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%)

3) Ofnau

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12) Rhagfarn

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22) Teilyngdod

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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 = 0.033

Dosbarthiad nad yw'n arferol, gan Spearman r = 0.0013

Dangos canlyniadau yn unig > r = 0.033

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 0.0559	Gadarnhaol gwan 0.0315	Negyddol gwan -0.0170	Gadarnhaol gwan 0.0920	Gadarnhaol gwan 0.0294	Negyddol gwan -0.0124	Negyddol gwan -0.1539
Answer 2	-	Gadarnhaol gwan 0.0229	Negyddol gwan -0.0002	Negyddol gwan -0.0448	Gadarnhaol gwan 0.0636	Gadarnhaol gwan 0.0445	Gadarnhaol gwan 0.0134	Negyddol gwan -0.0939
Answer 3	-	Negyddol gwan -0.0032	Negyddol gwan -0.0121	Negyddol gwan -0.0416	Negyddol gwan -0.0462	Gadarnhaol gwan 0.0466	Gadarnhaol gwan 0.0788	Negyddol gwan -0.0195
Answer 4	-	Gadarnhaol gwan 0.0438	Gadarnhaol gwan 0.0348	Negyddol gwan -0.0195	Gadarnhaol gwan 0.0153	Gadarnhaol gwan 0.0300	Gadarnhaol gwan 0.0207	Negyddol gwan -0.0980
Answer 5	-	Gadarnhaol gwan 0.0304	Gadarnhaol gwan 0.1282	Gadarnhaol gwan 0.0135	Gadarnhaol gwan 0.0734	Negyddol gwan -0.0013	Negyddol gwan -0.0200	Negyddol gwan -0.1757
Answer 6	-	Negyddol gwan -0.0002	Gadarnhaol gwan 0.0082	Negyddol gwan -0.0627	Negyddol gwan -0.0083	Gadarnhaol gwan 0.0193	Gadarnhaol gwan 0.0831	Negyddol gwan -0.0315
Answer 7	-	Gadarnhaol gwan 0.0126	Gadarnhaol gwan 0.0381	Negyddol gwan -0.0687	Negyddol gwan -0.0243	Gadarnhaol gwan 0.0469	Gadarnhaol gwan 0.0642	Negyddol gwan -0.0515
Answer 8	-	Gadarnhaol gwan 0.0698	Gadarnhaol gwan 0.0848	Negyddol gwan -0.0327	Gadarnhaol gwan 0.0148	Gadarnhaol gwan 0.0345	Gadarnhaol gwan 0.0134	Negyddol gwan -0.1365
Answer 9	-	Gadarnhaol gwan 0.0668	Gadarnhaol gwan 0.1676	Gadarnhaol gwan 0.0083	Gadarnhaol gwan 0.0693	Negyddol gwan -0.0131	Negyddol gwan -0.0516	Negyddol gwan -0.1818
Answer 10	-	Gadarnhaol gwan 0.0782	Gadarnhaol gwan 0.0753	Negyddol gwan -0.0204	Gadarnhaol gwan 0.0247	Gadarnhaol gwan 0.0342	Negyddol gwan -0.0131	Negyddol gwan -0.1304
Answer 11	-	Gadarnhaol gwan 0.0578	Gadarnhaol gwan 0.0532	Negyddol gwan -0.0096	Gadarnhaol gwan 0.0087	Gadarnhaol gwan 0.0195	Gadarnhaol gwan 0.0311	Negyddol gwan -0.1196
Answer 12	-	Gadarnhaol gwan 0.0390	Gadarnhaol gwan 0.1037	Negyddol gwan -0.0358	Gadarnhaol gwan 0.0358	Gadarnhaol gwan 0.0250	Gadarnhaol gwan 0.0299	Negyddol gwan -0.1520
Answer 13	-	Gadarnhaol gwan 0.0644	Gadarnhaol gwan 0.1048	Negyddol gwan -0.0448	Gadarnhaol gwan 0.0268	Gadarnhaol gwan 0.0417	Gadarnhaol gwan 0.0178	Negyddol gwan -0.1600
Answer 14	-	Gadarnhaol gwan 0.0712	Gadarnhaol gwan 0.1021	Negyddol gwan -0.0007	Negyddol gwan -0.0088	Negyddol gwan -0.0011	Gadarnhaol gwan 0.0088	Negyddol gwan -0.1169
Answer 15	-	Gadarnhaol gwan 0.0557	Gadarnhaol gwan 0.1365	Negyddol gwan -0.0423	Gadarnhaol gwan 0.0177	Negyddol gwan -0.0162	Gadarnhaol gwan 0.0224	Negyddol gwan -0.1179
Answer 16	-	Gadarnhaol gwan 0.0591	Gadarnhaol gwan 0.0273	Negyddol gwan -0.0386	Negyddol gwan -0.0400	Gadarnhaol gwan 0.0653	Gadarnhaol gwan 0.0284	Negyddol gwan -0.0708

Allforio i MS Excel

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Iawn

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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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