Namai/Dienoraštis/Mathematical Psychology

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.

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1) Įmonės veiksmai, susiję su personalu per pastarąjį mėnesį (taip / ne)

2) Įmonių veiksmai, susiję su personalo per pastarąjį mėnesį (tai)

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9) Kas daro žmones sėkmingus darbe?

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16) Pasitikėjimas (#WVS)

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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.

Baimė

Grafikai Koreliacija

VUCA

Kritinė reikšmė koreliacijos koeficientas

Normalus platinimas, pateikė William Sealy Gosset (studentas) r = 0.0353

Ne normalus pasiskirstymas, autorius Spearman r = 0.0014

Rodyti tik rezultatus > r = 0.0353

Paskirstymas	Ne normalu	Normalus	Ne normalu	Normalus	Normalus	Normalus	Normalus	Normalus
Visi klausimai Visi klausimai Mano didžiausia baimė yra
Mano didžiausia baimė yra
Answer 1	-	Silpnas teigiamas 0.0297	Silpnas teigiamas 0.0298	Silpnas neigiamas -0.0106	Silpnas teigiamas 0.0970	Silpnas teigiamas 0.0325	Silpnas neigiamas -0.0019	Silpnas neigiamas -0.1558
Answer 2	-	Silpnas teigiamas 0.0188	Silpnas teigiamas 0.0076	Silpnas neigiamas -0.0360	Silpnas teigiamas 0.0711	Silpnas teigiamas 0.0387	Silpnas teigiamas 0.0082	Silpnas neigiamas -0.1011
Answer 3	-	Silpnas teigiamas 0.0026	Silpnas neigiamas -0.0170	Silpnas neigiamas -0.0443	Silpnas neigiamas -0.0458	Silpnas teigiamas 0.0547	Silpnas teigiamas 0.0808	Silpnas neigiamas -0.0270
Answer 4	-	Silpnas teigiamas 0.0332	Silpnas teigiamas 0.0285	Silpnas neigiamas -0.0006	Silpnas teigiamas 0.0155	Silpnas teigiamas 0.0276	Silpnas teigiamas 0.0105	Silpnas neigiamas -0.0917
Answer 5	-	Silpnas teigiamas 0.0122	Silpnas teigiamas 0.1193	Silpnas teigiamas 0.0095	Silpnas teigiamas 0.0721	Silpnas teigiamas 0.0057	Silpnas neigiamas -0.0083	Silpnas neigiamas -0.1687
Answer 6	-	Silpnas teigiamas 0.0044	Silpnas teigiamas 0.0005	Silpnas neigiamas -0.0582	Silpnas neigiamas -0.0004	Silpnas teigiamas 0.0210	Silpnas teigiamas 0.0830	Silpnas neigiamas -0.0418
Answer 7	-	Silpnas teigiamas 0.0242	Silpnas teigiamas 0.0368	Silpnas neigiamas -0.0521	Silpnas neigiamas -0.0234	Silpnas teigiamas 0.0403	Silpnas teigiamas 0.0568	Silpnas neigiamas -0.0597
Answer 8	-	Silpnas teigiamas 0.0707	Silpnas teigiamas 0.0781	Silpnas neigiamas -0.0244	Silpnas teigiamas 0.0140	Silpnas teigiamas 0.0303	Silpnas teigiamas 0.0137	Silpnas neigiamas -0.1334
Answer 9	-	Silpnas teigiamas 0.0564	Silpnas teigiamas 0.1531	Silpnas teigiamas 0.0127	Silpnas teigiamas 0.0769	Silpnas neigiamas -0.0136	Silpnas neigiamas -0.0495	Silpnas neigiamas -0.1752
Answer 10	-	Silpnas teigiamas 0.0711	Silpnas teigiamas 0.0700	Silpnas neigiamas -0.0127	Silpnas teigiamas 0.0246	Silpnas teigiamas 0.0363	Silpnas neigiamas -0.0156	Silpnas neigiamas -0.1273
Answer 11	-	Silpnas teigiamas 0.0542	Silpnas teigiamas 0.0488	Silpnas teigiamas 0.0086	Silpnas teigiamas 0.0078	Silpnas teigiamas 0.0162	Silpnas teigiamas 0.0315	Silpnas neigiamas -0.1248
Answer 12	-	Silpnas teigiamas 0.0281	Silpnas teigiamas 0.0929	Silpnas neigiamas -0.0325	Silpnas teigiamas 0.0361	Silpnas teigiamas 0.0276	Silpnas teigiamas 0.0365	Silpnas neigiamas -0.1482
Answer 13	-	Silpnas teigiamas 0.0643	Silpnas teigiamas 0.0916	Silpnas neigiamas -0.0418	Silpnas teigiamas 0.0237	Silpnas teigiamas 0.0425	Silpnas teigiamas 0.0239	Silpnas neigiamas -0.1558
Answer 14	-	Silpnas teigiamas 0.0697	Silpnas teigiamas 0.1017	Silpnas teigiamas 0.0149	Silpnas neigiamas -0.0062	Silpnas neigiamas -0.0087	Silpnas neigiamas -0.0002	Silpnas neigiamas -0.1161
Answer 15	-	Silpnas teigiamas 0.0603	Silpnas teigiamas 0.1299	Silpnas neigiamas -0.0379	Silpnas teigiamas 0.0163	Silpnas neigiamas -0.0091	Silpnas teigiamas 0.0164	Silpnas neigiamas -0.1204
Answer 16	-	Silpnas teigiamas 0.0691	Silpnas teigiamas 0.0221	Silpnas neigiamas -0.0305	Silpnas neigiamas -0.0515	Silpnas teigiamas 0.0750	Silpnas teigiamas 0.0187	Silpnas neigiamas -0.0696

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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

Produkto savininkas „Saa Pet Project SDTest®“

1993 m. Valerii buvo kvalifikuotas kaip socialinis pedagogo-psichologas ir nuo to laiko pritaikė savo žinias projektų valdyme.
2013 m. Valerii įgijo magistro laipsnį ir projekto bei programų vadovo kvalifikaciją. Vykdydamas magistro programą, jis susipažino su projekto planu (GPM Deutsche Gesellschaft Für Projektmanagement e. V.) ir „Spiral Dynamics“.
Valerii ėmėsi įvairių „Spiral Dynamics“ testų ir panaudojo savo žinias bei patirtį, kad pritaikytų dabartinę SDTEST versiją.
Valerii yra autorius tyrinėti V.U.C.A. Koncepcija naudojant spiralinę dinamiką ir matematinę statistiką psichologijoje, daugiau nei 20 tarptautinių apklausų.

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