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) Actiones de societatibus in relatione ad personas in ultimo mense (sic / no)

2) De actionibus de societatibus in relatione ad personas in ultimo mense (quod in%)

3) Timoribus

4) Maximus difficultates adversus patria

5) Quales et ACCIPIO facere bonum duces uti cum aedificationem felix teams?

6) Google. Factors quod impulsum quadrigis EFICENTEN

7) Pelagus priorities ex Job conquisitor

8) Quid facit bulla magna princeps?

9) Quid facit populus felix ad opus?

10) Tu paratus accipere minus stipendium opus remotius?

11) Non agism est?

12) Ageism in Career

13) Ageism in Vita

14) Causas de ageism

15) Causa quare populus deficere (a Anna vitalis)

16) Confido (#WVS)

17) Oxford beatitudo Survey

18) Psychologicum bene

19) Ubi esset proximus maxime excitando occasionem?

20) Quid facietis hoc septimana ut vultus post mentis?

21) Ego vivere cogitandi de praeteritis, praesenti vel futurum

22) Meritocracy

23) Artificialis intelligentia et finis civilization

24) Quid faciunt homines procrastinate?

25) Gender difference in aedificationem sui fiducia (IFD Allensbach)

26) Xing.com culturae taxationem

27) Patrick Lencioni scriptor "quinque dysfunctions a quadrigis"

28) Empathy est ...

29) Quid est de necessitate ad eam specialists in eligens officium offer?

30) Quid populus resistere mutatio (per Siobhán Mchale)

31) Quid tibi moderari vestra affectuum? (Per Nawal Mustafa M.A.)

32) XXI artes, qui solvere te in aeternum (per Jeremiah Teo / 赵汉昇)

33) Verus libertas est ...

34) XII Vias aedificare fiducia cum aliis (per Justin Wright)

35) De ingenio employee (per Talentum Management Institutum)

36) X claves ad motivum tuum dolor

37) Algebra Conscientiae (auctore Vladimir Lefebvre)

38) Three possibilitates Future (by 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.

Timoribus

charts Triticum

VUCA

Critica valorem coefficientis est influxus reciproci

Normalis distribution, by William marcescet (Student) r = 0.0331

Non normalis distribution, a speedman r = 0.0013

Ostende tantum results > r = 0.0331

Distributio	Non normalis	Non normalis	Non normalis	Normalis	Normalis	Normalis	Normalis	Normalis
Omnes quaestionum Omnes quaestionum Mihi maxima timor
Mihi maxima timor
Answer 1	-	Positivum infirma 0.0563	Positivum infirma 0.0317	Negans infirma -0.0161	Positivum infirma 0.0907	Positivum infirma 0.0298	Negans infirma -0.0126	Negans infirma -0.1537
Answer 2	-	Positivum infirma 0.0216	Positivum infirma 0.0002	Negans infirma -0.0458	Positivum infirma 0.0654	Positivum infirma 0.0445	Positivum infirma 0.0124	Negans infirma -0.0937
Answer 3	-	Negans infirma -0.0035	Negans infirma -0.0111	Negans infirma -0.0421	Negans infirma -0.0456	Positivum infirma 0.0466	Positivum infirma 0.0786	Negans infirma -0.0201
Answer 4	-	Positivum infirma 0.0435	Positivum infirma 0.0353	Negans infirma -0.0181	Positivum infirma 0.0145	Positivum infirma 0.0301	Positivum infirma 0.0197	Negans infirma -0.0979
Answer 5	-	Positivum infirma 0.0299	Positivum infirma 0.1279	Positivum infirma 0.0136	Positivum infirma 0.0730	Negans infirma -0.0007	Negans infirma -0.0207	Negans infirma -0.1746
Answer 6	-	Negans infirma -0.0004	Positivum infirma 0.0082	Negans infirma -0.0629	Negans infirma -0.0078	Positivum infirma 0.0193	Positivum infirma 0.0830	Negans infirma -0.0318
Answer 7	-	Positivum infirma 0.0122	Positivum infirma 0.0381	Negans infirma -0.0686	Negans infirma -0.0242	Positivum infirma 0.0471	Positivum infirma 0.0636	Negans infirma -0.0513
Answer 8	-	Positivum infirma 0.0698	Positivum infirma 0.0849	Negans infirma -0.0321	Positivum infirma 0.0146	Positivum infirma 0.0345	Positivum infirma 0.0130	Negans infirma -0.1368
Answer 9	-	Positivum infirma 0.0665	Positivum infirma 0.1674	Positivum infirma 0.0092	Positivum infirma 0.0691	Negans infirma -0.0128	Negans infirma -0.0528	Negans infirma -0.1812
Answer 10	-	Positivum infirma 0.0778	Positivum infirma 0.0755	Negans infirma -0.0180	Positivum infirma 0.0231	Positivum infirma 0.0346	Negans infirma -0.0146	Negans infirma -0.1298
Answer 11	-	Positivum infirma 0.0584	Positivum infirma 0.0524	Negans infirma -0.0096	Positivum infirma 0.0081	Positivum infirma 0.0199	Positivum infirma 0.0318	Negans infirma -0.1197
Answer 12	-	Positivum infirma 0.0380	Positivum infirma 0.1042	Negans infirma -0.0352	Positivum infirma 0.0357	Positivum infirma 0.0254	Positivum infirma 0.0286	Negans infirma -0.1515
Answer 13	-	Positivum infirma 0.0644	Positivum infirma 0.1057	Negans infirma -0.0448	Positivum infirma 0.0268	Positivum infirma 0.0416	Positivum infirma 0.0169	Negans infirma -0.1600
Answer 14	-	Positivum infirma 0.0717	Positivum infirma 0.1026	Negans infirma -0.0006	Negans infirma -0.0089	Negans infirma -0.0012	Positivum infirma 0.0080	Negans infirma -0.1168
Answer 15	-	Positivum infirma 0.0549	Positivum infirma 0.1375	Negans infirma -0.0420	Positivum infirma 0.0178	Negans infirma -0.0160	Positivum infirma 0.0216	Negans infirma -0.1180
Answer 16	-	Positivum infirma 0.0591	Positivum infirma 0.0273	Negans infirma -0.0386	Negans infirma -0.0399	Positivum infirma 0.0653	Positivum infirma 0.0282	Negans infirma -0.0708

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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

Product dominus Saas Pet Project Sdtest®

Valerii erat qualified ut socialis paedagogue, psychologist in MCMXCIII et quod applicari in scientia in project administratione.
Valerii adeptus est magister scriptor gradus et project et progressio procurator simpliciter in 2013. Per suum domini progressio, qui est nota cum project roadmap (GPM deutsche gesellschaft für projektmanagment e. V.) et spirae dynamics.
Valerii Tulit variis spirae dynamics probat et usus eius scientia et experientia ad aptet ad current versionem SDTest.
Valerii est auctor explorandi in dubitationem de V.U.C.A. Conceptum per spiralem dynamics et mathematical statistics in Psychology, magis quam XX International Polls.

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