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) Ibikorwa byamasosiyete bijyanye nabakozi mukwezi gushize (yego / oya)

2) Ibikorwa byamasosiyete bijyanye nabakozi mukwezi gushize (Ukuri muri%)

3) Ubwoba

4) Ibibazo bikomeye byugarije igihugu cyanjye

5) Ni izihe mico n'ubushobozi bakoresha abayobozi beza bakoresha mugihe wubaka amakipe yatsinze?

6) Google. Ibintu bigira ingaruka kumatsinda

7) Ibyingenzi byihutirwa byabashaka akazi

8) Niki gituma shebuja umuyobozi ukomeye?

9) Niki gituma abantu batsinze akazi?

10) Witeguye kwakira umushahara muto kugirango ukore kure?

11) Ese imyaka irahari?

12) Ingero mu mwuga

13) Ingero mubuzima

14) Impamvu Zitera Imyaka

15) Impamvu zituma abantu bareka (na Anna ari ngombwa)

16) Kwizerana (#WVS)

17) Ubushakashatsi bwa Oxford

18) Imibereho myiza ya psychologiya

19) Ni hehe wakubera amahirwe ashimishije?

20) Uzakora iki muri iki cyumweru kugirango urebe ubuzima bwawe bwo mumutwe?

21) Mbaho ntekereza ibyahise, ubungubu cyangwa ejo hazaza

22) Mertocracy

23) Ubwenge bwubuhanga no kurangiza umuco

24) Kuki abantu batangara?

25) Itandukaniro ryuburinganire mu kubaka kwigirira icyizere (IFD AllenBach)

26) Xing.com Isuzuma ry'umuco

27) Patrick Lencioni's "Ingaruka eshanu z'ikipe"

28) Kubabarana ni ...

29) Ni ikihe kintu cy'ingenzi kuri kontorwa muguhitamo gutanga akazi?

30) Impamvu abantu barwanya impinduka (by Siobhán Mchale)

31) Nigute ushobora kugenga amarangamutima yawe? (by nawal mustafa m.a.)

32) 21 Ubuhanga bukwishura ubuziraherezo (by Yeremiya Teo / 赵汉昇)

33) Ubwisanzure nyabwo ni ...

34) Inzira 12 zo kubaka ikizere nabandi (by Justin Wright)

35) Ibiranga umukozi ufite impano (ukoresheje ikigo cyubuyobozi cyanditse)

36) Imfunguzo 10 zo gushishikariza ikipe yawe

37) Algebra y'umutimanama (by Vladimir Lefebvre)

38) Ibintu bitatu bitandukanye by'ejo hazaza (by 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.

Ubwoba

Ibishushanyo Isano

VUCA

Bitoroshe agaciro isano coefficient

Isaranganya risanzwe, na William Swal Sset (Umunyeshuri) r = 0.033

Kugabura bisanzwe, by umucumu r = 0.0013

Erekana ibisubizo gusa > r = 0.033

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

Valeri Kosenko

Nyirubwite nyirubwite umushinga sdtest®

Valerii yujuje ibisabwa nka Pedagoge ya Pedagoge-psychologue mu 1993 kandi kuva yakoresheje ubumenyi mu micungire y'umushinga.
Valerii yabonye impamyabumenyi y'ikirenga n'umushinga n'umuyobozi wa gahunda umuyobozi wa 2013. Mu Mushinga wa Shebuja, GPM Deutsche Gür ProjekTagement E. V.) N'imbaraga zigendanwa.
Valerii yakuye ibizamini bitandukanye bya kashe kandi akoresha ubumenyi n'uburambe kugira ngo amenyereho verisiyo y'ubu.
Valerii niwe mwanditsi ushakisha gushidikanya V.U.C. Igitekerezo ukoresheje imbaraga zidasanzwe hamwe n'imibare yimibare muri psychologiya, amatora arenga 20 mpuzamahanga.

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