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) 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

Gambar Korélasi

VUCA

Nilai kritis koefisien gathukane

Distribusi normal, dening William Sefery Gosset (siswa) r = 0.0329

Distribusi Non Non, dening Spearman r = 0.0013

Tampilake asil mung > r = 0.0329

Distribusi	Ora normal	Ora normal	Ora normal	Normal	Normal	Normal	Normal	Normal
Kabeh pitakon Kabeh pitakon Wedi paling gedhe yaiku
Wedi paling gedhe yaiku
Answer 1	-	Positif ringkih 0.0566	Positif ringkih 0.0332	Negatif lemah -0.0170	Positif ringkih 0.0912	Positif ringkih 0.0308	Negatif lemah -0.0153	Negatif lemah -0.1537
Answer 2	-	Positif ringkih 0.0223	Positif ringkih 0.0011	Negatif lemah -0.0442	Positif ringkih 0.0639	Positif ringkih 0.0464	Positif ringkih 0.0120	Negatif lemah -0.0960
Answer 3	-	Negatif lemah -0.0031	Negatif lemah -0.0104	Negatif lemah -0.0407	Negatif lemah -0.0463	Positif ringkih 0.0475	Positif ringkih 0.0779	Negatif lemah -0.0213
Answer 4	-	Positif ringkih 0.0437	Positif ringkih 0.0357	Negatif lemah -0.0197	Positif ringkih 0.0161	Positif ringkih 0.0311	Positif ringkih 0.0187	Negatif lemah -0.0987
Answer 5	-	Positif ringkih 0.0296	Positif ringkih 0.1300	Positif ringkih 0.0124	Positif ringkih 0.0749	Positif ringkih 0.0014	Negatif lemah -0.0231	Negatif lemah -0.1771
Answer 6	-	Negatif lemah -0.0008	Positif ringkih 0.0090	Negatif lemah -0.0613	Negatif lemah -0.0070	Positif ringkih 0.0196	Positif ringkih 0.0803	Negatif lemah -0.0321
Answer 7	-	Positif ringkih 0.0118	Positif ringkih 0.0401	Negatif lemah -0.0693	Negatif lemah -0.0246	Positif ringkih 0.0471	Positif ringkih 0.0623	Negatif lemah -0.0505
Answer 8	-	Positif ringkih 0.0697	Positif ringkih 0.0875	Negatif lemah -0.0316	Positif ringkih 0.0155	Positif ringkih 0.0346	Positif ringkih 0.0098	Negatif lemah -0.1373
Answer 9	-	Positif ringkih 0.0679	Positif ringkih 0.1707	Positif ringkih 0.0105	Positif ringkih 0.0676	Negatif lemah -0.0138	Negatif lemah -0.0545	Negatif lemah -0.1821
Answer 10	-	Positif ringkih 0.0793	Positif ringkih 0.0772	Negatif lemah -0.0208	Positif ringkih 0.0242	Positif ringkih 0.0343	Negatif lemah -0.0152	Negatif lemah -0.1300
Answer 11	-	Positif ringkih 0.0590	Positif ringkih 0.0559	Negatif lemah -0.0071	Positif ringkih 0.0082	Positif ringkih 0.0205	Positif ringkih 0.0266	Negatif lemah -0.1213
Answer 12	-	Positif ringkih 0.0405	Positif ringkih 0.1050	Negatif lemah -0.0363	Positif ringkih 0.0361	Positif ringkih 0.0253	Positif ringkih 0.0277	Negatif lemah -0.1522
Answer 13	-	Positif ringkih 0.0655	Positif ringkih 0.1056	Negatif lemah -0.0439	Positif ringkih 0.0270	Positif ringkih 0.0417	Positif ringkih 0.0152	Negatif lemah -0.1601
Answer 14	-	Positif ringkih 0.0728	Positif ringkih 0.1049	Negatif lemah -0.0002	Negatif lemah -0.0088	Negatif lemah -0.0007	Positif ringkih 0.0061	Negatif lemah -0.1187
Answer 15	-	Positif ringkih 0.0561	Positif ringkih 0.1378	Negatif lemah -0.0415	Positif ringkih 0.0178	Negatif lemah -0.0162	Positif ringkih 0.0194	Negatif lemah -0.1176
Answer 16	-	Positif ringkih 0.0606	Positif ringkih 0.0308	Negatif lemah -0.0348	Negatif lemah -0.0421	Positif ringkih 0.0642	Positif ringkih 0.0250	Negatif lemah -0.0717

Kaca kanggo MS Excel

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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

Pamilik Produk SaaS SDTEST®

Valerii nduweni kualifikasi minangka pedagogue-psikolog sosial ing 1993 lan wiwit nggunakake kawruh ing manajemen proyek.
Valerii pikantuk gelar Master lan kualifikasi manajer proyek lan program ing 2013. Sajrone program Master, dheweke kenal karo Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) lan Spiral Dynamics.
Valerii punika penulis njelajah kahanan sing durung mesthi saka V.U.C.A. konsep nggunakake Spiral Dynamics lan statistik matematika ing psikologi, lan 38 polling internasional.

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