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) Nga mahi a nga kamupene e pa ana ki nga kaimahi i te marama kua hipa (ae / kaore)

2) Nga mahi a nga kamupene e pa ana ki nga kaimahi i te marama whakamutunga (meka i te%)

3) Mataku

4) Nga raru nui e anga atu ana ki taku whenua

5) He aha nga kounga me nga kaha e whakamahia ana e nga rangatira i te wa e mahi ana nga ropu angitu?

6) Google. Āhuatanga e whai kiko ana te roopu roopu

7) Nga kaupapa matua o nga kaiwhaiwhai mahi

8) He aha te mea e tino rangatira ana te rangatira?

9) He aha te mea e angitu ai te tangata ki te mahi?

10) Kua rite koe ki te tango i te utu iti ake ki te mahi mamao?

11) Kei te mau tonu te kaupapa?

12) Ko te kaupapa i roto i te mahi

13) Nga mea nui i roto i te koiora

14) Tuhinga o mua

15) Te take he aha te take o te iwi (na Anna Fital)

16) Whakapono (#WVS)

17) Oxford te koa o te rangahau

18) Te oranga hinengaro

19) Kei hea koe e whai waahi pai rawa atu?

20) Ka aha koe i tenei wiki ki te tirotiro i to hauora hinengaro?

21) Kei te ora ahau mo te whakaaro mo aku mua, o mua me te heke mai ranei

22) Merirotocicy

23) Te mohio mohio me te mutunga o te ao

24) He aha te iwi e tuku ai?

25) Te rereketanga o te ira tangata ki te hanga i te maia-whaiaro (Ifd Allensbach)

26) Xing.com Te Aromatawai Ahuwhenua

27) Ko Patrick Lencioni's "nga kohinga e rima o te roopu"

28) Ko te ngakau nui ...

29) He aha te mea nui mo te mea motuhake ki te whiriwhiri i tetahi tuku mahi?

30) He aha te tangata e whakahē i te whakarereke (na Siobhán Mchale)

31) Me pehea e whakariterite ai i o kare? (Na Nawal Mustafa M.A.)

32) 21 Nga pukenga e utua ana e koe ake ake (na Jeremiah Teo / 赵汉昇)

33) Ko te tino rangatiratanga ko ...

34) 12 nga huarahi hei hanga i te whakawhirinaki ki etahi atu (na Justin Wright)

35) Nga ahuatanga o te kaimahi mohio (na te taranata whakahaere i te roopu whakahaere)

36) 10 taviri hei akiaki i to roopu

37) Algebra of Conscience (na Vladimir Lefebvre)

38) E toru nga mea rereke mo te heke mai (na Takuta 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.

Mataku

Ngā tūtohi Ine

VUCA

uara Critical o te whakarea te faatanoraa

Tohatoha noa, na William Sealy Gospes (akonga) r = 0.0331

Ko te tohatoha noa, na te taote r = 0.0013

Whakaatuhia anake nga hua > r = 0.0331

Whakaratonga	Kore noa	Kore noa	Kore noa	Tonu	Tonu	Tonu	Tonu	Tonu
Nga paatai katoa Nga paatai katoa Ko taku wehi nui ko
Ko taku wehi nui ko
Answer 1	-	Pai ngoikore 0.0562	Pai ngoikore 0.0311	Negative ngoikore -0.0164	Pai ngoikore 0.0903	Pai ngoikore 0.0301	Negative ngoikore -0.0120	Negative ngoikore -0.1534
Answer 2	-	Pai ngoikore 0.0217	Pai ngoikore 0.0011	Negative ngoikore -0.0455	Pai ngoikore 0.0660	Pai ngoikore 0.0440	Pai ngoikore 0.0117	Negative ngoikore -0.0942
Answer 3	-	Negative ngoikore -0.0034	Negative ngoikore -0.0104	Negative ngoikore -0.0419	Negative ngoikore -0.0451	Pai ngoikore 0.0462	Pai ngoikore 0.0780	Negative ngoikore -0.0204
Answer 4	-	Pai ngoikore 0.0436	Pai ngoikore 0.0362	Negative ngoikore -0.0177	Pai ngoikore 0.0150	Pai ngoikore 0.0296	Pai ngoikore 0.0189	Negative ngoikore -0.0984
Answer 5	-	Pai ngoikore 0.0298	Pai ngoikore 0.1270	Pai ngoikore 0.0133	Pai ngoikore 0.0724	Negative ngoikore -0.0002	Negative ngoikore -0.0199	Negative ngoikore -0.1742
Answer 6	-	Negative ngoikore -0.0003	Pai ngoikore 0.0089	Negative ngoikore -0.0627	Negative ngoikore -0.0074	Pai ngoikore 0.0190	Pai ngoikore 0.0825	Negative ngoikore -0.0321
Answer 7	-	Pai ngoikore 0.0123	Pai ngoikore 0.0388	Negative ngoikore -0.0684	Negative ngoikore -0.0238	Pai ngoikore 0.0468	Pai ngoikore 0.0631	Negative ngoikore -0.0517
Answer 8	-	Pai ngoikore 0.0699	Pai ngoikore 0.0857	Negative ngoikore -0.0318	Pai ngoikore 0.0150	Pai ngoikore 0.0341	Pai ngoikore 0.0125	Negative ngoikore -0.1372
Answer 9	-	Pai ngoikore 0.0666	Pai ngoikore 0.1681	Pai ngoikore 0.0094	Pai ngoikore 0.0694	Negative ngoikore -0.0131	Negative ngoikore -0.0533	Negative ngoikore -0.1815
Answer 10	-	Pai ngoikore 0.0776	Pai ngoikore 0.0744	Negative ngoikore -0.0185	Pai ngoikore 0.0224	Pai ngoikore 0.0352	Negative ngoikore -0.0135	Negative ngoikore -0.1293
Answer 11	-	Pai ngoikore 0.0585	Pai ngoikore 0.0531	Negative ngoikore -0.0094	Pai ngoikore 0.0086	Pai ngoikore 0.0195	Pai ngoikore 0.0313	Negative ngoikore -0.1200
Answer 12	-	Pai ngoikore 0.0378	Pai ngoikore 0.1030	Negative ngoikore -0.0357	Pai ngoikore 0.0350	Pai ngoikore 0.0261	Pai ngoikore 0.0297	Negative ngoikore -0.1510
Answer 13	-	Pai ngoikore 0.0642	Pai ngoikore 0.1044	Negative ngoikore -0.0454	Pai ngoikore 0.0259	Pai ngoikore 0.0424	Pai ngoikore 0.0183	Negative ngoikore -0.1595
Answer 14	-	Pai ngoikore 0.0718	Pai ngoikore 0.1034	Negative ngoikore -0.0003	Negative ngoikore -0.0085	Negative ngoikore -0.0016	Pai ngoikore 0.0074	Negative ngoikore -0.1172
Answer 15	-	Pai ngoikore 0.0550	Pai ngoikore 0.1382	Negative ngoikore -0.0418	Pai ngoikore 0.0181	Negative ngoikore -0.0163	Pai ngoikore 0.0211	Negative ngoikore -0.1183
Answer 16	-	Pai ngoikore 0.0591	Pai ngoikore 0.0276	Negative ngoikore -0.0384	Negative ngoikore -0.0397	Pai ngoikore 0.0651	Pai ngoikore 0.0280	Negative ngoikore -0.0710

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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

Kaipupuri Hua Saas Pet Project SDtest®

Ko Valerii te tohu he kaupapa hinengaro-hinengaro-a-iwi i te tau 1993, mai i te mea kua paahitia tona matauranga ki te whakahaere kaupapa.
I whiwhi a Valerii i te tohu a te rangatira me te kaupapa me te Kaiwhakahaere Kaupapa Kaupapa i te tau 2013. I te wa e mohio ana ia ki te kaupapa o tona rangatira (GPM deutsche geselschaft f.
I mau a Valeyii i nga whakamatautau o te shomics spiro me te whakamahi i tona mohiotanga me tana wheako ki te whakariterite i te putanga o te SDtest.
Ko Valeyi te kaituhi o te torotoro i te koretake o te V.U.C.A. Te ariā ma te whakamahi i nga hihiri a te spiro me nga tatauranga pāngarau i roto i te hinengaro hinengaro, neke atu i te 20 nga pooti o te ao.

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