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) ʻO nā hana o nāʻoihana e pili ana i nā limahana i ka mahina i hala (ʻae /ʻaʻole)

2) ʻO nā hana o nāʻoihana e pili ana i nā limahana i ka mahina i hala (ʻoiaʻiʻo i%)

3) Makau

4) Nā pilikia nui e kū nei i kuʻu'āina

5) He aha nā hiʻohiʻona a me nā pono e hoʻohana ai i nā alakaʻi maikaʻi i ka wā e kūkulu ai nā hui maikaʻi?

6) Google. Nā mea e hiki ai i ka hui o ka hui

7) ʻO nā mea nui o nā mea eʻimi nei

8) He aha ka mea e hoʻokau ai i kahi alakaʻi nui?

9) He aha ka mea e pōmaikaʻi ai nā kānaka ma ka hana?

10) Mākaukauʻoe e loaʻa ka uku uku e hana mamao?

11) Noho anei ka hoa?

12) ʻO ka huiʻana i ka hana

13) Overism i ke ola

14) Nā kumu o ka Ageries

15) ʻO nā kumu e hāʻawi ai i nā poʻe (e ka mea waiwai)

16) Paulele (#WVS)

17) ʻO ka loiloi hauʻoli o Oxford

18) ʻO ka noʻonoʻo noʻonoʻo noʻonoʻo

19) Ma hea e noho ai kāu manawa hou aʻe?

20) He aha kāu e hana ai i kēia pule e nānā i kāu olakino noʻonoʻo?

21) Noho wau i ka noʻonoʻoʻana i kaʻu mea i hala, i kēia manawa a iʻole e hiki mai ana

22) Mertocracy

23) Ka naʻauao a me ka hopena o ke kīwī

24) No ke aha ka poʻe e hōʻoia ai i nā kānaka?

25) ʻO keʻano hana kāne ma ke kūkuluʻana i ka hilinaʻi (inā Allensbach)

26) Xing.com cture loiloi

27) ʻO Patrick Lenciona's "kaʻelima mauʻelima o kahi hui"

28) Empathy ...

29) He aha ka mea nui no nā mea loea i ke kohoʻana i kahi hana hana?

30) No ke aha e hoʻololi ai nā kānaka i kahi hoʻololi (e Siobhán mchale)

31) Peheaʻoe e hoʻoponopono ai i kāu mau manaʻo? (e Nawal Mustafa M.a.)

32) 21 mau mākaukau e uku mau loa iāʻoe (Na Jeremia Too / 赵汉昇)

33) ʻO ke kūʻokoʻa maoli ...

34) 12 ala e kūkulu ai i ka hilinaʻi me nā poʻe'ē aʻe (e Justin Wright)

35) Nā hiʻohiʻona o kahi limahana talena (e talenagengement hoʻokele)

36) 10 mau kī e hoʻoikaika i kāu hui

37) Algebra of Conscience (na Vladimir Lefebvre)

38) ʻEkolu mau mea ʻokoʻa o ka wā e hiki mai ana (na 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.

Makau

nńnń Mea hoʻopili

VUCA

Pilikia waiwai o ka mea hoʻopili kaʻi lau waiwai

ʻO ka hoʻokaʻawale maʻamau, e William Sealy Gosset (haumāna) r = 0.0331

ʻO ka māhele maʻamauʻole, e ka'ōlelo r = 0.0013

Hōʻike i nā hopena wale nō > r = 0.0331

Ka Hoʻohanohano	Non maʻamau	Non maʻamau	Non maʻamau	Maʻamau	Maʻamau	Maʻamau	Maʻamau	Maʻamau
Nā nīnau āpau Nā nīnau āpau ʻO koʻu makaʻu nui loa
ʻO koʻu makaʻu nui loa
Answer 1	-	Nawaliwali maikaʻi 0.0563	Nawaliwali maikaʻi 0.0317	Nawaliwali hopena maikaʻi -0.0161	Nawaliwali maikaʻi 0.0907	Nawaliwali maikaʻi 0.0298	Nawaliwali hopena maikaʻi -0.0126	Nawaliwali hopena maikaʻi -0.1537
Answer 2	-	Nawaliwali maikaʻi 0.0216	Nawaliwali maikaʻi 0.0002	Nawaliwali hopena maikaʻi -0.0458	Nawaliwali maikaʻi 0.0654	Nawaliwali maikaʻi 0.0445	Nawaliwali maikaʻi 0.0124	Nawaliwali hopena maikaʻi -0.0937
Answer 3	-	Nawaliwali hopena maikaʻi -0.0035	Nawaliwali hopena maikaʻi -0.0111	Nawaliwali hopena maikaʻi -0.0421	Nawaliwali hopena maikaʻi -0.0456	Nawaliwali maikaʻi 0.0466	Nawaliwali maikaʻi 0.0786	Nawaliwali hopena maikaʻi -0.0201
Answer 4	-	Nawaliwali maikaʻi 0.0435	Nawaliwali maikaʻi 0.0353	Nawaliwali hopena maikaʻi -0.0181	Nawaliwali maikaʻi 0.0145	Nawaliwali maikaʻi 0.0301	Nawaliwali maikaʻi 0.0197	Nawaliwali hopena maikaʻi -0.0979
Answer 5	-	Nawaliwali maikaʻi 0.0299	Nawaliwali maikaʻi 0.1279	Nawaliwali maikaʻi 0.0136	Nawaliwali maikaʻi 0.0730	Nawaliwali hopena maikaʻi -0.0007	Nawaliwali hopena maikaʻi -0.0207	Nawaliwali hopena maikaʻi -0.1746
Answer 6	-	Nawaliwali hopena maikaʻi -0.0004	Nawaliwali maikaʻi 0.0082	Nawaliwali hopena maikaʻi -0.0629	Nawaliwali hopena maikaʻi -0.0078	Nawaliwali maikaʻi 0.0193	Nawaliwali maikaʻi 0.0830	Nawaliwali hopena maikaʻi -0.0318
Answer 7	-	Nawaliwali maikaʻi 0.0122	Nawaliwali maikaʻi 0.0381	Nawaliwali hopena maikaʻi -0.0686	Nawaliwali hopena maikaʻi -0.0242	Nawaliwali maikaʻi 0.0471	Nawaliwali maikaʻi 0.0636	Nawaliwali hopena maikaʻi -0.0513
Answer 8	-	Nawaliwali maikaʻi 0.0698	Nawaliwali maikaʻi 0.0849	Nawaliwali hopena maikaʻi -0.0321	Nawaliwali maikaʻi 0.0146	Nawaliwali maikaʻi 0.0345	Nawaliwali maikaʻi 0.0130	Nawaliwali hopena maikaʻi -0.1368
Answer 9	-	Nawaliwali maikaʻi 0.0665	Nawaliwali maikaʻi 0.1674	Nawaliwali maikaʻi 0.0092	Nawaliwali maikaʻi 0.0691	Nawaliwali hopena maikaʻi -0.0128	Nawaliwali hopena maikaʻi -0.0528	Nawaliwali hopena maikaʻi -0.1812
Answer 10	-	Nawaliwali maikaʻi 0.0778	Nawaliwali maikaʻi 0.0755	Nawaliwali hopena maikaʻi -0.0180	Nawaliwali maikaʻi 0.0231	Nawaliwali maikaʻi 0.0346	Nawaliwali hopena maikaʻi -0.0146	Nawaliwali hopena maikaʻi -0.1298
Answer 11	-	Nawaliwali maikaʻi 0.0584	Nawaliwali maikaʻi 0.0524	Nawaliwali hopena maikaʻi -0.0096	Nawaliwali maikaʻi 0.0081	Nawaliwali maikaʻi 0.0199	Nawaliwali maikaʻi 0.0318	Nawaliwali hopena maikaʻi -0.1197
Answer 12	-	Nawaliwali maikaʻi 0.0380	Nawaliwali maikaʻi 0.1042	Nawaliwali hopena maikaʻi -0.0352	Nawaliwali maikaʻi 0.0357	Nawaliwali maikaʻi 0.0254	Nawaliwali maikaʻi 0.0286	Nawaliwali hopena maikaʻi -0.1515
Answer 13	-	Nawaliwali maikaʻi 0.0644	Nawaliwali maikaʻi 0.1057	Nawaliwali hopena maikaʻi -0.0448	Nawaliwali maikaʻi 0.0268	Nawaliwali maikaʻi 0.0416	Nawaliwali maikaʻi 0.0169	Nawaliwali hopena maikaʻi -0.1600
Answer 14	-	Nawaliwali maikaʻi 0.0717	Nawaliwali maikaʻi 0.1026	Nawaliwali hopena maikaʻi -0.0006	Nawaliwali hopena maikaʻi -0.0089	Nawaliwali hopena maikaʻi -0.0012	Nawaliwali maikaʻi 0.0080	Nawaliwali hopena maikaʻi -0.1168
Answer 15	-	Nawaliwali maikaʻi 0.0549	Nawaliwali maikaʻi 0.1375	Nawaliwali hopena maikaʻi -0.0420	Nawaliwali maikaʻi 0.0178	Nawaliwali hopena maikaʻi -0.0160	Nawaliwali maikaʻi 0.0216	Nawaliwali hopena maikaʻi -0.1180
Answer 16	-	Nawaliwali maikaʻi 0.0591	Nawaliwali maikaʻi 0.0273	Nawaliwali hopena maikaʻi -0.0386	Nawaliwali hopena maikaʻi -0.0399	Nawaliwali maikaʻi 0.0653	Nawaliwali maikaʻi 0.0282	Nawaliwali hopena maikaʻi -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

ʻO ka mea nona ka huahanaʻo Saas Bank Project SDTest®

Ua loaʻa iā Valerii i kahi mea hoʻokūkū kanaka ma keʻano he psychologist
Loaʻaʻo Valerii i kahi keken o ka haku a me ka papahana a me ka hana ma 2013. I ka wā o kāna papahana,ʻikeʻiaʻo ia me ka papahana o kona haku
Laweʻo Valerii i nā hōʻike Spiral Denamics e hoʻohana a hoʻohana i konaʻike a me konaʻike e hoʻoponopono i ka mana o keʻano o ka sdtest.
ʻO Valerii ka mea kākau o kaʻimiʻana i ka maopopoʻole o ka v.U.C.a. Manaʻo e hoʻohana ana i nā kiʻi spiral spimal a me nā helu helu matematika ma ka psychology,ʻoi aku ma mua o 20 mau koho balota.

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