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:

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3) Ibẹru

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7) Awọn pataki akọkọ ti awọn ti n wa ni iṣẹ

8) Kini o jẹ ki Oga kan ni oludari nla?

9) Kini o mu ki eniyan ṣaṣeyọri ni ibi iṣẹ?

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11) Ṣe ọjọ-ori wa?

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13) Ognsm ni igbesi aye

14) Awọn okunfa ti ọjọ ori

15) Awọn idi ti awọn eniyan fi fun (nipasẹ anna pataki)

16) Igbẹkẹle (#WVS)

17) Oxford Ayọ Iwadi

18) Ooye imọ-ara

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22) Ibararan

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24) Kini idi ti eniyan fi ṣe ipin?

25) Iyato akọ-ọrọ ni kikọ lati kọ igbẹkẹle ara ẹni (Ifer AlnsBach)

26) Xing.com asa igbelewọn

27) Patrick Levension ká "awọn dysfocnu marun ti ẹgbẹ kan"

28) Ifoju jẹ ...

29) Kini o ṣe pataki fun awọn alamọja ni yiyan ipese iṣẹ?

30) Kilode ti awọn eniyan tako iyipada (nipasẹ Siobhán MChale)

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32) Awọn ọgbọn 21 ti o sanwo fun ọ lailai (nipasẹ Jeremiah Teo / 赵汉昇)

33) Ominira gidi ni ...

34) Awọn ọna 12 lati kọ igbẹkẹle pẹlu awọn miiran (nipasẹ Justin Winght)

35) Awọn abuda ti oṣiṣẹ talenti kan (nipasẹ Ile-ẹkọ Talenti)

36) 10 awọn bọtini lati rubọ ẹgbẹ rẹ

37) Algebra ti Ẹri (nipasẹ Vladimir Lefebvre)

38) Awọn aye Iyatọ Meta ti Ọjọ iwaju (nipasẹ Dokita 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.

Ibẹru

shatti Ibamu

VUCA

Lominu ni iye ti awọn ibamu olùsọdipúpọ

Pinpin deede, nipasẹ William Searin (ọmọ ile-iwe) r = 0.0335

Pinpin deede, nipasẹ Spearman r = 0.0014

Fihan awọn abajade nikan > r = 0.0335

Pinpin	Ti kii ṣe deede	Ti kii ṣe deede	Ti kii ṣe deede	Deedee	Deedee	Deedee	Deedee	Deedee
Gbogbo awọn ibeere Gbogbo awọn ibeere Ibẹru nla mi jẹ
Ibẹru nla mi jẹ
Answer 1	-	Alailagbara 0.0521	Alailagbara 0.0294	Alailagbara odi -0.0147	Alailagbara 0.0885	Alailagbara 0.0316	Alailagbara odi -0.0110	Alailagbara odi -0.1513
Answer 2	-	Alailagbara 0.0213	Alailagbara 0.0013	Alailagbara odi -0.0432	Alailagbara 0.0618	Alailagbara 0.0453	Alailagbara 0.0103	Alailagbara odi -0.0918
Answer 3	-	Alailagbara odi -0.0042	Alailagbara odi -0.0116	Alailagbara odi -0.0406	Alailagbara odi -0.0477	Alailagbara 0.0487	Alailagbara 0.0767	Alailagbara odi -0.0191
Answer 4	-	Alailagbara 0.0421	Alailagbara 0.0350	Alailagbara odi -0.0115	Alailagbara 0.0112	Alailagbara 0.0307	Alailagbara 0.0175	Alailagbara odi -0.0980
Answer 5	-	Alailagbara 0.0288	Alailagbara 0.1272	Alailagbara 0.0146	Alailagbara 0.0697	Alailagbara 0.0037	Alailagbara odi -0.0215	Alailagbara odi -0.1746
Answer 6	-	Alailagbara odi -0.0001	Alailagbara 0.0042	Alailagbara odi -0.0607	Alailagbara odi -0.0115	Alailagbara 0.0231	Alailagbara 0.0826	Alailagbara odi -0.0309
Answer 7	-	Alailagbara 0.0117	Alailagbara 0.0372	Alailagbara odi -0.0653	Alailagbara odi -0.0283	Alailagbara 0.0495	Alailagbara 0.0626	Alailagbara odi -0.0505
Answer 8	-	Alailagbara 0.0658	Alailagbara 0.0830	Alailagbara odi -0.0310	Alailagbara 0.0139	Alailagbara 0.0334	Alailagbara 0.0134	Alailagbara odi -0.1322
Answer 9	-	Alailagbara 0.0660	Alailagbara 0.1658	Alailagbara 0.0051	Alailagbara 0.0691	Alailagbara odi -0.0093	Alailagbara odi -0.0498	Alailagbara odi -0.1820
Answer 10	-	Alailagbara 0.0758	Alailagbara 0.0724	Alailagbara odi -0.0173	Alailagbara 0.0236	Alailagbara 0.0312	Alailagbara odi -0.0115	Alailagbara odi -0.1263
Answer 11	-	Alailagbara 0.0577	Alailagbara 0.0544	Alailagbara odi -0.0075	Alailagbara 0.0082	Alailagbara 0.0185	Alailagbara 0.0293	Alailagbara odi -0.1190
Answer 12	-	Alailagbara 0.0376	Alailagbara 0.1007	Alailagbara odi -0.0342	Alailagbara 0.0296	Alailagbara 0.0273	Alailagbara 0.0341	Alailagbara odi -0.1500
Answer 13	-	Alailagbara 0.0627	Alailagbara 0.1017	Alailagbara odi -0.0443	Alailagbara 0.0248	Alailagbara 0.0434	Alailagbara 0.0189	Alailagbara odi -0.1576
Answer 14	-	Alailagbara 0.0732	Alailagbara 0.1036	Alailagbara 0.0048	Alailagbara odi -0.0105	Alailagbara odi -0.0039	Alailagbara 0.0041	Alailagbara odi -0.1157
Answer 15	-	Alailagbara 0.0539	Alailagbara 0.1381	Alailagbara odi -0.0424	Alailagbara 0.0163	Alailagbara odi -0.0147	Alailagbara 0.0216	Alailagbara odi -0.1173
Answer 16	-	Alailagbara 0.0590	Alailagbara 0.0274	Alailagbara odi -0.0375	Alailagbara odi -0.0429	Alailagbara 0.0687	Alailagbara 0.0253	Alailagbara odi -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

Valeriii Kosenko

Ọja Sus Pet Project Sdtest®

A ṣe oṣiṣẹ Valerii gẹgẹbi onimọ-jinlẹ ti o jẹ aṣoju-ọrọ ti o jẹ aṣoju ọdun 1993 ati pe o ti lo imo rẹ ni iṣakoso iṣẹ akanṣe.
Valerii gba ìyí ti oluwa rẹ ati iṣẹ akanṣe ati ilana ilana eto eto ni ọdun 2013. Lakoko eto oluwa rẹ, o jẹ ipinya ti agbekale (GPM Rutscherschaft Für ProjekThatamencationscramentamencationscramentamencation
Valerii mu ọpọlọpọ awọn idanwo awọn idanwo shanics ati lo imoye rẹ ati iriri lati mu ẹya ti isiyi ṣe deede.
Valerii ni onkọwe ti ṣawari aidaniloju ti V.u.c.i. Erongba nipa lilo awọn agbara ajira ati awọn iṣiro iṣiro iṣiro ni ọpọlọ, diẹ ẹ sii ju 20 ibo ibo kariaye.

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