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) Aktiounen vun de Firmen a Relatioun mam Personal am leschte Mount (jo / nee)

2) Aktiounen vun Firmen a Relatioun mam Personal am leschte Mount (Fakt an%)

3) Ängschen

4) Gréisste Probleemer vis-à-vis vum Land

5) Wat Qualitéiten a Fäegkeeten maachen gutt Leadere benotzen wann Dir erfollegräich Équipë baut?

6) Google. Facteuren déi den Teacher Effectivess

7) D'Haaptprioritéite vun Aarbechtssiche

8) Wat mécht e Patron e grousse Leader?

9) Wat mécht d'Leit erfollegräich op der Aarbecht?

10) Sidd Dir prett manner bezuelt fir Remote ze kréien?

11) Ass de Alterismus?

12) Alterismus an der Carrière

13) Agenmus am Liewen

14) Ursaachen vum Avisismus

15) Grënn firwat d'Leit opginn (vum Anna vital)

16) Vertrau méi trau (#WVS)

17) Oxford Gléck Ëmfro

18) Psychologesch Wuelbefannen

19) Wou wier Är nächst spannendst Geleeënheet?

20) Wat maacht Dir dës Woch fir Är mental Gesondheet ze kucken?

21) Ech wunnen iwwer meng Vergaangenheet, präsent oder zukünfteg

22) Merichokratie

23) Kënschtlech Intelligenz an d'Enn vun der Zivilisatioun

24) Firwat procrastinéieren?

25) Geschlecht Ënnerscheed am Gebai Selbstvertrauen (ifed Allensbach)

26) Xing.com Kultur Bewäertung

27) De Patrick Lncioni ass "déi fënnef Dysfunktiounen vun engem Team"

28) Empathie ass ...

29) Wat ass essentiell fir et Spezialisten fir eng Joboffer ze wielen?

30) Firwat Leit widderstoen änneren (vum Siobhán Machle)

31) Wéi regléiert Dir Är Emotiounen? (vum Nawal Mustafa M.a.)

32) 21 Fäegkeeten déi Iech fir ëmmer bezuelen (vum Jeremiah Teo / 赵汉昇)

33) Richteg Fräiheet ass ...

34) 12 Weeër fir Vertrauen mat aneren ze bauen (vum Justin Wright)

35) Charakteristike vun engem talentéierten Employé (duerch Talent Managementinstitut)

36) 10 Schlësselen fir Äert Team motivéieren

37) Algebra of Conscience (vum Vladimir Lefebvre)

38) Dräi Distinct Méiglechkeeten vun der Zukunft (vum Dr. Clare W. Graves)

39) Aktiounen fir onwahrscheinlech Selbstvertrauen ze bauen (vum 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.

Ängschen

Charts Korrelatioun

VUCA

Kritescher Wäert vun der Korrelatioun souguer gemaach

Normal Verdeelung, vum William Sighty Goesset (Student) r = 0.0317

Net normal Verdeelung, vum Spärman r = 0.0013

Weisen nëmme Resultater > r = 0.0317

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

Export zu MS Excel

Dës Funktionalitéit wäert an Ären eegene VUCA Ëmfroen sinn

You can not only just create your poll in the Tarif- «V.U.C.A Emfro Designer» (with a unique link and your logo) but also you can earn money by selling its results in the Tarif- «Poll Butteker», as already the authors of polls.

If you participated in VUCA polls, you can see your results and compare them with the overall polls results, which are constantly growing, in your personal account after purchasing Tarif- «Meng SDT»

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

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

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

2023.10.13

Valerii Kosenko

Produit Besëtzer SaaS SDTEST®

De Valerii gouf 1993 als Sozialpädagog-Psycholog qualifizéiert an huet zënterhier säi Wëssen an der Projektmanagement applizéiert.
De Valerii krut e Masterstudium an d'Qualifikatioun vum Projet a Programmmanager am Joer 2013. Während sengem Masterprogramm huet hie sech mam Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) a Spiral Dynamics vertraut.
Valerii ass den Auteur fir d'Onsécherheet vun der V.U.C.A. Konzept mat Spiral Dynamik a mathematesch Statistiken an der Psychologie, an 38 international Ëmfroen.

Dëse Post huet 0 Kommentarer

Äntwert op

Annuléieren eng Äntwert

Entlooss Äre Kommentar