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?

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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)

31) Bawo ni o ṣe ṣe ilana awọn ẹdun rẹ? (nipasẹ Nawal Mustafa m.a.)

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 = 0.033

Pinpin deede, nipasẹ Spearman r = 0.0013

Fihan awọn abajade nikan > r = 0.033

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 0.0559	Alailagbara 0.0315	Alailagbara odi -0.0170	Alailagbara 0.0920	Alailagbara 0.0294	Alailagbara odi -0.0124	Alailagbara odi -0.1539
Answer 2	-	Alailagbara 0.0229	Alailagbara odi -0.0002	Alailagbara odi -0.0448	Alailagbara 0.0636	Alailagbara 0.0445	Alailagbara 0.0134	Alailagbara odi -0.0939
Answer 3	-	Alailagbara odi -0.0032	Alailagbara odi -0.0121	Alailagbara odi -0.0416	Alailagbara odi -0.0462	Alailagbara 0.0466	Alailagbara 0.0788	Alailagbara odi -0.0195
Answer 4	-	Alailagbara 0.0438	Alailagbara 0.0348	Alailagbara odi -0.0195	Alailagbara 0.0153	Alailagbara 0.0300	Alailagbara 0.0207	Alailagbara odi -0.0980
Answer 5	-	Alailagbara 0.0304	Alailagbara 0.1282	Alailagbara 0.0135	Alailagbara 0.0734	Alailagbara odi -0.0013	Alailagbara odi -0.0200	Alailagbara odi -0.1757
Answer 6	-	Alailagbara odi -0.0002	Alailagbara 0.0082	Alailagbara odi -0.0627	Alailagbara odi -0.0083	Alailagbara 0.0193	Alailagbara 0.0831	Alailagbara odi -0.0315
Answer 7	-	Alailagbara 0.0126	Alailagbara 0.0381	Alailagbara odi -0.0687	Alailagbara odi -0.0243	Alailagbara 0.0469	Alailagbara 0.0642	Alailagbara odi -0.0515
Answer 8	-	Alailagbara 0.0698	Alailagbara 0.0848	Alailagbara odi -0.0327	Alailagbara 0.0148	Alailagbara 0.0345	Alailagbara 0.0134	Alailagbara odi -0.1365
Answer 9	-	Alailagbara 0.0668	Alailagbara 0.1676	Alailagbara 0.0083	Alailagbara 0.0693	Alailagbara odi -0.0131	Alailagbara odi -0.0516	Alailagbara odi -0.1818
Answer 10	-	Alailagbara 0.0782	Alailagbara 0.0753	Alailagbara odi -0.0204	Alailagbara 0.0247	Alailagbara 0.0342	Alailagbara odi -0.0131	Alailagbara odi -0.1304
Answer 11	-	Alailagbara 0.0578	Alailagbara 0.0532	Alailagbara odi -0.0096	Alailagbara 0.0087	Alailagbara 0.0195	Alailagbara 0.0311	Alailagbara odi -0.1196
Answer 12	-	Alailagbara 0.0390	Alailagbara 0.1037	Alailagbara odi -0.0358	Alailagbara 0.0358	Alailagbara 0.0250	Alailagbara 0.0299	Alailagbara odi -0.1520
Answer 13	-	Alailagbara 0.0644	Alailagbara 0.1048	Alailagbara odi -0.0448	Alailagbara 0.0268	Alailagbara 0.0417	Alailagbara 0.0178	Alailagbara odi -0.1600
Answer 14	-	Alailagbara 0.0712	Alailagbara 0.1021	Alailagbara odi -0.0007	Alailagbara odi -0.0088	Alailagbara odi -0.0011	Alailagbara 0.0088	Alailagbara odi -0.1169
Answer 15	-	Alailagbara 0.0557	Alailagbara 0.1365	Alailagbara odi -0.0423	Alailagbara 0.0177	Alailagbara odi -0.0162	Alailagbara 0.0224	Alailagbara odi -0.1179
Answer 16	-	Alailagbara 0.0591	Alailagbara 0.0273	Alailagbara odi -0.0386	Alailagbara odi -0.0400	Alailagbara 0.0653	Alailagbara 0.0284	Alailagbara odi -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

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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