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)

39) Mga Pagkilos upang Bumuo ng Hindi Natitinag na Tiwala sa Sarili (ni 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.

Takot

chart Ugnayan

VUCA

Kritikal ang halaga ng ugnayan koepisyent

Normal na pamamahagi, ni William Sealy Gosset (mag -aaral) r = 0.0318

Hindi normal na pamamahagi, ni Spearman r = 0.0013

Ipakita lamang ang mga resulta > r = 0.0318

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 0.0526	Mahina positibo 0.0260	Mahina negatibo -0.0183	Mahina positibo 0.0946	Mahina positibo 0.0358	Mahina negatibo -0.0143	Mahina negatibo -0.1540
Answer 2	-	Mahina positibo 0.0175	Mahina negatibo -0.0058	Mahina negatibo -0.0388	Mahina positibo 0.0668	Mahina positibo 0.0496	Mahina positibo 0.0117	Mahina negatibo -0.0970
Answer 3	-	Mahina negatibo -0.0035	Mahina negatibo -0.0091	Mahina negatibo -0.0441	Mahina negatibo -0.0435	Mahina positibo 0.0478	Mahina positibo 0.0747	Mahina negatibo -0.0200
Answer 4	-	Mahina positibo 0.0414	Mahina positibo 0.0257	Mahina negatibo -0.0232	Mahina positibo 0.0188	Mahina positibo 0.0356	Mahina positibo 0.0249	Mahina negatibo -0.0993
Answer 5	-	Mahina positibo 0.0226	Mahina positibo 0.1270	Mahina positibo 0.0111	Mahina positibo 0.0773	Mahina negatibo -0.0008	Mahina negatibo -0.0177	Mahina negatibo -0.1772
Answer 6	-	Mahina negatibo -0.0057	Mahina positibo 0.0040	Mahina negatibo -0.0620	Mahina negatibo -0.0076	Mahina positibo 0.0246	Mahina positibo 0.0860	Mahina negatibo -0.0351
Answer 7	-	Mahina positibo 0.0082	Mahina positibo 0.0329	Mahina negatibo -0.0653	Mahina negatibo -0.0294	Mahina positibo 0.0519	Mahina positibo 0.0693	Mahina negatibo -0.0520
Answer 8	-	Mahina positibo 0.0627	Mahina positibo 0.0709	Mahina negatibo -0.0265	Mahina positibo 0.0134	Mahina positibo 0.0376	Mahina positibo 0.0181	Mahina negatibo -0.1337
Answer 9	-	Mahina positibo 0.0710	Mahina positibo 0.1600	Mahina positibo 0.0074	Mahina positibo 0.0646	Mahina negatibo -0.0109	Mahina negatibo -0.0487	Mahina negatibo -0.1817
Answer 10	-	Mahina positibo 0.0739	Mahina positibo 0.0654	Mahina negatibo -0.0147	Mahina positibo 0.0296	Mahina positibo 0.0318	Mahina negatibo -0.0126	Mahina negatibo -0.1357
Answer 11	-	Mahina positibo 0.0627	Mahina positibo 0.0522	Mahina negatibo -0.0096	Mahina positibo 0.0108	Mahina positibo 0.0250	Mahina positibo 0.0244	Mahina negatibo -0.1268
Answer 12	-	Mahina positibo 0.0431	Mahina positibo 0.0920	Mahina negatibo -0.0336	Mahina positibo 0.0339	Mahina positibo 0.0327	Mahina positibo 0.0254	Mahina negatibo -0.1537
Answer 13	-	Mahina positibo 0.0685	Mahina positibo 0.0956	Mahina negatibo -0.0394	Mahina positibo 0.0308	Mahina positibo 0.0405	Mahina positibo 0.0148	Mahina negatibo -0.1628
Answer 14	-	Mahina positibo 0.0779	Mahina positibo 0.0883	Mahina negatibo -0.0001	Mahina negatibo -0.0092	Mahina positibo 0.0046	Mahina positibo 0.0135	Mahina negatibo -0.1225
Answer 15	-	Mahina positibo 0.0537	Mahina positibo 0.1267	Mahina negatibo -0.0337	Mahina positibo 0.0152	Mahina negatibo -0.0175	Mahina positibo 0.0234	Mahina negatibo -0.1158
Answer 16	-	Mahina positibo 0.0689	Mahina positibo 0.0247	Mahina negatibo -0.0371	Mahina negatibo -0.0383	Mahina positibo 0.0702	Mahina positibo 0.0203	Mahina negatibo -0.0791

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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 SDTEST®

Si Valerii ay kwalipikado bilang isang social pedagogue-psychologist noong 1993 at mula noon ay inilapat ang kanyang kaalaman sa pamamahala ng proyekto.
Nakakuha si Valerii ng Master's degree at ang project at program manager qualification noong 2013. Sa panahon ng kanyang Master's program, naging pamilyar siya sa Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) at Spiral Dynamics.
Si Valerii ang may-akda ng paggalugad sa kawalan ng katiyakan ng V.U.C.A. konsepto gamit ang Spiral Dynamics at mathematical statistics sa psychology, at 38 international poll.

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