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) Dejanja podjetij v zvezi z osebjem v zadnjem mesecu (da / ne)

2) Ukrepi podjetij v zvezi z osebjem v zadnjem mesecu (dejstvo v%)

3) Strahovi

4) Največji problemi, s katerimi se sooča moja država

5) Katere lastnosti in sposobnosti uporabljajo dobre voditelje pri gradnji uspešnih ekip?

6) Google. Dejavniki, ki vplivajo na učinkovitost ekipe

7) Glavne prioritete iskalcev zaposlitve

8) Kaj naredi šefa odličnega voditelja?

9) Kaj naredi ljudje uspešni v službi?

10) Ste pripravljeni prejeti manj plačila za delo na daljavo?

11) Ali obstaja ageizem?

12) Ageizem v karieri

13) Ageizem v življenju

14) Vzroki za starost

15) Razlogi, zakaj se ljudje odpovedujejo (avtor Anna Vital)

16) ZAUPANJE (#WVS)

17) Oxfordska raziskava sreče

18) Psihološko počutje

19) Kje bi bila vaša naslednja najbolj vznemirljiva priložnost?

20) Kaj boste storili ta teden, da boste skrbeli za svoje duševno zdravje?

21) Živim razmišljam o svoji preteklosti, sedanjosti ali prihodnosti

22) Meritokracija

23) Umetna inteligenca in konec civilizacije

24) Zakaj ljudje odlašajo?

25) Razlika med spoloma pri gradnji samozavesti (IFD Allensbach)

26) Xing.com ocena kulture

27) Patricka Lencionija "Pet disfunkcij ekipe"

28) Empatija je ...

29) Kaj je bistvenega pomena za strokovnjake za izbiro ponudbe za delo?

30) Zakaj se ljudje upirajo spremembam (avtor Siobhán McHale)

31) Kako urejate svoja čustva? (avtor Nawal Mustafa M.A.)

32) 21 spretnosti, ki vam plačajo za vedno (avtor Jeremiah Teo / 赵汉昇)

33) Prava svoboda je ...

34) 12 načinov za vzpostavitev zaupanja z drugimi (Justin Wright)

35) Značilnosti nadarjenega zaposlenega (avtorice za upravljanje talentov)

36) 10 tipk za motiviranje vaše ekipe

37) Algebra vesti (avtor Vladimir Lefebvre)

38) Tri različne možnosti prihodnosti (dr. Clare W. Graves)

39) Ukrepi za izgradnjo neomajljivega samozaupanja (avtor 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.

Strahovi

Grafikoni Korelacija

VUCA

Kritična vrednost koeficienta korelacije

Običajna distribucija, William Sealy Gosset (študent) r = 0.0317

Ne običajna porazdelitev, Spearman r = 0.0013

Pokažite samo rezultate > r = 0.0317

Porazdelitev	Ne normalno	Ne normalno	Ne normalno	Normalno	Normalno	Normalno	Normalno	Normalno
Vsa vprašanja Vsa vprašanja Moj največji strah je
Moj največji strah je
Answer 1	-	Šibko pozitivno 0.0537	Šibko pozitivno 0.0288	Šibko negativno -0.0175	Šibko pozitivno 0.0948	Šibko pozitivno 0.0381	Šibko negativno -0.0178	Šibko negativno -0.1563
Answer 2	-	Šibko pozitivno 0.0194	Šibko negativno -0.0048	Šibko negativno -0.0385	Šibko pozitivno 0.0655	Šibko pozitivno 0.0495	Šibko pozitivno 0.0106	Šibko negativno -0.0982
Answer 3	-	Šibko negativno -0.0001	Šibko negativno -0.0084	Šibko negativno -0.0449	Šibko negativno -0.0445	Šibko pozitivno 0.0485	Šibko pozitivno 0.0742	Šibko negativno -0.0207
Answer 4	-	Šibko pozitivno 0.0433	Šibko pozitivno 0.0291	Šibko negativno -0.0232	Šibko pozitivno 0.0163	Šibko pozitivno 0.0367	Šibko pozitivno 0.0226	Šibko negativno -0.0996
Answer 5	-	Šibko pozitivno 0.0277	Šibko pozitivno 0.1291	Šibko pozitivno 0.0108	Šibko pozitivno 0.0745	Šibko pozitivno 0.0012	Šibko negativno -0.0177	Šibko negativno -0.1783
Answer 6	-	Šibko negativno -0.0015	Šibko pozitivno 0.0058	Šibko negativno -0.0607	Šibko negativno -0.0094	Šibko pozitivno 0.0255	Šibko pozitivno 0.0844	Šibko negativno -0.0363
Answer 7	-	Šibko pozitivno 0.0113	Šibko pozitivno 0.0348	Šibko negativno -0.0657	Šibko negativno -0.0305	Šibko pozitivno 0.0521	Šibko pozitivno 0.0686	Šibko negativno -0.0532
Answer 8	-	Šibko pozitivno 0.0657	Šibko pozitivno 0.0728	Šibko negativno -0.0255	Šibko pozitivno 0.0124	Šibko pozitivno 0.0386	Šibko pozitivno 0.0153	Šibko negativno -0.1345
Answer 9	-	Šibko pozitivno 0.0757	Šibko pozitivno 0.1605	Šibko pozitivno 0.0066	Šibko pozitivno 0.0612	Šibko negativno -0.0063	Šibko negativno -0.0492	Šibko negativno -0.1822
Answer 10	-	Šibko pozitivno 0.0764	Šibko pozitivno 0.0669	Šibko negativno -0.0124	Šibko pozitivno 0.0271	Šibko pozitivno 0.0365	Šibko negativno -0.0130	Šibko negativno -0.1348
Answer 11	-	Šibko pozitivno 0.0634	Šibko pozitivno 0.0526	Šibko negativno -0.0075	Šibko pozitivno 0.0096	Šibko pozitivno 0.0264	Šibko pozitivno 0.0242	Šibko negativno -0.1270
Answer 12	-	Šibko pozitivno 0.0450	Šibko pozitivno 0.0944	Šibko negativno -0.0323	Šibko pozitivno 0.0307	Šibko pozitivno 0.0343	Šibko pozitivno 0.0260	Šibko negativno -0.1530
Answer 13	-	Šibko pozitivno 0.0725	Šibko pozitivno 0.0947	Šibko negativno -0.0389	Šibko pozitivno 0.0265	Šibko pozitivno 0.0443	Šibko pozitivno 0.0144	Šibko negativno -0.1631
Answer 14	-	Šibko pozitivno 0.0820	Šibko pozitivno 0.0897	Šibko negativno -0.0030	Šibko negativno -0.0122	Šibko pozitivno 0.0060	Šibko pozitivno 0.0135	Šibko negativno -0.1213
Answer 15	-	Šibko pozitivno 0.0549	Šibko pozitivno 0.1265	Šibko negativno -0.0334	Šibko pozitivno 0.0119	Šibko negativno -0.0153	Šibko pozitivno 0.0242	Šibko negativno -0.1157
Answer 16	-	Šibko pozitivno 0.0732	Šibko pozitivno 0.0242	Šibko negativno -0.0373	Šibko negativno -0.0398	Šibko pozitivno 0.0729	Šibko pozitivno 0.0169	Šibko negativno -0.0774

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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

Lastnik izdelka SaaS SDTEST®

Valerii je leta 1993 pridobil izobrazbo socialnega pedagoga-psihologa in od takrat svoje znanje uporablja pri vodenju projektov.
Valerii je leta 2013 pridobil magisterij in kvalifikacijo projektnega in programskega vodje. Med magistrskim študijem se je seznanil s Projektnim načrtom (GPM Deutsche Gesellschaft für Projektmanagement e. V.) in Spiralno dinamiko.
Valerii je avtor raziskovanja negotovosti V.U.C.A. koncept z uporabo spiralne dinamike in matematične statistike v psihologiji ter 38 mednarodnih anket.

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