Panimalay/Balabag/Mathematical Psychology

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) Mga aksyon sa mga kompanya nga may kalabutan sa mga kawani sa miaging bulan (oo / dili)

2) Mga aksyon sa mga kompanya nga may kalabutan sa mga kawani sa miaging bulan (kamatuoran sa%)

3) Gikahadlokan

4) Labing dako nga mga problema nga giatubang sa akong nasud

5) Unsang mga hiyas ug katakos ang gigamit sa maayong mga lider sa pagtukod sa malampuson nga mga koponan?

6) Google. Mga hinungdan nga nakaapekto sa tim nga pagkaayo

7) Ang nag-unang mga prayoridad sa mga nangita sa trabaho

8) Unsa man ang naghimo sa usa ka boss nga usa ka maayo nga lider?

9) Unsa man ang naghimo sa mga tawo nga malampuson sa trabaho?

10) Andam ka ba nga makadawat gamay nga bayad aron magtrabaho nga layo?

11) Adunay ba ang edad?

12) Ageism sa karera

13) Ageism sa kinabuhi

14) Mga Hinungdan sa Ageismo

15) Mga hinungdan ngano nga ang mga tawo mihunong (ni Anna hinungdanon)

16) Mosalig (#WVS)

17) Surbey sa Kalipay sa Oxford

18) Psychological Wellbeing

19) Asa ang imong sunod nga labing kulbahinam nga oportunidad?

20) Unsa man ang imong buhaton karong semanaha aron maatiman ang imong kahimsog sa pangisip?

21) Nagpuyo ko nga naghunahuna sa akong nangagi, karon o sa umaabot

22) Meritocracy

23) Artipisyal nga salabutan ug ang katapusan sa sibilisasyon

24) Ngano nga ang mga tawo nag-procrastinate?

25) Pagkalainlain sa Gender sa Pagtukod sa Kaugalingon nga Pagsalig (IFD Allensbach)

26) Xing.com Pag-asayn sa Kultura

27) Patrick Lencioni's "Ang Lima nga Dysfunction sa usa ka Team"

28) Empatiya ...

29) Unsa ang hinungdanon alang sa mga espesyalista sa pagpili sa usa ka tanyag sa trabaho?

30) Ngano nga Batok sa mga Tawo ang Pagbag-o (ni Siobhán MCHALE)

31) Giunsa nimo pag-regulate ang imong emosyon? (ni Nawal Mustafa M.a.)

32) 21 Mga Kahanas nga Nagabayad Kanimo sa Kahangturan (ni Jeremiah Teo / 赵汉昇)

33) Tinuod nga Kagawasan ang ...

34) 12 Mga Paagi Aron Mabuhat ang Pagsalig sa Uban (Ni Justin Wright)

35) Mga Kinaiya sa usa ka Talento nga Empleyado (pinaagi sa Talent Management Institute)

36) 10 mga yawi sa pagdasig sa imong team

37) Algebra of Conscience (ni Vladimir Lefebvre)

38) Tulo ka Lahi nga Posibilidad sa Umaabot (ni 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.

Gikahadlokan

tsart Correlation

VUCA

Critical bili sa correlation coefficient

Kasagaran nga pag-apod-apod, ni William Sedy Gosset (Estudyante) r = 0.0329

Dili normal nga pag-apod-apod, pinaagi sa Spearman r = 0.0013

Ipakita ang mga resulta > r = 0.0329

Pag-apod-apod	Dili normal	Dili normal	Dili normal	Kasagaran	Kasagaran	Kasagaran	Kasagaran	Kasagaran
Tanan nga mga pangutana Tanan nga mga pangutana Ang akong labing dako nga kahadlok mao ang
Ang akong labing dako nga kahadlok mao ang
Answer 1	-	Maluya nga positibo 0.0566	Maluya nga positibo 0.0332	Naluya nga negatibo -0.0170	Maluya nga positibo 0.0912	Maluya nga positibo 0.0308	Naluya nga negatibo -0.0153	Naluya nga negatibo -0.1537
Answer 2	-	Maluya nga positibo 0.0223	Maluya nga positibo 0.0011	Naluya nga negatibo -0.0442	Maluya nga positibo 0.0639	Maluya nga positibo 0.0464	Maluya nga positibo 0.0120	Naluya nga negatibo -0.0960
Answer 3	-	Naluya nga negatibo -0.0031	Naluya nga negatibo -0.0104	Naluya nga negatibo -0.0407	Naluya nga negatibo -0.0463	Maluya nga positibo 0.0475	Maluya nga positibo 0.0779	Naluya nga negatibo -0.0213
Answer 4	-	Maluya nga positibo 0.0437	Maluya nga positibo 0.0357	Naluya nga negatibo -0.0197	Maluya nga positibo 0.0161	Maluya nga positibo 0.0311	Maluya nga positibo 0.0187	Naluya nga negatibo -0.0987
Answer 5	-	Maluya nga positibo 0.0296	Maluya nga positibo 0.1300	Maluya nga positibo 0.0124	Maluya nga positibo 0.0749	Maluya nga positibo 0.0014	Naluya nga negatibo -0.0231	Naluya nga negatibo -0.1771
Answer 6	-	Naluya nga negatibo -0.0008	Maluya nga positibo 0.0090	Naluya nga negatibo -0.0613	Naluya nga negatibo -0.0070	Maluya nga positibo 0.0196	Maluya nga positibo 0.0803	Naluya nga negatibo -0.0321
Answer 7	-	Maluya nga positibo 0.0118	Maluya nga positibo 0.0401	Naluya nga negatibo -0.0693	Naluya nga negatibo -0.0246	Maluya nga positibo 0.0471	Maluya nga positibo 0.0623	Naluya nga negatibo -0.0505
Answer 8	-	Maluya nga positibo 0.0697	Maluya nga positibo 0.0875	Naluya nga negatibo -0.0316	Maluya nga positibo 0.0155	Maluya nga positibo 0.0346	Maluya nga positibo 0.0098	Naluya nga negatibo -0.1373
Answer 9	-	Maluya nga positibo 0.0679	Maluya nga positibo 0.1707	Maluya nga positibo 0.0105	Maluya nga positibo 0.0676	Naluya nga negatibo -0.0138	Naluya nga negatibo -0.0545	Naluya nga negatibo -0.1821
Answer 10	-	Maluya nga positibo 0.0793	Maluya nga positibo 0.0772	Naluya nga negatibo -0.0208	Maluya nga positibo 0.0242	Maluya nga positibo 0.0343	Naluya nga negatibo -0.0152	Naluya nga negatibo -0.1300
Answer 11	-	Maluya nga positibo 0.0590	Maluya nga positibo 0.0559	Naluya nga negatibo -0.0071	Maluya nga positibo 0.0082	Maluya nga positibo 0.0205	Maluya nga positibo 0.0266	Naluya nga negatibo -0.1213
Answer 12	-	Maluya nga positibo 0.0405	Maluya nga positibo 0.1050	Naluya nga negatibo -0.0363	Maluya nga positibo 0.0361	Maluya nga positibo 0.0253	Maluya nga positibo 0.0277	Naluya nga negatibo -0.1522
Answer 13	-	Maluya nga positibo 0.0655	Maluya nga positibo 0.1056	Naluya nga negatibo -0.0439	Maluya nga positibo 0.0270	Maluya nga positibo 0.0417	Maluya nga positibo 0.0152	Naluya nga negatibo -0.1601
Answer 14	-	Maluya nga positibo 0.0728	Maluya nga positibo 0.1049	Naluya nga negatibo -0.0002	Naluya nga negatibo -0.0088	Naluya nga negatibo -0.0007	Maluya nga positibo 0.0061	Naluya nga negatibo -0.1187
Answer 15	-	Maluya nga positibo 0.0561	Maluya nga positibo 0.1378	Naluya nga negatibo -0.0415	Maluya nga positibo 0.0178	Naluya nga negatibo -0.0162	Maluya nga positibo 0.0194	Naluya nga negatibo -0.1176
Answer 16	-	Maluya nga positibo 0.0606	Maluya nga positibo 0.0308	Naluya nga negatibo -0.0348	Naluya nga negatibo -0.0421	Maluya nga positibo 0.0642	Maluya nga positibo 0.0250	Naluya nga negatibo -0.0717

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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 Kesenko

Tag-iya sa Produkto SaaS SDTEST®

Si Valerii kuwalipikado isip usa ka social pedagogue-psychologist niadtong 1993 ug sukad niadto migamit sa iyang kahibalo sa pagdumala sa proyekto.
Nakakuha si Valerii og Master's degree ug ang kwalipikasyon sa project ug program manager sa 2013. Atol sa iyang Master's program, nasinati niya ang Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) ug Spiral Dynamics.
Si Valerii ang tagsulat sa pagsuhid sa kawalay kasiguruhan sa V.U.C.A. konsepto gamit ang Spiral Dynamics ug mathematical statistics sa psychology, ug 38 international polls.

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