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.

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Here are reports of polls which SDTEST^® makes:

1) Soňky aýda işgärler bilen baglanyşykly kompaniýalaryň hereketleri (hawa / ýok)

2) Soňky aýda işgärler bilen baglanyşykly kompaniýalaryň hereketleri (% -de fakt)

3) Gorkuz

4) Meniň ýurduma ýüzbe-ýüz bolýan iň uly meseleler

5) Üstünlikli toparlary guranyňyzda haýsy häsiýetleri we başarnyklary ulanýarlar?

6) Google. Toparyň netijeliligine täsir edýän faktorlar

7) Iş gözleýänleriň esasy ileri tutulýan ugurlary

8) Bosbiýa uly lider näme edýär?

9) Adamlary işde üstünlik gazanýan näme edýär?

10) Uzakdan işlemek üçin az aýlyk almaga taýynmy?

11) Ageaşizm barmy?

12) Karýeradaky ýaşizm

13) Durmuşda ýaşizm

14) Ageaşylygyň sebäpleri

15) Adamlaryň ýüz öwürmeginiň sebäpleri (Anna witan tarapyndan)

16) Ynam (#WVS)

17) Oksford bagty gözleg

18) Psihologiki abadançylyk

19) Indiki iň tolgundyryjy pursatyňyz nirede?

20) Akyl saglygyňyza seretmek üçin bu hepde näme ederdiňiz?

21) Geçmişim, häzirki ýa-da geljegi barada pikir edýärin

22) Meritokratiýa

23) Emeli intellekt we siwilizasiýanyň soňy

24) Adamlar näme üçin adamlar gijä galýarlar?

25) Özüňe ynam döretmekdäki jyns tapawudy (ifd solnsach)

26) Xing.com medeniýetine baha bermek

27) Patrik Lencioniniň "toparyň bäş sany" -ny "

28) Duýgudaşlyk ...

29) Iş teklibini saýlamagyndaky hünärmenler üçin zerur zat näme?

30) Adamlar näme üçin üýtgemeýärler (Siobhán mchalele)

31) Duýgularyňyzy nädip kadaňyzy düzedip bilersiňiz? (Nawal Musta M.a.)

32) Size baky töleýän 21 başarnyk (Jeremiahermeýa teo / 赵汉昇)

33) Hakyky erkinlik ...

34) Başgalaryna ynam döretmegiň 12 usuly (Jastin Wraýt bilen)

35) Zehinli işgäriň aýratynlyklary (zehinli dolandyryş instituty)

36) Toparyňyzy höweslendirmek üçin 10 açar

37) Wyciencedan algebrasy (Wladimir Lefebvre)

38) Geljegiň üç aýratyn mümkinçiligi (Dr. Klar W. Graves tarapyndan)

39) Sarsmaz özüne ynam döretmek üçin hereketler (Suren Samarhýan tarapyndan)

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.

Gorkuz

grafikler Baradaky

VUCA

Korrelýasiýa koeffisiýentiniň möhüm bahasy

Adaty paýlanyş, William Sealyom tarapyndan (talyp) r = 0.0316

Adaty däl paýlanma, naýza bilen r = 0.0013

Diňe netijeleri görkeziň > r = 0.0316

Paýlamak	Kadaly däl	Kadaly däl	Kadaly däl	Adaty	Adaty	Adaty	Adaty	Adaty
Allhli soraglar Allhli soraglar Iň uly gorkym
Iň uly gorkym
Answer 1	-	Gowşak oňyn 0.0547	Gowşak oňyn 0.0292	Gowşak negatiw -0.0172	Gowşak oňyn 0.0944	Gowşak oňyn 0.0380	Gowşak negatiw -0.0182	Gowşak negatiw -0.1566
Answer 2	-	Gowşak oňyn 0.0186	Gowşak negatiw -0.0057	Gowşak negatiw -0.0380	Gowşak oňyn 0.0644	Gowşak oňyn 0.0501	Gowşak oňyn 0.0112	Gowşak negatiw -0.0975
Answer 3	-	Gowşak negatiw -0.0003	Gowşak negatiw -0.0090	Gowşak negatiw -0.0451	Gowşak negatiw -0.0446	Gowşak oňyn 0.0498	Gowşak oňyn 0.0750	Gowşak negatiw -0.0219
Answer 4	-	Gowşak oňyn 0.0438	Gowşak oňyn 0.0304	Gowşak negatiw -0.0229	Gowşak oňyn 0.0164	Gowşak oňyn 0.0371	Gowşak oňyn 0.0228	Gowşak negatiw -0.1017
Answer 5	-	Gowşak oňyn 0.0273	Gowşak oňyn 0.1287	Gowşak oňyn 0.0112	Gowşak oňyn 0.0739	Gowşak oňyn 0.0004	Gowşak negatiw -0.0165	Gowşak negatiw -0.1777
Answer 6	-	Gowşak negatiw -0.0001	Gowşak oňyn 0.0049	Gowşak negatiw -0.0605	Gowşak negatiw -0.0103	Gowşak oňyn 0.0258	Gowşak oňyn 0.0852	Gowşak negatiw -0.0370
Answer 7	-	Gowşak oňyn 0.0120	Gowşak oňyn 0.0336	Gowşak negatiw -0.0656	Gowşak negatiw -0.0309	Gowşak oňyn 0.0526	Gowşak oňyn 0.0690	Gowşak negatiw -0.0535
Answer 8	-	Gowşak oňyn 0.0660	Gowşak oňyn 0.0725	Gowşak negatiw -0.0261	Gowşak oňyn 0.0132	Gowşak oňyn 0.0387	Gowşak oňyn 0.0158	Gowşak negatiw -0.1354
Answer 9	-	Gowşak oňyn 0.0764	Gowşak oňyn 0.1613	Gowşak oňyn 0.0055	Gowşak oňyn 0.0619	Gowşak negatiw -0.0064	Gowşak negatiw -0.0488	Gowşak negatiw -0.1833
Answer 10	-	Gowşak oňyn 0.0769	Gowşak oňyn 0.0664	Gowşak negatiw -0.0128	Gowşak oňyn 0.0271	Gowşak oňyn 0.0355	Gowşak negatiw -0.0113	Gowşak negatiw -0.1349
Answer 11	-	Gowşak oňyn 0.0638	Gowşak oňyn 0.0514	Gowşak negatiw -0.0082	Gowşak oňyn 0.0105	Gowşak oňyn 0.0262	Gowşak oňyn 0.0257	Gowşak negatiw -0.1280
Answer 12	-	Gowşak oňyn 0.0440	Gowşak oňyn 0.0919	Gowşak negatiw -0.0326	Gowşak oňyn 0.0309	Gowşak oňyn 0.0353	Gowşak oňyn 0.0281	Gowşak negatiw -0.1535
Answer 13	-	Gowşak oňyn 0.0720	Gowşak oňyn 0.0932	Gowşak negatiw -0.0393	Gowşak oňyn 0.0270	Gowşak oňyn 0.0450	Gowşak oňyn 0.0162	Gowşak negatiw -0.1640
Answer 14	-	Gowşak oňyn 0.0816	Gowşak oňyn 0.0889	Gowşak negatiw -0.0040	Gowşak negatiw -0.0115	Gowşak oňyn 0.0058	Gowşak oňyn 0.0144	Gowşak negatiw -0.1209
Answer 15	-	Gowşak oňyn 0.0546	Gowşak oňyn 0.1258	Gowşak negatiw -0.0333	Gowşak oňyn 0.0120	Gowşak negatiw -0.0144	Gowşak oňyn 0.0249	Gowşak negatiw -0.1165
Answer 16	-	Gowşak oňyn 0.0731	Gowşak oňyn 0.0231	Gowşak negatiw -0.0381	Gowşak negatiw -0.0378	Gowşak oňyn 0.0729	Gowşak oňyn 0.0176	Gowşak negatiw -0.0784

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[1] https://twitter.com/wileyprof

[2] https://colinallen.dnsalias.org

[3] https://philpeople.org/profiles/colin-allen

2023.10.13

Waleri Kosenko

Önümiň eýesi SaaS SDTEST®

Waleriý 1993-nji ýylda sosial pedagog-psiholog hökmünde saýlandy we şondan soň bilimini taslamany dolandyrmakda ulandy.
Waleri 2013-nji ýylda magistr derejesini we taslama we programma menejeri derejesini aldy. Magistr programmasynyň dowamynda Taslamanyň mol kartasy (GPM Doýçe Gesellschaft für Projektmanagement e. V.) we Spiral Dynamics bilen tanyşdy.
Waleriý V.U.C.A.-nyň näbelliligini öwrenmegiň awtory. Psihologiýada Spiral Dynamics we matematiki statistika we 38 halkara pikir soralyşygy ulanmak düşünjesi.

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