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 0.0524	Slabo pozitívne 0.0258	Slabý negatívny -0.0180	Slabo pozitívne 0.0949	Slabo pozitívne 0.0355	Slabý negatívny -0.0146	Slabý negatívny -0.1537
Answer 2	-	Slabo pozitívne 0.0175	Slabý negatívny -0.0058	Slabý negatívny -0.0387	Slabo pozitívne 0.0669	Slabo pozitívne 0.0494	Slabo pozitívne 0.0116	Slabý negatívny -0.0969
Answer 3	-	Slabý negatívny -0.0035	Slabý negatívny -0.0091	Slabý negatívny -0.0441	Slabý negatívny -0.0435	Slabo pozitívne 0.0477	Slabo pozitívne 0.0747	Slabý negatívny -0.0199
Answer 4	-	Slabo pozitívne 0.0412	Slabo pozitívne 0.0255	Slabý negatívny -0.0229	Slabo pozitívne 0.0192	Slabo pozitívne 0.0353	Slabo pozitívne 0.0246	Slabý negatívny -0.0990
Answer 5	-	Slabo pozitívne 0.0227	Slabo pozitívne 0.1271	Slabo pozitívne 0.0109	Slabo pozitívne 0.0770	Slabý negatívny -0.0005	Slabý negatívny -0.0175	Slabý negatívny -0.1774
Answer 6	-	Slabý negatívny -0.0055	Slabo pozitívne 0.0042	Slabý negatívny -0.0622	Slabý negatívny -0.0080	Slabo pozitívne 0.0249	Slabo pozitívne 0.0863	Slabý negatívny -0.0354
Answer 7	-	Slabo pozitívne 0.0084	Slabo pozitívne 0.0331	Slabý negatívny -0.0656	Slabý negatívny -0.0297	Slabo pozitívne 0.0523	Slabo pozitívne 0.0696	Slabý negatívny -0.0522
Answer 8	-	Slabo pozitívne 0.0629	Slabo pozitívne 0.0710	Slabý negatívny -0.0267	Slabo pozitívne 0.0130	Slabo pozitívne 0.0379	Slabo pozitívne 0.0184	Slabý negatívny -0.1339
Answer 9	-	Slabo pozitívne 0.0711	Slabo pozitívne 0.1602	Slabo pozitívne 0.0072	Slabo pozitívne 0.0643	Slabý negatívny -0.0106	Slabý negatívny -0.0484	Slabý negatívny -0.1819
Answer 10	-	Slabo pozitívne 0.0740	Slabo pozitívne 0.0656	Slabý negatívny -0.0150	Slabo pozitívne 0.0292	Slabo pozitívne 0.0321	Slabý negatívny -0.0123	Slabý negatívny -0.1359
Answer 11	-	Slabo pozitívne 0.0629	Slabo pozitívne 0.0524	Slabý negatívny -0.0098	Slabo pozitívne 0.0104	Slabo pozitívne 0.0253	Slabo pozitívne 0.0247	Slabý negatívny -0.1270
Answer 12	-	Slabo pozitívne 0.0433	Slabo pozitívne 0.0921	Slabý negatívny -0.0338	Slabo pozitívne 0.0335	Slabo pozitívne 0.0331	Slabo pozitívne 0.0257	Slabý negatívny -0.1540
Answer 13	-	Slabo pozitívne 0.0687	Slabo pozitívne 0.0957	Slabý negatívny -0.0396	Slabo pozitívne 0.0304	Slabo pozitívne 0.0408	Slabo pozitívne 0.0151	Slabý negatívny -0.1630
Answer 14	-	Slabo pozitívne 0.0781	Slabo pozitívne 0.0884	Slabý negatívny -0.0003	Slabý negatívny -0.0096	Slabo pozitívne 0.0050	Slabo pozitívne 0.0138	Slabý negatívny -0.1228
Answer 15	-	Slabo pozitívne 0.0539	Slabo pozitívne 0.1269	Slabý negatívny -0.0339	Slabo pozitívne 0.0148	Slabý negatívny -0.0172	Slabo pozitívne 0.0237	Slabý negatívny -0.1160
Answer 16	-	Slabo pozitívne 0.0690	Slabo pozitívne 0.0248	Slabý negatívny -0.0372	Slabý negatívny -0.0385	Slabo pozitívne 0.0703	Slabo pozitívne 0.0205	Slabý negatívny -0.0792

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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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