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

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 = 0.0353

Non parasts sadalījums, autors Spearman r = 0.0014

Parādīt tikai rezultātus > r = 0.0353

Sadalījums	Nenormāls	Normāls	Nenormāls	Normāls	Normāls	Normāls	Normāls	Normāls
Visi jautājumi Visi jautājumi Mana lielākā bailes ir
Mana lielākā bailes ir
Answer 1	-	Vāji pozitīvi 0.0297	Vāji pozitīvi 0.0298	Vāja negatīva -0.0106	Vāji pozitīvi 0.0970	Vāji pozitīvi 0.0325	Vāja negatīva -0.0019	Vāja negatīva -0.1558
Answer 2	-	Vāji pozitīvi 0.0188	Vāji pozitīvi 0.0076	Vāja negatīva -0.0360	Vāji pozitīvi 0.0711	Vāji pozitīvi 0.0387	Vāji pozitīvi 0.0082	Vāja negatīva -0.1011
Answer 3	-	Vāji pozitīvi 0.0026	Vāja negatīva -0.0170	Vāja negatīva -0.0443	Vāja negatīva -0.0458	Vāji pozitīvi 0.0547	Vāji pozitīvi 0.0808	Vāja negatīva -0.0270
Answer 4	-	Vāji pozitīvi 0.0332	Vāji pozitīvi 0.0285	Vāja negatīva -0.0006	Vāji pozitīvi 0.0155	Vāji pozitīvi 0.0276	Vāji pozitīvi 0.0105	Vāja negatīva -0.0917
Answer 5	-	Vāji pozitīvi 0.0122	Vāji pozitīvi 0.1193	Vāji pozitīvi 0.0095	Vāji pozitīvi 0.0721	Vāji pozitīvi 0.0057	Vāja negatīva -0.0083	Vāja negatīva -0.1687
Answer 6	-	Vāji pozitīvi 0.0044	Vāji pozitīvi 0.0005	Vāja negatīva -0.0582	Vāja negatīva -0.0004	Vāji pozitīvi 0.0210	Vāji pozitīvi 0.0830	Vāja negatīva -0.0418
Answer 7	-	Vāji pozitīvi 0.0242	Vāji pozitīvi 0.0368	Vāja negatīva -0.0521	Vāja negatīva -0.0234	Vāji pozitīvi 0.0403	Vāji pozitīvi 0.0568	Vāja negatīva -0.0597
Answer 8	-	Vāji pozitīvi 0.0707	Vāji pozitīvi 0.0781	Vāja negatīva -0.0244	Vāji pozitīvi 0.0140	Vāji pozitīvi 0.0303	Vāji pozitīvi 0.0137	Vāja negatīva -0.1334
Answer 9	-	Vāji pozitīvi 0.0564	Vāji pozitīvi 0.1531	Vāji pozitīvi 0.0127	Vāji pozitīvi 0.0769	Vāja negatīva -0.0136	Vāja negatīva -0.0495	Vāja negatīva -0.1752
Answer 10	-	Vāji pozitīvi 0.0711	Vāji pozitīvi 0.0700	Vāja negatīva -0.0127	Vāji pozitīvi 0.0246	Vāji pozitīvi 0.0363	Vāja negatīva -0.0156	Vāja negatīva -0.1273
Answer 11	-	Vāji pozitīvi 0.0542	Vāji pozitīvi 0.0488	Vāji pozitīvi 0.0086	Vāji pozitīvi 0.0078	Vāji pozitīvi 0.0162	Vāji pozitīvi 0.0315	Vāja negatīva -0.1248
Answer 12	-	Vāji pozitīvi 0.0281	Vāji pozitīvi 0.0929	Vāja negatīva -0.0325	Vāji pozitīvi 0.0361	Vāji pozitīvi 0.0276	Vāji pozitīvi 0.0365	Vāja negatīva -0.1482
Answer 13	-	Vāji pozitīvi 0.0643	Vāji pozitīvi 0.0916	Vāja negatīva -0.0418	Vāji pozitīvi 0.0237	Vāji pozitīvi 0.0425	Vāji pozitīvi 0.0239	Vāja negatīva -0.1558
Answer 14	-	Vāji pozitīvi 0.0697	Vāji pozitīvi 0.1017	Vāji pozitīvi 0.0149	Vāja negatīva -0.0062	Vāja negatīva -0.0087	Vāja negatīva -0.0002	Vāja negatīva -0.1161
Answer 15	-	Vāji pozitīvi 0.0603	Vāji pozitīvi 0.1299	Vāja negatīva -0.0379	Vāji pozitīvi 0.0163	Vāja negatīva -0.0091	Vāji pozitīvi 0.0164	Vāja negatīva -0.1204
Answer 16	-	Vāji pozitīvi 0.0691	Vāji pozitīvi 0.0221	Vāja negatīva -0.0305	Vāja negatīva -0.0515	Vāji pozitīvi 0.0750	Vāji pozitīvi 0.0187	Vāja negatīva -0.0696

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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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