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)

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 = 0.0335

Non parasts sadalījums, autors Spearman r = 0.0014

Parādīt tikai rezultātus > r = 0.0335

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 0.0521	Vāji pozitīvi 0.0294	Vāja negatīva -0.0147	Vāji pozitīvi 0.0885	Vāji pozitīvi 0.0316	Vāja negatīva -0.0110	Vāja negatīva -0.1513
Answer 2	-	Vāji pozitīvi 0.0213	Vāji pozitīvi 0.0013	Vāja negatīva -0.0432	Vāji pozitīvi 0.0618	Vāji pozitīvi 0.0453	Vāji pozitīvi 0.0103	Vāja negatīva -0.0918
Answer 3	-	Vāja negatīva -0.0042	Vāja negatīva -0.0116	Vāja negatīva -0.0406	Vāja negatīva -0.0477	Vāji pozitīvi 0.0487	Vāji pozitīvi 0.0767	Vāja negatīva -0.0191
Answer 4	-	Vāji pozitīvi 0.0421	Vāji pozitīvi 0.0350	Vāja negatīva -0.0115	Vāji pozitīvi 0.0112	Vāji pozitīvi 0.0307	Vāji pozitīvi 0.0175	Vāja negatīva -0.0980
Answer 5	-	Vāji pozitīvi 0.0288	Vāji pozitīvi 0.1272	Vāji pozitīvi 0.0146	Vāji pozitīvi 0.0697	Vāji pozitīvi 0.0037	Vāja negatīva -0.0215	Vāja negatīva -0.1746
Answer 6	-	Vāja negatīva -0.0001	Vāji pozitīvi 0.0042	Vāja negatīva -0.0607	Vāja negatīva -0.0115	Vāji pozitīvi 0.0231	Vāji pozitīvi 0.0826	Vāja negatīva -0.0309
Answer 7	-	Vāji pozitīvi 0.0117	Vāji pozitīvi 0.0372	Vāja negatīva -0.0653	Vāja negatīva -0.0283	Vāji pozitīvi 0.0495	Vāji pozitīvi 0.0626	Vāja negatīva -0.0505
Answer 8	-	Vāji pozitīvi 0.0658	Vāji pozitīvi 0.0830	Vāja negatīva -0.0310	Vāji pozitīvi 0.0139	Vāji pozitīvi 0.0334	Vāji pozitīvi 0.0134	Vāja negatīva -0.1322
Answer 9	-	Vāji pozitīvi 0.0660	Vāji pozitīvi 0.1658	Vāji pozitīvi 0.0051	Vāji pozitīvi 0.0691	Vāja negatīva -0.0093	Vāja negatīva -0.0498	Vāja negatīva -0.1820
Answer 10	-	Vāji pozitīvi 0.0758	Vāji pozitīvi 0.0724	Vāja negatīva -0.0173	Vāji pozitīvi 0.0236	Vāji pozitīvi 0.0312	Vāja negatīva -0.0115	Vāja negatīva -0.1263
Answer 11	-	Vāji pozitīvi 0.0577	Vāji pozitīvi 0.0544	Vāja negatīva -0.0075	Vāji pozitīvi 0.0082	Vāji pozitīvi 0.0185	Vāji pozitīvi 0.0293	Vāja negatīva -0.1190
Answer 12	-	Vāji pozitīvi 0.0376	Vāji pozitīvi 0.1007	Vāja negatīva -0.0342	Vāji pozitīvi 0.0296	Vāji pozitīvi 0.0273	Vāji pozitīvi 0.0341	Vāja negatīva -0.1500
Answer 13	-	Vāji pozitīvi 0.0627	Vāji pozitīvi 0.1017	Vāja negatīva -0.0443	Vāji pozitīvi 0.0248	Vāji pozitīvi 0.0434	Vāji pozitīvi 0.0189	Vāja negatīva -0.1576
Answer 14	-	Vāji pozitīvi 0.0732	Vāji pozitīvi 0.1036	Vāji pozitīvi 0.0048	Vāja negatīva -0.0105	Vāja negatīva -0.0039	Vāji pozitīvi 0.0041	Vāja negatīva -0.1157
Answer 15	-	Vāji pozitīvi 0.0539	Vāji pozitīvi 0.1381	Vāja negatīva -0.0424	Vāji pozitīvi 0.0163	Vāja negatīva -0.0147	Vāji pozitīvi 0.0216	Vāja negatīva -0.1173
Answer 16	-	Vāji pozitīvi 0.0590	Vāji pozitīvi 0.0274	Vāja negatīva -0.0375	Vāja negatīva -0.0429	Vāji pozitīvi 0.0687	Vāji pozitīvi 0.0253	Vāja negatīva -0.0698

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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 Pet Project SDTest®

Valerii tika kvalificēts kā sociālais pedagogu psihologs 1993. gadā un kopš tā laika ir izmantojis savas zināšanas projektu vadībā.
Valerii ieguva maģistra grādu un projekta un programmas vadītāja kvalifikāciju 2013. gadā. Viņa maģistra programmas laikā viņš iepazinās ar projekta ceļvedi (GPM Deutsche Gesellschaft Für Projektmanagement E. V.) un spirāles dinamika.
Valerii veica dažādus spirāles dinamikas testus un izmantoja savas zināšanas un pieredzi, lai pielāgotu pašreizējo Sdtest versiju.
Valerii ir autors, lai izpētītu V.U.C.A. nenoteiktību. Koncepcija, izmantojot spirāles dinamiku un matemātisko statistiku psiholoģijā, vairāk nekā 20 starptautiskas aptaujas.

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