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

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 = 0.0353

Usambazaji usio wa kawaida, na Spearman r = 0.0014

Onyesha matokeo tu > r = 0.0353

Usambazaji	Sio kawaida	Kawaida	Sio kawaida	Kawaida	Kawaida	Kawaida	Kawaida	Kawaida
Maswali yote Maswali yote Hofu yangu kubwa ni
Hofu yangu kubwa ni
Answer 1	-	Chanya dhaifu 0.0297	Chanya dhaifu 0.0298	Hasi dhaifu -0.0106	Chanya dhaifu 0.0970	Chanya dhaifu 0.0325	Hasi dhaifu -0.0019	Hasi dhaifu -0.1558
Answer 2	-	Chanya dhaifu 0.0188	Chanya dhaifu 0.0076	Hasi dhaifu -0.0360	Chanya dhaifu 0.0711	Chanya dhaifu 0.0387	Chanya dhaifu 0.0082	Hasi dhaifu -0.1011
Answer 3	-	Chanya dhaifu 0.0026	Hasi dhaifu -0.0170	Hasi dhaifu -0.0443	Hasi dhaifu -0.0458	Chanya dhaifu 0.0547	Chanya dhaifu 0.0808	Hasi dhaifu -0.0270
Answer 4	-	Chanya dhaifu 0.0332	Chanya dhaifu 0.0285	Hasi dhaifu -0.0006	Chanya dhaifu 0.0155	Chanya dhaifu 0.0276	Chanya dhaifu 0.0105	Hasi dhaifu -0.0917
Answer 5	-	Chanya dhaifu 0.0122	Chanya dhaifu 0.1193	Chanya dhaifu 0.0095	Chanya dhaifu 0.0721	Chanya dhaifu 0.0057	Hasi dhaifu -0.0083	Hasi dhaifu -0.1687
Answer 6	-	Chanya dhaifu 0.0044	Chanya dhaifu 0.0005	Hasi dhaifu -0.0582	Hasi dhaifu -0.0004	Chanya dhaifu 0.0210	Chanya dhaifu 0.0830	Hasi dhaifu -0.0418
Answer 7	-	Chanya dhaifu 0.0242	Chanya dhaifu 0.0368	Hasi dhaifu -0.0521	Hasi dhaifu -0.0234	Chanya dhaifu 0.0403	Chanya dhaifu 0.0568	Hasi dhaifu -0.0597
Answer 8	-	Chanya dhaifu 0.0707	Chanya dhaifu 0.0781	Hasi dhaifu -0.0244	Chanya dhaifu 0.0140	Chanya dhaifu 0.0303	Chanya dhaifu 0.0137	Hasi dhaifu -0.1334
Answer 9	-	Chanya dhaifu 0.0564	Chanya dhaifu 0.1531	Chanya dhaifu 0.0127	Chanya dhaifu 0.0769	Hasi dhaifu -0.0136	Hasi dhaifu -0.0495	Hasi dhaifu -0.1752
Answer 10	-	Chanya dhaifu 0.0711	Chanya dhaifu 0.0700	Hasi dhaifu -0.0127	Chanya dhaifu 0.0246	Chanya dhaifu 0.0363	Hasi dhaifu -0.0156	Hasi dhaifu -0.1273
Answer 11	-	Chanya dhaifu 0.0542	Chanya dhaifu 0.0488	Chanya dhaifu 0.0086	Chanya dhaifu 0.0078	Chanya dhaifu 0.0162	Chanya dhaifu 0.0315	Hasi dhaifu -0.1248
Answer 12	-	Chanya dhaifu 0.0281	Chanya dhaifu 0.0929	Hasi dhaifu -0.0325	Chanya dhaifu 0.0361	Chanya dhaifu 0.0276	Chanya dhaifu 0.0365	Hasi dhaifu -0.1482
Answer 13	-	Chanya dhaifu 0.0643	Chanya dhaifu 0.0916	Hasi dhaifu -0.0418	Chanya dhaifu 0.0237	Chanya dhaifu 0.0425	Chanya dhaifu 0.0239	Hasi dhaifu -0.1558
Answer 14	-	Chanya dhaifu 0.0697	Chanya dhaifu 0.1017	Chanya dhaifu 0.0149	Hasi dhaifu -0.0062	Hasi dhaifu -0.0087	Hasi dhaifu -0.0002	Hasi dhaifu -0.1161
Answer 15	-	Chanya dhaifu 0.0603	Chanya dhaifu 0.1299	Hasi dhaifu -0.0379	Chanya dhaifu 0.0163	Hasi dhaifu -0.0091	Chanya dhaifu 0.0164	Hasi dhaifu -0.1204
Answer 16	-	Chanya dhaifu 0.0691	Chanya dhaifu 0.0221	Hasi dhaifu -0.0305	Hasi dhaifu -0.0515	Chanya dhaifu 0.0750	Chanya dhaifu 0.0187	Hasi dhaifu -0.0696

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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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