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) Lampah perusahaan dina hubungan personil di bulan kamari (leres / henteu)

2) Lampah perusahaan dina hubungan personil dina bulan kamari (kanyataan di%)

3) Sieun

4) Masalah panggedéna nyanghareupan nagara kuring

5) Naon sipat sareng kamampuan ngalakukeun pimpinan anu saé dianggo nalika ngawangun tim anu suksés?

6) Google. Faktor anu dampak tim épéktipitas

7) Prioritas utama pangurus padamelan

8) Naon anu ngajadikeun boss pamimpin hébat?

9) Naon anu ngajadikeun jalma suksés di damel?

10) Naha anjeun siap nampi anu kirang mayar jarak jauh?

11) Naha umurna aya?

12) Umur dina karir

13) Yamanisme dina kahirupan

14) Nyababkeun yuswa

15) Alesan kunaon jalma nyerah (ku Anna penting)

16) Amanah (#WVS)

17) Survey Kabagjaan

18) Sumanget psikologis

19) Dimana kasempetan anu paling pikaresepeun anjeun?

20) Naon anu anjeun bakal laksanakeun minggu ieu pikeun ngarawat kaséhatan méntal anjeun?

21) Kuring cicing mikir ngeunaan jaman baheula, ayeuna atanapi masa depan

22) Meritokrasi

23) Intelijen jieunan sareng tungtung peradaban

24) Naha jalma-jalma singricinate?

25) Bédana gender dina ngawangun kapercayaan diri (ift Allensbach)

26) Xing.com convigasi budaya

27) Patrick Lenconi's "lima dysfunction tina tim"

28) Empati nyaéta ...

29) Naon penting pikeun spesialis dina milih tawaran padamelan?

30) Naha jalma nolak parobahan (ku SiobHán mchale)

31) Kumaha anjeun ngatasi émosi anjeun? (ku Nawalsafa Maya M.a.)

32) 21 Kaahlian anu mayar anjeun salamina (ku Jeremiah Too / 赵汉昇)

33) Kabébasan nyata ...

34) 12 cara pikeun ngawangun kapercayaan sareng batur (ku justin witht)

35) Ciri tina karyawan anu berakat (ku Nebus manajemén bakat

36) 10 konci pikeun motivasi tim anjeun

37) Aljabar Nurani (ku Vladimir Lefebvre)

38) Tilu Kemungkinan Béda tina Masa Depan (ku 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.

Sieun

grafik Korelasi

VUCA

Nilai kritis koefisien korélasi

Sebaran normal, ku William laut anu gumpal (mahasiswa) r = 0.033

Sebaran non normal, ku Spearman r = 0.0013

Nunjukkeun ngan hasil > r = 0.033

Sebaran	Non normal	Non normal	Non normal	Normal	Normal	Normal	Normal	Normal
Kabeh patarosan Kabeh patarosan Kasieun kuring
Kasieun kuring
Answer 1	-	Positip lemah 0.0559	Positip lemah 0.0315	Négatip lemah -0.0170	Positip lemah 0.0920	Positip lemah 0.0294	Négatip lemah -0.0124	Négatip lemah -0.1539
Answer 2	-	Positip lemah 0.0229	Négatip lemah -0.0002	Négatip lemah -0.0448	Positip lemah 0.0636	Positip lemah 0.0445	Positip lemah 0.0134	Négatip lemah -0.0939
Answer 3	-	Négatip lemah -0.0032	Négatip lemah -0.0121	Négatip lemah -0.0416	Négatip lemah -0.0462	Positip lemah 0.0466	Positip lemah 0.0788	Négatip lemah -0.0195
Answer 4	-	Positip lemah 0.0438	Positip lemah 0.0348	Négatip lemah -0.0195	Positip lemah 0.0153	Positip lemah 0.0300	Positip lemah 0.0207	Négatip lemah -0.0980
Answer 5	-	Positip lemah 0.0304	Positip lemah 0.1282	Positip lemah 0.0135	Positip lemah 0.0734	Négatip lemah -0.0013	Négatip lemah -0.0200	Négatip lemah -0.1757
Answer 6	-	Négatip lemah -0.0002	Positip lemah 0.0082	Négatip lemah -0.0627	Négatip lemah -0.0083	Positip lemah 0.0193	Positip lemah 0.0831	Négatip lemah -0.0315
Answer 7	-	Positip lemah 0.0126	Positip lemah 0.0381	Négatip lemah -0.0687	Négatip lemah -0.0243	Positip lemah 0.0469	Positip lemah 0.0642	Négatip lemah -0.0515
Answer 8	-	Positip lemah 0.0698	Positip lemah 0.0848	Négatip lemah -0.0327	Positip lemah 0.0148	Positip lemah 0.0345	Positip lemah 0.0134	Négatip lemah -0.1365
Answer 9	-	Positip lemah 0.0668	Positip lemah 0.1676	Positip lemah 0.0083	Positip lemah 0.0693	Négatip lemah -0.0131	Négatip lemah -0.0516	Négatip lemah -0.1818
Answer 10	-	Positip lemah 0.0782	Positip lemah 0.0753	Négatip lemah -0.0204	Positip lemah 0.0247	Positip lemah 0.0342	Négatip lemah -0.0131	Négatip lemah -0.1304
Answer 11	-	Positip lemah 0.0578	Positip lemah 0.0532	Négatip lemah -0.0096	Positip lemah 0.0087	Positip lemah 0.0195	Positip lemah 0.0311	Négatip lemah -0.1196
Answer 12	-	Positip lemah 0.0390	Positip lemah 0.1037	Négatip lemah -0.0358	Positip lemah 0.0358	Positip lemah 0.0250	Positip lemah 0.0299	Négatip lemah -0.1520
Answer 13	-	Positip lemah 0.0644	Positip lemah 0.1048	Négatip lemah -0.0448	Positip lemah 0.0268	Positip lemah 0.0417	Positip lemah 0.0178	Négatip lemah -0.1600
Answer 14	-	Positip lemah 0.0712	Positip lemah 0.1021	Négatip lemah -0.0007	Négatip lemah -0.0088	Négatip lemah -0.0011	Positip lemah 0.0088	Négatip lemah -0.1169
Answer 15	-	Positip lemah 0.0557	Positip lemah 0.1365	Négatip lemah -0.0423	Positip lemah 0.0177	Négatip lemah -0.0162	Positip lemah 0.0224	Négatip lemah -0.1179
Answer 16	-	Positip lemah 0.0591	Positip lemah 0.0273	Négatip lemah -0.0386	Négatip lemah -0.0400	Positip lemah 0.0653	Positip lemah 0.0284	Négatip lemah -0.0708

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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

Pitunjuk produk saas petas piaraan SDTest®

Valeri dibébas salaku psagog sosial-psagolog di 1993 sareng parantos ngalarapkeun kanyaho-daya dina manajemén Prakték.
Valeri ngagaduhan gelar Master sareng proyék sareng Program Ku Kode Kualifikasi dina taun 2013. Salila program jalanna, gpm dysellschman Für prondekherch.) sareng dinamis spelykschman.
Valeri nyandak sababaraha dinamika deadika sareng nganggo kanyaho sareng pangalaman na pikeun adaptasi versi ayeuna halaman sdtest.
Valeri nyaéta panulis ngajalajah kateupastian tina V.u.A.A. Konsep nganggo dinamika spiral sareng statistik matematika dina psikologi, langkung ti 20 pemancip internasional.

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