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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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 0.0569	Gadarnhaol gwan 0.0313	Negyddol gwan -0.0161	Gadarnhaol gwan 0.0906	Gadarnhaol gwan 0.0297	Negyddol gwan -0.0118	Negyddol gwan -0.1544
Answer 2	-	Gadarnhaol gwan 0.0225	Gadarnhaol gwan 0.0002	Negyddol gwan -0.0450	Gadarnhaol gwan 0.0644	Gadarnhaol gwan 0.0442	Gadarnhaol gwan 0.0128	Negyddol gwan -0.0940
Answer 3	-	Negyddol gwan -0.0030	Negyddol gwan -0.0116	Negyddol gwan -0.0411	Negyddol gwan -0.0465	Gadarnhaol gwan 0.0466	Gadarnhaol gwan 0.0786	Negyddol gwan -0.0200
Answer 4	-	Gadarnhaol gwan 0.0440	Gadarnhaol gwan 0.0354	Negyddol gwan -0.0189	Gadarnhaol gwan 0.0150	Gadarnhaol gwan 0.0299	Gadarnhaol gwan 0.0204	Negyddol gwan -0.0986
Answer 5	-	Gadarnhaol gwan 0.0309	Gadarnhaol gwan 0.1278	Gadarnhaol gwan 0.0137	Gadarnhaol gwan 0.0728	Negyddol gwan -0.0011	Negyddol gwan -0.0195	Negyddol gwan -0.1757
Answer 6	-	Negyddol gwan -0.0001	Gadarnhaol gwan 0.0086	Negyddol gwan -0.0623	Negyddol gwan -0.0085	Gadarnhaol gwan 0.0193	Gadarnhaol gwan 0.0829	Negyddol gwan -0.0319
Answer 7	-	Gadarnhaol gwan 0.0127	Gadarnhaol gwan 0.0385	Negyddol gwan -0.0683	Negyddol gwan -0.0246	Gadarnhaol gwan 0.0468	Gadarnhaol gwan 0.0640	Negyddol gwan -0.0519
Answer 8	-	Gadarnhaol gwan 0.0700	Gadarnhaol gwan 0.0853	Negyddol gwan -0.0322	Gadarnhaol gwan 0.0146	Gadarnhaol gwan 0.0344	Gadarnhaol gwan 0.0132	Negyddol gwan -0.1370
Answer 9	-	Gadarnhaol gwan 0.0670	Gadarnhaol gwan 0.1680	Gadarnhaol gwan 0.0087	Gadarnhaol gwan 0.0692	Negyddol gwan -0.0132	Negyddol gwan -0.0518	Negyddol gwan -0.1822
Answer 10	-	Gadarnhaol gwan 0.0784	Gadarnhaol gwan 0.0758	Negyddol gwan -0.0199	Gadarnhaol gwan 0.0245	Gadarnhaol gwan 0.0342	Negyddol gwan -0.0133	Negyddol gwan -0.1308
Answer 11	-	Gadarnhaol gwan 0.0586	Gadarnhaol gwan 0.0528	Negyddol gwan -0.0091	Gadarnhaol gwan 0.0074	Gadarnhaol gwan 0.0198	Gadarnhaol gwan 0.0318	Negyddol gwan -0.1198
Answer 12	-	Gadarnhaol gwan 0.0392	Gadarnhaol gwan 0.1042	Negyddol gwan -0.0353	Gadarnhaol gwan 0.0357	Gadarnhaol gwan 0.0249	Gadarnhaol gwan 0.0297	Negyddol gwan -0.1526
Answer 13	-	Gadarnhaol gwan 0.0646	Gadarnhaol gwan 0.1052	Negyddol gwan -0.0444	Gadarnhaol gwan 0.0266	Gadarnhaol gwan 0.0416	Gadarnhaol gwan 0.0176	Negyddol gwan -0.1605
Answer 14	-	Gadarnhaol gwan 0.0714	Gadarnhaol gwan 0.1026	Negyddol gwan -0.0002	Negyddol gwan -0.0090	Negyddol gwan -0.0012	Gadarnhaol gwan 0.0086	Negyddol gwan -0.1174
Answer 15	-	Gadarnhaol gwan 0.0558	Gadarnhaol gwan 0.1369	Negyddol gwan -0.0419	Gadarnhaol gwan 0.0176	Negyddol gwan -0.0163	Gadarnhaol gwan 0.0222	Negyddol gwan -0.1183
Answer 16	-	Gadarnhaol gwan 0.0592	Gadarnhaol gwan 0.0275	Negyddol gwan -0.0384	Negyddol gwan -0.0402	Gadarnhaol gwan 0.0652	Gadarnhaol gwan 0.0283	Negyddol gwan -0.0710

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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