ringkih
0.0686
Negatif lemah
-0.0121
Negatif lemah
-0.0519
Negatif lemah
-0.1824
Answer 10-
Positif ringkih
0.0754
Positif ringkih
0.0707
Negatif lemah
-0.0182
Positif ringkih
0.0232
Positif ringkih
0.0331
Negatif lemah
-0.0156
Negatif lemah
-0.1307
Answer 11-
Positif ringkih
0.0578
Positif ringkih
0.0517
Negatif lemah
-0.0105
Positif ringkih
0.0074
Positif ringkih
0.0211
Positif ringkih
0.0311
Negatif lemah
-0.1220
Answer 12-
Positif ringkih
0.0365
Positif ringkih
0.1003
Negatif lemah
-0.0360
Positif ringkih
0.0342
Positif ringkih
0.0263
Positif ringkih
0.0299
Negatif lemah
-0.1515
Answer 13-
Positif ringkih
0.0619
Positif ringkih
0.1037
Negatif lemah
-0.0455
Positif ringkih
0.0266
Positif ringkih
0.0436
Positif ringkih
0.0179
Negatif lemah
-0.1611
Answer 14-
Positif ringkih
0.0713
Positif ringkih
0.1013
Positif ringkih
0.0011
Negatif lemah
-0.0088
Negatif lemah
-0.0007
Positif ringkih
0.0058
Negatif lemah
-0.1177
Answer 15-
Positif ringkih
0.0542
Positif ringkih
0.1353
Negatif lemah
-0.0401
Positif ringkih
0.0170
Negatif lemah
-0.0152
Positif ringkih
0.0209
Negatif lemah
-0.1185
Answer 16-
Positif ringkih
0.0584
Positif ringkih
0.0254
Negatif lemah
-0.0382
Negatif lemah
-0.0402
Positif ringkih
0.0657
Positif ringkih
0.0271
Negatif lemah
-0.0723


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

2023.10.13
Valerii Kosenko
Pemilik Produk Saas Pet Project SDTES®

Valerii layak minangka psikologi pedagoga sosial ing taun 1993 lan wiwit ngetrapake pengetahuan ing Manajemen Proyek.
Valerii entuk gelar master lan kualifikasi proyek lan manajer program ing taun 2013. Sajrone program Master dheweke, dheweke wis kenal karo Proyek Roadmap (GPM DeutscheFTFFT Für Projektmanagement E. V.) lan Dinamika Spiral.
Valerii njupuk macem-macem tes Dinamika spiral lan nggunakake kawruh lan pengalaman kanggo adaptasi versi SDTTTTTt.
Valerii minangka penulis kanggo njelajah kahanan sing durung mesthi ing V.U.C.A. Konsep nggunakake Dinamika Spiral lan statistik matematika ing Psikologi, luwih saka 20 jajak pendapat internasional.
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Hai ana! Ayo kula takon, apa sampeyan wis kenal karo dinamika spiral?