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) Akcije tvrtki u odnosu na osoblje u posljednjih mjesec dana (da / ne)

2) Djelovanja poduzeća u odnosu na osoblje u prošlom mjesecu (činjenica u%)

3) Strahovi

4) Najveći problemi s kojima se suočava moja zemlja

5) Koje osobine i sposobnosti dobri vođe koriste prilikom izgradnje uspješnih timova?

6) Google. Čimbenici koji utječu na efikasnost tima

7) Glavni prioriteti tražitelja posla

8) Zbog čega šefa čini sjajnim vođom?

9) Što ljude čini uspješnim na poslu?

10) Jeste li spremni primiti manje plaće za daljinski rad?

11) Postoji li ageizam?

12) Ageizam u karijeri

13) Ageizam u životu

14) Uzroci ageizma

15) Razlozi zbog kojih ljudi odustaju (od Anna Vital)

16) POVJERENJE (#WVS)

17) Anketa o Oxfordskoj sreći

18) Psihološko dobrobit

19) Gdje bi vam bila sljedeća najuzbudljivija prilika?

20) Što ćete učiniti ovaj tjedan da biste se brinuli o svom mentalnom zdravlju?

21) Živim razmišljajući o svojoj prošlosti, sadašnjosti ili budućnosti

22) Meritokracija

23) Umjetna inteligencija i kraj civilizacije

24) Zašto ljudi odgađaju?

25) Razlika u spolu u izgradnji samopouzdanja (IFD Allensbach)

26) Xing.com kultura procjena

27) Patrick Lencioni "Pet disfunkcija tima"

28) Empatija je ...

29) Što je bitno za IT stručnjake za odabir ponude za posao?

30) Zašto se ljudi odupiru promjenama (Siobhán McHale)

31) Kako regulirate svoje emocije? (Nawal Mustafa M.A.

32) 21 vještine koje vam plaćaju zauvijek (Jeremiah Teo / 赵汉昇)

33) Prava sloboda je ...

34) 12 načina za izgradnju povjerenja s drugima (Justin Wright)

35) Karakteristike talentiranog zaposlenika (Institutom za upravljanje talentima)

36) 10 ključeva za motiviranje vašeg tima

37) Algebra savjesti (Vladimir Lefebvre)

38) Tri različite mogućnosti budućnosti (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.

Strahovi

Karte Poveznica

VUCA

Kritična vrijednost koeficijenta korelacije

Normalna distribucija, William Sealy Gosset (student) r = 0.0329

Ne normalna distribucija, Spearman r = 0.0013

Pokažite samo rezultate > r = 0.0329

Distribucija	Ne normalan	Ne normalan	Ne normalan	Normalan	Normalan	Normalan	Normalan	Normalan
Sva pitanja Sva pitanja Moj najveći strah je
Moj najveći strah je
Answer 1	-	Slaba pozitivan 0.0566	Slaba pozitivan 0.0332	Slaba negativan -0.0170	Slaba pozitivan 0.0912	Slaba pozitivan 0.0308	Slaba negativan -0.0153	Slaba negativan -0.1537
Answer 2	-	Slaba pozitivan 0.0223	Slaba pozitivan 0.0011	Slaba negativan -0.0442	Slaba pozitivan 0.0639	Slaba pozitivan 0.0464	Slaba pozitivan 0.0120	Slaba negativan -0.0960
Answer 3	-	Slaba negativan -0.0031	Slaba negativan -0.0104	Slaba negativan -0.0407	Slaba negativan -0.0463	Slaba pozitivan 0.0475	Slaba pozitivan 0.0779	Slaba negativan -0.0213
Answer 4	-	Slaba pozitivan 0.0437	Slaba pozitivan 0.0357	Slaba negativan -0.0197	Slaba pozitivan 0.0161	Slaba pozitivan 0.0311	Slaba pozitivan 0.0187	Slaba negativan -0.0987
Answer 5	-	Slaba pozitivan 0.0296	Slaba pozitivan 0.1300	Slaba pozitivan 0.0124	Slaba pozitivan 0.0749	Slaba pozitivan 0.0014	Slaba negativan -0.0231	Slaba negativan -0.1771
Answer 6	-	Slaba negativan -0.0008	Slaba pozitivan 0.0090	Slaba negativan -0.0613	Slaba negativan -0.0070	Slaba pozitivan 0.0196	Slaba pozitivan 0.0803	Slaba negativan -0.0321
Answer 7	-	Slaba pozitivan 0.0118	Slaba pozitivan 0.0401	Slaba negativan -0.0693	Slaba negativan -0.0246	Slaba pozitivan 0.0471	Slaba pozitivan 0.0623	Slaba negativan -0.0505
Answer 8	-	Slaba pozitivan 0.0697	Slaba pozitivan 0.0875	Slaba negativan -0.0316	Slaba pozitivan 0.0155	Slaba pozitivan 0.0346	Slaba pozitivan 0.0098	Slaba negativan -0.1373
Answer 9	-	Slaba pozitivan 0.0679	Slaba pozitivan 0.1707	Slaba pozitivan 0.0105	Slaba pozitivan 0.0676	Slaba negativan -0.0138	Slaba negativan -0.0545	Slaba negativan -0.1821
Answer 10	-	Slaba pozitivan 0.0793	Slaba pozitivan 0.0772	Slaba negativan -0.0208	Slaba pozitivan 0.0242	Slaba pozitivan 0.0343	Slaba negativan -0.0152	Slaba negativan -0.1300
Answer 11	-	Slaba pozitivan 0.0590	Slaba pozitivan 0.0559	Slaba negativan -0.0071	Slaba pozitivan 0.0082	Slaba pozitivan 0.0205	Slaba pozitivan 0.0266	Slaba negativan -0.1213
Answer 12	-	Slaba pozitivan 0.0405	Slaba pozitivan 0.1050	Slaba negativan -0.0363	Slaba pozitivan 0.0361	Slaba pozitivan 0.0253	Slaba pozitivan 0.0277	Slaba negativan -0.1522
Answer 13	-	Slaba pozitivan 0.0655	Slaba pozitivan 0.1056	Slaba negativan -0.0439	Slaba pozitivan 0.0270	Slaba pozitivan 0.0417	Slaba pozitivan 0.0152	Slaba negativan -0.1601
Answer 14	-	Slaba pozitivan 0.0728	Slaba pozitivan 0.1049	Slaba negativan -0.0002	Slaba negativan -0.0088	Slaba negativan -0.0007	Slaba pozitivan 0.0061	Slaba negativan -0.1187
Answer 15	-	Slaba pozitivan 0.0561	Slaba pozitivan 0.1378	Slaba negativan -0.0415	Slaba pozitivan 0.0178	Slaba negativan -0.0162	Slaba pozitivan 0.0194	Slaba negativan -0.1176
Answer 16	-	Slaba pozitivan 0.0606	Slaba pozitivan 0.0308	Slaba negativan -0.0348	Slaba negativan -0.0421	Slaba pozitivan 0.0642	Slaba pozitivan 0.0250	Slaba negativan -0.0717

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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

Vlasnik proizvoda SaaS SDTEST®

Valerii je 1993. godine stekao zvanje socijalnog pedagoga-psihologa i od tada svoje znanje primjenjuje u upravljanju projektima.
Valerii je 2013. stekao magisterij i kvalifikaciju voditelja projekta i programa. Tijekom magistarskog programa upoznao se s Planom projekta (GPM Deutsche Gesellschaft für Projektmanagement e. V.) i Spiralnom dinamikom.
Valerii je autor istraživanja neizvjesnosti V.U.C.A. koncept koji koristi Spiralnu dinamiku i matematičku statistiku u psihologiji, te 38 međunarodnih anketa.

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