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 = 0.0335

Distribuzzjoni mhux normali, minn Spearman r = 0.0014

Juru biss ir-riżultati > r = 0.0335

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 0.0521	Pożittiv dgħajjef 0.0294	Negattiv dgħajjef -0.0147	Pożittiv dgħajjef 0.0885	Pożittiv dgħajjef 0.0316	Negattiv dgħajjef -0.0110	Negattiv dgħajjef -0.1513
Answer 2	-	Pożittiv dgħajjef 0.0213	Pożittiv dgħajjef 0.0013	Negattiv dgħajjef -0.0432	Pożittiv dgħajjef 0.0618	Pożittiv dgħajjef 0.0453	Pożittiv dgħajjef 0.0103	Negattiv dgħajjef -0.0918
Answer 3	-	Negattiv dgħajjef -0.0042	Negattiv dgħajjef -0.0116	Negattiv dgħajjef -0.0406	Negattiv dgħajjef -0.0477	Pożittiv dgħajjef 0.0487	Pożittiv dgħajjef 0.0767	Negattiv dgħajjef -0.0191
Answer 4	-	Pożittiv dgħajjef 0.0421	Pożittiv dgħajjef 0.0350	Negattiv dgħajjef -0.0115	Pożittiv dgħajjef 0.0112	Pożittiv dgħajjef 0.0307	Pożittiv dgħajjef 0.0175	Negattiv dgħajjef -0.0980
Answer 5	-	Pożittiv dgħajjef 0.0288	Pożittiv dgħajjef 0.1272	Pożittiv dgħajjef 0.0146	Pożittiv dgħajjef 0.0697	Pożittiv dgħajjef 0.0037	Negattiv dgħajjef -0.0215	Negattiv dgħajjef -0.1746
Answer 6	-	Negattiv dgħajjef -0.0001	Pożittiv dgħajjef 0.0042	Negattiv dgħajjef -0.0607	Negattiv dgħajjef -0.0115	Pożittiv dgħajjef 0.0231	Pożittiv dgħajjef 0.0826	Negattiv dgħajjef -0.0309
Answer 7	-	Pożittiv dgħajjef 0.0117	Pożittiv dgħajjef 0.0372	Negattiv dgħajjef -0.0653	Negattiv dgħajjef -0.0283	Pożittiv dgħajjef 0.0495	Pożittiv dgħajjef 0.0626	Negattiv dgħajjef -0.0505
Answer 8	-	Pożittiv dgħajjef 0.0658	Pożittiv dgħajjef 0.0830	Negattiv dgħajjef -0.0310	Pożittiv dgħajjef 0.0139	Pożittiv dgħajjef 0.0334	Pożittiv dgħajjef 0.0134	Negattiv dgħajjef -0.1322
Answer 9	-	Pożittiv dgħajjef 0.0660	Pożittiv dgħajjef 0.1658	Pożittiv dgħajjef 0.0051	Pożittiv dgħajjef 0.0691	Negattiv dgħajjef -0.0093	Negattiv dgħajjef -0.0498	Negattiv dgħajjef -0.1820
Answer 10	-	Pożittiv dgħajjef 0.0758	Pożittiv dgħajjef 0.0724	Negattiv dgħajjef -0.0173	Pożittiv dgħajjef 0.0236	Pożittiv dgħajjef 0.0312	Negattiv dgħajjef -0.0115	Negattiv dgħajjef -0.1263
Answer 11	-	Pożittiv dgħajjef 0.0577	Pożittiv dgħajjef 0.0544	Negattiv dgħajjef -0.0075	Pożittiv dgħajjef 0.0082	Pożittiv dgħajjef 0.0185	Pożittiv dgħajjef 0.0293	Negattiv dgħajjef -0.1190
Answer 12	-	Pożittiv dgħajjef 0.0376	Pożittiv dgħajjef 0.1007	Negattiv dgħajjef -0.0342	Pożittiv dgħajjef 0.0296	Pożittiv dgħajjef 0.0273	Pożittiv dgħajjef 0.0341	Negattiv dgħajjef -0.1500
Answer 13	-	Pożittiv dgħajjef 0.0627	Pożittiv dgħajjef 0.1017	Negattiv dgħajjef -0.0443	Pożittiv dgħajjef 0.0248	Pożittiv dgħajjef 0.0434	Pożittiv dgħajjef 0.0189	Negattiv dgħajjef -0.1576
Answer 14	-	Pożittiv dgħajjef 0.0732	Pożittiv dgħajjef 0.1036	Pożittiv dgħajjef 0.0048	Negattiv dgħajjef -0.0105	Negattiv dgħajjef -0.0039	Pożittiv dgħajjef 0.0041	Negattiv dgħajjef -0.1157
Answer 15	-	Pożittiv dgħajjef 0.0539	Pożittiv dgħajjef 0.1381	Negattiv dgħajjef -0.0424	Pożittiv dgħajjef 0.0163	Negattiv dgħajjef -0.0147	Pożittiv dgħajjef 0.0216	Negattiv dgħajjef -0.1173
Answer 16	-	Pożittiv dgħajjef 0.0590	Pożittiv dgħajjef 0.0274	Negattiv dgħajjef -0.0375	Negattiv dgħajjef -0.0429	Pożittiv dgħajjef 0.0687	Pożittiv dgħajjef 0.0253	Negattiv dgħajjef -0.0698

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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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