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) Radnje preduzeća u odnosu na osoblje u poslednjem mesecu (da / ne)

2) Radnje preduzeća u odnosu na osoblje u poslednjem mesecu (činjenica u%)

3) Strahovi

4) Najveći problemi s kojima se suočava moja zemlja

5) Koje kvalitete i sposobnosti koriste dobri lideri kada izgradite uspješne timove?

6) Google. Čimbenici koji utječu na timušku efikasnost

7) Glavni prioriteti tražitelja posla

8) Šta šefe čini sjajnim vođom?

9) Šta ljudi čini uspješnim na poslu?

10) Jeste li spremni dobiti manje plaćanja za rad na daljinu?

11) Da li ageizam postoji?

12) Ageizam u karijeri

13) Ageizam u životu

14) Uzroci ageizma

15) Razlozi zbog kojih se ljudi odustaju (od strane Ane Vital)

16) Povjerenje (#WVS)

17) Anketa o sreći Oxford

18) Psihološka blagostanja

19) Gdje bi bila vaša sljedeća najuzbudljivija prilika?

20) Šta ćete raditi ove sedmice da biste pazili na vaše mentalno zdravlje?

21) Živim razmišljajući o svojoj prošlosti, sadašnjosti ili budućnosti

22) Meritokracija

23) Umjetna inteligencija i kraj civilizacije

24) Zašto ljudi oduzimaju?

25) Rodna razlika u izgradnji samopouzdanja (IFD Allensbach)

26) Xing.com Procjena kulture

27) Patrick Lencioni's "Pet disfunkcije tima"

28) Empatija je ...

29) Šta je neophodno za IT stručnjake u odabiru ponude za posao?

30) Zašto se ljudi odupiruju promjenama (od strane Siobhán Mchale)

31) Kako regulišete svoje emocije? (Autor NAWAL MUSTAFA M.A.)

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

33) Prava sloboda je ...

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

35) Karakteristike talentovanog zaposlenika (od strane Instituta za upravljanje talentima)

36) 10 tipki za motiviranje vašeg tima

37) Algebra savesti (Vladimir Lefevr)

38) Tri različite mogućnosti budućnosti (dr. Clare W. Graves)

39) Akcije za izgradnju nepokolebljivog samopouzdanja (Suren Samarchyan)

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.

Strahovi

Charts Korelacija

VUCA

Kritične vrijednosti koeficijenta korelacije

Normalna distribucija, William Sealy Gosset (student) r = 0.0318

Non Normalna distribucija, od Spearman r = 0.0013

Prikaži samo rezultate > r = 0.0318

Distribucija	Ne normalno	Ne normalno	Ne normalno	Normalan	Normalan	Normalan	Normalan	Normalan
Sva pitanja Sva pitanja Moj najveći strah je
Moj najveći strah je
Answer 1	-	Slabo pozitivno 0.0548	Slabo pozitivno 0.0285	Slab negativan -0.0173	Slabo pozitivno 0.0940	Slabo pozitivno 0.0358	Slab negativan -0.0156	Slab negativan -0.1560
Answer 2	-	Slabo pozitivno 0.0192	Slab negativan -0.0048	Slab negativan -0.0394	Slabo pozitivno 0.0659	Slabo pozitivno 0.0491	Slabo pozitivno 0.0117	Slab negativan -0.0981
Answer 3	-	Slab negativan -0.0003	Slab negativan -0.0088	Slab negativan -0.0450	Slab negativan -0.0440	Slabo pozitivno 0.0471	Slabo pozitivno 0.0739	Slab negativan -0.0191
Answer 4	-	Slabo pozitivno 0.0429	Slabo pozitivno 0.0271	Slab negativan -0.0230	Slabo pozitivno 0.0182	Slabo pozitivno 0.0351	Slabo pozitivno 0.0239	Slab negativan -0.0995
Answer 5	-	Slabo pozitivno 0.0273	Slabo pozitivno 0.1298	Slabo pozitivno 0.0101	Slabo pozitivno 0.0772	Slab negativan -0.0006	Slab negativan -0.0183	Slab negativan -0.1784
Answer 6	-	Slab negativan -0.0026	Slabo pozitivno 0.0050	Slab negativan -0.0621	Slab negativan -0.0081	Slabo pozitivno 0.0240	Slabo pozitivno 0.0856	Slab negativan -0.0346
Answer 7	-	Slabo pozitivno 0.0105	Slabo pozitivno 0.0339	Slab negativan -0.0661	Slab negativan -0.0304	Slabo pozitivno 0.0517	Slabo pozitivno 0.0686	Slab negativan -0.0515
Answer 8	-	Slabo pozitivno 0.0635	Slabo pozitivno 0.0732	Slab negativan -0.0275	Slabo pozitivno 0.0143	Slabo pozitivno 0.0370	Slabo pozitivno 0.0172	Slab negativan -0.1336
Answer 9	-	Slabo pozitivno 0.0734	Slabo pozitivno 0.1618	Slabo pozitivno 0.0069	Slabo pozitivno 0.0644	Slab negativan -0.0109	Slab negativan -0.0489	Slab negativan -0.1811
Answer 10	-	Slabo pozitivno 0.0764	Slabo pozitivno 0.0679	Slab negativan -0.0139	Slabo pozitivno 0.0290	Slabo pozitivno 0.0338	Slab negativan -0.0123	Slab negativan -0.1342
Answer 11	-	Slabo pozitivno 0.0634	Slabo pozitivno 0.0535	Slab negativan -0.0091	Slabo pozitivno 0.0113	Slabo pozitivno 0.0238	Slabo pozitivno 0.0247	Slab negativan -0.1260
Answer 12	-	Slabo pozitivno 0.0449	Slabo pozitivno 0.0941	Slab negativan -0.0341	Slabo pozitivno 0.0342	Slabo pozitivno 0.0332	Slabo pozitivno 0.0255	Slab negativan -0.1534
Answer 13	-	Slabo pozitivno 0.0691	Slabo pozitivno 0.0966	Slab negativan -0.0393	Slabo pozitivno 0.0295	Slabo pozitivno 0.0417	Slabo pozitivno 0.0148	Slab negativan -0.1626
Answer 14	-	Slabo pozitivno 0.0775	Slabo pozitivno 0.0903	Slab negativan -0.0019	Slab negativan -0.0089	Slabo pozitivno 0.0048	Slabo pozitivno 0.0140	Slab negativan -0.1223
Answer 15	-	Slabo pozitivno 0.0544	Slabo pozitivno 0.1280	Slab negativan -0.0345	Slabo pozitivno 0.0152	Slab negativan -0.0178	Slabo pozitivno 0.0236	Slab negativan -0.1158
Answer 16	-	Slabo pozitivno 0.0703	Slabo pozitivno 0.0262	Slab negativan -0.0371	Slab negativan -0.0377	Slabo pozitivno 0.0697	Slabo pozitivno 0.0204	Slab negativan -0.0788

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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 kvalifikaciju socijalnog pedagoga-psihologa i od tada primjenjuje svoje znanje u upravljanju projektima.
Valerii je magistrirao i kvalifikaciju menadžera projekta i programa 2013. godine. Tokom magistarskog programa upoznao se sa Planom puta projekta (GPM Deutsche Gesellschaft für Projektmanagement e. V.) i Spiral Dynamics.
Valerii je autor istraživanja neizvjesnosti V.U.C.A. koncept koji koristi spiralnu dinamiku i matematičku statistiku u psihologiji i 38 međunarodnih anketa.

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