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) Veprimet e kompanive në lidhje me personelin në muajin e fundit (po / jo)

2) Veprimet e kompanive në raport me personelin në muajin e fundit (fakt në%)

3) Frikësoj

4) Problemet më të mëdha me të cilat përballet vendi im

5) Cilat cilësi dhe aftësi përdorin udhëheqësit e mirë kur ndërtojnë ekipe të suksesshme?

6) Google. Faktorët që ndikojnë në efikasitetin e ekipit

7) Përparësitë kryesore të punëkërkuesve

8) Makesfarë e bën një shef një udhëheqës të shkëlqyeshëm?

9) Makesfarë i bën njerëzit të suksesshëm në punë?

10) A jeni gati të merrni më pak pagë për të punuar nga distanca?

11) A ekziston ageism?

12) Ageism në karrierë

13) Ageism në jetë

14) Shkaqet e ageizmit

15) Arsyet pse njerëzit heqin dorë (nga Anna Vital)

16) BESIM (#WVS)

17) Sondazhi i lumturisë në Oksford

18) Mirëqenie psikologjike

19) Ku do të ishte mundësia juaj tjetër më tërheqëse?

20) Çfarë do të bëni këtë javë për t'u kujdesur për shëndetin tuaj mendor?

21) Unë jetoj duke menduar për të kaluarën time, të tashmen ose të ardhmen

22) Meritokraci

23) Inteligjenca artificiale dhe fundi i civilizimit

24) Pse njerëzit zvarriten?

25) Diferenca gjinore në ndërtimin e vetëbesimit (IFD Allensbach)

26) Xing.com Vlerësimi i Kulturës

27) Patrick Lencioni "Pesë Mosfunksionimet e një ekipi"

28) Empatia është ...

29) Isfarë është thelbësore për specialistët e IT në zgjedhjen e një oferte pune?

30) Pse njerëzit i rezistojnë ndryshimit (nga Siobhán McHale)

31) Si i rregulloni emocionet tuaja? (Nga Nawal Mustafa M.A.)

32) 21 Aftësi që ju paguajnë përgjithmonë (nga Jeremiah Teo / 赵汉昇)

33) Liria e vërtetë është ...

34) 12 mënyra për të ndërtuar besim me të tjerët (nga Justin Wright)

35) Karakteristikat e një punonjësi të talentuar (nga Instituti i Menaxhimit të Talentëve)

36) 10 çelësa për të motivuar ekipin tuaj

37) Algjebra e ndërgjegjes (nga Vladimir Lefebvre)

38) Tre mundësi të dallueshme të së ardhmes (nga 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.

Frikësoj

Charts Korrelacion

VUCA

Vlera kritike e koeficient korrelacioni

Shpërndarja normale, nga William Sealy Gosset (Student) r = 0.033

Shpërndarje jo normale, nga Spearman r = 0.0013

Tregoni vetëm rezultate > r = 0.033

Shpërndarje	Jo normal	Jo normal	Jo normal	Normal	Normal	Normal	Normal	Normal
Të gjitha pyetjet Të gjitha pyetjet Frika ime më e madhe është
Frika ime më e madhe është
Answer 1	-	Pozitiv i dobët 0.0559	Pozitiv i dobët 0.0315	Negative dobët -0.0170	Pozitiv i dobët 0.0920	Pozitiv i dobët 0.0294	Negative dobët -0.0124	Negative dobët -0.1539
Answer 2	-	Pozitiv i dobët 0.0229	Negative dobët -0.0002	Negative dobët -0.0448	Pozitiv i dobët 0.0636	Pozitiv i dobët 0.0445	Pozitiv i dobët 0.0134	Negative dobët -0.0939
Answer 3	-	Negative dobët -0.0032	Negative dobët -0.0121	Negative dobët -0.0416	Negative dobët -0.0462	Pozitiv i dobët 0.0466	Pozitiv i dobët 0.0788	Negative dobët -0.0195
Answer 4	-	Pozitiv i dobët 0.0438	Pozitiv i dobët 0.0348	Negative dobët -0.0195	Pozitiv i dobët 0.0153	Pozitiv i dobët 0.0300	Pozitiv i dobët 0.0207	Negative dobët -0.0980
Answer 5	-	Pozitiv i dobët 0.0304	Pozitiv i dobët 0.1282	Pozitiv i dobët 0.0135	Pozitiv i dobët 0.0734	Negative dobët -0.0013	Negative dobët -0.0200	Negative dobët -0.1757
Answer 6	-	Negative dobët -0.0002	Pozitiv i dobët 0.0082	Negative dobët -0.0627	Negative dobët -0.0083	Pozitiv i dobët 0.0193	Pozitiv i dobët 0.0831	Negative dobët -0.0315
Answer 7	-	Pozitiv i dobët 0.0126	Pozitiv i dobët 0.0381	Negative dobët -0.0687	Negative dobët -0.0243	Pozitiv i dobët 0.0469	Pozitiv i dobët 0.0642	Negative dobët -0.0515
Answer 8	-	Pozitiv i dobët 0.0698	Pozitiv i dobët 0.0848	Negative dobët -0.0327	Pozitiv i dobët 0.0148	Pozitiv i dobët 0.0345	Pozitiv i dobët 0.0134	Negative dobët -0.1365
Answer 9	-	Pozitiv i dobët 0.0668	Pozitiv i dobët 0.1676	Pozitiv i dobët 0.0083	Pozitiv i dobët 0.0693	Negative dobët -0.0131	Negative dobët -0.0516	Negative dobët -0.1818
Answer 10	-	Pozitiv i dobët 0.0782	Pozitiv i dobët 0.0753	Negative dobët -0.0204	Pozitiv i dobët 0.0247	Pozitiv i dobët 0.0342	Negative dobët -0.0131	Negative dobët -0.1304
Answer 11	-	Pozitiv i dobët 0.0578	Pozitiv i dobët 0.0532	Negative dobët -0.0096	Pozitiv i dobët 0.0087	Pozitiv i dobët 0.0195	Pozitiv i dobët 0.0311	Negative dobët -0.1196
Answer 12	-	Pozitiv i dobët 0.0390	Pozitiv i dobët 0.1037	Negative dobët -0.0358	Pozitiv i dobët 0.0358	Pozitiv i dobët 0.0250	Pozitiv i dobët 0.0299	Negative dobët -0.1520
Answer 13	-	Pozitiv i dobët 0.0644	Pozitiv i dobët 0.1048	Negative dobët -0.0448	Pozitiv i dobët 0.0268	Pozitiv i dobët 0.0417	Pozitiv i dobët 0.0178	Negative dobët -0.1600
Answer 14	-	Pozitiv i dobët 0.0712	Pozitiv i dobët 0.1021	Negative dobët -0.0007	Negative dobët -0.0088	Negative dobët -0.0011	Pozitiv i dobët 0.0088	Negative dobët -0.1169
Answer 15	-	Pozitiv i dobët 0.0557	Pozitiv i dobët 0.1365	Negative dobët -0.0423	Pozitiv i dobët 0.0177	Negative dobët -0.0162	Pozitiv i dobët 0.0224	Negative dobët -0.1179
Answer 16	-	Pozitiv i dobët 0.0591	Pozitiv i dobët 0.0273	Negative dobët -0.0386	Negative dobët -0.0400	Pozitiv i dobët 0.0653	Pozitiv i dobët 0.0284	Negative dobët -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

Pronari i produktit SaaS Pet Project SDTEST®

Valerii u kualifikua si pedagog-psikolog social në 1993 dhe që atëherë ka zbatuar njohuritë e tij në menaxhimin e projektit.
Valerii mori një diplomë master dhe kualifikimin e menaxherit të projektit dhe programit në 2013. Gjatë programit të tij master, ai u njoh me hartën e rrugës së projektit (GPM Deutsche Gesellschaft Für Projektmanagement e. V.) dhe Spiral Dynamics.
Valerii mori teste të ndryshme të dinamikës spirale dhe përdori njohuritë dhe përvojën e tij për të përshtatur versionin aktual të SDTest.
Valerii është autori i eksplorimit të pasigurisë së V.U.C.A. Koncepti duke përdorur dinamikën spirale dhe statistikat matematikore në psikologji, më shumë se 20 sondazhe ndërkombëtare.

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