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) Yritysten toimet henkilöstön suhteen viime kuussa (kyllä / ei)

2) Yritysten toimet suhteessa henkilöstöön viime kuussa (tosiasia%)

3) Pelot

4) Suurimmat ongelmat kotimaani

5) Mitä ominaisuuksia ja kykyjä hyvät johtajat käyttävät rakennettaessa menestyviä joukkueita?

6) Google. Tekijät, jotka vaikuttavat ryhmän tehokkuuteen

7) Työnhakijoiden tärkeimmät prioriteetit

8) Mikä tekee pomosta suuren johtajan?

9) Mikä tekee ihmisistä menestyviä töissä?

10) Oletko valmis vastaanottamaan vähemmän palkkaa työskennelläkseen etäyhteydessä?

11) Onko ageismia olemassa?

12) Ageismi uran aikana

13) Ageismi elämässä

14) Ageismin syyt

15) Syyt miksi ihmiset luopuvat (Anna Vital)

16) LUOTTAMUS (#WVS)

17) Oxfordin onnellisuustutkimus

18) Psykologinen hyvinvointi

19) Missä olisi seuraava mielenkiintoisin tilaisuutesi?

20) Mitä teet tällä viikolla huolehtiaksesi mielenterveydestäsi?

21) Asun ajatellessani menneisyyttäni, nykyisyyttäni tai tulevaisuutta

22) Meritokratia

23) Keinotekoinen älykkyys ja sivilisaation loppu

24) Miksi ihmiset viivyttävät?

25) Sukupuoliero itseluottamuksen rakentamisessa (IFD Allensbach)

26) Xing.com -kulttuurin arviointi

27) Patrick Lencionin "joukkueen viisi toimintahäiriötä"

28) Empatia on ...

29) Mikä on välttämätöntä IT -asiantuntijoille työtarjouksen valinnassa?

30) Miksi ihmiset vastustavat muutosta (kirjoittanut Siobhán McHale)

31) Kuinka säätelet tunteitasi? (Nawal Mustafa M.A.)

32) 21 taidot, jotka maksavat sinulle ikuisesti (kirjoittanut Jeremiah Teo / 赵汉昇)

33) Todellinen vapaus on ...

34) 12 tapaa rakentaa luottamus muiden kanssa (kirjoittanut Justin Wright)

35) Lahjakkaan työntekijän ominaisuudet (Talent Management Institute)

36) 10 avainta tiimisi motivointiin

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.

Pelot

kaavioita Korrelaatio

VUCA

Kriittinen arvo korrelaatiokertoimen

Normaalijakelu, kirjoittanut William Sealy Gosset (opiskelija) r = 0.0353

Ei normaali jakauma, keihäsmies r = 0.0014

Näytä vain tulokset > r = 0.0353

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

Vie MS Excel

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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

Tuotteen omistaja SaaS Pet Project SDTEST®

Valerii oli pätevä sosiaaliseksi pedagogipsykologiksi vuonna 1993, ja hän on sittemmin soveltanut tietämystä projektijohtamisessa.
Valerii sai maisterin tutkinnon ja projekti- ja ohjelmapäällikön pätevyyden vuonna 2013. Hänen maisteriohjelmansa aikana hän tutustui Project -etenemissuunnitelmaan (GPM Deutsche Gesellschaft für ProjektManagement e. V.) ja Spiral Dynamics.
Valerii suoritti erilaisia spiraalidynamiikkatestejä ja käytti tietonsa ja kokemuksensa SDTEST: n nykyisen version mukauttamiseen.
Valerii on kirjoittanut V.U.C.A. Konsepti käyttämällä spiraalidynamiikkaa ja psykologian matemaattisia tilastoja, yli 20 kansainvälistä kyselyä.

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