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 = 0.033

Non Normalna distribucija, od Spearman r = 0.0013

Prikaži samo rezultate > r = 0.033

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 0.0559	Slabo pozitivno 0.0315	Slab negativan -0.0170	Slabo pozitivno 0.0920	Slabo pozitivno 0.0294	Slab negativan -0.0124	Slab negativan -0.1539
Answer 2	-	Slabo pozitivno 0.0229	Slab negativan -0.0002	Slab negativan -0.0448	Slabo pozitivno 0.0636	Slabo pozitivno 0.0445	Slabo pozitivno 0.0134	Slab negativan -0.0939
Answer 3	-	Slab negativan -0.0032	Slab negativan -0.0121	Slab negativan -0.0416	Slab negativan -0.0462	Slabo pozitivno 0.0466	Slabo pozitivno 0.0788	Slab negativan -0.0195
Answer 4	-	Slabo pozitivno 0.0438	Slabo pozitivno 0.0348	Slab negativan -0.0195	Slabo pozitivno 0.0153	Slabo pozitivno 0.0300	Slabo pozitivno 0.0207	Slab negativan -0.0980
Answer 5	-	Slabo pozitivno 0.0304	Slabo pozitivno 0.1282	Slabo pozitivno 0.0135	Slabo pozitivno 0.0734	Slab negativan -0.0013	Slab negativan -0.0200	Slab negativan -0.1757
Answer 6	-	Slab negativan -0.0002	Slabo pozitivno 0.0082	Slab negativan -0.0627	Slab negativan -0.0083	Slabo pozitivno 0.0193	Slabo pozitivno 0.0831	Slab negativan -0.0315
Answer 7	-	Slabo pozitivno 0.0126	Slabo pozitivno 0.0381	Slab negativan -0.0687	Slab negativan -0.0243	Slabo pozitivno 0.0469	Slabo pozitivno 0.0642	Slab negativan -0.0515
Answer 8	-	Slabo pozitivno 0.0698	Slabo pozitivno 0.0848	Slab negativan -0.0327	Slabo pozitivno 0.0148	Slabo pozitivno 0.0345	Slabo pozitivno 0.0134	Slab negativan -0.1365
Answer 9	-	Slabo pozitivno 0.0668	Slabo pozitivno 0.1676	Slabo pozitivno 0.0083	Slabo pozitivno 0.0693	Slab negativan -0.0131	Slab negativan -0.0516	Slab negativan -0.1818
Answer 10	-	Slabo pozitivno 0.0782	Slabo pozitivno 0.0753	Slab negativan -0.0204	Slabo pozitivno 0.0247	Slabo pozitivno 0.0342	Slab negativan -0.0131	Slab negativan -0.1304
Answer 11	-	Slabo pozitivno 0.0578	Slabo pozitivno 0.0532	Slab negativan -0.0096	Slabo pozitivno 0.0087	Slabo pozitivno 0.0195	Slabo pozitivno 0.0311	Slab negativan -0.1196
Answer 12	-	Slabo pozitivno 0.0390	Slabo pozitivno 0.1037	Slab negativan -0.0358	Slabo pozitivno 0.0358	Slabo pozitivno 0.0250	Slabo pozitivno 0.0299	Slab negativan -0.1520
Answer 13	-	Slabo pozitivno 0.0644	Slabo pozitivno 0.1048	Slab negativan -0.0448	Slabo pozitivno 0.0268	Slabo pozitivno 0.0417	Slabo pozitivno 0.0178	Slab negativan -0.1600
Answer 14	-	Slabo pozitivno 0.0712	Slabo pozitivno 0.1021	Slab negativan -0.0007	Slab negativan -0.0088	Slab negativan -0.0011	Slabo pozitivno 0.0088	Slab negativan -0.1169
Answer 15	-	Slabo pozitivno 0.0557	Slabo pozitivno 0.1365	Slab negativan -0.0423	Slabo pozitivno 0.0177	Slab negativan -0.0162	Slabo pozitivno 0.0224	Slab negativan -0.1179
Answer 16	-	Slabo pozitivno 0.0591	Slabo pozitivno 0.0273	Slab negativan -0.0386	Slab negativan -0.0400	Slabo pozitivno 0.0653	Slabo pozitivno 0.0284	Slab negativan -0.0708

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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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