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) Vitendo vya kampuni zinazohusiana na wafanyikazi katika mwezi uliopita (ndio / hapana)

2) Vitendo vya makampuni kuhusiana na wafanyakazi katika mwezi uliopita (ukweli katika%)

3) Hofu

4) Shida kubwa zinazoikabili nchi yangu

5) Je! Ni sifa gani na uwezo gani ambao viongozi wazuri hutumia wakati wa kujenga timu zilizofanikiwa?

6) Google. Mambo ambayo yanaathiri ufanisi wa timu

7) Vipaumbele vikuu vya wanaotafuta kazi

8) Ni nini kinachomfanya bosi kuwa kiongozi mkubwa?

9) Ni nini hufanya watu kufanikiwa kazini?

10) Uko tayari kupokea malipo kidogo kufanya kazi kwa mbali?

11) Je! Umri upo?

12) Umri katika kazi

13) Umri katika maisha

14) Sababu za uzee

15) Sababu Kwa nini Watu Wape Up (na Anna Vital)

16) Imani (#WVS)

17) Utafiti wa Furaha ya Oxford

18) Ustawi wa kisaikolojia

19) Ambapo itakuwa fursa yako ijayo ya kufurahisha zaidi?

20) Je! Utafanya nini wiki hii kutunza afya yako ya akili?

21) Ninaishi nikifikiria zamani, za sasa au za baadaye

22) Meritocracy

23) Ujuzi wa bandia na mwisho wa maendeleo

24) Kwa nini watu huchelewesha?

25) Tofauti ya kijinsia katika kujenga kujiamini (IFD Allensbach)

26) Xing.com tathmini ya utamaduni

27) Patrick Lencioni "dysfunctions tano za timu"

28) Huruma ni ...

29) Ni nini muhimu kwa wataalamu wa IT katika kuchagua toleo la kazi?

30) Kwa nini watu wanapinga mabadiliko (na Siobhán McHale)

31) Je! Unasimamiaje hisia zako? (Na Nawal Mustafa M.A.)

32) Ujuzi 21 ambao unakulipa milele (na Jeremiah Teo / 赵汉昇)

33) Uhuru wa kweli ni ...

34) Njia 12 za kujenga uaminifu na wengine (na Justin Wright)

35) Tabia za mfanyakazi mwenye talanta (na Taasisi ya Usimamizi wa Vipaji)

36) Funguo 10 za kuhamasisha timu yako

37) Algebra ya Dhamiri (na Vladimir Lefebvre)

38) Uwezekano Tatu Tofauti wa Wakati Ujao (na Dk. 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.

Hofu

chati Uwiano

VUCA

Muhimu thamani ya mgawo uwiano

Usambazaji wa kawaida, na William Sealy Gosset (Mwanafunzi) r = 0.0335

Usambazaji usio wa kawaida, na Spearman r = 0.0014

Onyesha matokeo tu > r = 0.0335

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

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