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)

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 = 0.033

Ne običajna porazdelitev, Spearman r = 0.0013

Pokažite samo rezultate > r = 0.033

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 0.0558	Šibko pozitivno 0.0311	Šibko negativno -0.0169	Šibko pozitivno 0.0917	Šibko pozitivno 0.0304	Šibko negativno -0.0128	Šibko negativno -0.1541
Answer 2	-	Šibko pozitivno 0.0229	Šibko negativno -0.0006	Šibko negativno -0.0443	Šibko pozitivno 0.0632	Šibko pozitivno 0.0453	Šibko pozitivno 0.0130	Šibko negativno -0.0942
Answer 3	-	Šibko negativno -0.0032	Šibko negativno -0.0122	Šibko negativno -0.0413	Šibko negativno -0.0464	Šibko pozitivno 0.0469	Šibko pozitivno 0.0786	Šibko negativno -0.0196
Answer 4	-	Šibko pozitivno 0.0437	Šibko pozitivno 0.0345	Šibko negativno -0.0196	Šibko pozitivno 0.0152	Šibko pozitivno 0.0307	Šibko pozitivno 0.0204	Šibko negativno -0.0981
Answer 5	-	Šibko pozitivno 0.0303	Šibko pozitivno 0.1280	Šibko pozitivno 0.0134	Šibko pozitivno 0.0733	Šibko negativno -0.0005	Šibko negativno -0.0203	Šibko negativno -0.1759
Answer 6	-	Šibko negativno -0.0003	Šibko pozitivno 0.0082	Šibko negativno -0.0630	Šibko negativno -0.0082	Šibko pozitivno 0.0195	Šibko pozitivno 0.0830	Šibko negativno -0.0315
Answer 7	-	Šibko pozitivno 0.0124	Šibko pozitivno 0.0382	Šibko negativno -0.0694	Šibko negativno -0.0241	Šibko pozitivno 0.0473	Šibko pozitivno 0.0641	Šibko negativno -0.0514
Answer 8	-	Šibko pozitivno 0.0696	Šibko pozitivno 0.0850	Šibko negativno -0.0333	Šibko pozitivno 0.0150	Šibko pozitivno 0.0346	Šibko pozitivno 0.0134	Šibko negativno -0.1364
Answer 9	-	Šibko pozitivno 0.0667	Šibko pozitivno 0.1676	Šibko pozitivno 0.0077	Šibko pozitivno 0.0694	Šibko negativno -0.0128	Šibko negativno -0.0517	Šibko negativno -0.1817
Answer 10	-	Šibko pozitivno 0.0780	Šibko pozitivno 0.0754	Šibko negativno -0.0211	Šibko pozitivno 0.0249	Šibko pozitivno 0.0347	Šibko negativno -0.0132	Šibko negativno -0.1303
Answer 11	-	Šibko pozitivno 0.0579	Šibko pozitivno 0.0528	Šibko negativno -0.0090	Šibko pozitivno 0.0083	Šibko pozitivno 0.0201	Šibko pozitivno 0.0308	Šibko negativno -0.1198
Answer 12	-	Šibko pozitivno 0.0389	Šibko pozitivno 0.1036	Šibko negativno -0.0362	Šibko pozitivno 0.0359	Šibko pozitivno 0.0255	Šibko pozitivno 0.0297	Šibko negativno -0.1521
Answer 13	-	Šibko pozitivno 0.0645	Šibko pozitivno 0.1041	Šibko negativno -0.0438	Šibko pozitivno 0.0262	Šibko pozitivno 0.0423	Šibko pozitivno 0.0174	Šibko negativno -0.1603
Answer 14	-	Šibko pozitivno 0.0710	Šibko pozitivno 0.1022	Šibko negativno -0.0015	Šibko negativno -0.0085	Šibko negativno -0.0006	Šibko pozitivno 0.0087	Šibko negativno -0.1169
Answer 15	-	Šibko pozitivno 0.0555	Šibko pozitivno 0.1365	Šibko negativno -0.0429	Šibko pozitivno 0.0179	Šibko negativno -0.0158	Šibko pozitivno 0.0223	Šibko negativno -0.1178
Answer 16	-	Šibko pozitivno 0.0591	Šibko pozitivno 0.0271	Šibko negativno -0.0384	Šibko negativno -0.0401	Šibko pozitivno 0.0655	Šibko pozitivno 0.0283	Šibko negativno -0.0709

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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 Pet Project Sdtest®

Valerii je bil leta 1993 kvalificiran kot socialni pedagog-psiholog in je od takrat uporabil svoje znanje pri upravljanju projektov.
Valerii je magistriral in kvalifikacijo projekta in vodje programa leta 2013. Med magistrskim programom se je seznanil s projektnim načrtom (GPM Deutsche Gesellschaft Für Projektmanagement e. V.) in spiralno dinamiko.
Valerii je opravil različne teste spiralne dinamike in svoje znanje in izkušnje uporabil za prilagoditev trenutne različice SDTest.
Valerii je avtor raziskovanja negotovosti V.U.C.A. Koncept z uporabo spiralne dinamike in matematične statistike v psihologiji, več kot 20 mednarodnih anket.

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