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)

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 = 0.0335

Non Normalna distribucija, od Spearman r = 0.0014

Prikaži samo rezultate > r = 0.0335

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

Vlasnik proizvoda Saas Pet Project SDTEST®

Valerii je bio kvalificiran kao socijalni pedagogi psiholog 1993. godine i od tada je primijenio svoje znanje u upravljanju projektima.
Valerii je stekao magisterij i kvalifikaciju projekta i programskih menadžera u 2013. tokom svog master programa postao je upoznat sa projektnim mapama (GPM Deutsche Gesellschaft für projektmanagement e. V.) i spiralna dinamika.
Valerii je preuzeo razne testove spiralne dinamike i koristio svoje znanje i iskustvo kako bi prilagodili trenutnu verziju SDTEST-a.
Valerii je autor istraživanja neizvjesnosti V..c.a. Koncept koristeći spiralnu dinamiku i matematičku statistiku u psihologiji, više od 20 međunarodnih anketa.

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