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) Rädsla

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11) Finns ageism?

12) Ageism i karriären

13) Ageism i livet

14) Causes of Ageism

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16) FÖRTROENDE (#WVS)

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18) Psykologiskt välmående

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21) Jag lever och tänker på mitt förflutna, nutid eller framtid

22) Meritokrati

23) Konstgjord intelligens och slutet på civilisationen

24) Varför skjuter människor?

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28) Empati är ...

29) Vad är viktigt för IT -specialisterna för att välja ett jobberbjudande?

30) Varför människor motstår förändring (av Siobhán McHale)

31) Hur reglerar du dina känslor? (av Nawal Mustafa M.A.)

32) 21 färdigheter som betalar dig för alltid (av Jeremiah Teo / 赵汉昇)

33) Verklig frihet är ...

34) 12 sätt att bygga förtroende med andra (av Justin Wright)

35) Egenskaper hos en begåvad anställd (av Talent Management Institute)

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38) Framtidens tre distinkta möjligheter (av 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.

Rädsla

diagram Korrelation

VUCA

Kritiska värdet av korrelationskoefficienten

Normal Distribution, av William Sealy Gosset (Student) r = 0.0329

Icke normal distribution, av Spearman r = 0.0013

Visa endast resultat > r = 0.0329

Distribution	Icke normal	Icke normal	Icke normal	Vanligt	Vanligt	Vanligt	Vanligt	Vanligt
Alla frågor Alla frågor Min största rädsla är
Min största rädsla är
Answer 1	-	Svagt positivt 0.0566	Svagt positivt 0.0332	Svagt negativt -0.0170	Svagt positivt 0.0912	Svagt positivt 0.0308	Svagt negativt -0.0153	Svagt negativt -0.1537
Answer 2	-	Svagt positivt 0.0223	Svagt positivt 0.0011	Svagt negativt -0.0442	Svagt positivt 0.0639	Svagt positivt 0.0464	Svagt positivt 0.0120	Svagt negativt -0.0960
Answer 3	-	Svagt negativt -0.0031	Svagt negativt -0.0104	Svagt negativt -0.0407	Svagt negativt -0.0463	Svagt positivt 0.0475	Svagt positivt 0.0779	Svagt negativt -0.0213
Answer 4	-	Svagt positivt 0.0437	Svagt positivt 0.0357	Svagt negativt -0.0197	Svagt positivt 0.0161	Svagt positivt 0.0311	Svagt positivt 0.0187	Svagt negativt -0.0987
Answer 5	-	Svagt positivt 0.0296	Svagt positivt 0.1300	Svagt positivt 0.0124	Svagt positivt 0.0749	Svagt positivt 0.0014	Svagt negativt -0.0231	Svagt negativt -0.1771
Answer 6	-	Svagt negativt -0.0008	Svagt positivt 0.0090	Svagt negativt -0.0613	Svagt negativt -0.0070	Svagt positivt 0.0196	Svagt positivt 0.0803	Svagt negativt -0.0321
Answer 7	-	Svagt positivt 0.0118	Svagt positivt 0.0401	Svagt negativt -0.0693	Svagt negativt -0.0246	Svagt positivt 0.0471	Svagt positivt 0.0623	Svagt negativt -0.0505
Answer 8	-	Svagt positivt 0.0697	Svagt positivt 0.0875	Svagt negativt -0.0316	Svagt positivt 0.0155	Svagt positivt 0.0346	Svagt positivt 0.0098	Svagt negativt -0.1373
Answer 9	-	Svagt positivt 0.0679	Svagt positivt 0.1707	Svagt positivt 0.0105	Svagt positivt 0.0676	Svagt negativt -0.0138	Svagt negativt -0.0545	Svagt negativt -0.1821
Answer 10	-	Svagt positivt 0.0793	Svagt positivt 0.0772	Svagt negativt -0.0208	Svagt positivt 0.0242	Svagt positivt 0.0343	Svagt negativt -0.0152	Svagt negativt -0.1300
Answer 11	-	Svagt positivt 0.0590	Svagt positivt 0.0559	Svagt negativt -0.0071	Svagt positivt 0.0082	Svagt positivt 0.0205	Svagt positivt 0.0266	Svagt negativt -0.1213
Answer 12	-	Svagt positivt 0.0405	Svagt positivt 0.1050	Svagt negativt -0.0363	Svagt positivt 0.0361	Svagt positivt 0.0253	Svagt positivt 0.0277	Svagt negativt -0.1522
Answer 13	-	Svagt positivt 0.0655	Svagt positivt 0.1056	Svagt negativt -0.0439	Svagt positivt 0.0270	Svagt positivt 0.0417	Svagt positivt 0.0152	Svagt negativt -0.1601
Answer 14	-	Svagt positivt 0.0728	Svagt positivt 0.1049	Svagt negativt -0.0002	Svagt negativt -0.0088	Svagt negativt -0.0007	Svagt positivt 0.0061	Svagt negativt -0.1187
Answer 15	-	Svagt positivt 0.0561	Svagt positivt 0.1378	Svagt negativt -0.0415	Svagt positivt 0.0178	Svagt negativt -0.0162	Svagt positivt 0.0194	Svagt negativt -0.1176
Answer 16	-	Svagt positivt 0.0606	Svagt positivt 0.0308	Svagt negativt -0.0348	Svagt negativt -0.0421	Svagt positivt 0.0642	Svagt positivt 0.0250	Svagt negativt -0.0717

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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

Produktägare SaaS SDTEST®

Valerii utbildades till socialpedagog-psykolog 1993 och har sedan dess tillämpat sina kunskaper inom projektledning.
Valerii tog en magisterexamen och projekt- och programledarexamen 2013. Under masterprogrammet blev han bekant med Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) och Spiral Dynamics.
Valerii är författaren till att utforska osäkerheten i V.U.C.A. koncept med Spiral Dynamics och matematisk statistik i psykologi, och 38 internationella undersökningar.

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