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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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

siartiau Cydberthyniad

VUCA

Gwerth feirniadol o'r cyfernod cydberthyniad

Dosbarthiad Arferol, gan William Sealy Gosset (Myfyriwr) r = 0.0335

Dosbarthiad nad yw'n arferol, gan Spearman r = 0.0014

Dangos canlyniadau yn unig > r = 0.0335

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 0.0521	Gadarnhaol gwan 0.0294	Negyddol gwan -0.0147	Gadarnhaol gwan 0.0885	Gadarnhaol gwan 0.0316	Negyddol gwan -0.0110	Negyddol gwan -0.1513
Answer 2	-	Gadarnhaol gwan 0.0213	Gadarnhaol gwan 0.0013	Negyddol gwan -0.0432	Gadarnhaol gwan 0.0618	Gadarnhaol gwan 0.0453	Gadarnhaol gwan 0.0103	Negyddol gwan -0.0918
Answer 3	-	Negyddol gwan -0.0042	Negyddol gwan -0.0116	Negyddol gwan -0.0406	Negyddol gwan -0.0477	Gadarnhaol gwan 0.0487	Gadarnhaol gwan 0.0767	Negyddol gwan -0.0191
Answer 4	-	Gadarnhaol gwan 0.0421	Gadarnhaol gwan 0.0350	Negyddol gwan -0.0115	Gadarnhaol gwan 0.0112	Gadarnhaol gwan 0.0307	Gadarnhaol gwan 0.0175	Negyddol gwan -0.0980
Answer 5	-	Gadarnhaol gwan 0.0288	Gadarnhaol gwan 0.1272	Gadarnhaol gwan 0.0146	Gadarnhaol gwan 0.0697	Gadarnhaol gwan 0.0037	Negyddol gwan -0.0215	Negyddol gwan -0.1746
Answer 6	-	Negyddol gwan -0.0001	Gadarnhaol gwan 0.0042	Negyddol gwan -0.0607	Negyddol gwan -0.0115	Gadarnhaol gwan 0.0231	Gadarnhaol gwan 0.0826	Negyddol gwan -0.0309
Answer 7	-	Gadarnhaol gwan 0.0117	Gadarnhaol gwan 0.0372	Negyddol gwan -0.0653	Negyddol gwan -0.0283	Gadarnhaol gwan 0.0495	Gadarnhaol gwan 0.0626	Negyddol gwan -0.0505
Answer 8	-	Gadarnhaol gwan 0.0658	Gadarnhaol gwan 0.0830	Negyddol gwan -0.0310	Gadarnhaol gwan 0.0139	Gadarnhaol gwan 0.0334	Gadarnhaol gwan 0.0134	Negyddol gwan -0.1322
Answer 9	-	Gadarnhaol gwan 0.0660	Gadarnhaol gwan 0.1658	Gadarnhaol gwan 0.0051	Gadarnhaol gwan 0.0691	Negyddol gwan -0.0093	Negyddol gwan -0.0498	Negyddol gwan -0.1820
Answer 10	-	Gadarnhaol gwan 0.0758	Gadarnhaol gwan 0.0724	Negyddol gwan -0.0173	Gadarnhaol gwan 0.0236	Gadarnhaol gwan 0.0312	Negyddol gwan -0.0115	Negyddol gwan -0.1263
Answer 11	-	Gadarnhaol gwan 0.0577	Gadarnhaol gwan 0.0544	Negyddol gwan -0.0075	Gadarnhaol gwan 0.0082	Gadarnhaol gwan 0.0185	Gadarnhaol gwan 0.0293	Negyddol gwan -0.1190
Answer 12	-	Gadarnhaol gwan 0.0376	Gadarnhaol gwan 0.1007	Negyddol gwan -0.0342	Gadarnhaol gwan 0.0296	Gadarnhaol gwan 0.0273	Gadarnhaol gwan 0.0341	Negyddol gwan -0.1500
Answer 13	-	Gadarnhaol gwan 0.0627	Gadarnhaol gwan 0.1017	Negyddol gwan -0.0443	Gadarnhaol gwan 0.0248	Gadarnhaol gwan 0.0434	Gadarnhaol gwan 0.0189	Negyddol gwan -0.1576
Answer 14	-	Gadarnhaol gwan 0.0732	Gadarnhaol gwan 0.1036	Gadarnhaol gwan 0.0048	Negyddol gwan -0.0105	Negyddol gwan -0.0039	Gadarnhaol gwan 0.0041	Negyddol gwan -0.1157
Answer 15	-	Gadarnhaol gwan 0.0539	Gadarnhaol gwan 0.1381	Negyddol gwan -0.0424	Gadarnhaol gwan 0.0163	Negyddol gwan -0.0147	Gadarnhaol gwan 0.0216	Negyddol gwan -0.1173
Answer 16	-	Gadarnhaol gwan 0.0590	Gadarnhaol gwan 0.0274	Negyddol gwan -0.0375	Negyddol gwan -0.0429	Gadarnhaol gwan 0.0687	Gadarnhaol gwan 0.0253	Negyddol gwan -0.0698

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

Valerii Kosenko

Perchennog y Cynnyrch Saas Pet Project Sdtest®

Roedd Valerii yn gymwys fel addysgegydd cymdeithasol-seicolegydd ym 1993 ac ers hynny mae wedi cymhwyso ei wybodaeth mewn rheoli prosiect.
Cafodd Valerii radd meistr a chymhwyster y prosiect a rheolwr rhaglen yn 2013. Yn ystod rhaglen ei feistr, daeth yn gyfarwydd â Map Ffordd Project (GPM Deutsche Gesellschaft für Projektmanagement e. V.) a Spiral Dynamics.
Cipiodd Valerii amryw o brofion dynameg troellog a defnyddio ei wybodaeth a'i brofiad i addasu'r fersiwn gyfredol o SDTest.
Valerii yw awdur archwilio ansicrwydd y V.U.C.A. Cysyniad gan ddefnyddio dynameg troellog ac ystadegau mathemategol mewn seicoleg, mwy nag 20 o bolau rhyngwladol.

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