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 ng mga kumpanya na may kaugnayan sa mga tauhan sa nakaraang buwan (oo / hindi)

2) Mga aksyon ng mga kumpanya na may kaugnayan sa mga tauhan sa nakaraang buwan (katotohanan sa%)

3) Takot

4) Pinakamalaking problema na kinakaharap ng aking bansa

5) Anong mga katangian at kakayahan ang ginagamit ng mabubuting pinuno kapag nagtatayo ng matagumpay na koponan?

6) Google. Mga kadahilanan na nakakaapekto sa pagiging epektibo ng koponan

7) Ang pangunahing mga prayoridad ng mga naghahanap ng trabaho

8) Ano ang gumagawa ng isang boss na isang mahusay na pinuno?

9) Ano ang nagtatagumpay sa mga tao sa trabaho?

10) Handa ka na bang makatanggap ng mas kaunting suweldo upang gumana nang malayuan?

11) Mayroon bang Ageism?

12) Ageism sa karera

13) Ageism sa buhay

14) Mga Sanhi ng Ageism

15) Mga dahilan kung bakit sumuko ang mga tao (ni Anna Vital)

16) Tiwala (#WVS)

17) Oxford kaligayahan survey

18) Sikolohikal na kabutihan

19) Saan ang iyong susunod na pinaka -kapana -panabik na pagkakataon?

20) Ano ang gagawin mo sa linggong ito upang alagaan ang iyong kalusugan sa kaisipan?

21) Nabubuhay ako sa pag -iisip tungkol sa aking nakaraan, kasalukuyan o hinaharap

22) Meritocracy

23) Artipisyal na katalinuhan at pagtatapos ng sibilisasyon

24) Bakit nag -procrastinate ang mga tao?

25) Pagkakaiba ng kasarian sa pagbuo ng tiwala sa sarili (IFD Allensbach)

26) Xing.com Culture Assessment

27) Ang Limang Dysfunctions ng isang Koponan ni Patrick Lencioni

28) Ang empatiya ay ...

29) Ano ang mahalaga para sa mga espesyalista sa IT sa pagpili ng isang alok sa trabaho?

30) Bakit Nilalabanan ng Mga Tao ang Pagbabago (ni Siobhán McHale)

31) Paano mo maiayos ang iyong emosyon? (Ni Nawal Mustafa M.A.)

32) 21 mga kasanayan na magbabayad sa iyo magpakailanman (ni Jeremiah Teo / 赵汉昇)

33) Ang totoong kalayaan ay ...

34) 12 mga paraan upang mabuo ang tiwala sa iba (ni Justin Wright)

35) Mga Katangian ng isang Talentado na Empleyado (ng Talent Management Institute)

36) 10 mga susi sa pag -uudyok sa iyong koponan

37) Algebra of Conscience (ni Vladimir Lefebvre)

38) Tatlong Magkakaibang Posibilidad ng Hinaharap (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.

Takot

chart Ugnayan

VUCA

Kritikal ang halaga ng ugnayan koepisyent

Normal na pamamahagi, ni William Sealy Gosset (mag -aaral) r = 0.033

Hindi normal na pamamahagi, ni Spearman r = 0.0013

Ipakita lamang ang mga resulta > r = 0.033

Pamamahagi	Hindi normal	Hindi normal	Hindi normal	Normal	Normal	Normal	Normal	Normal
Lahat ng mga katanungan Lahat ng mga katanungan Ang pinakadakilang takot ko
Ang pinakadakilang takot ko
Answer 1	-	Mahina positibo 0.0559	Mahina positibo 0.0315	Mahina negatibo -0.0170	Mahina positibo 0.0920	Mahina positibo 0.0294	Mahina negatibo -0.0124	Mahina negatibo -0.1539
Answer 2	-	Mahina positibo 0.0229	Mahina negatibo -0.0002	Mahina negatibo -0.0448	Mahina positibo 0.0636	Mahina positibo 0.0445	Mahina positibo 0.0134	Mahina negatibo -0.0939
Answer 3	-	Mahina negatibo -0.0032	Mahina negatibo -0.0121	Mahina negatibo -0.0416	Mahina negatibo -0.0462	Mahina positibo 0.0466	Mahina positibo 0.0788	Mahina negatibo -0.0195
Answer 4	-	Mahina positibo 0.0438	Mahina positibo 0.0348	Mahina negatibo -0.0195	Mahina positibo 0.0153	Mahina positibo 0.0300	Mahina positibo 0.0207	Mahina negatibo -0.0980
Answer 5	-	Mahina positibo 0.0304	Mahina positibo 0.1282	Mahina positibo 0.0135	Mahina positibo 0.0734	Mahina negatibo -0.0013	Mahina negatibo -0.0200	Mahina negatibo -0.1757
Answer 6	-	Mahina negatibo -0.0002	Mahina positibo 0.0082	Mahina negatibo -0.0627	Mahina negatibo -0.0083	Mahina positibo 0.0193	Mahina positibo 0.0831	Mahina negatibo -0.0315
Answer 7	-	Mahina positibo 0.0126	Mahina positibo 0.0381	Mahina negatibo -0.0687	Mahina negatibo -0.0243	Mahina positibo 0.0469	Mahina positibo 0.0642	Mahina negatibo -0.0515
Answer 8	-	Mahina positibo 0.0698	Mahina positibo 0.0848	Mahina negatibo -0.0327	Mahina positibo 0.0148	Mahina positibo 0.0345	Mahina positibo 0.0134	Mahina negatibo -0.1365
Answer 9	-	Mahina positibo 0.0668	Mahina positibo 0.1676	Mahina positibo 0.0083	Mahina positibo 0.0693	Mahina negatibo -0.0131	Mahina negatibo -0.0516	Mahina negatibo -0.1818
Answer 10	-	Mahina positibo 0.0782	Mahina positibo 0.0753	Mahina negatibo -0.0204	Mahina positibo 0.0247	Mahina positibo 0.0342	Mahina negatibo -0.0131	Mahina negatibo -0.1304
Answer 11	-	Mahina positibo 0.0578	Mahina positibo 0.0532	Mahina negatibo -0.0096	Mahina positibo 0.0087	Mahina positibo 0.0195	Mahina positibo 0.0311	Mahina negatibo -0.1196
Answer 12	-	Mahina positibo 0.0390	Mahina positibo 0.1037	Mahina negatibo -0.0358	Mahina positibo 0.0358	Mahina positibo 0.0250	Mahina positibo 0.0299	Mahina negatibo -0.1520
Answer 13	-	Mahina positibo 0.0644	Mahina positibo 0.1048	Mahina negatibo -0.0448	Mahina positibo 0.0268	Mahina positibo 0.0417	Mahina positibo 0.0178	Mahina negatibo -0.1600
Answer 14	-	Mahina positibo 0.0712	Mahina positibo 0.1021	Mahina negatibo -0.0007	Mahina negatibo -0.0088	Mahina negatibo -0.0011	Mahina positibo 0.0088	Mahina negatibo -0.1169
Answer 15	-	Mahina positibo 0.0557	Mahina positibo 0.1365	Mahina negatibo -0.0423	Mahina positibo 0.0177	Mahina negatibo -0.0162	Mahina positibo 0.0224	Mahina negatibo -0.1179
Answer 16	-	Mahina positibo 0.0591	Mahina positibo 0.0273	Mahina negatibo -0.0386	Mahina negatibo -0.0400	Mahina positibo 0.0653	Mahina positibo 0.0284	Mahina negatibo -0.0708

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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

May -ari ng Produkto SaaS Pet Project Sdtest®

Si Valerii ay kwalipikado bilang isang panlipunang pedagogue-psychologist noong 1993 at mula nang inilapat ang kanyang kaalaman sa pamamahala ng proyekto.
Nakuha ni Valerii ang isang Master's Degree at ang Project and Program Manager Qualification noong 2013. Sa panahon ng kanyang programa ng Master, naging pamilyar siya sa Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) at Spiral Dynamics.
Kinuha ni Valerii ang iba't ibang mga pagsubok sa dinamika ng spiral at ginamit ang kanyang kaalaman at karanasan upang iakma ang kasalukuyang bersyon ng Sdtest.
Si Valerii ay may -akda ng paggalugad ng kawalan ng katiyakan ng V.U.C.A. Konsepto gamit ang mga spiral dinamika at istatistika ng matematika sa sikolohiya, higit sa 20 internasyonal na botohan.

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