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^®

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3) Mantha

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8) Kodi chimapangitsa bwanji bwana mtsogoleri wamkulu?

9) Nchiyani chimapangitsa anthu kukhala opambana kuntchito?

10) Kodi mwakonzeka kulandira ndalama zochepa kuti mugwire ntchito kutali?

11) Kodi kusachita zinthu zilipo?

12) Kutsatira Ntchito Yantchito

13) Kuchita Zinthu m'moyo

14) Zomwe Zimayambitsa

15) Zifukwa Zomwe Anthu Amataya (ndi Anna Chofunika)

16) Kukhulupilira (#WVS)

17) Kafukufuku wa Oxford

18) Kupatsa Maganizo

19) Kodi mungakhale kuti mwayi wanu wotsatira?

20) Kodi mungatani sabata ino kuyang'ana thanzi lanu la m'maganizo?

21) Ndimakhala ndikuganiza zakale, zomwe zilipo kapena zamtsogolo

22) Zangomsi

23) Luntha lamphamvu ndi kutha kwa chitukuko

24) N 'chifukwa Chiyani Anthu Amachita Chidwi?

25) Kusiyana kwa amuna ndi akazi podzilimbitsa mtima (ngati allensbach)

26) Xing.com Kuyeserera Kwachikhalidwe

27) Patrick Lencioni's "

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32) 21 Maluso omwe amakulipirani kwamuyaya (ndi Yeremiya / 赵汉昇)

33) Ufulu weniweni ndi ...

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39) Zochita Kuti Mumange Kudzidalira Kosagwedezeka (wolemba 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.

Mantha

Charts Malumikizanidwe

VUCA

Tili mtengo wa malumikizanidwe koyefishienti

Kugawa kofananira, ndi William ku Alliamly Gosset (wophunzira) r = 0.0318

Kugawidwa kwakwabwino kwanthawi zonse, kwa Spearman r = 0.0013

Onetsani zotsatira zokha > r = 0.0318

Kugawa	Osakhala wamba	Osakhala wamba	Osakhala wamba	Mwamasikuonse	Mwamasikuonse	Mwamasikuonse	Mwamasikuonse	Mwamasikuonse
Mafunso Onse Mafunso Onse Mantha anga kwambiri ndi
Mantha anga kwambiri ndi
Answer 1	-	Ofooka zabwino 0.0548	Ofooka zabwino 0.0285	Ofooka zoipa -0.0173	Ofooka zabwino 0.0940	Ofooka zabwino 0.0358	Ofooka zoipa -0.0156	Ofooka zoipa -0.1560
Answer 2	-	Ofooka zabwino 0.0192	Ofooka zoipa -0.0048	Ofooka zoipa -0.0394	Ofooka zabwino 0.0659	Ofooka zabwino 0.0491	Ofooka zabwino 0.0117	Ofooka zoipa -0.0981
Answer 3	-	Ofooka zoipa -0.0003	Ofooka zoipa -0.0088	Ofooka zoipa -0.0450	Ofooka zoipa -0.0440	Ofooka zabwino 0.0471	Ofooka zabwino 0.0739	Ofooka zoipa -0.0191
Answer 4	-	Ofooka zabwino 0.0429	Ofooka zabwino 0.0271	Ofooka zoipa -0.0230	Ofooka zabwino 0.0182	Ofooka zabwino 0.0351	Ofooka zabwino 0.0239	Ofooka zoipa -0.0995
Answer 5	-	Ofooka zabwino 0.0273	Ofooka zabwino 0.1298	Ofooka zabwino 0.0101	Ofooka zabwino 0.0772	Ofooka zoipa -0.0006	Ofooka zoipa -0.0183	Ofooka zoipa -0.1784
Answer 6	-	Ofooka zoipa -0.0026	Ofooka zabwino 0.0050	Ofooka zoipa -0.0621	Ofooka zoipa -0.0081	Ofooka zabwino 0.0240	Ofooka zabwino 0.0856	Ofooka zoipa -0.0346
Answer 7	-	Ofooka zabwino 0.0105	Ofooka zabwino 0.0339	Ofooka zoipa -0.0661	Ofooka zoipa -0.0304	Ofooka zabwino 0.0517	Ofooka zabwino 0.0686	Ofooka zoipa -0.0515
Answer 8	-	Ofooka zabwino 0.0635	Ofooka zabwino 0.0732	Ofooka zoipa -0.0275	Ofooka zabwino 0.0143	Ofooka zabwino 0.0370	Ofooka zabwino 0.0172	Ofooka zoipa -0.1336
Answer 9	-	Ofooka zabwino 0.0734	Ofooka zabwino 0.1618	Ofooka zabwino 0.0069	Ofooka zabwino 0.0644	Ofooka zoipa -0.0109	Ofooka zoipa -0.0489	Ofooka zoipa -0.1811
Answer 10	-	Ofooka zabwino 0.0764	Ofooka zabwino 0.0679	Ofooka zoipa -0.0139	Ofooka zabwino 0.0290	Ofooka zabwino 0.0338	Ofooka zoipa -0.0123	Ofooka zoipa -0.1342
Answer 11	-	Ofooka zabwino 0.0634	Ofooka zabwino 0.0535	Ofooka zoipa -0.0091	Ofooka zabwino 0.0113	Ofooka zabwino 0.0238	Ofooka zabwino 0.0247	Ofooka zoipa -0.1260
Answer 12	-	Ofooka zabwino 0.0449	Ofooka zabwino 0.0941	Ofooka zoipa -0.0341	Ofooka zabwino 0.0342	Ofooka zabwino 0.0332	Ofooka zabwino 0.0255	Ofooka zoipa -0.1534
Answer 13	-	Ofooka zabwino 0.0691	Ofooka zabwino 0.0966	Ofooka zoipa -0.0393	Ofooka zabwino 0.0295	Ofooka zabwino 0.0417	Ofooka zabwino 0.0148	Ofooka zoipa -0.1626
Answer 14	-	Ofooka zabwino 0.0775	Ofooka zabwino 0.0903	Ofooka zoipa -0.0019	Ofooka zoipa -0.0089	Ofooka zabwino 0.0048	Ofooka zabwino 0.0140	Ofooka zoipa -0.1223
Answer 15	-	Ofooka zabwino 0.0544	Ofooka zabwino 0.1280	Ofooka zoipa -0.0345	Ofooka zabwino 0.0152	Ofooka zoipa -0.0178	Ofooka zabwino 0.0236	Ofooka zoipa -0.1158
Answer 16	-	Ofooka zabwino 0.0703	Ofooka zabwino 0.0262	Ofooka zoipa -0.0371	Ofooka zoipa -0.0377	Ofooka zabwino 0.0697	Ofooka zabwino 0.0204	Ofooka zoipa -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

Mwini Zinthu SaaS SDTEST®

Valerii anayenerera kukhala katswiri wa zamaganizo mu 1993 ndipo wakhala akugwiritsa ntchito chidziwitso chake pa kayendetsedwe ka polojekiti.
Valerii adalandira digiri ya Master ndi qualification ya polojekiti ndi pulogalamu ya 2013. Pa pulogalamu ya Master, adadziwa bwino Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) ndi Spiral Dynamics.
Valerii ndi mlembi wofufuza za kusatsimikizika kwa V.U.C.A. Lingaliro logwiritsa ntchito Spiral Dynamics ndi masamu masamu mu psychology, ndi mavoti 38 apadziko lonse lapansi.

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