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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3) Pelot

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10) Oletko valmis vastaanottamaan vähemmän palkkaa työskennelläkseen etäyhteydessä?

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13) Ageismi elämässä

14) Ageismin syyt

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16) LUOTTAMUS (#WVS)

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18) Psykologinen hyvinvointi

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20) Mitä teet tällä viikolla huolehtiaksesi mielenterveydestäsi?

21) Asun ajatellessani menneisyyttäni, nykyisyyttäni tai tulevaisuutta

22) Meritokratia

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24) Miksi ihmiset viivyttävät?

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26) Xing.com -kulttuurin arviointi

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31) Kuinka säätelet tunteitasi? (Nawal Mustafa M.A.)

32) 21 taidot, jotka maksavat sinulle ikuisesti (kirjoittanut Jeremiah Teo / 赵汉昇)

33) Todellinen vapaus on ...

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38) Kolme erilaista tulevaisuuden mahdollisuutta (tohtori Clare W. Graves)

39) Toimet horjumattoman itseluottamuksen rakentamiseksi (Suren Samarchyan)

40)

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.

Pelot

kaavioita Korrelaatio

VUCA

Kriittinen arvo korrelaatiokertoimen

Normaalijakelu, kirjoittanut William Sealy Gosset (opiskelija) r = 0.0317

Ei normaali jakauma, keihäsmies r = 0.0013

Näytä vain tulokset > r = 0.0317

Jakelu	Normaali	Normaali	Normaali	Normaali	Normaali	Normaali	Normaali	Normaali
Kaikki kysymykset Kaikki kysymykset Suurin pelkoni on
Suurin pelkoni on
Answer 1	-	Heikko positiivinen 0.0537	Heikko positiivinen 0.0288	Heikko negatiivinen -0.0175	Heikko positiivinen 0.0948	Heikko positiivinen 0.0381	Heikko negatiivinen -0.0178	Heikko negatiivinen -0.1563
Answer 2	-	Heikko positiivinen 0.0194	Heikko negatiivinen -0.0048	Heikko negatiivinen -0.0385	Heikko positiivinen 0.0655	Heikko positiivinen 0.0495	Heikko positiivinen 0.0106	Heikko negatiivinen -0.0982
Answer 3	-	Heikko negatiivinen -0.0001	Heikko negatiivinen -0.0084	Heikko negatiivinen -0.0449	Heikko negatiivinen -0.0445	Heikko positiivinen 0.0485	Heikko positiivinen 0.0742	Heikko negatiivinen -0.0207
Answer 4	-	Heikko positiivinen 0.0433	Heikko positiivinen 0.0291	Heikko negatiivinen -0.0232	Heikko positiivinen 0.0163	Heikko positiivinen 0.0367	Heikko positiivinen 0.0226	Heikko negatiivinen -0.0996
Answer 5	-	Heikko positiivinen 0.0277	Heikko positiivinen 0.1291	Heikko positiivinen 0.0108	Heikko positiivinen 0.0745	Heikko positiivinen 0.0012	Heikko negatiivinen -0.0177	Heikko negatiivinen -0.1783
Answer 6	-	Heikko negatiivinen -0.0015	Heikko positiivinen 0.0058	Heikko negatiivinen -0.0607	Heikko negatiivinen -0.0094	Heikko positiivinen 0.0255	Heikko positiivinen 0.0844	Heikko negatiivinen -0.0363
Answer 7	-	Heikko positiivinen 0.0113	Heikko positiivinen 0.0348	Heikko negatiivinen -0.0657	Heikko negatiivinen -0.0305	Heikko positiivinen 0.0521	Heikko positiivinen 0.0686	Heikko negatiivinen -0.0532
Answer 8	-	Heikko positiivinen 0.0657	Heikko positiivinen 0.0728	Heikko negatiivinen -0.0255	Heikko positiivinen 0.0124	Heikko positiivinen 0.0386	Heikko positiivinen 0.0153	Heikko negatiivinen -0.1345
Answer 9	-	Heikko positiivinen 0.0757	Heikko positiivinen 0.1605	Heikko positiivinen 0.0066	Heikko positiivinen 0.0612	Heikko negatiivinen -0.0063	Heikko negatiivinen -0.0492	Heikko negatiivinen -0.1822
Answer 10	-	Heikko positiivinen 0.0764	Heikko positiivinen 0.0669	Heikko negatiivinen -0.0124	Heikko positiivinen 0.0271	Heikko positiivinen 0.0365	Heikko negatiivinen -0.0130	Heikko negatiivinen -0.1348
Answer 11	-	Heikko positiivinen 0.0634	Heikko positiivinen 0.0526	Heikko negatiivinen -0.0075	Heikko positiivinen 0.0096	Heikko positiivinen 0.0264	Heikko positiivinen 0.0242	Heikko negatiivinen -0.1270
Answer 12	-	Heikko positiivinen 0.0450	Heikko positiivinen 0.0944	Heikko negatiivinen -0.0323	Heikko positiivinen 0.0307	Heikko positiivinen 0.0343	Heikko positiivinen 0.0260	Heikko negatiivinen -0.1530
Answer 13	-	Heikko positiivinen 0.0725	Heikko positiivinen 0.0947	Heikko negatiivinen -0.0389	Heikko positiivinen 0.0265	Heikko positiivinen 0.0443	Heikko positiivinen 0.0144	Heikko negatiivinen -0.1631
Answer 14	-	Heikko positiivinen 0.0820	Heikko positiivinen 0.0897	Heikko negatiivinen -0.0030	Heikko negatiivinen -0.0122	Heikko positiivinen 0.0060	Heikko positiivinen 0.0135	Heikko negatiivinen -0.1213
Answer 15	-	Heikko positiivinen 0.0549	Heikko positiivinen 0.1265	Heikko negatiivinen -0.0334	Heikko positiivinen 0.0119	Heikko negatiivinen -0.0153	Heikko positiivinen 0.0242	Heikko negatiivinen -0.1157
Answer 16	-	Heikko positiivinen 0.0732	Heikko positiivinen 0.0242	Heikko negatiivinen -0.0373	Heikko negatiivinen -0.0398	Heikko positiivinen 0.0729	Heikko positiivinen 0.0169	Heikko negatiivinen -0.0774

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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

Tuotteen omistaja SaaS SDTEST®

Valerii valmistui sosiaalipedagogiksi-psykologiksi vuonna 1993 ja on sittemmin soveltanut osaamistaan projektijohtamiseen.
Valerii suoritti maisterin tutkinnon sekä projekti- ja ohjelmapäällikön tutkinnon vuonna 2013. Maisteriohjelmansa aikana hän tutustui Project Roadmapiin (GPM Deutsche Gesellschaft für Projektmanagement e. V.) ja Spiral Dynamicsiin.
Valerii on kirjoittanut V.U.C.A.:n epävarmuutta. konsepti käyttäen spiraalidynamiikkaa ja matemaattisia tilastoja psykologiassa sekä 38 kansainvälistä kyselyä.

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