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) Actions of companies in relation to personnel in the last month (yes / no)

2) Actions of companies in relation to personnel in the last month (fact in %)

3) Fears

4) Biggest problems facing my country

5) What qualities and abilities do good leaders use when building successful teams?

6) Google. Factors that impact team effectiveness

7) The main priorities of job seekers

8) What makes a boss a great leader?

9) What makes people successful at work?

10) Are you ready to receive less pay to work remotely?

11) Does ageism exist?

12) Ageism in career

13) Ageism in life

14) Ageism's causes

15) Reasons why people give up (by Anna Vital)

16) TRUST (by WVS)

17) Oxford Happiness Survey

18) Psychological Wellbeing (by Carol D. Ryff)

19) Where would be your next most exciting opportunity?

20) What will you do this week to look after your mental health?

21) I live thinking about my past, present or future

22) Meritocracy

23) A.I. and the end of civilization

24) Why do people procrastinate?

25) Gender difference in building self-confidence (IFD Allensbach)

26) Xing.com culture assessment

27) Patrick Lencioni's "The Five Dysfunctions of a Team"

28) Empathy is...

29) What is essential for IT specialists in choosing a job offer?

30) Why People Resist Change (by Siobhán McHale)

31) How Do You Regulate Your Emotions? (by Nawal Mustafa M.A.)

32) 21 skills that pay you forever (by Jeremiah Teo / 赵汉昇)

33) Real freedom is ...

34) 12 ways to build trust with others (by Justin Wright)

35) Characteristics of a talented employee (by Talent Management Institute)

36) 10 Keys to Motivating Your Team

37) Algebra of Conscience (by Vladimir Lefebvre)

38) Three Distinct Possibilities of the Future (by Dr. Clare W. Graves)

39) Actions to Build Unshakable Self-Trust (by Suren Samarchyan)

40) Rating of Top and Anti-top companies according to the IT community of Kazakhstan

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.

Fears

ChartsCorrelation

VUCA

Correlation Type	Linear (Pearson) Linear (Pearson) Nonlinear (Spearman)
Critical value of the correlation coefficient	Normal distribution, by William Sealy Gosset (Student) Normal distribution, by William Sealy Gosset (Student) Non Normal distribution, by Spearman	Show only results > r = 0.0296

Distribution	Non Normal	Non Normal	Non Normal	Normal	Normal	Normal	Normal	Normal
All questions All questions My greatest fears are
My greatest fears are
Answer 1	-	Weak positive 0.0485	Weak positive 0.0201	Weak negative -0.0234	Weak positive 0.0985	Weak positive 0.0335	Weak negative -0.0084	Weak negative -0.1486
Answer 2	-	Weak positive 0.0200	Weak positive 0.0021	Weak negative -0.0369	Weak positive 0.0592	Weak positive 0.0447	Weak positive 0.0121	Weak negative -0.0956
Answer 3	-	Weak negative -0.0001	Weak positive 0.0017	Weak negative -0.0434	Weak negative -0.0468	Weak positive 0.0437	Weak positive 0.0762	Weak negative -0.0244
Answer 4	-	Weak positive 0.0419	Weak positive 0.0308	Weak negative -0.0278	Weak positive 0.0177	Weak positive 0.0341	Weak positive 0.0250	Weak negative -0.0973
Answer 5	-	Weak positive 0.0213	Weak positive 0.1264	Weak positive 0.0047	Weak positive 0.0821	Weak negative -0.0002	Weak negative -0.0085	Weak negative -0.1814
Answer 6	-	Weak positive 0.0074	Weak positive 0.0162	Weak negative -0.0617	Weak negative -0.0144	Weak positive 0.0161	Weak positive 0.0877	Weak negative -0.0388
Answer 7	-	Weak positive 0.0148	Weak positive 0.0443	Weak negative -0.0694	Weak negative -0.0395	Weak positive 0.0433	Weak positive 0.0766	Weak negative -0.0500
Answer 8	-	Weak positive 0.0592	Weak positive 0.0833	Weak negative -0.0254	Weak positive 0.0082	Weak positive 0.0369	Weak positive 0.0192	Weak negative -0.1372
Answer 9	-	Weak positive 0.0699	Weak positive 0.1578	Weak positive 0.0012	Weak positive 0.0595	Weak negative -0.0084	Weak negative -0.0453	Weak negative -0.1737
Answer 10	-	Weak positive 0.0742	Weak positive 0.0578	Weak negative -0.0120	Weak positive 0.0217	Weak positive 0.0392	Weak negative -0.0049	Weak negative -0.1325
Answer 11	-	Weak positive 0.0602	Weak positive 0.0545	Weak negative -0.0022	Weak positive 0.0085	Weak positive 0.0238	Weak positive 0.0211	Weak negative -0.1258
Answer 12	-	Weak positive 0.0399	Weak positive 0.1025	Weak negative -0.0363	Weak positive 0.0346	Weak positive 0.0269	Weak positive 0.0287	Weak negative -0.1526
Answer 13	-	Weak positive 0.0736	Weak positive 0.0993	Weak negative -0.0351	Weak positive 0.0247	Weak positive 0.0326	Weak positive 0.0168	Weak negative -0.1605
Answer 14	-	Weak positive 0.0844	Weak positive 0.0904	Weak negative -0.0038	Weak negative -0.0160	Weak positive 0.0024	Weak positive 0.0115	Weak negative -0.1151
Answer 15	-	Weak positive 0.0548	Weak positive 0.1257	Weak negative -0.0279	Weak positive 0.0100	Weak negative -0.0215	Weak positive 0.0281	Weak negative -0.1175
Answer 16	-	Weak positive 0.0658	Weak positive 0.0294	Weak negative -0.0341	Weak negative -0.0490	Weak positive 0.0642	Weak positive 0.0202	Weak negative -0.0654

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

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

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

2023.10.13

FearpersonqualitiesprojectorganizationalstructureRACIresponsibilitymatrixCritical ChainProject Managementfocus factorJiraempathyleadersbossGermanyChinaPolicyUkraineRussiawarvolatilityuncertaintycomplexityambiguityVUCArelocatejobproblemcountryreasongive upobjectivekeyresultmathematicalpsychologyMBTIHR metricsstandardDEIcorrelationriskscoringmodelGame TheoryPrisoner's Dilemma

Valerii Kosenko

Product Owner SaaS SDTEST®

Valerii was qualified as a social pedagogue-psychologist in 1993 and has since applied his knowledge in project management.
Valerii obtained a Master's degree and the project and program manager qualification in 2013. During his Master's program, he became familiar with Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) and Spiral Dynamics.
Valerii is the author of exploring the uncertainty of the V.U.C.A. concept using Spiral Dynamics and mathematical statistics in psychology, and 38 international polls.

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