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) Uzņēmumu darbības saistībā ar personālu pēdējā mēneša laikā (jā / nē)

2) Uzņēmumu darbības attiecībā uz personālu pēdējā mēneša laikā (fakts%)

3) Bailes

4) Lielākās problēmas, ar kurām saskaras mana valsts

5) Kādas īpašības un spējas labas vadītājus izmanto, veidojot veiksmīgas komandas?

6) Google. Faktori, kas ietekmē komandas efektivitāti

7) Galvenās darba meklētāju prioritātes

8) Kas padara priekšnieku par lielisku vadītāju?

9) Kas padara cilvēkus par veiksmīgiem darbā?

10) Vai esat gatavs saņemt mazāk atalgojuma par darbu attālināti?

11) Vai vecums pastāv?

12) Ageisms karjerā

13) Vecums dzīvē

14) Agisma cēloņi

15) Iemesli, kāpēc cilvēki atsakās (Anna Vital)

16) Uzticība (#WVS)

17) Oksfordas laimes aptauja

18) Psiholoģiskā labklājība

19) Kur būtu jūsu nākamā aizraujošākā iespēja?

20) Ko jūs darīsit šonedēļ, lai rūpētos par savu garīgo veselību?

21) Es dzīvoju, domājot par savu pagātni, tagadni vai nākotni

22) Meritokrātija

23) Mākslīgais intelekts un civilizācijas beigas

24) Kāpēc cilvēki kavējas?

25) Dzimumu atšķirība pašpārliecinātības veidošanā (ifd allensbach)

26) Xing.com kultūras novērtējums

27) Patrika Lencioni "Piecas komandas disfunkcijas"

28) Empātija ir ...

29) Kas ir svarīgi IT speciālistiem, izvēloties darba piedāvājumu?

30) Kāpēc cilvēki pretojas pārmaiņām (autors Siobhán McHale)

31) Kā jūs regulējat savas emocijas? (autors Nawal Mustafa M.A.)

32) 21 prasmes, kas jums maksā mūžīgi (Jeremiah Teo / 赵汉昇)

33) Īsta brīvība ir ...

34) 12 veidi, kā veidot uzticību citiem (autors Džastins Raits)

35) Talantīga darbinieka raksturojums (autors talantu vadības institūts)

36) 10 atslēgas jūsu komandas motivēšanai

37) Sirdsapziņas algebra (Vladimirs Lefevrs)

38) Trīs atšķirīgas nākotnes iespējas (autors. Dr. Clare W. Graves)

39) Darbības nesatricināmas pašapziņas veidošanai (autors Surens Samarčjans)

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.

Bailes

charts Korelācija

VUCA

Kritiskais vērtību korelācijas koeficienta

Normāla izplatīšana, autors Viljams Sealijs Gossets (students) r = 0.0315

Non parasts sadalījums, autors Spearman r = 0.0013

Parādīt tikai rezultātus > r = 0.0315

Sadalījums	Nenormāls	Nenormāls	Nenormāls	Normāls	Normāls	Normāls	Normāls	Normāls
Visi jautājumi Visi jautājumi Mana lielākā bailes ir
Mana lielākā bailes ir
Answer 1	-	Vāji pozitīvi 0.0518	Vāji pozitīvi 0.0257	Vāja negatīva -0.0203	Vāji pozitīvi 0.0942	Vāji pozitīvi 0.0391	Vāja negatīva -0.0141	Vāja negatīva -0.1546
Answer 2	-	Vāji pozitīvi 0.0178	Vāja negatīva -0.0071	Vāja negatīva -0.0376	Vāji pozitīvi 0.0631	Vāji pozitīvi 0.0501	Vāji pozitīvi 0.0133	Vāja negatīva -0.0955
Answer 3	-	Vāja negatīva -0.0025	Vāja negatīva -0.0083	Vāja negatīva -0.0456	Vāja negatīva -0.0432	Vāji pozitīvi 0.0498	Vāji pozitīvi 0.0768	Vāja negatīva -0.0241
Answer 4	-	Vāji pozitīvi 0.0428	Vāji pozitīvi 0.0297	Vāja negatīva -0.0259	Vāji pozitīvi 0.0175	Vāji pozitīvi 0.0374	Vāji pozitīvi 0.0266	Vāja negatīva -0.1027
Answer 5	-	Vāji pozitīvi 0.0228	Vāji pozitīvi 0.1240	Vāji pozitīvi 0.0115	Vāji pozitīvi 0.0735	Vāji pozitīvi 0.0010	Vāja negatīva -0.0152	Vāja negatīva -0.1755
Answer 6	-	Vāja negatīva -0.0021	Vāji pozitīvi 0.0028	Vāja negatīva -0.0619	Vāja negatīva -0.0110	Vāji pozitīvi 0.0269	Vāji pozitīvi 0.0872	Vāja negatīva -0.0366
Answer 7	-	Vāji pozitīvi 0.0107	Vāji pozitīvi 0.0313	Vāja negatīva -0.0667	Vāja negatīva -0.0310	Vāji pozitīvi 0.0538	Vāji pozitīvi 0.0715	Vāja negatīva -0.0532
Answer 8	-	Vāji pozitīvi 0.0653	Vāji pozitīvi 0.0688	Vāja negatīva -0.0267	Vāji pozitīvi 0.0117	Vāji pozitīvi 0.0398	Vāji pozitīvi 0.0185	Vāja negatīva -0.1345
Answer 9	-	Vāji pozitīvi 0.0740	Vāji pozitīvi 0.1594	Vāji pozitīvi 0.0050	Vāji pozitīvi 0.0612	Vāja negatīva -0.0067	Vāja negatīva -0.0464	Vāja negatīva -0.1836
Answer 10	-	Vāji pozitīvi 0.0754	Vāji pozitīvi 0.0624	Vāja negatīva -0.0144	Vāji pozitīvi 0.0273	Vāji pozitīvi 0.0336	Vāja negatīva -0.0107	Vāja negatīva -0.1359
Answer 11	-	Vāji pozitīvi 0.0626	Vāji pozitīvi 0.0495	Vāja negatīva -0.0084	Vāji pozitīvi 0.0094	Vāji pozitīvi 0.0277	Vāji pozitīvi 0.0251	Vāja negatīva -0.1276
Answer 12	-	Vāji pozitīvi 0.0429	Vāji pozitīvi 0.0889	Vāja negatīva -0.0323	Vāji pozitīvi 0.0317	Vāji pozitīvi 0.0350	Vāji pozitīvi 0.0265	Vāja negatīva -0.1531
Answer 13	-	Vāji pozitīvi 0.0705	Vāji pozitīvi 0.0917	Vāja negatīva -0.0384	Vāji pozitīvi 0.0287	Vāji pozitīvi 0.0437	Vāji pozitīvi 0.0151	Vāja negatīva -0.1634
Answer 14	-	Vāji pozitīvi 0.0812	Vāji pozitīvi 0.0862	Vāja negatīva -0.0035	Vāja negatīva -0.0129	Vāji pozitīvi 0.0076	Vāji pozitīvi 0.0152	Vāja negatīva -0.1208
Answer 15	-	Vāji pozitīvi 0.0555	Vāji pozitīvi 0.1235	Vāja negatīva -0.0340	Vāji pozitīvi 0.0113	Vāja negatīva -0.0139	Vāji pozitīvi 0.0261	Vāja negatīva -0.1160
Answer 16	-	Vāji pozitīvi 0.0715	Vāji pozitīvi 0.0212	Vāja negatīva -0.0388	Vāja negatīva -0.0401	Vāji pozitīvi 0.0745	Vāji pozitīvi 0.0178	Vāja negatīva -0.0772

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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

Produkta īpašnieks SaaS SDTEST®

Valērijs 1993. gadā ieguva sociālā pedagoga-psihologa kvalifikāciju un kopš tā laika ir pielietojis savas zināšanas projektu vadībā.
Valērijs 2013. gadā ieguva maģistra grādu un projektu un programmu vadītāja kvalifikāciju. Maģistra programmas laikā viņš iepazinās ar Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) un Spiral Dynamics.
Valerii ir V.U.C.A. nenoteiktības izpētes autors. koncepcija, izmantojot spirālveida dinamiku un matemātisko statistiku psiholoģijā, un 38 starptautiskas aptaujas.

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