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:

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26) Su'esu'ega aganu'u a Xing.com

27) Patrick LenCioni's "O le Lima Dysfanotions o le 'au"

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29) O le a le mea e taua mo ia i le filifilia o se galuega ofo?

30) Aisea e teteʻe ai tagata i suiga (e Siobhán Mchale)

31) Faʻafefea ona e faʻatonutonu ou lagona? (SAUNIA E NAWAL LE MUTATA M.A.)

32) 21 Tomai e Totogi Oe e Faavavau (SAUNIA E SAMA TOO / 赵汉昇)

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35) Uiga o se tagata talenia tagata faigaluega (e le taleni pulega inisitituti)

36) 10 ki e faaosofia ai lau 'au

37) Algebra of Conscience (saunia e Vladimir Lefebvre)

38) E Tolu Tulaga Eseese o le Lumanai (saunia e Dr. Clare W. Graves)

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.

Fefe

siata Faamaopoopo

VUCA

Tau aogā taua o le coefficient faamaopoopoga

Masani tufatufaina, saunia e William Sealy Gosset (Tamaiti Aoga) r = 0.0331

Le masani ai tufatufaina, saunia e Spearman r = 0.0013

Faʻailoa naʻo faʻaiuga > r = 0.0331

Tufatufaina	Le masani	Le masani	Le masani	Masani	Masani	Masani	Masani	Masani
Fesili uma Fesili uma O loʻu fefe silisili o
O loʻu fefe silisili o
Answer 1	-	Lelei vaivai 0.0562	Lelei vaivai 0.0311	Leaga vaivai -0.0164	Lelei vaivai 0.0903	Lelei vaivai 0.0301	Leaga vaivai -0.0120	Leaga vaivai -0.1534
Answer 2	-	Lelei vaivai 0.0217	Lelei vaivai 0.0011	Leaga vaivai -0.0455	Lelei vaivai 0.0660	Lelei vaivai 0.0440	Lelei vaivai 0.0117	Leaga vaivai -0.0942
Answer 3	-	Leaga vaivai -0.0034	Leaga vaivai -0.0104	Leaga vaivai -0.0419	Leaga vaivai -0.0451	Lelei vaivai 0.0462	Lelei vaivai 0.0780	Leaga vaivai -0.0204
Answer 4	-	Lelei vaivai 0.0436	Lelei vaivai 0.0362	Leaga vaivai -0.0177	Lelei vaivai 0.0150	Lelei vaivai 0.0296	Lelei vaivai 0.0189	Leaga vaivai -0.0984
Answer 5	-	Lelei vaivai 0.0298	Lelei vaivai 0.1270	Lelei vaivai 0.0133	Lelei vaivai 0.0724	Leaga vaivai -0.0002	Leaga vaivai -0.0199	Leaga vaivai -0.1742
Answer 6	-	Leaga vaivai -0.0003	Lelei vaivai 0.0089	Leaga vaivai -0.0627	Leaga vaivai -0.0074	Lelei vaivai 0.0190	Lelei vaivai 0.0825	Leaga vaivai -0.0321
Answer 7	-	Lelei vaivai 0.0123	Lelei vaivai 0.0388	Leaga vaivai -0.0684	Leaga vaivai -0.0238	Lelei vaivai 0.0468	Lelei vaivai 0.0631	Leaga vaivai -0.0517
Answer 8	-	Lelei vaivai 0.0699	Lelei vaivai 0.0857	Leaga vaivai -0.0318	Lelei vaivai 0.0150	Lelei vaivai 0.0341	Lelei vaivai 0.0125	Leaga vaivai -0.1372
Answer 9	-	Lelei vaivai 0.0666	Lelei vaivai 0.1681	Lelei vaivai 0.0094	Lelei vaivai 0.0694	Leaga vaivai -0.0131	Leaga vaivai -0.0533	Leaga vaivai -0.1815
Answer 10	-	Lelei vaivai 0.0776	Lelei vaivai 0.0744	Leaga vaivai -0.0185	Lelei vaivai 0.0224	Lelei vaivai 0.0352	Leaga vaivai -0.0135	Leaga vaivai -0.1293
Answer 11	-	Lelei vaivai 0.0585	Lelei vaivai 0.0531	Leaga vaivai -0.0094	Lelei vaivai 0.0086	Lelei vaivai 0.0195	Lelei vaivai 0.0313	Leaga vaivai -0.1200
Answer 12	-	Lelei vaivai 0.0378	Lelei vaivai 0.1030	Leaga vaivai -0.0357	Lelei vaivai 0.0350	Lelei vaivai 0.0261	Lelei vaivai 0.0297	Leaga vaivai -0.1510
Answer 13	-	Lelei vaivai 0.0642	Lelei vaivai 0.1044	Leaga vaivai -0.0454	Lelei vaivai 0.0259	Lelei vaivai 0.0424	Lelei vaivai 0.0183	Leaga vaivai -0.1595
Answer 14	-	Lelei vaivai 0.0718	Lelei vaivai 0.1034	Leaga vaivai -0.0003	Leaga vaivai -0.0085	Leaga vaivai -0.0016	Lelei vaivai 0.0074	Leaga vaivai -0.1172
Answer 15	-	Lelei vaivai 0.0550	Lelei vaivai 0.1382	Leaga vaivai -0.0418	Lelei vaivai 0.0181	Leaga vaivai -0.0163	Lelei vaivai 0.0211	Leaga vaivai -0.1183
Answer 16	-	Lelei vaivai 0.0591	Lelei vaivai 0.0276	Leaga vaivai -0.0384	Leaga vaivai -0.0397	Lelei vaivai 0.0651	Lelei vaivai 0.0280	Leaga vaivai -0.0710

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

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

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

2023.10.13

Valeri Kosenko

Oloa oloa sas as fagafao poloketi sdtest®

Sa agavaa ai le valeri o le lautele o le pergogogy-psychogist i le 1993 ma ua uma ona faʻaaoga lona iloa i le puleaina o le poloketi.
Na maua e Valeri tikeri o le matai ma le Polokalame agavaa ma Polokalama Manaoga i le 2013. I le polokalame a lona master, na ia masani ai ma le Polokalame o le Polokalama FIA. V.) ma Spiral Dynamics E. V.
Na faia e le valeriri le tele o suʻega o faʻataʻitaʻiga ma faʻaaoga lona iloa ma le poto masani e faʻafetaui ai le taimi nei o le sctest.
Vuleri o le tusitala o le suesueina o le le mautonu o le v.u.c.a. manatu o le faʻaaogaina o le spiral dynamictics ma matematika fuainumera i psychology, sili atu nai lo le 20 vaitusi faʻavaomalo.

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