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

37) Omantunnon algebra (Vladimir Lefebvre)

38) Kolme erilaista tulevaisuuden mahdollisuutta (tohtori Clare W. Graves)

39) Toimet horjumattoman itseluottamuksen rakentamiseksi (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.

Pelot

kaavioita Korrelaatio

VUCA

Kriittinen arvo korrelaatiokertoimen

Normaalijakelu, kirjoittanut William Sealy Gosset (opiskelija) r = 0.0325

Ei normaali jakauma, keihäsmies r = 0.0013

Näytä vain tulokset > r = 0.0325

Jakelu	Normaali	Normaali	Normaali	Normaali	Normaali	Normaali	Normaali	Normaali
Kaikki kysymykset Kaikki kysymykset Suurin pelkoni on
Suurin pelkoni on
Answer 1	-	Heikko positiivinen 0.0509	Heikko positiivinen 0.0310	Heikko negatiivinen -0.0164	Heikko positiivinen 0.0960	Heikko positiivinen 0.0348	Heikko negatiivinen -0.0171	Heikko negatiivinen -0.1562
Answer 2	-	Heikko positiivinen 0.0186	Heikko positiivinen 8.59E-5	Heikko negatiivinen -0.0431	Heikko positiivinen 0.0656	Heikko positiivinen 0.0473	Heikko positiivinen 0.0120	Heikko negatiivinen -0.0955
Answer 3	-	Heikko negatiivinen -0.0033	Heikko negatiivinen -0.0107	Heikko negatiivinen -0.0468	Heikko negatiivinen -0.0442	Heikko positiivinen 0.0495	Heikko positiivinen 0.0774	Heikko negatiivinen -0.0201
Answer 4	-	Heikko positiivinen 0.0417	Heikko positiivinen 0.0267	Heikko negatiivinen -0.0217	Heikko positiivinen 0.0174	Heikko positiivinen 0.0329	Heikko positiivinen 0.0228	Heikko negatiivinen -0.0960
Answer 5	-	Heikko positiivinen 0.0218	Heikko positiivinen 0.1307	Heikko positiivinen 0.0096	Heikko positiivinen 0.0789	Heikko positiivinen 0.0014	Heikko negatiivinen -0.0224	Heikko negatiivinen -0.1783
Answer 6	-	Heikko negatiivinen -0.0056	Heikko positiivinen 0.0104	Heikko negatiivinen -0.0685	Heikko negatiivinen -0.0063	Heikko positiivinen 0.0223	Heikko positiivinen 0.0843	Heikko negatiivinen -0.0321
Answer 7	-	Heikko positiivinen 0.0115	Heikko positiivinen 0.0405	Heikko negatiivinen -0.0745	Heikko negatiivinen -0.0266	Heikko positiivinen 0.0498	Heikko positiivinen 0.0676	Heikko negatiivinen -0.0512
Answer 8	-	Heikko positiivinen 0.0684	Heikko positiivinen 0.0829	Heikko negatiivinen -0.0340	Heikko positiivinen 0.0167	Heikko positiivinen 0.0360	Heikko positiivinen 0.0133	Heikko negatiivinen -0.1373
Answer 9	-	Heikko positiivinen 0.0697	Heikko positiivinen 0.1669	Heikko positiivinen 0.0052	Heikko positiivinen 0.0666	Heikko negatiivinen -0.0119	Heikko negatiivinen -0.0541	Heikko negatiivinen -0.1802
Answer 10	-	Heikko positiivinen 0.0789	Heikko positiivinen 0.0731	Heikko negatiivinen -0.0235	Heikko positiivinen 0.0279	Heikko positiivinen 0.0328	Heikko negatiivinen -0.0160	Heikko negatiivinen -0.1337
Answer 11	-	Heikko positiivinen 0.0625	Heikko positiivinen 0.0575	Heikko negatiivinen -0.0095	Heikko positiivinen 0.0096	Heikko positiivinen 0.0225	Heikko positiivinen 0.0210	Heikko negatiivinen -0.1247
Answer 12	-	Heikko positiivinen 0.0392	Heikko positiivinen 0.1011	Heikko negatiivinen -0.0409	Heikko positiivinen 0.0359	Heikko positiivinen 0.0310	Heikko positiivinen 0.0258	Heikko negatiivinen -0.1524
Answer 13	-	Heikko positiivinen 0.0650	Heikko positiivinen 0.1026	Heikko negatiivinen -0.0443	Heikko positiivinen 0.0293	Heikko positiivinen 0.0452	Heikko positiivinen 0.0145	Heikko negatiivinen -0.1646
Answer 14	-	Heikko positiivinen 0.0702	Heikko positiivinen 0.0990	Heikko negatiivinen -0.0016	Heikko negatiivinen -0.0071	Heikko positiivinen 0.0046	Heikko positiivinen 0.0070	Heikko negatiivinen -0.1209
Answer 15	-	Heikko positiivinen 0.0535	Heikko positiivinen 0.1346	Heikko negatiivinen -0.0385	Heikko positiivinen 0.0206	Heikko negatiivinen -0.0182	Heikko positiivinen 0.0177	Heikko negatiivinen -0.1166
Answer 16	-	Heikko positiivinen 0.0660	Heikko positiivinen 0.0305	Heikko negatiivinen -0.0380	Heikko negatiivinen -0.0413	Heikko positiivinen 0.0660	Heikko positiivinen 0.0218	Heikko negatiivinen -0.0755

Vie MS Excel

Tämä toiminto on saatavilla omassa VUCA-kyselyt

Hyvä

You can not only just create your poll in the tulli «V.U.C.A kysely suunnittelija» (with a unique link and your logo) but also you can earn money by selling its results in the tulli «Äänesalli», as already the authors of polls.

If you participated in VUCA polls, you can see your results and compare them with the overall polls results, which are constantly growing, in your personal account after purchasing tulli «Minun SDT»

[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 SDTEST®

Valerii valmistui sosiaalipedagogiksi-psykologiksi vuonna 1993 ja on sittemmin soveltanut osaamistaan projektijohtamiseen.
Valerii suoritti maisterin tutkinnon sekä projekti- ja ohjelmapäällikön tutkinnon vuonna 2013. Maisteriohjelmansa aikana hän tutustui Project Roadmapiin (GPM Deutsche Gesellschaft für Projektmanagement e. V.) ja Spiral Dynamicsiin.
Valerii on kirjoittanut V.U.C.A.:n epävarmuutta. konsepti käyttäen spiraalidynamiikkaa ja matemaattisia tilastoja psykologiassa sekä 38 kansainvälistä kyselyä.

Tällä viestillä on 0 Kommentit

Vastata

Peruuta vastaus

Jätä kommentti