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) Kiryarên pargîdaniyên di têkiliyên bi personelê de di meha paşîn de (erê / na)

2) Kiryarên pargîdaniyan di derbarê personelê de di meha paşîn de (di %%)

3) Tirsa

4) Pirsgirêkên herî mezin ku li welatê min rû didin

5) Kîjan taybetmendî û jêhatî rêberên baş dikin dema ku tîmên serfiraz ava dikin?

6) Google. Faktorên ku bandora tîmê bandor dikin

7) Pêşînên sereke yên lêgerîna kar

8) Whati dibe sedema serokatiyek mezin?

9) Makesi dibe ku mirov di kar de serfiraz bibe?

10) Ma hûn amade ne ku ji bo ku hûn ji dûr ve bixebitin kêmtir bidin?

11) Halgeîzm heye?

12) Halûn di karîzasyonê de

13) Halûn di jiyanê de

14) Sedemên temenîzmê

15) Sedemên ku mirov dane (ji hêla Anna Vital)

16) BAWERÎ (#WVS)

17) Lêkolîna Xemgîniya Oxford

18) Welatparêziya Psîkolojîk

19) Li ku derê dê derfeta herî balkêş ya we be?

20) Hûn ê vê hefteyê çi bikin da ku hûn li tenduristiya giyanî ya xwe binêrin?

21) Ez li ser paşeroja xwe, niha an pêşerojê difikirim

22) Meritokrasî

23) Îstîxbarata artificial û dawiya şaristaniyê

24) Whyima mirov paşve dikin?

25) Cûdahiya zayendî di avakirina xwe-bawerî (IFD ALLENSBACH)

26) XING.COM Nirxandina Cultureîna

27) Patrick Lencioni "Pênc Dysfunctions of a tîm"

28) Empatî ye ...

29) Di hilbijartina pêşniyarek karekî de ji bo pisporên wê çi girîng e?

30) Whyima mirov li dijî guhertinê radiwestin (ji hêla Siobhán Mchale)

31) Ma hûn çawa hestên xwe rêz dikin? (ji hêla Nawal Mustafa M.A.)

32) 21 Hişmendiyên ku we her dem didin (ji hêla Jeremiah Teo / 赵汉昇)

33) Azadiya rastîn e ...

34) 12 awayên ji bo avakirina baweriyê bi yên din re (ji hêla Justin Wright)

35) Taybetmendiyên karmendek jêhatî (ji hêla Enstîtuya Rêveberiya Talent)

36) 10 Keys ji bo motîfkirina tîmê xwe

37) Algebra of Wijdan (ji hêla Vladimir Lefebvre)

38) Sê îmkanên cuda yên pêşerojê (ji hêla 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.

Tirsa

Charts Correlation

VUCA

Nirxa krîtîkî ya hevkêşeya têkeliyê

Belavkirina normal, ji hêla William Sealy Gosset (xwendekar) r = 0.033

Belavkirina ne normal, ji hêla spearman r = 0.0013

Tenê encaman nîşan bide > r = 0.033

Belavkirinî	Ne normal	Ne normal	Ne normal	Normal	Normal	Normal	Normal	Normal
Hemî pirs Hemî pirs Tirsa min a herî mezin e
Tirsa min a herî mezin e
Answer 1	-	Erênî qels 0.0559	Erênî qels 0.0315	Neyînî qels -0.0170	Erênî qels 0.0920	Erênî qels 0.0294	Neyînî qels -0.0124	Neyînî qels -0.1539
Answer 2	-	Erênî qels 0.0229	Neyînî qels -0.0002	Neyînî qels -0.0448	Erênî qels 0.0636	Erênî qels 0.0445	Erênî qels 0.0134	Neyînî qels -0.0939
Answer 3	-	Neyînî qels -0.0032	Neyînî qels -0.0121	Neyînî qels -0.0416	Neyînî qels -0.0462	Erênî qels 0.0466	Erênî qels 0.0788	Neyînî qels -0.0195
Answer 4	-	Erênî qels 0.0438	Erênî qels 0.0348	Neyînî qels -0.0195	Erênî qels 0.0153	Erênî qels 0.0300	Erênî qels 0.0207	Neyînî qels -0.0980
Answer 5	-	Erênî qels 0.0304	Erênî qels 0.1282	Erênî qels 0.0135	Erênî qels 0.0734	Neyînî qels -0.0013	Neyînî qels -0.0200	Neyînî qels -0.1757
Answer 6	-	Neyînî qels -0.0002	Erênî qels 0.0082	Neyînî qels -0.0627	Neyînî qels -0.0083	Erênî qels 0.0193	Erênî qels 0.0831	Neyînî qels -0.0315
Answer 7	-	Erênî qels 0.0126	Erênî qels 0.0381	Neyînî qels -0.0687	Neyînî qels -0.0243	Erênî qels 0.0469	Erênî qels 0.0642	Neyînî qels -0.0515
Answer 8	-	Erênî qels 0.0698	Erênî qels 0.0848	Neyînî qels -0.0327	Erênî qels 0.0148	Erênî qels 0.0345	Erênî qels 0.0134	Neyînî qels -0.1365
Answer 9	-	Erênî qels 0.0668	Erênî qels 0.1676	Erênî qels 0.0083	Erênî qels 0.0693	Neyînî qels -0.0131	Neyînî qels -0.0516	Neyînî qels -0.1818
Answer 10	-	Erênî qels 0.0782	Erênî qels 0.0753	Neyînî qels -0.0204	Erênî qels 0.0247	Erênî qels 0.0342	Neyînî qels -0.0131	Neyînî qels -0.1304
Answer 11	-	Erênî qels 0.0578	Erênî qels 0.0532	Neyînî qels -0.0096	Erênî qels 0.0087	Erênî qels 0.0195	Erênî qels 0.0311	Neyînî qels -0.1196
Answer 12	-	Erênî qels 0.0390	Erênî qels 0.1037	Neyînî qels -0.0358	Erênî qels 0.0358	Erênî qels 0.0250	Erênî qels 0.0299	Neyînî qels -0.1520
Answer 13	-	Erênî qels 0.0644	Erênî qels 0.1048	Neyînî qels -0.0448	Erênî qels 0.0268	Erênî qels 0.0417	Erênî qels 0.0178	Neyînî qels -0.1600
Answer 14	-	Erênî qels 0.0712	Erênî qels 0.1021	Neyînî qels -0.0007	Neyînî qels -0.0088	Neyînî qels -0.0011	Erênî qels 0.0088	Neyînî qels -0.1169
Answer 15	-	Erênî qels 0.0557	Erênî qels 0.1365	Neyînî qels -0.0423	Erênî qels 0.0177	Neyînî qels -0.0162	Erênî qels 0.0224	Neyînî qels -0.1179
Answer 16	-	Erênî qels 0.0591	Erênî qels 0.0273	Neyînî qels -0.0386	Neyînî qels -0.0400	Erênî qels 0.0653	Erênî qels 0.0284	Neyînî qels -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

Xwediyê hilberê Saas Pet Project Sdtest®

Valerii di sala 1993-an de wekî pedagojiya civakî-psîkolojiyê-psîkologê hate qiyas kirin û ji ber ku zanîna wî di rêveberiya projeyê de bicîh kir.
Valerii di sala 2013-an de asta masterê û rêvebirê rêveberê master û projeyê û bernameya xwe peyda kir, ew bi projeya projeya projeyê (GPM Deutsche Gesellschaft für projektman e. V.) û dînamîka spiral.
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Valerii nivîskarê lêgerîna nediyarbûna v.u.c.A. Têgihiştin ku di psîkolojiyê de, zêdetirî 20 anketên navneteweyî bêtir bikar bînin.

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