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) Tindakan syarikat berhubung dengan kakitangan pada bulan lalu (ya / tidak)

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

3) Ketakutan

4) Masalah terbesar yang dihadapi negara saya

5) Apakah kualiti dan kebolehan yang digunakan oleh pemimpin yang baik ketika membina pasukan yang berjaya?

6) Google. Faktor yang memberi kesan kepada pasukan yang kuat

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8) Apa yang menjadikan bos sebagai pemimpin yang hebat?

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?

21) Saya hidup memikirkan masa lalu, masa kini atau masa depan saya

22) Meritokrasi

23) Kecerdasan buatan dan akhir tamadun

24) Mengapa orang menunda -nunda?

25) Perbezaan jantina dalam membina keyakinan diri (IFD Allensbach)

26) Xing.com Penilaian Budaya

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29) Apa yang penting untuk pakar IT dalam memilih tawaran pekerjaan?

30) Mengapa Orang Menentang Perubahan (oleh Siobhán McHale)

31) Bagaimana anda mengawal emosi anda? (Oleh Nawal Mustafa M.A.)

32) 21 Kemahiran yang Membayar Anda Selamanya (oleh Jeremiah Teo / 赵汉昇)

33) Kebebasan sebenar adalah ...

34) 12 cara untuk membina kepercayaan dengan orang lain (oleh Justin Wright)

35) Ciri -ciri pekerja berbakat (oleh Institut Pengurusan Bakat)

36) 10 kunci untuk memotivasi pasukan anda

37) Algebra of Conscience (oleh Vladimir Lefebvre)

38) Tiga Kemungkinan Berbeza Masa Depan (oleh 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.

Ketakutan

carta Korelasi

VUCA

Nilai kritikal pekali korelasi

Pengagihan Normal, oleh William Sealy Gosset (Pelajar) r = 0.0331

Pengedaran tidak normal, oleh Spearman r = 0.0013

Tunjukkan hanya hasil > r = 0.0331

Pengedaran	Tidak normal	Tidak normal	Tidak normal	Biasa	Biasa	Biasa	Biasa	Biasa
Semua soalan Semua soalan Ketakutan terbesar saya adalah
Ketakutan terbesar saya adalah
Answer 1	-	Lemah positif 0.0562	Lemah positif 0.0311	Lemah negatif -0.0164	Lemah positif 0.0903	Lemah positif 0.0301	Lemah negatif -0.0120	Lemah negatif -0.1534
Answer 2	-	Lemah positif 0.0217	Lemah positif 0.0011	Lemah negatif -0.0455	Lemah positif 0.0660	Lemah positif 0.0440	Lemah positif 0.0117	Lemah negatif -0.0942
Answer 3	-	Lemah negatif -0.0034	Lemah negatif -0.0104	Lemah negatif -0.0419	Lemah negatif -0.0451	Lemah positif 0.0462	Lemah positif 0.0780	Lemah negatif -0.0204
Answer 4	-	Lemah positif 0.0436	Lemah positif 0.0362	Lemah negatif -0.0177	Lemah positif 0.0150	Lemah positif 0.0296	Lemah positif 0.0189	Lemah negatif -0.0984
Answer 5	-	Lemah positif 0.0298	Lemah positif 0.1270	Lemah positif 0.0133	Lemah positif 0.0724	Lemah negatif -0.0002	Lemah negatif -0.0199	Lemah negatif -0.1742
Answer 6	-	Lemah negatif -0.0003	Lemah positif 0.0089	Lemah negatif -0.0627	Lemah negatif -0.0074	Lemah positif 0.0190	Lemah positif 0.0825	Lemah negatif -0.0321
Answer 7	-	Lemah positif 0.0123	Lemah positif 0.0388	Lemah negatif -0.0684	Lemah negatif -0.0238	Lemah positif 0.0468	Lemah positif 0.0631	Lemah negatif -0.0517
Answer 8	-	Lemah positif 0.0699	Lemah positif 0.0857	Lemah negatif -0.0318	Lemah positif 0.0150	Lemah positif 0.0341	Lemah positif 0.0125	Lemah negatif -0.1372
Answer 9	-	Lemah positif 0.0666	Lemah positif 0.1681	Lemah positif 0.0094	Lemah positif 0.0694	Lemah negatif -0.0131	Lemah negatif -0.0533	Lemah negatif -0.1815
Answer 10	-	Lemah positif 0.0776	Lemah positif 0.0744	Lemah negatif -0.0185	Lemah positif 0.0224	Lemah positif 0.0352	Lemah negatif -0.0135	Lemah negatif -0.1293
Answer 11	-	Lemah positif 0.0585	Lemah positif 0.0531	Lemah negatif -0.0094	Lemah positif 0.0086	Lemah positif 0.0195	Lemah positif 0.0313	Lemah negatif -0.1200
Answer 12	-	Lemah positif 0.0378	Lemah positif 0.1030	Lemah negatif -0.0357	Lemah positif 0.0350	Lemah positif 0.0261	Lemah positif 0.0297	Lemah negatif -0.1510
Answer 13	-	Lemah positif 0.0642	Lemah positif 0.1044	Lemah negatif -0.0454	Lemah positif 0.0259	Lemah positif 0.0424	Lemah positif 0.0183	Lemah negatif -0.1595
Answer 14	-	Lemah positif 0.0718	Lemah positif 0.1034	Lemah negatif -0.0003	Lemah negatif -0.0085	Lemah negatif -0.0016	Lemah positif 0.0074	Lemah negatif -0.1172
Answer 15	-	Lemah positif 0.0550	Lemah positif 0.1382	Lemah negatif -0.0418	Lemah positif 0.0181	Lemah negatif -0.0163	Lemah positif 0.0211	Lemah negatif -0.1183
Answer 16	-	Lemah positif 0.0591	Lemah positif 0.0276	Lemah negatif -0.0384	Lemah negatif -0.0397	Lemah positif 0.0651	Lemah positif 0.0280	Lemah negatif -0.0710

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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 SDTest®

Valerii layak sebagai ahli pedagogi sosial-psikologi pada tahun 1993 dan sejak itu telah menggunakan pengetahuannya dalam pengurusan projek.
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