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) Omume nke ụlọ ọrụ metụtara ndị ọrụ nọ n'ọnwa gara aga (ee / Mba)

2) Omume nke ụlọ ọrụ metụtara ndị ọrụ nọ n'ọnwa gara aga (eziokwu na%)

3) Atughi egwu

4) Nnukwu nsogbu chere obodo m

5) Olee àgwà na ikike na-eme ezi ndị nduzi na-eji mgbe ha na-eme ihe ọma?

6) Google. Ihe ndị na-emetụta otu ndị otu

7) Isi ihe ndị na-achọ ọrụ

8) Kedu ihe na-eme onye isi nnukwu onye ndu?

9) Gịnị na-eme ka ndị mmadụ nwee ihe ịga nke ọma n'ọrụ?

10) Ready dịla njikere ịnata obere ụgwọ ịrụ ọrụ?

11) Ọdịbi dị adị?

12) Ọhụrụ na Ọrụ

13) Ọhụrụ na ndụ

14) Na-akpata afọ ojuju

15) Ihe kpatara ndị mmadụ ji hapụ (site na Anna dị mkpa)

16) Ntukwasi obi (#WVS)

17) Nnyocha nyocha Oxford

18) Ime Ihe Oche

19) Ebee ka ị ga-eme gị na-atọ ụtọ?

20) Kedu ihe ị ga - eme n'izu a iji lekọta ahụike gị?

21) M na-eche banyere m gara aga, ugbu a ma ọ bụ ọdịnihu

22) Ebere

23) Ọgụgụ isi na njedebe nke mmepe

24) Gịnị mere ndị mmadụ ji ewe iwe?

25) Ime ihe dị iche na iji wuo ntụkwasị obi onwe ya (IFD nonsbach)

26) Xing.com omenala

27) Patrick Lengsioni's "Dysfuntions nke otu"

28) Mmetụta ọmịiko bụ ...

29) Gịnị dị mkpa maka ya na ndị ọkachamara n'ịhọrọ ọrụ?

30) Ihe mere ndị mmadụ ji emegide mgbanwe (site na Siobhán Mchale)

31) Kedu ka ị ga - esi chịkwaa obi gị? (site na mulhalla m.a.)

32) 21 nkà na-akwụ gị ụgwọ ruo mgbe ebighi ebi (nke Jeremaịa Teo / 赵汉昇)

33) Ezigbo nnwere onwe bụ ...

34) 12 Wayzọ iji wuo ntụkwasị obi na ndị ọzọ (site na Justin Wright)

35) Njirimara nke onye na-arụ ọrụ (nke Talent Magent)

36) Igodo 10 iji kpalie ndị otu gị

37) Algebra nke akọ na uche (nke Vladimir Lefebvre)

38) Ohere atọ pụrụ iche nke ọdịnihu (nke Dr. Clare W. Graves)

39) Omume iji wulite ntụkwasị obi onwe onye na-enweghị mgbagha (nke Suren Samarchyan)

40)

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.

Atughi egwu

chaatị dị iche iche Mmekọrịta

VUCA

Critical uru nke mmekọrịta ọnụọgụ

Ngalaba nkịtị, site na William Stel r = 0.0317

Ntinye na-abụghị ọrụ, site na Spearman r = 0.0013

Gosiputa nsonaazụ > r = 0.0317

Nkesa	Na-abụghị nkịtị	Na-abụghị nkịtị	Na-abụghị nkịtị	Nke kwesiri	Nke kwesiri	Nke kwesiri	Nke kwesiri	Nke kwesiri
Ajụjụ niile Ajụjụ niile Egwu m kachasị
Egwu m kachasị
Answer 1	-	Na-adịghị ike mma 0.0537	Na-adịghị ike mma 0.0288	Na-adịghị ike na-adịghị mma -0.0175	Na-adịghị ike mma 0.0948	Na-adịghị ike mma 0.0381	Na-adịghị ike na-adịghị mma -0.0178	Na-adịghị ike na-adịghị mma -0.1563
Answer 2	-	Na-adịghị ike mma 0.0194	Na-adịghị ike na-adịghị mma -0.0048	Na-adịghị ike na-adịghị mma -0.0385	Na-adịghị ike mma 0.0655	Na-adịghị ike mma 0.0495	Na-adịghị ike mma 0.0106	Na-adịghị ike na-adịghị mma -0.0982
Answer 3	-	Na-adịghị ike na-adịghị mma -0.0001	Na-adịghị ike na-adịghị mma -0.0084	Na-adịghị ike na-adịghị mma -0.0449	Na-adịghị ike na-adịghị mma -0.0445	Na-adịghị ike mma 0.0485	Na-adịghị ike mma 0.0742	Na-adịghị ike na-adịghị mma -0.0207
Answer 4	-	Na-adịghị ike mma 0.0433	Na-adịghị ike mma 0.0291	Na-adịghị ike na-adịghị mma -0.0232	Na-adịghị ike mma 0.0163	Na-adịghị ike mma 0.0367	Na-adịghị ike mma 0.0226	Na-adịghị ike na-adịghị mma -0.0996
Answer 5	-	Na-adịghị ike mma 0.0277	Na-adịghị ike mma 0.1291	Na-adịghị ike mma 0.0108	Na-adịghị ike mma 0.0745	Na-adịghị ike mma 0.0012	Na-adịghị ike na-adịghị mma -0.0177	Na-adịghị ike na-adịghị mma -0.1783
Answer 6	-	Na-adịghị ike na-adịghị mma -0.0015	Na-adịghị ike mma 0.0058	Na-adịghị ike na-adịghị mma -0.0607	Na-adịghị ike na-adịghị mma -0.0094	Na-adịghị ike mma 0.0255	Na-adịghị ike mma 0.0844	Na-adịghị ike na-adịghị mma -0.0363
Answer 7	-	Na-adịghị ike mma 0.0113	Na-adịghị ike mma 0.0348	Na-adịghị ike na-adịghị mma -0.0657	Na-adịghị ike na-adịghị mma -0.0305	Na-adịghị ike mma 0.0521	Na-adịghị ike mma 0.0686	Na-adịghị ike na-adịghị mma -0.0532
Answer 8	-	Na-adịghị ike mma 0.0657	Na-adịghị ike mma 0.0728	Na-adịghị ike na-adịghị mma -0.0255	Na-adịghị ike mma 0.0124	Na-adịghị ike mma 0.0386	Na-adịghị ike mma 0.0153	Na-adịghị ike na-adịghị mma -0.1345
Answer 9	-	Na-adịghị ike mma 0.0757	Na-adịghị ike mma 0.1605	Na-adịghị ike mma 0.0066	Na-adịghị ike mma 0.0612	Na-adịghị ike na-adịghị mma -0.0063	Na-adịghị ike na-adịghị mma -0.0492	Na-adịghị ike na-adịghị mma -0.1822
Answer 10	-	Na-adịghị ike mma 0.0764	Na-adịghị ike mma 0.0669	Na-adịghị ike na-adịghị mma -0.0124	Na-adịghị ike mma 0.0271	Na-adịghị ike mma 0.0365	Na-adịghị ike na-adịghị mma -0.0130	Na-adịghị ike na-adịghị mma -0.1348
Answer 11	-	Na-adịghị ike mma 0.0634	Na-adịghị ike mma 0.0526	Na-adịghị ike na-adịghị mma -0.0075	Na-adịghị ike mma 0.0096	Na-adịghị ike mma 0.0264	Na-adịghị ike mma 0.0242	Na-adịghị ike na-adịghị mma -0.1270
Answer 12	-	Na-adịghị ike mma 0.0450	Na-adịghị ike mma 0.0944	Na-adịghị ike na-adịghị mma -0.0323	Na-adịghị ike mma 0.0307	Na-adịghị ike mma 0.0343	Na-adịghị ike mma 0.0260	Na-adịghị ike na-adịghị mma -0.1530
Answer 13	-	Na-adịghị ike mma 0.0725	Na-adịghị ike mma 0.0947	Na-adịghị ike na-adịghị mma -0.0389	Na-adịghị ike mma 0.0265	Na-adịghị ike mma 0.0443	Na-adịghị ike mma 0.0144	Na-adịghị ike na-adịghị mma -0.1631
Answer 14	-	Na-adịghị ike mma 0.0820	Na-adịghị ike mma 0.0897	Na-adịghị ike na-adịghị mma -0.0030	Na-adịghị ike na-adịghị mma -0.0122	Na-adịghị ike mma 0.0060	Na-adịghị ike mma 0.0135	Na-adịghị ike na-adịghị mma -0.1213
Answer 15	-	Na-adịghị ike mma 0.0549	Na-adịghị ike mma 0.1265	Na-adịghị ike na-adịghị mma -0.0334	Na-adịghị ike mma 0.0119	Na-adịghị ike na-adịghị mma -0.0153	Na-adịghị ike mma 0.0242	Na-adịghị ike na-adịghị mma -0.1157
Answer 16	-	Na-adịghị ike mma 0.0732	Na-adịghị ike mma 0.0242	Na-adịghị ike na-adịghị mma -0.0373	Na-adịghị ike na-adịghị mma -0.0398	Na-adịghị ike mma 0.0729	Na-adịghị ike mma 0.0169	Na-adịghị ike na-adịghị mma -0.0774

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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

Onye nwe ngwaahịa SaaS SDTEST®

Valerii tozuru oke dị ka onye nkuzi mmekọrịta mmadụ na mmụọ na 1993 wee tinye ihe ọmụma ya n'ọrụ na njikwa ọrụ.
Valerii nwetara nzere Master na oru ngo na mmemme njikwa mmemme na 2013. N'oge mmemme Nna-ukwu ya, ọ maara Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) na Spiral Dynamics.
Valerii bụ onye dere nyocha nke ejighị n'aka nke V.U.C.A. echiche iji Spiral Dynamics na mgbakọ na mwepụ mgbakọ na mwepụ na akparamaagwa, na 38 mba ntuli aka.

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