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) Falalka shirkadaha la xiriira shaqaalaha bishii la soo dhaafay (haa / maya)

2) Falalka shirkadaha la xiriira shaqaalaha bishii ugu dambeysay (xaqiiqda%)

3) Cabsi

4) Dhibaatooyinka ugu weyn ee wajahaya dalkayga

5) Waa maxay tayada iyo awoodaha ay sameeyaan hoggaamiyeyaal wanaagsan marka loo dhiso kooxaha guuleysta?

6) Google. Waxyaabaha ay saameeyaan kooxda saameynta ku leh

7) Ahmiyadaha ugu weyn ee shaqo doonka

8) Maxaa madaxa ka dhigaya hoggaamiye weyn?

9) Maxaa dadka ka dhigaya inay ku guuleystaan shaqada?

10) Diyaar ma u tahay inaad hesho mushahar yar si aad uga fogaato meel fog?

11) Da 'ma jiraa?

12) Da 'xirfadeed ee shaqada

13) Darooyinka nolosha

14) Sababaha da '

15) Sababaha ay dadku u quustaan (Anna muhiim ah)

16) Aamminid (#WVS)

17) Sahaminta farxadda ee Oxford

18) Samafal maskaxeed

19) Xagee bay noqon doontaa fursaddaada ugu xiisaha badan?

20) Maxaad sameyn doontaa toddobaadkan si aad u daryeesho caafimaadkaaga maskaxda?

21) Waxaan ku noolahay inaan ka fikiro wixii aan soo maray, xaadirkan ama mustaqbalkeyga

22) Dareen

23) Sirdoonka macmalka ah iyo dhamaadka ilbaxnimada

24) Maxay dadku u daneeyaan?

25) Farqiga u dhexeeya lamaanaha ee dhisida isku kalsoonida (ifd alnsbach)

26) Xing.com Qiimaynta Dhaqanka

27) Patrick Lencioni "shanta qof ee koox ahaaneed ee koox"

28) Naxariistu waa ...

29) Maxaa muhiim u ah khabiirada ay ku takhasusay doorashada shaqo?

30) Maxay dadku u diidayaan isbedelka (by Siibhán mchale)

31) Sideed u nidaamisaa shucuurtaada? (by Nawal Mustafa M.A.)

32) 21 xirfado oo adiga ku siinaya weligaa (oo ah Yeremyaah teo / 赵汉昇)

33) Xorriyadda dhabta ahi waa ...

34) 12 siyaabood oo lagu dhiso kalsoonida dadka kale (by justin wright)

35) Astaamaha shaqaale karti leh (oo ay ku qoran yihiin machadka maaraynta kartida)

36) 10 Furayaasha si loo dhiiri geliyo kooxdaada

37) Aljebra ee Damiirka (waxaa qoray Vladimir Lefebvre)

38) Saddexda suurtagal ee mustaqbalka ee kala duwan (waxaa qoray 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.

Cabsi

gooldhalinta Xiriir

VUCA

Qiimaha Halis ah Wehliyaha xiriir ah

Qaybinta caadiga ah, by William Bads Gossist (Ardayga) r = 0.0331

Qaybinta aan caadiga ahayn, by spearman r = 0.0013

Muuji kaliya natiijooyinka > r = 0.0331

Qaybinta	Aan caadi ahayn	Aan caadi ahayn	Aan caadi ahayn	Caadi ah	Caadi ah	Caadi ah	Caadi ah	Caadi ah
Dhammaan su'aalaha Dhammaan su'aalaha Cabsida ugu weyn waa
Cabsida ugu weyn waa
Answer 1	-	Positive daciif ah 0.0563	Positive daciif ah 0.0317	Negative daciif ah -0.0161	Positive daciif ah 0.0907	Positive daciif ah 0.0298	Negative daciif ah -0.0126	Negative daciif ah -0.1537
Answer 2	-	Positive daciif ah 0.0216	Positive daciif ah 0.0002	Negative daciif ah -0.0458	Positive daciif ah 0.0654	Positive daciif ah 0.0445	Positive daciif ah 0.0124	Negative daciif ah -0.0937
Answer 3	-	Negative daciif ah -0.0035	Negative daciif ah -0.0111	Negative daciif ah -0.0421	Negative daciif ah -0.0456	Positive daciif ah 0.0466	Positive daciif ah 0.0786	Negative daciif ah -0.0201
Answer 4	-	Positive daciif ah 0.0435	Positive daciif ah 0.0353	Negative daciif ah -0.0181	Positive daciif ah 0.0145	Positive daciif ah 0.0301	Positive daciif ah 0.0197	Negative daciif ah -0.0979
Answer 5	-	Positive daciif ah 0.0299	Positive daciif ah 0.1279	Positive daciif ah 0.0136	Positive daciif ah 0.0730	Negative daciif ah -0.0007	Negative daciif ah -0.0207	Negative daciif ah -0.1746
Answer 6	-	Negative daciif ah -0.0004	Positive daciif ah 0.0082	Negative daciif ah -0.0629	Negative daciif ah -0.0078	Positive daciif ah 0.0193	Positive daciif ah 0.0830	Negative daciif ah -0.0318
Answer 7	-	Positive daciif ah 0.0122	Positive daciif ah 0.0381	Negative daciif ah -0.0686	Negative daciif ah -0.0242	Positive daciif ah 0.0471	Positive daciif ah 0.0636	Negative daciif ah -0.0513
Answer 8	-	Positive daciif ah 0.0698	Positive daciif ah 0.0849	Negative daciif ah -0.0321	Positive daciif ah 0.0146	Positive daciif ah 0.0345	Positive daciif ah 0.0130	Negative daciif ah -0.1368
Answer 9	-	Positive daciif ah 0.0665	Positive daciif ah 0.1674	Positive daciif ah 0.0092	Positive daciif ah 0.0691	Negative daciif ah -0.0128	Negative daciif ah -0.0528	Negative daciif ah -0.1812
Answer 10	-	Positive daciif ah 0.0778	Positive daciif ah 0.0755	Negative daciif ah -0.0180	Positive daciif ah 0.0231	Positive daciif ah 0.0346	Negative daciif ah -0.0146	Negative daciif ah -0.1298
Answer 11	-	Positive daciif ah 0.0584	Positive daciif ah 0.0524	Negative daciif ah -0.0096	Positive daciif ah 0.0081	Positive daciif ah 0.0199	Positive daciif ah 0.0318	Negative daciif ah -0.1197
Answer 12	-	Positive daciif ah 0.0380	Positive daciif ah 0.1042	Negative daciif ah -0.0352	Positive daciif ah 0.0357	Positive daciif ah 0.0254	Positive daciif ah 0.0286	Negative daciif ah -0.1515
Answer 13	-	Positive daciif ah 0.0644	Positive daciif ah 0.1057	Negative daciif ah -0.0448	Positive daciif ah 0.0268	Positive daciif ah 0.0416	Positive daciif ah 0.0169	Negative daciif ah -0.1600
Answer 14	-	Positive daciif ah 0.0717	Positive daciif ah 0.1026	Negative daciif ah -0.0006	Negative daciif ah -0.0089	Negative daciif ah -0.0012	Positive daciif ah 0.0080	Negative daciif ah -0.1168
Answer 15	-	Positive daciif ah 0.0549	Positive daciif ah 0.1375	Negative daciif ah -0.0420	Positive daciif ah 0.0178	Negative daciif ah -0.0160	Positive daciif ah 0.0216	Negative daciif ah -0.1180
Answer 16	-	Positive daciif ah 0.0591	Positive daciif ah 0.0273	Negative daciif ah -0.0386	Negative daciif ah -0.0399	Positive daciif ah 0.0653	Positive daciif ah 0.0282	Negative daciif ah -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

Milkiilaha wax soo saarka ee SAS PET PROSS SDTEst®

Valeri waxay u qalmay sidii barbaarin bulsheed-cilmi-nafsi-cilmu-nafsi sanadkii 1993, ilaa iyo markaasna wuxuu aqoon u yeeshay aqoontiisa mashruuca.
Valerikai waxay heshay shahaadada Masterka iyo is-ka-shaashadda mashruuca iyo heerka tababarka barnaamijka 2013. Intii uu socday barnaamijka sayidkiisa, wuxuu caan ku noqday mashruuca Qorshe-hawleedka (GPM Deutsche Gesellschaft für projektnaft für projektnaft) iyo dhaqdhaqaaqa dhaqdhaqaaqa.
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