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)

39) Nā hana e kūkulu ai i ka hilinaʻi ponoʻī ʻole (na Suren Samarchyan)

40)

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 = 0.0318

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

Hōʻike i nā hopena wale nō > r = 0.0318

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 0.0548	Nawaliwali maikaʻi 0.0285	Nawaliwali hopena maikaʻi -0.0173	Nawaliwali maikaʻi 0.0940	Nawaliwali maikaʻi 0.0358	Nawaliwali hopena maikaʻi -0.0156	Nawaliwali hopena maikaʻi -0.1560
Answer 2	-	Nawaliwali maikaʻi 0.0192	Nawaliwali hopena maikaʻi -0.0048	Nawaliwali hopena maikaʻi -0.0394	Nawaliwali maikaʻi 0.0659	Nawaliwali maikaʻi 0.0491	Nawaliwali maikaʻi 0.0117	Nawaliwali hopena maikaʻi -0.0981
Answer 3	-	Nawaliwali hopena maikaʻi -0.0003	Nawaliwali hopena maikaʻi -0.0088	Nawaliwali hopena maikaʻi -0.0450	Nawaliwali hopena maikaʻi -0.0440	Nawaliwali maikaʻi 0.0471	Nawaliwali maikaʻi 0.0739	Nawaliwali hopena maikaʻi -0.0191
Answer 4	-	Nawaliwali maikaʻi 0.0429	Nawaliwali maikaʻi 0.0271	Nawaliwali hopena maikaʻi -0.0230	Nawaliwali maikaʻi 0.0182	Nawaliwali maikaʻi 0.0351	Nawaliwali maikaʻi 0.0239	Nawaliwali hopena maikaʻi -0.0995
Answer 5	-	Nawaliwali maikaʻi 0.0273	Nawaliwali maikaʻi 0.1298	Nawaliwali maikaʻi 0.0101	Nawaliwali maikaʻi 0.0772	Nawaliwali hopena maikaʻi -0.0006	Nawaliwali hopena maikaʻi -0.0183	Nawaliwali hopena maikaʻi -0.1784
Answer 6	-	Nawaliwali hopena maikaʻi -0.0026	Nawaliwali maikaʻi 0.0050	Nawaliwali hopena maikaʻi -0.0621	Nawaliwali hopena maikaʻi -0.0081	Nawaliwali maikaʻi 0.0240	Nawaliwali maikaʻi 0.0856	Nawaliwali hopena maikaʻi -0.0346
Answer 7	-	Nawaliwali maikaʻi 0.0105	Nawaliwali maikaʻi 0.0339	Nawaliwali hopena maikaʻi -0.0661	Nawaliwali hopena maikaʻi -0.0304	Nawaliwali maikaʻi 0.0517	Nawaliwali maikaʻi 0.0686	Nawaliwali hopena maikaʻi -0.0515
Answer 8	-	Nawaliwali maikaʻi 0.0635	Nawaliwali maikaʻi 0.0732	Nawaliwali hopena maikaʻi -0.0275	Nawaliwali maikaʻi 0.0143	Nawaliwali maikaʻi 0.0370	Nawaliwali maikaʻi 0.0172	Nawaliwali hopena maikaʻi -0.1336
Answer 9	-	Nawaliwali maikaʻi 0.0734	Nawaliwali maikaʻi 0.1618	Nawaliwali maikaʻi 0.0069	Nawaliwali maikaʻi 0.0644	Nawaliwali hopena maikaʻi -0.0109	Nawaliwali hopena maikaʻi -0.0489	Nawaliwali hopena maikaʻi -0.1811
Answer 10	-	Nawaliwali maikaʻi 0.0764	Nawaliwali maikaʻi 0.0679	Nawaliwali hopena maikaʻi -0.0139	Nawaliwali maikaʻi 0.0290	Nawaliwali maikaʻi 0.0338	Nawaliwali hopena maikaʻi -0.0123	Nawaliwali hopena maikaʻi -0.1342
Answer 11	-	Nawaliwali maikaʻi 0.0634	Nawaliwali maikaʻi 0.0535	Nawaliwali hopena maikaʻi -0.0091	Nawaliwali maikaʻi 0.0113	Nawaliwali maikaʻi 0.0238	Nawaliwali maikaʻi 0.0247	Nawaliwali hopena maikaʻi -0.1260
Answer 12	-	Nawaliwali maikaʻi 0.0449	Nawaliwali maikaʻi 0.0941	Nawaliwali hopena maikaʻi -0.0341	Nawaliwali maikaʻi 0.0342	Nawaliwali maikaʻi 0.0332	Nawaliwali maikaʻi 0.0255	Nawaliwali hopena maikaʻi -0.1534
Answer 13	-	Nawaliwali maikaʻi 0.0691	Nawaliwali maikaʻi 0.0966	Nawaliwali hopena maikaʻi -0.0393	Nawaliwali maikaʻi 0.0295	Nawaliwali maikaʻi 0.0417	Nawaliwali maikaʻi 0.0148	Nawaliwali hopena maikaʻi -0.1626
Answer 14	-	Nawaliwali maikaʻi 0.0775	Nawaliwali maikaʻi 0.0903	Nawaliwali hopena maikaʻi -0.0019	Nawaliwali hopena maikaʻi -0.0089	Nawaliwali maikaʻi 0.0048	Nawaliwali maikaʻi 0.0140	Nawaliwali hopena maikaʻi -0.1223
Answer 15	-	Nawaliwali maikaʻi 0.0544	Nawaliwali maikaʻi 0.1280	Nawaliwali hopena maikaʻi -0.0345	Nawaliwali maikaʻi 0.0152	Nawaliwali hopena maikaʻi -0.0178	Nawaliwali maikaʻi 0.0236	Nawaliwali hopena maikaʻi -0.1158
Answer 16	-	Nawaliwali maikaʻi 0.0703	Nawaliwali maikaʻi 0.0262	Nawaliwali hopena maikaʻi -0.0371	Nawaliwali hopena maikaʻi -0.0377	Nawaliwali maikaʻi 0.0697	Nawaliwali maikaʻi 0.0204	Nawaliwali hopena maikaʻi -0.0788

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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

Mea nona ka huahana SaaS SDTEST®

Ua kūpono ʻo Valerii ma ke ʻano he kanaka aʻoaʻo-psychologist ma 1993 a ua hoʻohana ʻo ia i kona ʻike i ka hoʻokele papahana.
Ua loaʻa iā Valerii ke kēkelē laeoʻo a me ka hōʻailona papahana a me ka manakia papahana ma 2013. I ka wā o kāna papahana Master, ua kamaʻāina ʻo ia me Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) a me Spiral Dynamics.
ʻO Valerii ka mea kākau o ka ʻimi ʻana i ka maopopo ʻole o ka V.U.C.A. manaʻo e hoʻohana ana i ka Spiral Dynamics a me ka helu makemakika i loko o ka psychology, a me 38 mau koho balota.

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