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) Gweithredoedd cwmnïau mewn perthynas â phersonél yn ystod y mis diwethaf (ie / na)

2) Gweithredoedd cwmnïau mewn perthynas â phersonél yn ystod y mis diwethaf (ffaith mewn%)

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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.

Ofnau

siartiauCydberthyniad

VUCA

Math Cydberthynas	llinellol (Pearson) llinellol (Pearson) Aflinol (Spearman)
Gwerth feirniadol o'r cyfernod cydberthyniad	Dosbarthiad Arferol, gan William Sealy Gosset (Myfyriwr) Dosbarthiad Arferol, gan William Sealy Gosset (Myfyriwr) Dosbarthiad nad yw'n arferol, gan Spearman	Dangos canlyniadau yn unig > r = 0.03

Nosbarthiadau	Nad yw'n normal	Nad yw'n normal	Nad yw'n normal	Normal	Normal	Normal	Normal	Normal
Pob cwestiwn Pob cwestiwn Fy ofn mwyaf yw
Fy ofn mwyaf yw
Answer 1	-	Gadarnhaol gwan 0.0482	Gadarnhaol gwan 0.0259	Negyddol gwan -0.0250	Gadarnhaol gwan 0.0985	Gadarnhaol gwan 0.0348	Negyddol gwan -0.0113	Negyddol gwan -0.1504
Answer 2	-	Gadarnhaol gwan 0.0235	Gadarnhaol gwan 0.0009	Negyddol gwan -0.0417	Gadarnhaol gwan 0.0619	Gadarnhaol gwan 0.0463	Gadarnhaol gwan 0.0123	Negyddol gwan -0.0971
Answer 3	-	Negyddol gwan -0.0021	Gadarnhaol gwan 0.0040	Negyddol gwan -0.0483	Negyddol gwan -0.0428	Gadarnhaol gwan 0.0428	Gadarnhaol gwan 0.0749	Negyddol gwan -0.0225
Answer 4	-	Gadarnhaol gwan 0.0446	Gadarnhaol gwan 0.0326	Negyddol gwan -0.0296	Gadarnhaol gwan 0.0197	Gadarnhaol gwan 0.0346	Gadarnhaol gwan 0.0227	Negyddol gwan -0.0997
Answer 5	-	Gadarnhaol gwan 0.0222	Gadarnhaol gwan 0.1291	Gadarnhaol gwan 0.0029	Gadarnhaol gwan 0.0839	Negyddol gwan -1.80E-5	Negyddol gwan -0.0119	Negyddol gwan -0.1816
Answer 6	-	Gadarnhaol gwan 0.0043	Gadarnhaol gwan 0.0158	Negyddol gwan -0.0643	Negyddol gwan -0.0108	Gadarnhaol gwan 0.0149	Gadarnhaol gwan 0.0867	Negyddol gwan -0.0357
Answer 7	-	Gadarnhaol gwan 0.0100	Gadarnhaol gwan 0.0445	Negyddol gwan -0.0687	Negyddol gwan -0.0339	Gadarnhaol gwan 0.0441	Gadarnhaol gwan 0.0736	Negyddol gwan -0.0512
Answer 8	-	Gadarnhaol gwan 0.0624	Gadarnhaol gwan 0.0845	Negyddol gwan -0.0295	Gadarnhaol gwan 0.0114	Gadarnhaol gwan 0.0354	Gadarnhaol gwan 0.0169	Negyddol gwan -0.1364
Answer 9	-	Gadarnhaol gwan 0.0735	Gadarnhaol gwan 0.1609	Negyddol gwan -0.0009	Gadarnhaol gwan 0.0628	Negyddol gwan -0.0084	Negyddol gwan -0.0493	Negyddol gwan -0.1765
Answer 10	-	Gadarnhaol gwan 0.0756	Gadarnhaol gwan 0.0622	Negyddol gwan -0.0152	Gadarnhaol gwan 0.0242	Gadarnhaol gwan 0.0376	Negyddol gwan -0.0052	Negyddol gwan -0.1348
Answer 11	-	Gadarnhaol gwan 0.0658	Gadarnhaol gwan 0.0561	Negyddol gwan -0.0086	Gadarnhaol gwan 0.0102	Gadarnhaol gwan 0.0243	Gadarnhaol gwan 0.0198	Negyddol gwan -0.1260
Answer 12	-	Gadarnhaol gwan 0.0415	Gadarnhaol gwan 0.1046	Negyddol gwan -0.0390	Gadarnhaol gwan 0.0361	Gadarnhaol gwan 0.0275	Gadarnhaol gwan 0.0255	Negyddol gwan -0.1523
Answer 13	-	Gadarnhaol gwan 0.0744	Gadarnhaol gwan 0.1011	Negyddol gwan -0.0390	Gadarnhaol gwan 0.0271	Gadarnhaol gwan 0.0325	Gadarnhaol gwan 0.0140	Negyddol gwan -0.1591
Answer 14	-	Gadarnhaol gwan 0.0831	Gadarnhaol gwan 0.0922	Negyddol gwan -0.0086	Negyddol gwan -0.0139	Gadarnhaol gwan 0.0030	Gadarnhaol gwan 0.0101	Negyddol gwan -0.1131
Answer 15	-	Gadarnhaol gwan 0.0556	Gadarnhaol gwan 0.1306	Negyddol gwan -0.0297	Gadarnhaol gwan 0.0122	Negyddol gwan -0.0229	Gadarnhaol gwan 0.0240	Negyddol gwan -0.1175
Answer 16	-	Gadarnhaol gwan 0.0685	Gadarnhaol gwan 0.0315	Negyddol gwan -0.0348	Negyddol gwan -0.0426	Gadarnhaol gwan 0.0629	Gadarnhaol gwan 0.0163	Negyddol gwan -0.0701

Allforio i MS Excel

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[1] https://twitter.com/wileyprof

[2] https://colinallen.dnsalias.org

[3] https://philpeople.org/profiles/colin-allen

2023.10.13

FearpersonqualitiesprojectorganizationalstructureRACIresponsibilitymatrixCritical ChainProject Managementfocus factorJiraempathyleadersbossGermanyChinaPolicyUkraineRussiawarvolatilityuncertaintycomplexityambiguityVUCArelocatejobproblemcountryreasongive upobjectivekeyresultmathematicalpsychologyMBTIHR metricsstandardDEIcorrelationriskscoringmodelGame TheoryPrisoner's Dilemma

Valerii Kosenko

Perchennog Cynnyrch SaaS SDTEST®

Cymhwyswyd Valerii fel pedagog-seicolegydd cymdeithasol yn 1993 ac ers hynny mae wedi cymhwyso ei wybodaeth mewn rheoli prosiectau.
Enillodd Valerii radd Meistr a chymhwyster rheolwr prosiect a rhaglen yn 2013. Yn ystod ei raglen Meistr, daeth yn gyfarwydd â Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) a Spiral Dynamics.
Mae Valerii yn awdur ar archwilio ansicrwydd y V.U.C.A. cysyniad defnyddio Spiral Dynamics ac ystadegau mathemategol mewn seicoleg, a 38 polau rhyngwladol.

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