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)

39) Çalakiyên Avakirina Xwebaweriya Bêşik (ji aliyê Suren Saarchyan)

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.

Tirsa

Charts Correlation

VUCA

Nirxa krîtîkî ya hevkêşeya têkeliyê

Belavkirina normal, ji hêla William Sealy Gosset (xwendekar) r = 0.0323

Belavkirina ne normal, ji hêla spearman r = 0.0013

Tenê encaman nîşan bide > r = 0.0323

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 0.0502	Erênî qels 0.0357	Neyînî qels -0.0172	Erênî qels 0.0940	Erênî qels 0.0354	Neyînî qels -0.0173	Neyînî qels -0.1560
Answer 2	-	Erênî qels 0.0193	Erênî qels 0.0013	Neyînî qels -0.0422	Erênî qels 0.0635	Erênî qels 0.0459	Erênî qels 0.0132	Neyînî qels -0.0958
Answer 3	-	Neyînî qels -0.0017	Neyînî qels -0.0096	Neyînî qels -0.0461	Neyînî qels -0.0465	Erênî qels 0.0478	Erênî qels 0.0763	Neyînî qels -0.0168
Answer 4	-	Erênî qels 0.0404	Erênî qels 0.0319	Neyînî qels -0.0225	Erênî qels 0.0182	Erênî qels 0.0304	Erênî qels 0.0228	Neyînî qels -0.0960
Answer 5	-	Erênî qels 0.0288	Erênî qels 0.1333	Erênî qels 0.0088	Erênî qels 0.0794	Erênî qels 0.0003	Neyînî qels -0.0229	Neyînî qels -0.1791
Answer 6	-	Neyînî qels -0.0041	Erênî qels 0.0112	Neyînî qels -0.0655	Neyînî qels -0.0094	Erênî qels 0.0206	Erênî qels 0.0841	Neyînî qels -0.0292
Answer 7	-	Erênî qels 0.0116	Erênî qels 0.0421	Neyînî qels -0.0703	Neyînî qels -0.0290	Erênî qels 0.0476	Erênî qels 0.0654	Neyînî qels -0.0490
Answer 8	-	Erênî qels 0.0647	Erênî qels 0.0822	Neyînî qels -0.0307	Erênî qels 0.0153	Erênî qels 0.0349	Erênî qels 0.0139	Neyînî qels -0.1337
Answer 9	-	Erênî qels 0.0686	Erênî qels 0.1685	Erênî qels 0.0058	Erênî qels 0.0669	Neyînî qels -0.0138	Neyînî qels -0.0513	Neyînî qels -0.1785
Answer 10	-	Erênî qels 0.0773	Erênî qels 0.0732	Neyînî qels -0.0203	Erênî qels 0.0262	Erênî qels 0.0316	Neyînî qels -0.0108	Neyînî qels -0.1291
Answer 11	-	Erênî qels 0.0619	Erênî qels 0.0581	Neyînî qels -0.0053	Erênî qels 0.0087	Erênî qels 0.0181	Erênî qels 0.0240	Neyînî qels -0.1226
Answer 12	-	Erênî qels 0.0425	Erênî qels 0.1009	Neyînî qels -0.0359	Erênî qels 0.0356	Erênî qels 0.0309	Erênî qels 0.0238	Neyînî qels -0.1519
Answer 13	-	Erênî qels 0.0670	Erênî qels 0.1023	Neyînî qels -0.0394	Erênî qels 0.0276	Erênî qels 0.0415	Erênî qels 0.0143	Neyînî qels -0.1617
Answer 14	-	Erênî qels 0.0719	Erênî qels 0.0988	Neyînî qels -0.0036	Neyînî qels -0.0064	Erênî qels 0.0035	Erênî qels 0.0112	Neyînî qels -0.1212
Answer 15	-	Erênî qels 0.0544	Erênî qels 0.1343	Neyînî qels -0.0337	Erênî qels 0.0178	Neyînî qels -0.0194	Erênî qels 0.0202	Neyînî qels -0.1183
Answer 16	-	Erênî qels 0.0671	Erênî qels 0.0284	Neyînî qels -0.0337	Neyînî qels -0.0421	Erênî qels 0.0641	Erênî qels 0.0255	Neyînî qels -0.0753

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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 SDTEST®

Valerii di sala 1993-an de wek pedagog-psîkologê civakî hat hilbijartin û ji wê demê ve zanîna xwe di rêvebirina projeyê de bi kar anî.
Valerii di sala 2013-an de bawernameya masterê û qayimbûna rêveberê proje û bernameyê wergirt. Di dema bernameya masterê de, ew bi Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) û Spiral Dynamics nas bû.
Valerii nivîskarê vekolîna nezelaliya V.U.C.A ye. konsepta bikaranîna Dînamîkên Spiral û statîstîkên matematîkî di psîkolojiyê de, û 38 anketên navneteweyî.

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