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) Aksyon nan konpayi an relasyon ak pèsonèl nan dènye mwa a (wi / non)

2) Aksyon de konpayi an relasyon ak pèsonèl nan dènye mwa a (reyalite nan%)

3) Pè

4) Pi gwo pwoblèm fè fas a peyi mwen an

5) Ki kalite ak kapasite bon lidè yo itilize lè bati ekip siksè?

6) Google. Faktè ki afekte efikasite ekip la

7) Priyorite prensipal yo nan moun k ap chèche travay

8) Ki sa ki fè yon bòs yon gwo lidè?

9) Ki sa ki fè moun ki gen siksè nan travay?

10) Èske ou pare yo resevwa mwens peye nan travay adistans?

11) Ageism egziste?

12) Ageism nan karyè

13) Ageism nan lavi

14) Kòz Ageism

15) Rezon ki fè moun bay moute (pa Anna Vital)

16) Fè konfyans (#WVS)

17) Sondaj Oxford Bonè

18) Byennèt sikolojik

19) Ki kote ta pwochen opòtinite ki pi enteresan ou a?

20) Kisa ou pral fè semèn sa a yo gade apre sante mantal ou a?

21) Mwen ap viv panse sou sot pase mwen, prezan oswa nan lavni

22) Meritokrasi

23) Entèlijans atifisyèl ak nan fen sivilizasyon

24) Poukisa moun ap gentan?

25) Diferans sèks nan bilding konfyans nan tèt (IFD Allensbach)

26) Xing.com Kilti Evalyasyon

27) Patrick Lencioni a "Senk disfonksyon yo nan yon ekip"

28) Anpati se ...

29) Ki sa ki esansyèl pou li espesyalis nan chwazi yon òf travay?

30) Poukisa moun reziste chanjman (pa Siobhán McHale)

31) Ki jan ou kontwole emosyon ou a? (pa Nawal Mustafa M.A.)

32) 21 ladrès ki peye ou pou tout tan (pa Jeremi Teo / 赵汉昇)

33) Libète reyèl se ...

34) 12 fason yo bati konfyans ak lòt moun (pa Justin Wright)

35) Karakteristik yon anplwaye talan (pa Enstiti Jesyon Talent)

36) 10 kle pou motive ekip ou a

37) Aljèb Konsyans (pa Vladimir Lefebvre)

38) Twa posiblite diferan nan tan kap vini an (pa 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.

Pè

Charts Korelasyon

VUCA

Kritik valè de koyefisyan an korelasyon

Distribisyon nòmal, pa William Sealy Gosset (Elèv) r = 0.0331

Distribisyon ki pa nòmal, pa Spearman r = 0.0013

Montre rezilta sèlman > r = 0.0331

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

Ekspòtasyon nan MS Excel

Sa a fonksyonalite yo ap disponib nan pwòp biwo vòt VUCA ou yo

You can not only just create your poll in the tarif «V.U.C.A biwo vòt designer» (with a unique link and your logo) but also you can earn money by selling its results in the tarif «Bouton Biwo Vòt», 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 «Mwen SDT»

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

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

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

2023.10.13

Valerii Kosenko

Pwopriyetè pwodwi SaaS bèt kay pwojè sdtest®

Valerii te kalifye kòm yon pedagòg sosyal-sikològ nan 1993 e li te depi aplike konesans li nan jesyon pwojè.
Valerii te jwenn yon degre Mèt la ak Pwojè a ak Kalifikasyon Manadjè Pwogram nan 2013. Pandan pwogram Mèt li a, li te vin abitye ak Pwojè Roadmap (GPM Deutsche Gesellschaft für Projektmanagement E. V.) ak dinamik espiral.
Valerii te pran divès kalite tès dinamik espiral ak itilize konesans li ak eksperyans yo adapte vèsyon aktyèl la nan SDTest.
Valerii se otè a nan eksplore ensèten a nan V.U.C.A. Konsèp lè l sèvi avèk dinamik espiral ak estatistik matematik nan sikoloji, plis pase 20 biwo vòt entènasyonal yo.

Pòs sa a genyen 0 Kòmantè

Reponn a

Anile yon repons

Kite kòmantè ou