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) ባለፈው ወር ከሠራተኞች ጋር በተያያዘ የኩባንያዎች እርምጃዎች (አዎ / አይ)

2) ባለፈው ወር ከሠራተኞች ጋር በተያያዘ የኩባንያዎች እርምጃዎች (በእውነቱ በ%)

3) ፍራቻዎች

4) በአገሬ ፊት ለፊት ትልቁ ችግሮች

5) ስኬታማ ቡድኖችን በሚገነቡበት ጊዜ ጥሩ መሪዎች ምን ዓይነት መመሪያዎች እና ችሎታ ይጠቀማሉ?

6) ጉግል. የቡድን ውጤታማነት ላይ ተጽዕኖ የሚያሳድሩ ምክንያቶች

7) የስራ ፈላጊዎች ዋና ዋና ጉዳዮች

8) አለቃ ታላቅ መሪ የሚያደርገው ምንድን ነው?

9) ሰዎች በሥራ ላይ ስኬታማ የሚያደርጉት ምንድን ነው?

10) በርቀት ለመስራት አነስተኛ ክፍያ ለመቀበል ዝግጁ ነዎት?

11) አሃድኒዝም አለ?

12) በሙያ ውስጥ ያለው አማካይነት

13) ሕይወት በህይወት ውስጥ

14) የአካላዊ ምክንያቶች

15) ሰዎች ተስፋ እንዲቆርጡ የሚያደርጉ ምክንያቶች (አና አና አስፈላጊ)

16) መተማመን (#WVS)

17) ኦክስፎርድ ደስታ ጥናት

18) ሥነ ልቦናዊ ደህንነት

19) የሚቀጥለው በጣም አስደሳች አጋጣሚዎ የት ይኖራል?

20) የአእምሮ ጤንነትዎን ለመንከባከብ በዚህ ሳምንት ምን ያደርጋሉ?

21) እኔ ያለኝን ያለፈውን, የአሁኑ ወይም የወደፊቱ ማሰብ ነው

22) መሬታዊነት

23) ሰው ሰራሽ የማሰብ ችሎታ እና ስልጣኔ መጨረሻ

24) ሰዎች ዛሬ ነገረው የሚሉት ለምንድን ነው?

25) የሥርዓተ- gender ታ ልዩነት በራስ መተማመንን በመገንባት (IFD Aldsabach)

26) Xing.com የኮም አገልግሎት ግምገማ

27) ፓትሪክ ሌንኪዮ "አምስት የቡድን ዲስኮች"

28) የሌላውን ችግር መረዳዳት ነው ...

29) የሥራ አቅርቦትን በመምረጥ ረገድ ልዩ ባለሙያተኞች ምን አስፈላጊ ነገር አለ?

30) ለምን ሰዎች ለውጥን የሚቃወሙበት ምክንያት (በ Sibhánn Mchare)

31) ስሜትዎን እንዴት ይቆጣጠራሉ? (በ NAWAN SUNAFAFA.A.)

32) 21 ለዘላለም የሚከፍሉዎት 21 ችሎታዎች (በኤርሚያስ TEO / 赵汉昇)

33) እውነተኛ ነፃነት ...

34) ከሌሎች ጋር መተማመንን የሚገነቡበት 12 መንገዶች (ጀስቲን ዌም)

35) የታካሚ ሠራተኛ ባህሪያትን (ችሎታ ያለው አስተዳደር ተቋም)

36) ቡድንዎን ለማነቃቃት 10 ቁልፍ

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.

ፍራቻዎች

ሠንጠረዦች ትሰስር

VUCA

የ ትሰስር የጠቋሚ የሚተቹ ዋጋ

መደበኛ ስርጭት, ዊሊያምስ በዊሊያም ጎሳዎች (ተማሪ) r = 0.0353

መደበኛ ያልሆነ ስርጭት, በፓርቲው r = 0.0014

ውጤቶችን ብቻ ያሳዩ > r = 0.0353

ስርጭት	መደበኛ ያልሆነ	መደበኛ	መደበኛ ያልሆነ	መደበኛ	መደበኛ	መደበኛ	መደበኛ	መደበኛ
ሁሉም ጥያቄዎች ሁሉም ጥያቄዎች የእኔ ትልቁ ፍርሃት ነው
የእኔ ትልቁ ፍርሃት ነው
Answer 1	-	ደካማ አዎንታዊ 0.0297	ደካማ አዎንታዊ 0.0298	ደካማ አሉታዊ -0.0106	ደካማ አዎንታዊ 0.0970	ደካማ አዎንታዊ 0.0325	ደካማ አሉታዊ -0.0019	ደካማ አሉታዊ -0.1558
Answer 2	-	ደካማ አዎንታዊ 0.0188	ደካማ አዎንታዊ 0.0076	ደካማ አሉታዊ -0.0360	ደካማ አዎንታዊ 0.0711	ደካማ አዎንታዊ 0.0387	ደካማ አዎንታዊ 0.0082	ደካማ አሉታዊ -0.1011
Answer 3	-	ደካማ አዎንታዊ 0.0026	ደካማ አሉታዊ -0.0170	ደካማ አሉታዊ -0.0443	ደካማ አሉታዊ -0.0458	ደካማ አዎንታዊ 0.0547	ደካማ አዎንታዊ 0.0808	ደካማ አሉታዊ -0.0270
Answer 4	-	ደካማ አዎንታዊ 0.0332	ደካማ አዎንታዊ 0.0285	ደካማ አሉታዊ -0.0006	ደካማ አዎንታዊ 0.0155	ደካማ አዎንታዊ 0.0276	ደካማ አዎንታዊ 0.0105	ደካማ አሉታዊ -0.0917
Answer 5	-	ደካማ አዎንታዊ 0.0122	ደካማ አዎንታዊ 0.1193	ደካማ አዎንታዊ 0.0095	ደካማ አዎንታዊ 0.0721	ደካማ አዎንታዊ 0.0057	ደካማ አሉታዊ -0.0083	ደካማ አሉታዊ -0.1687
Answer 6	-	ደካማ አዎንታዊ 0.0044	ደካማ አዎንታዊ 0.0005	ደካማ አሉታዊ -0.0582	ደካማ አሉታዊ -0.0004	ደካማ አዎንታዊ 0.0210	ደካማ አዎንታዊ 0.0830	ደካማ አሉታዊ -0.0418
Answer 7	-	ደካማ አዎንታዊ 0.0242	ደካማ አዎንታዊ 0.0368	ደካማ አሉታዊ -0.0521	ደካማ አሉታዊ -0.0234	ደካማ አዎንታዊ 0.0403	ደካማ አዎንታዊ 0.0568	ደካማ አሉታዊ -0.0597
Answer 8	-	ደካማ አዎንታዊ 0.0707	ደካማ አዎንታዊ 0.0781	ደካማ አሉታዊ -0.0244	ደካማ አዎንታዊ 0.0140	ደካማ አዎንታዊ 0.0303	ደካማ አዎንታዊ 0.0137	ደካማ አሉታዊ -0.1334
Answer 9	-	ደካማ አዎንታዊ 0.0564	ደካማ አዎንታዊ 0.1531	ደካማ አዎንታዊ 0.0127	ደካማ አዎንታዊ 0.0769	ደካማ አሉታዊ -0.0136	ደካማ አሉታዊ -0.0495	ደካማ አሉታዊ -0.1752
Answer 10	-	ደካማ አዎንታዊ 0.0711	ደካማ አዎንታዊ 0.0700	ደካማ አሉታዊ -0.0127	ደካማ አዎንታዊ 0.0246	ደካማ አዎንታዊ 0.0363	ደካማ አሉታዊ -0.0156	ደካማ አሉታዊ -0.1273
Answer 11	-	ደካማ አዎንታዊ 0.0542	ደካማ አዎንታዊ 0.0488	ደካማ አዎንታዊ 0.0086	ደካማ አዎንታዊ 0.0078	ደካማ አዎንታዊ 0.0162	ደካማ አዎንታዊ 0.0315	ደካማ አሉታዊ -0.1248
Answer 12	-	ደካማ አዎንታዊ 0.0281	ደካማ አዎንታዊ 0.0929	ደካማ አሉታዊ -0.0325	ደካማ አዎንታዊ 0.0361	ደካማ አዎንታዊ 0.0276	ደካማ አዎንታዊ 0.0365	ደካማ አሉታዊ -0.1482
Answer 13	-	ደካማ አዎንታዊ 0.0643	ደካማ አዎንታዊ 0.0916	ደካማ አሉታዊ -0.0418	ደካማ አዎንታዊ 0.0237	ደካማ አዎንታዊ 0.0425	ደካማ አዎንታዊ 0.0239	ደካማ አሉታዊ -0.1558
Answer 14	-	ደካማ አዎንታዊ 0.0697	ደካማ አዎንታዊ 0.1017	ደካማ አዎንታዊ 0.0149	ደካማ አሉታዊ -0.0062	ደካማ አሉታዊ -0.0087	ደካማ አሉታዊ -0.0002	ደካማ አሉታዊ -0.1161
Answer 15	-	ደካማ አዎንታዊ 0.0603	ደካማ አዎንታዊ 0.1299	ደካማ አሉታዊ -0.0379	ደካማ አዎንታዊ 0.0163	ደካማ አሉታዊ -0.0091	ደካማ አዎንታዊ 0.0164	ደካማ አሉታዊ -0.1204
Answer 16	-	ደካማ አዎንታዊ 0.0691	ደካማ አዎንታዊ 0.0221	ደካማ አሉታዊ -0.0305	ደካማ አሉታዊ -0.0515	ደካማ አዎንታዊ 0.0750	ደካማ አዎንታዊ 0.0187	ደካማ አሉታዊ -0.0696

MS Excel ላክ

ይህ ተግባር በራስዎ VUCA ምርጫዎች ውስጥ ይገኛል።

እሺ

You can not only just create your poll in the ቁርጥ ዋጋ «V.U.C.A መስጫ ዲዛይነር» (with a unique link and your logo) but also you can earn money by selling its results in the ቁርጥ ዋጋ «የሕዝብ ቁጥር ሱቅ», as already the authors of polls.

If you participated in VUCA polls, you can see your results and compare them with the overall polls results, which are constantly growing, in your personal account after purchasing ቁርጥ ዋጋ «የእኔ SDT»

[1] https://twitter.com/wileyprof

[2] https://colinallen.dnsalias.org

[3] https://philpeople.org/profiles/colin-allen

2023.10.13

Valeri Kosenko

የምርት ባለቤት ሳባ ፔት ethret ፕሮጀክት SDTEST®

እ.ኤ.አ. በ 1993 ወደ ማህበራዊ ፔድጎግ-ሳይኮሎጂስት ብቁ ሆነች እናም በፕሮጀክት አስተዳደር ውስጥ እውቀቱን ተግባራዊ አደረጉ.
እ.ኤ.አ. በ 2013 የፕሮጀክት ዲግሪ እና የፕሮጀክቱ ሥራ አስኪያጅ በመሆን የፕሮጀክት ሥራን አግኝቷል.
Valerii የተለያዩ የችሎታ ተለዋዋጭ ምርመራዎችን ወስዶ የአሁኑን የ SDTEST ስሪቱን ለማስተካከል እውቀቱን እና ልምዱን ተጠቅሟል.
Valerii የ v.u.a.a ን እርግጠኛ አለመሆኑን የማሰስ ደራሲ ነው. ከ 20 ቱ ዓለም አቀፍ ምርጫዎች, በስነ-ልቦና የተሞላ ተለዋዋጭ ተለዋዋጭ እና የሂሳብ ስታቲስቲክስን በመጠቀም ፅንሰ-ሀሳብ.

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