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 0.0532	Malforta pozitiva 0.0292	Malforta negativo -0.0175	Malforta pozitiva 0.0919	Malforta pozitiva 0.0301	Malforta negativo -0.0114	Malforta negativo -0.1523
Answer 2	-	Malforta pozitiva 0.0208	Malforta negativo -0.0014	Malforta negativo -0.0431	Malforta pozitiva 0.0641	Malforta pozitiva 0.0449	Malforta pozitiva 0.0130	Malforta negativo -0.0931
Answer 3	-	Malforta negativo -0.0053	Malforta negativo -0.0130	Malforta negativo -0.0406	Malforta negativo -0.0456	Malforta pozitiva 0.0474	Malforta pozitiva 0.0793	Malforta negativo -0.0204
Answer 4	-	Malforta pozitiva 0.0427	Malforta pozitiva 0.0328	Malforta negativo -0.0200	Malforta pozitiva 0.0158	Malforta pozitiva 0.0306	Malforta pozitiva 0.0217	Malforta negativo -0.0980
Answer 5	-	Malforta pozitiva 0.0255	Malforta pozitiva 0.1255	Malforta pozitiva 0.0143	Malforta pozitiva 0.0732	Malforta negativo -0.0019	Malforta negativo -0.0196	Malforta negativo -0.1747
Answer 6	-	Malforta negativo -0.0027	Malforta pozitiva 0.0074	Malforta negativo -0.0629	Malforta negativo -0.0074	Malforta pozitiva 0.0199	Malforta pozitiva 0.0835	Malforta negativo -0.0324
Answer 7	-	Malforta pozitiva 0.0110	Malforta pozitiva 0.0371	Malforta negativo -0.0688	Malforta negativo -0.0227	Malforta pozitiva 0.0471	Malforta pozitiva 0.0650	Malforta negativo -0.0523
Answer 8	-	Malforta pozitiva 0.0693	Malforta pozitiva 0.0825	Malforta negativo -0.0321	Malforta pozitiva 0.0139	Malforta pozitiva 0.0351	Malforta pozitiva 0.0147	Malforta negativo -0.1369
Answer 9	-	Malforta pozitiva 0.0643	Malforta pozitiva 0.1659	Malforta pozitiva 0.0082	Malforta pozitiva 0.0699	Malforta negativo -0.0136	Malforta negativo -0.0513	Malforta negativo -0.1826
Answer 10	-	Malforta pozitiva 0.0760	Malforta pozitiva 0.0730	Malforta negativo -0.0219	Malforta pozitiva 0.0254	Malforta pozitiva 0.0318	Malforta negativo -0.0138	Malforta negativo -0.1318
Answer 11	-	Malforta pozitiva 0.0571	Malforta pozitiva 0.0514	Malforta negativo -0.0099	Malforta pozitiva 0.0077	Malforta pozitiva 0.0206	Malforta pozitiva 0.0308	Malforta negativo -0.1211
Answer 12	-	Malforta pozitiva 0.0373	Malforta pozitiva 0.1013	Malforta negativo -0.0357	Malforta pozitiva 0.0357	Malforta pozitiva 0.0243	Malforta pozitiva 0.0296	Malforta negativo -0.1524
Answer 13	-	Malforta pozitiva 0.0621	Malforta pozitiva 0.1036	Malforta negativo -0.0438	Malforta pozitiva 0.0273	Malforta pozitiva 0.0414	Malforta pozitiva 0.0176	Malforta negativo -0.1608
Answer 14	-	Malforta pozitiva 0.0703	Malforta pozitiva 0.1007	Malforta pozitiva 9.54E-5	Malforta negativo -0.0088	Malforta negativo -0.0011	Malforta pozitiva 0.0084	Malforta negativo -0.1174
Answer 15	-	Malforta pozitiva 0.0554	Malforta pozitiva 0.1349	Malforta negativo -0.0418	Malforta pozitiva 0.0179	Malforta negativo -0.0165	Malforta pozitiva 0.0219	Malforta negativo -0.1181
Answer 16	-	Malforta pozitiva 0.0581	Malforta pozitiva 0.0255	Malforta negativo -0.0388	Malforta negativo -0.0407	Malforta pozitiva 0.0654	Malforta pozitiva 0.0283	Malforta negativo -0.0714

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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

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.

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