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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25) O le itupa o le itupa i le fausiaina o oe lava-talitonuina (pend Allensbach)

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 = 0.0335

Le masani ai tufatufaina, saunia e Spearman r = 0.0014

Faʻailoa naʻo faʻaiuga > r = 0.0335

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

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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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