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) Akcie spoločností vo vzťahu k personálu za posledný mesiac (áno / nie)

2) Akcie spoločností vo vzťahu k personálu v poslednom mesiaci (fakt v%)

3) Obávať

4) Najväčšie problémy, ktorým čelí moja krajina

5) Aké vlastnosti a schopnosti používajú dobrí vodcovia pri budovaní úspešných tímov?

6) Google. Faktory, ktoré ovplyvňujú efektívnosť tímu

7) Hlavné priority uchádzačov o zamestnanie

8) Čo robí šéfa skvelým vodcom?

9) Čo robí ľudí úspešnými v práci?

10) Ste pripravení na diaľku dostávať menej mzdy za prácu?

11) Existuje ageizmus?

12) Ageizmus v kariére

13) Ageizmus v živote

14) Príčiny ageizmu

15) Dôvody, prečo sa ľudia vzdávajú (Anna Vital)

16) Dôverovať (#WVS)

17) Prieskum o šťastí v Oxforde

18) Psychologický blahobyt

19) Kde by bola vaša ďalšia najzaujímavejšia príležitosť?

20) Čo urobíte tento týždeň, aby ste sa starali o svoje duševné zdravie?

21) Žijem premýšľam o svojej minulosti, prítomnosti alebo budúcnosti

22) Meritokracia

23) Umelá inteligencia a koniec civilizácie

24) Prečo ľudia odkladajú?

25) Rodové rozdiely v budovaní sebavedomia (IFD Allensbach)

26) Xing.com Hodnotenie kultúry

27) „Päť dysfunkcií tímu Patricka Lencioniho“

28) Empatia je ...

29) Čo je nevyhnutné pre IT špecialistov pri výbere ponuky práce?

30) Prečo ľudia odolávajú zmenám (od Siobhán McHale)

31) Ako regulujete svoje emócie? (Autor: Nawal Mustafa M.A.)

32) 21 zručností, ktoré vám platia navždy (od Jeremiáša Teo / 赵汉昇)

33) Skutočná sloboda je ...

34) 12 spôsobov, ako vybudovať dôveru s ostatnými (Justin Wright)

35) Charakteristiky talentovaného zamestnanca (Inštitút riadenia talentov)

36) 10 kľúčov k motivácii vášho tímu

37) Algebra svedomia (Vladimír Lefebvre)

38) Tri odlišné možnosti budúcnosti (Dr. Clare W. Graves)

39) Akcie na vybudovanie neotrasiteľnej sebadôvery (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.

Obávať

grafy Korelácia

VUCA

Kritická hodnota korelačného koeficientu

Normálne rozdelenie, od Williama Sealyho Gosset (študent) r = 0.0318

Normálne rozdelenie, Spearman r = 0.0013

Zobraziť iba výsledky > r = 0.0318

Distribúcia	Nekonečný	Nekonečný	Nekonečný	Normálny	Normálny	Normálny	Normálny	Normálny
Všetky otázky Všetky otázky Môj najväčší strach je
Môj najväčší strach je
Answer 1	-	Slabo pozitívne 0.0546	Slabo pozitívne 0.0291	Slabý negatívny -0.0174	Slabo pozitívne 0.0940	Slabo pozitívne 0.0348	Slabý negatívny -0.0152	Slabý negatívny -0.1554
Answer 2	-	Slabo pozitívne 0.0189	Slabý negatívny -0.0048	Slabý negatívny -0.0401	Slabo pozitívne 0.0658	Slabo pozitívne 0.0496	Slabo pozitívne 0.0122	Slabý negatívny -0.0981
Answer 3	-	Slabý negatívny -0.0017	Slabý negatívny -0.0085	Slabý negatívny -0.0455	Slabý negatívny -0.0447	Slabo pozitívne 0.0486	Slabo pozitívne 0.0747	Slabý negatívny -0.0193
Answer 4	-	Slabo pozitívne 0.0419	Slabo pozitívne 0.0279	Slabý negatívny -0.0240	Slabo pozitívne 0.0179	Slabo pozitívne 0.0357	Slabo pozitívne 0.0245	Slabý negatívny -0.0993
Answer 5	-	Slabo pozitívne 0.0268	Slabo pozitívne 0.1300	Slabo pozitívne 0.0098	Slabo pozitívne 0.0766	Slabo pozitívne 0.0004	Slabý negatívny -0.0175	Slabý negatívny -0.1790
Answer 6	-	Slabý negatívny -0.0033	Slabo pozitívne 0.0054	Slabý negatívny -0.0629	Slabý negatívny -0.0092	Slabo pozitívne 0.0253	Slabo pozitívne 0.0867	Slabý negatívny -0.0350
Answer 7	-	Slabo pozitívne 0.0099	Slabo pozitívne 0.0345	Slabý negatívny -0.0669	Slabý negatívny -0.0312	Slabo pozitívne 0.0528	Slabo pozitívne 0.0697	Slabý negatívny -0.0520
Answer 8	-	Slabo pozitívne 0.0632	Slabo pozitívne 0.0735	Slabý negatívny -0.0283	Slabo pozitívne 0.0143	Slabo pozitívne 0.0377	Slabo pozitívne 0.0180	Slabý negatívny -0.1342
Answer 9	-	Slabo pozitívne 0.0731	Slabo pozitívne 0.1624	Slabo pozitívne 0.0060	Slabo pozitívne 0.0639	Slabý negatívny -0.0102	Slabý negatívny -0.0481	Slabý negatívny -0.1814
Answer 10	-	Slabo pozitívne 0.0749	Slabo pozitívne 0.0681	Slabý negatívny -0.0133	Slabo pozitívne 0.0285	Slabo pozitívne 0.0335	Slabý negatívny -0.0110	Slabý negatívny -0.1340
Answer 11	-	Slabo pozitívne 0.0624	Slabo pozitívne 0.0537	Slabý negatívny -0.0091	Slabo pozitívne 0.0106	Slabo pozitívne 0.0239	Slabo pozitívne 0.0260	Slabý negatívny -0.1260
Answer 12	-	Slabo pozitívne 0.0438	Slabo pozitívne 0.0947	Slabý negatívny -0.0347	Slabo pozitívne 0.0335	Slabo pozitívne 0.0341	Slabo pozitívne 0.0267	Slabý negatívny -0.1538
Answer 13	-	Slabo pozitívne 0.0705	Slabo pozitívne 0.0964	Slabý negatívny -0.0397	Slabo pozitívne 0.0294	Slabo pozitívne 0.0421	Slabo pozitívne 0.0149	Slabý negatívny -0.1635
Answer 14	-	Slabo pozitívne 0.0787	Slabo pozitívne 0.0912	Slabý negatívny -0.0031	Slabý negatívny -0.0091	Slabo pozitívne 0.0050	Slabo pozitívne 0.0143	Slabý negatívny -0.1230
Answer 15	-	Slabo pozitívne 0.0535	Slabo pozitívne 0.1285	Slabý negatívny -0.0352	Slabo pozitívne 0.0145	Slabý negatívny -0.0166	Slabo pozitívne 0.0246	Slabý negatívny -0.1163
Answer 16	-	Slabo pozitívne 0.0698	Slabo pozitívne 0.0267	Slabý negatívny -0.0375	Slabý negatívny -0.0378	Slabo pozitívne 0.0701	Slabo pozitívne 0.0209	Slabý negatívny -0.0793

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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

Vlastník produktu SaaS SDTEST®

Valerii získal kvalifikáciu sociálneho pedagóga-psychológa v roku 1993 a odvtedy svoje znalosti uplatňuje v projektovom manažmente.
Valerii získal magisterský titul a kvalifikáciu projektového a programového manažéra v roku 2013. Počas magisterského štúdia sa zoznámil s Plánom projektu (GPM Deutsche Gesellschaft für Projektmanagement e. V.) a Špirálovou dynamikou.
Valerii je autorom skúmania neistoty V.U.C.A. koncept využívajúci špirálovú dynamiku a matematickú štatistiku v psychológii a 38 medzinárodných prieskumov verejnej mienky.

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