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:

1. What makes the use of mathematics in mathematical psychology reasonably practical, in contrast to other sciences like physics-inspired mathematical biology or symbolic cognitive science?
2. How does the mathematical approach in mathematical psychology differ from other branches of psychology, like psychophysics and psychometrics?
3. Given diverging perspectives on aligning with this field, what is the appropriate relationship of mathematical psychology to cognitive science?

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. Norwood Hanson stated that 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. Mathematical psychology's history is complex 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 significant 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 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 that psychology needed to become mathematical to be scientific. However, mathematizing psychology faced complications that needed to be addressed 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 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 a resistant subject matter helps reveal mathematics's evolving role and place 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 vital aspects stand out:

1. Advocating quantitative methods broadly. Mathematical psychology emerged partly to push psychology to embrace quantitative modeling and mathematics beyond basic statistics.
2. Drawing from diverse mathematical tools. With more excellent training in mathematics, mathematical psychologists utilize more advanced and varied mathematical techniques like topology and differential geometry.
3. Linking models and experiments. Mathematical psychologists emphasize tightly connecting experimental design and statistical analysis with experiments that test specific models.
4. Favoring theoretical models. Mathematical psychology incorporates "pure" mathematical results and prefers analytic, hand-fitted models over data-driven computer models.
5. Seeking general, cumulative theory. Unlike just describing data, mathematical psychology aspires to abstract, general theory supported across experiments, incremental 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, 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 takes a more critical stance towards purely simulation-based modeling in cognitive science, instead emphasizing iterative modeling tightly linked to experimentation.

Mathematical psychology significantly overlaps 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 that 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 critical 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. Also, 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. Are the models' accuracy and truth value significant 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 provides 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"

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.

Open the link to see the widget.

You can not only create your poll in the Tariff ?V.U.C.A. poll designer? (with a unique link and your logo), but you can also earn money by selling its results in the Tariff ?Poll Shop,? as already the authors of polls.

If you participated in VUCA polls, you can see and compare your results with the overall poll results, which are constantly growing, in your account after purchasing?the Tariff ?My SDT.?

Next, read Simple SDTEST? Gives Great Possibilities.

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

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

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