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:

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7) Zofunikira kwambiri zofunika pantchito

8) Kodi chimapangitsa bwanji bwana mtsogoleri wamkulu?

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11) Kodi kusachita zinthu zilipo?

12) Kutsatira Ntchito Yantchito

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15) Zifukwa Zomwe Anthu Amataya (ndi Anna Chofunika)

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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 "

28) Chisoni ndi ...

29) Kodi chofunikira ndi chiyani kwa akatswiri posankha ntchito?

30) Chifukwa Chomwe Anthu Amakana Kusintha (ndi Siobhán Mchale)

31) Kodi mumawongolera bwanji momwe mukumvera? (ndi Nawal IstafA M.a.)

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

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35) Makhalidwe a wogwira ntchito waluso (ndi talente yoyang'anira inshuwaransi)

36) 10 Chinsinsi Cholimbikitsa Gulu Lanu

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 = 0.0353

Kugawidwa kwakwabwino kwanthawi zonse, kwa Spearman r = 0.0014

Onetsani zotsatira zokha > r = 0.0353

Kugawa	Osakhala wamba	Mwamasikuonse	Osakhala wamba	Mwamasikuonse	Mwamasikuonse	Mwamasikuonse	Mwamasikuonse	Mwamasikuonse
Mafunso Onse Mafunso Onse Mantha anga kwambiri ndi
Mantha anga kwambiri ndi
Answer 1	-	Ofooka zabwino 0.0297	Ofooka zabwino 0.0298	Ofooka zoipa -0.0106	Ofooka zabwino 0.0970	Ofooka zabwino 0.0325	Ofooka zoipa -0.0019	Ofooka zoipa -0.1558
Answer 2	-	Ofooka zabwino 0.0188	Ofooka zabwino 0.0076	Ofooka zoipa -0.0360	Ofooka zabwino 0.0711	Ofooka zabwino 0.0387	Ofooka zabwino 0.0082	Ofooka zoipa -0.1011
Answer 3	-	Ofooka zabwino 0.0026	Ofooka zoipa -0.0170	Ofooka zoipa -0.0443	Ofooka zoipa -0.0458	Ofooka zabwino 0.0547	Ofooka zabwino 0.0808	Ofooka zoipa -0.0270
Answer 4	-	Ofooka zabwino 0.0332	Ofooka zabwino 0.0285	Ofooka zoipa -0.0006	Ofooka zabwino 0.0155	Ofooka zabwino 0.0276	Ofooka zabwino 0.0105	Ofooka zoipa -0.0917
Answer 5	-	Ofooka zabwino 0.0122	Ofooka zabwino 0.1193	Ofooka zabwino 0.0095	Ofooka zabwino 0.0721	Ofooka zabwino 0.0057	Ofooka zoipa -0.0083	Ofooka zoipa -0.1687
Answer 6	-	Ofooka zabwino 0.0044	Ofooka zabwino 0.0005	Ofooka zoipa -0.0582	Ofooka zoipa -0.0004	Ofooka zabwino 0.0210	Ofooka zabwino 0.0830	Ofooka zoipa -0.0418
Answer 7	-	Ofooka zabwino 0.0242	Ofooka zabwino 0.0368	Ofooka zoipa -0.0521	Ofooka zoipa -0.0234	Ofooka zabwino 0.0403	Ofooka zabwino 0.0568	Ofooka zoipa -0.0597
Answer 8	-	Ofooka zabwino 0.0707	Ofooka zabwino 0.0781	Ofooka zoipa -0.0244	Ofooka zabwino 0.0140	Ofooka zabwino 0.0303	Ofooka zabwino 0.0137	Ofooka zoipa -0.1334
Answer 9	-	Ofooka zabwino 0.0564	Ofooka zabwino 0.1531	Ofooka zabwino 0.0127	Ofooka zabwino 0.0769	Ofooka zoipa -0.0136	Ofooka zoipa -0.0495	Ofooka zoipa -0.1752
Answer 10	-	Ofooka zabwino 0.0711	Ofooka zabwino 0.0700	Ofooka zoipa -0.0127	Ofooka zabwino 0.0246	Ofooka zabwino 0.0363	Ofooka zoipa -0.0156	Ofooka zoipa -0.1273
Answer 11	-	Ofooka zabwino 0.0542	Ofooka zabwino 0.0488	Ofooka zabwino 0.0086	Ofooka zabwino 0.0078	Ofooka zabwino 0.0162	Ofooka zabwino 0.0315	Ofooka zoipa -0.1248
Answer 12	-	Ofooka zabwino 0.0281	Ofooka zabwino 0.0929	Ofooka zoipa -0.0325	Ofooka zabwino 0.0361	Ofooka zabwino 0.0276	Ofooka zabwino 0.0365	Ofooka zoipa -0.1482
Answer 13	-	Ofooka zabwino 0.0643	Ofooka zabwino 0.0916	Ofooka zoipa -0.0418	Ofooka zabwino 0.0237	Ofooka zabwino 0.0425	Ofooka zabwino 0.0239	Ofooka zoipa -0.1558
Answer 14	-	Ofooka zabwino 0.0697	Ofooka zabwino 0.1017	Ofooka zabwino 0.0149	Ofooka zoipa -0.0062	Ofooka zoipa -0.0087	Ofooka zoipa -0.0002	Ofooka zoipa -0.1161
Answer 15	-	Ofooka zabwino 0.0603	Ofooka zabwino 0.1299	Ofooka zoipa -0.0379	Ofooka zabwino 0.0163	Ofooka zoipa -0.0091	Ofooka zabwino 0.0164	Ofooka zoipa -0.1204
Answer 16	-	Ofooka zabwino 0.0691	Ofooka zabwino 0.0221	Ofooka zoipa -0.0305	Ofooka zoipa -0.0515	Ofooka zabwino 0.0750	Ofooka zabwino 0.0187	Ofooka zoipa -0.0696

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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 Wogulitsa Saas Pet Projekiti Sdtest®

Valerii anali woyenerera ngati katswiri wazamitundu yotsatsirana pakati pa zaka za 1993 ndipo kuyambira pa kuphunzira kwake pantchito.
Valerii adalandira digiri ya master komanso polojekiti ndi Computer Manege Oneger mu 2013. Pa pulogalamu ya Projekiti yake, adazidziwa bwino panjira ya Projelmat.
Valerii adayesa mayeso osiyanasiyana ozungulira ndipo adagwiritsa ntchito chidziwitso chake ndikusintha kusintha kwa sdtest.
Valerii ndi wolemba kufufuza kusatsimikizika kwa v.U.c.a. Lingaliro logwiritsira ntchito maluso ndi ziwerengero zamasamu mu psychology, oposa 20 ogwiritsa ntchito.

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