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) Azzjonijiet ta 'kumpaniji b'rabta mal-persunal fl-aħħar xahar (iva / le)

2) Azzjonijiet ta 'kumpaniji fir-rigward ta' persunal fl-aħħar xahar (fatt f '%)

3) Biża '

4) L-ikbar problemi li jiffaċċja lil pajjiżi

5) Liema kwalitajiet u abbiltajiet jużaw il-mexxejja tajbin meta jibnu timijiet ta 'suċċess?

6) Google. Fatturi li jolqtu l-effiċjenza tat-tim

7) Il-prijoritajiet ewlenin ta 'dawk li jfittxu impjieg

8) Dak li jagħmel lil imgħallem mexxej kbir?

9) Dak li jagħmel in-nies b'suċċess fuq ix-xogħol?

10) Lest li tirċievi inqas paga biex taħdem mill-bogħod?

11) L-etàżmu jeżisti?

12) Ageism fil-karriera

13) Ageism fil-ħajja

14) Kawżi ta 'l-Ageism

15) Raġunijiet għaliex in-nies jieqfu (minn Anna Vital)

16) Fiduċja (#WVS)

17) Stħarriġ tal-kuntentizza ta 'Oxford

18) Benesseri psikoloġiku

19) Fejn tkun l-iktar opportunità eċċitanti li jmiss tiegħek?

20) X'se tagħmel din il-ġimgħa biex tieħu ħsieb is-saħħa mentali tiegħek?

21) Jien ngħix naħseb dwar il-passat, il-preżent jew il-futur tiegħi

22) Meritokrazija

23) Intelliġenza artifiċjali u t-tmiem taċ-ċiviltà

24) In-nies għaliex jindirizzaw?

25) Differenza bejn is-sessi fil-bini ta 'kunfidenza fihom infushom (IFD Allensbach)

26) Xing.com Valutazzjoni tal-Kultura

27) Patrick Lencioni "Il-Ħames Disfunzjonijiet ta 'Tim"

28) L-empatija hija ...

29) X'inhu essenzjali għall-ispeċjalisti tal-IT fl-għażla ta 'offerta ta' xogħol?

30) Għaliex in-nies jirreżistu l-bidla (minn Siobhán Mchale)

31) Kif tirregola l-emozzjonijiet tiegħek? (minn Nawal Mustafa M.A.)

32) 21 Ħiliet li jħallsu għal dejjem (minn Jeremiah Teo / 赵汉昇)

33) Il-libertà vera hija ...

34) 12-il mod kif tibni fiduċja ma 'oħrajn (minn Justin Wright)

35) Karatteristiċi ta 'impjegat b'talent (mill-Istitut tal-Ġestjoni tat-Talenti)

36) 10 ċwievet biex jimmotivaw lit-tim tiegħek

37) Alġebra tal-Kuxjenza (minn Vladimir Lefebvre)

38) Tliet Possibbiltajiet Distinti tal-Futur (minn 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.

Biża '

mapep nawtiċi Korrelazzjoni

VUCA

Valur kritiku tal-koeffiċjent ta 'korrelazzjoni

Distribuzzjoni Normali, minn William Sealy Gosset (student) r = 0.0331

Distribuzzjoni mhux normali, minn Spearman r = 0.0013

Juru biss ir-riżultati > r = 0.0331

Distribuzzjoni	Mhux normali	Mhux normali	Mhux normali	Normali	Normali	Normali	Normali	Normali
Il-mistoqsijiet kollha Il-mistoqsijiet kollha L-akbar biża 'tiegħi hija
L-akbar biża 'tiegħi hija
Answer 1	-	Pożittiv dgħajjef 0.0563	Pożittiv dgħajjef 0.0317	Negattiv dgħajjef -0.0161	Pożittiv dgħajjef 0.0907	Pożittiv dgħajjef 0.0298	Negattiv dgħajjef -0.0126	Negattiv dgħajjef -0.1537
Answer 2	-	Pożittiv dgħajjef 0.0216	Pożittiv dgħajjef 0.0002	Negattiv dgħajjef -0.0458	Pożittiv dgħajjef 0.0654	Pożittiv dgħajjef 0.0445	Pożittiv dgħajjef 0.0124	Negattiv dgħajjef -0.0937
Answer 3	-	Negattiv dgħajjef -0.0035	Negattiv dgħajjef -0.0111	Negattiv dgħajjef -0.0421	Negattiv dgħajjef -0.0456	Pożittiv dgħajjef 0.0466	Pożittiv dgħajjef 0.0786	Negattiv dgħajjef -0.0201
Answer 4	-	Pożittiv dgħajjef 0.0435	Pożittiv dgħajjef 0.0353	Negattiv dgħajjef -0.0181	Pożittiv dgħajjef 0.0145	Pożittiv dgħajjef 0.0301	Pożittiv dgħajjef 0.0197	Negattiv dgħajjef -0.0979
Answer 5	-	Pożittiv dgħajjef 0.0299	Pożittiv dgħajjef 0.1279	Pożittiv dgħajjef 0.0136	Pożittiv dgħajjef 0.0730	Negattiv dgħajjef -0.0007	Negattiv dgħajjef -0.0207	Negattiv dgħajjef -0.1746
Answer 6	-	Negattiv dgħajjef -0.0004	Pożittiv dgħajjef 0.0082	Negattiv dgħajjef -0.0629	Negattiv dgħajjef -0.0078	Pożittiv dgħajjef 0.0193	Pożittiv dgħajjef 0.0830	Negattiv dgħajjef -0.0318
Answer 7	-	Pożittiv dgħajjef 0.0122	Pożittiv dgħajjef 0.0381	Negattiv dgħajjef -0.0686	Negattiv dgħajjef -0.0242	Pożittiv dgħajjef 0.0471	Pożittiv dgħajjef 0.0636	Negattiv dgħajjef -0.0513
Answer 8	-	Pożittiv dgħajjef 0.0698	Pożittiv dgħajjef 0.0849	Negattiv dgħajjef -0.0321	Pożittiv dgħajjef 0.0146	Pożittiv dgħajjef 0.0345	Pożittiv dgħajjef 0.0130	Negattiv dgħajjef -0.1368
Answer 9	-	Pożittiv dgħajjef 0.0665	Pożittiv dgħajjef 0.1674	Pożittiv dgħajjef 0.0092	Pożittiv dgħajjef 0.0691	Negattiv dgħajjef -0.0128	Negattiv dgħajjef -0.0528	Negattiv dgħajjef -0.1812
Answer 10	-	Pożittiv dgħajjef 0.0778	Pożittiv dgħajjef 0.0755	Negattiv dgħajjef -0.0180	Pożittiv dgħajjef 0.0231	Pożittiv dgħajjef 0.0346	Negattiv dgħajjef -0.0146	Negattiv dgħajjef -0.1298
Answer 11	-	Pożittiv dgħajjef 0.0584	Pożittiv dgħajjef 0.0524	Negattiv dgħajjef -0.0096	Pożittiv dgħajjef 0.0081	Pożittiv dgħajjef 0.0199	Pożittiv dgħajjef 0.0318	Negattiv dgħajjef -0.1197
Answer 12	-	Pożittiv dgħajjef 0.0380	Pożittiv dgħajjef 0.1042	Negattiv dgħajjef -0.0352	Pożittiv dgħajjef 0.0357	Pożittiv dgħajjef 0.0254	Pożittiv dgħajjef 0.0286	Negattiv dgħajjef -0.1515
Answer 13	-	Pożittiv dgħajjef 0.0644	Pożittiv dgħajjef 0.1057	Negattiv dgħajjef -0.0448	Pożittiv dgħajjef 0.0268	Pożittiv dgħajjef 0.0416	Pożittiv dgħajjef 0.0169	Negattiv dgħajjef -0.1600
Answer 14	-	Pożittiv dgħajjef 0.0717	Pożittiv dgħajjef 0.1026	Negattiv dgħajjef -0.0006	Negattiv dgħajjef -0.0089	Negattiv dgħajjef -0.0012	Pożittiv dgħajjef 0.0080	Negattiv dgħajjef -0.1168
Answer 15	-	Pożittiv dgħajjef 0.0549	Pożittiv dgħajjef 0.1375	Negattiv dgħajjef -0.0420	Pożittiv dgħajjef 0.0178	Negattiv dgħajjef -0.0160	Pożittiv dgħajjef 0.0216	Negattiv dgħajjef -0.1180
Answer 16	-	Pożittiv dgħajjef 0.0591	Pożittiv dgħajjef 0.0273	Negattiv dgħajjef -0.0386	Negattiv dgħajjef -0.0399	Pożittiv dgħajjef 0.0653	Pożittiv dgħajjef 0.0282	Negattiv dgħajjef -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

Sid tal-Prodott SaaS Pet Project SDTest®

Valerii kien ikkwalifikat bħala pedagoga soċjali-psikologu fl-1993 u minn dakinhar applika l-għarfien tiegħu fil-ġestjoni tal-proġett.
Valerii kiseb il-grad ta 'master u l-kwalifika tal-Proġett u l-Maniġer tal-Programm fl-2013. Matul il-programm tal-kaptan tiegħu, sar familjari mal-pjan direzzjonali tal-proġett (GPM Deutsche Gesellschaft Für Projektmanagement e. V.) u Spiral Dynamics.
Valerii ħa diversi testijiet ta 'dinamika spirali u uża l-għarfien u l-esperjenza tiegħu biex jadatta l-verżjoni attwali ta' SDTest.
Valerii huwa l-awtur tal-esplorazzjoni tal-inċertezza tal-V.U.C.A. Kunċett bl-użu ta 'dinamika spirali u statistika matematika fil-psikoloġija, aktar minn 20 stħarriġ internazzjonali.

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