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 = 0.033

Usambazaji usio wa kawaida, na Spearman r = 0.0013

Onyesha matokeo tu > r = 0.033

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

Valerii Kosenko

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