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) Agoj de kompanioj rilate al dungitaro en la lasta monato (jes / ne)

2) Agoj de kompanioj rilate al dungitaro en la lasta monato (fakto en%)

3) Timoj

4) Plej grandaj problemoj alfrontantaj mian landon

5) Kiajn kvalitojn kaj kapablojn uzas bonaj estroj dum konstruado de sukcesaj teamoj?

6) Google. Faktoroj, kiuj influas teaman efikecon

7) La ĉefaj prioritatoj de serĉantoj de laboro

8) Kio faras estron bonega gvidanto?

9) Kio sukcesigas homojn en la laboro?

10) Ĉu vi pretas ricevi malpli da salajro por funkcii remotamente?

11) Ĉu ageismo ekzistas?

12) Ageismo en kariero

13) Ageismo en la vivo

14) Kaŭzoj de Ageismo

15) Kialoj Kial Homoj Rezignas (De Anna Vital)

16) Fidu (#WVS)

17) Oksforda Feliĉa Enketo

18) Psikologia bonstato

19) Kie estus via sekva plej ekscita okazo?

20) Kion vi faros ĉi -semajne por prizorgi vian mensan sanon?

21) Mi vivas pensante pri mia pasinteco, nuno aŭ estonteco

22) Meritokratio

23) Artefarita inteligenteco kaj la fino de civilizo

24) Kial homoj prokrastas?

25) Seksa diferenco en konstruado de memfido (IFD Allensbach)

26) Xing.com kultur -takso

27) Patrick Lencioni "La Kvin Malfunkcioj de Teamo"

28) Empatio estas ...

29) Kio estas esenca por IT -specialistoj pri elekto de laborposteno?

30) Kial homoj rezistas ŝanĝon (de Siobhán McHale)

31) Kiel vi reguligas viajn emociojn? (de Nawal Mustafa M.A.)

32) 21 kapabloj, kiuj pagas vin por ĉiam (de Jeremiah Teo / 赵汉昇)

33) Vera libereco estas ...

34) 12 manieroj konstrui fidon kun aliaj (de Justin Wright)

35) Karakterizaĵoj de talenta dungito (de Talent Management Institute)

36) 10 Ŝlosiloj Por Motivigi Vian Teamon

37) Algebro de Konscienco (de Vladimir Lefebvre)

38) Tri Distingaj Eblecoj de la Estonteco (de 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.

Timoj

furorlisto Korelacio

VUCA

Kritika valoro de la korelacio

Normala distribuo, de William Sealy Gosset (studento) r = 0.033

Ne normala distribuo, de Spearman r = 0.0013

Montri nur rezultojn > r = 0.033

Distribuo	Ne normala	Ne normala	Ne normala	Normala	Normala	Normala	Normala	Normala
Ĉiuj demandoj Ĉiuj demandoj Mia plej granda timo estas
Mia plej granda timo estas
Answer 1	-	Malforta pozitiva 0.0567	Malforta pozitiva 0.0317	Malforta negativo -0.0161	Malforta pozitiva 0.0910	Malforta pozitiva 0.0295	Malforta negativo -0.0121	Malforta negativo -0.1545
Answer 2	-	Malforta pozitiva 0.0228	Malforta negativo -0.0002	Malforta negativo -0.0450	Malforta pozitiva 0.0639	Malforta pozitiva 0.0444	Malforta pozitiva 0.0133	Malforta negativo -0.0938
Answer 3	-	Malforta negativo -0.0028	Malforta negativo -0.0120	Malforta negativo -0.0410	Malforta negativo -0.0470	Malforta pozitiva 0.0467	Malforta pozitiva 0.0790	Malforta negativo -0.0198
Answer 4	-	Malforta pozitiva 0.0443	Malforta pozitiva 0.0349	Malforta negativo -0.0188	Malforta pozitiva 0.0144	Malforta pozitiva 0.0301	Malforta pozitiva 0.0209	Malforta negativo -0.0984
Answer 5	-	Malforta pozitiva 0.0305	Malforta pozitiva 0.1282	Malforta pozitiva 0.0136	Malforta pozitiva 0.0734	Malforta negativo -0.0013	Malforta negativo -0.0200	Malforta negativo -0.1758
Answer 6	-	Malforta pozitiva 8.40E-5	Malforta pozitiva 0.0083	Malforta negativo -0.0622	Malforta negativo -0.0089	Malforta pozitiva 0.0194	Malforta pozitiva 0.0832	Malforta negativo -0.0318
Answer 7	-	Malforta pozitiva 0.0130	Malforta pozitiva 0.0382	Malforta negativo -0.0683	Malforta negativo -0.0250	Malforta pozitiva 0.0470	Malforta pozitiva 0.0644	Malforta negativo -0.0518
Answer 8	-	Malforta pozitiva 0.0702	Malforta pozitiva 0.0849	Malforta negativo -0.0322	Malforta pozitiva 0.0141	Malforta pozitiva 0.0345	Malforta pozitiva 0.0136	Malforta negativo -0.1369
Answer 9	-	Malforta pozitiva 0.0672	Malforta pozitiva 0.1676	Malforta pozitiva 0.0087	Malforta pozitiva 0.0689	Malforta negativo -0.0131	Malforta negativo -0.0515	Malforta negativo -0.1820
Answer 10	-	Malforta pozitiva 0.0786	Malforta pozitiva 0.0755	Malforta negativo -0.0199	Malforta pozitiva 0.0241	Malforta pozitiva 0.0343	Malforta negativo -0.0129	Malforta negativo -0.1307
Answer 11	-	Malforta pozitiva 0.0582	Malforta pozitiva 0.0533	Malforta negativo -0.0091	Malforta pozitiva 0.0080	Malforta pozitiva 0.0196	Malforta pozitiva 0.0313	Malforta negativo -0.1199
Answer 12	-	Malforta pozitiva 0.0394	Malforta pozitiva 0.1038	Malforta negativo -0.0353	Malforta pozitiva 0.0352	Malforta pozitiva 0.0251	Malforta pozitiva 0.0300	Malforta negativo -0.1524
Answer 13	-	Malforta pozitiva 0.0648	Malforta pozitiva 0.1049	Malforta negativo -0.0443	Malforta pozitiva 0.0262	Malforta pozitiva 0.0417	Malforta pozitiva 0.0179	Malforta negativo -0.1604
Answer 14	-	Malforta pozitiva 0.0716	Malforta pozitiva 0.1022	Malforta negativo -0.0002	Malforta negativo -0.0094	Malforta negativo -0.0010	Malforta pozitiva 0.0089	Malforta negativo -0.1173
Answer 15	-	Malforta pozitiva 0.0560	Malforta pozitiva 0.1366	Malforta negativo -0.0419	Malforta pozitiva 0.0172	Malforta negativo -0.0161	Malforta pozitiva 0.0225	Malforta negativo -0.1182
Answer 16	-	Malforta pozitiva 0.0593	Malforta pozitiva 0.0274	Malforta negativo -0.0384	Malforta negativo -0.0403	Malforta pozitiva 0.0653	Malforta pozitiva 0.0285	Malforta negativo -0.0710

Eksporti al MS Excel

Ĉi tiu funkcio estos havebla en viaj propraj VUCA-enketoj

Bone

You can not only just create your poll in the tarifo «V.U.C.A balotenketo diseñador» (with a unique link and your logo) but also you can earn money by selling its results in the tarifo «Pollbutiko», 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 tarifo «Mia SDT»

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

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

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

2023.10.13

Valerii Kosenko

Produktposedanto SaaS Pet Project SDTest®

Valerii estis kvalifikita kiel socia pedagogo-psikologo en 1993 kaj de tiam aplikis sian scion en projektadministrado.
Valerii akiris magistron kaj la Projekta kaj Programadministranto en 2013. Dum sia majstra programo, li konatiĝis kun Project Roadmap (GPM Deutsche Gesellschaft Für ProjektManagement e. V.) kaj Spiral Dynamics.
Valerii prenis diversajn spiralajn dinamikajn testojn kaj uzis siajn sciojn kaj sperton por adapti la aktualan version de SDTest.
Valerii estas la aŭtoro de esplorado de la necerteco de la V.U.C.A. Koncepto uzanta spiralan dinamikon kaj matematikajn statistikojn en psikologio, pli ol 20 internaciaj balotoj.

Ĉi tiu afiŝo havas 0 Komentoj

Respondi al

Nuligu respondon

Lasu vian komenton