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) Gnìomhan companaidhean a thaobh luchd-obrach sa mhìos a chaidh (tha / chan eil)

2) Gnìomhan companaidhean a thaobh luchd-obrach sa mhìos a chaidh (fìrinn ann an%)

3) Eagal

4) Na duilgheadasan as motha a tha mu choinneamh mo dhùthaich

5) Dè na feartan agus na comasan a bhios a 'cleachdadh stiùirichean math nuair a bhios tu a' togail sgiobaidhean soirbheachail?

6) Google. Factaran a tha a 'toirt buaidh air èifeachdas sgioba

7) Na prìomh phrìomhachasan luchd-siridh obrach

8) Dè a tha a 'dèanamh stiùiriche ceannard air stiùiriche?

9) Dè a tha a 'dèanamh daoine soirbheachail aig an obair?

10) A bheil thu deiseil airson nas lugha de phàigheadh fhaighinn airson obair air astar?

11) A bheil Aitisism ann?

12) Aimsir ann an dreuchd

13) Aimsir ann am beatha

14) Adhbharan Agemism

15) Adhbharan carson a bheir daoine seachad (le Anna deatamach)

16) Earbsa (#WVS)

17) Sgrùdadh Solas Oxford Oxford

18) Sunnd saidhgeòlach

19) Càite am biodh an ath chothrom as inntinniche agad?

20) Dè a nì thu an t-seachdain seo airson coimhead às dèidh do shlàinte inntinn?

21) Tha mi a 'fuireach a' smaoineachadh mun àm a dh'fhalbh, an-diugh no an àm ri teachd

22) Airidheachd

23) Eòlas fuadain agus deireadh sìobhaltachd

24) Carson a tha daoine a 'cur fo smachd?

25) Eadar-dhealachadh gnè ann a bhith a 'togail fèin-mhisneachd (ifd allensbach)

26) Measadh cultar Xing.com

27) Na còig Dyspunctions aig Patrick Lencioni le sgioba

28) Tha co-fhaireachdainn ...

29) Dè a tha riatanach dha eòlaichean airson a bhith a 'taghadh tairgse obrach?

30) Carson a dh 'atharraicheas daoine atharrachadh (le Sioilgán Machale)

31) Ciamar a bhios tu a 'riaghladh na faireachdainnean agad? (le canafa mawa m.a.)

32) 21 Sgilean a phàigheas tu gu bràth (le Jeremiah Teo / 赵汉昇)

33) Is e fìor shaorsa ...

34) 12 Dòighean air earbsa a thogail le feadhainn eile (le Justin Wright)

35) Feartan neach-obrach tàlantach (le Institiùd Riaghlaidh Tàlant)

36) 10 iuchraichean gus do sgioba a bhrosnachadh

37) Ailseabra na Coguis (le Vladimir Lefebvre)

38) Trì Comasan Sònraichte san Àm ri Teachd (leis an Dr. 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.

Eagal

Charts Co-dhàimh

VUCA

Critical luach na co-dhàimh coefficient

Sgaoileadh àbhaisteach, le Uilleam Sealy Howet (Oileanach) r = 0.033

Sgaoileadh neo-àbhaisteach, le spearman r = 0.0013

Seall a-mhàin toraidhean a-mhàin > r = 0.033

Sgaoileadh	Neo-àbhaisteach	Neo-àbhaisteach	Neo-àbhaisteach	Àbhaisteach	Àbhaisteach	Àbhaisteach	Àbhaisteach	Àbhaisteach
A h-uile ceist A h-uile ceist Tha an t-eagal as motha agam
Tha an t-eagal as motha agam
Answer 1	-	Lag deimhinneach 0.0569	Lag deimhinneach 0.0313	Lag àicheil -0.0161	Lag deimhinneach 0.0906	Lag deimhinneach 0.0297	Lag àicheil -0.0118	Lag àicheil -0.1544
Answer 2	-	Lag deimhinneach 0.0225	Lag deimhinneach 0.0002	Lag àicheil -0.0450	Lag deimhinneach 0.0644	Lag deimhinneach 0.0442	Lag deimhinneach 0.0128	Lag àicheil -0.0940
Answer 3	-	Lag àicheil -0.0030	Lag àicheil -0.0116	Lag àicheil -0.0411	Lag àicheil -0.0465	Lag deimhinneach 0.0466	Lag deimhinneach 0.0786	Lag àicheil -0.0200
Answer 4	-	Lag deimhinneach 0.0440	Lag deimhinneach 0.0354	Lag àicheil -0.0189	Lag deimhinneach 0.0150	Lag deimhinneach 0.0299	Lag deimhinneach 0.0204	Lag àicheil -0.0986
Answer 5	-	Lag deimhinneach 0.0309	Lag deimhinneach 0.1278	Lag deimhinneach 0.0137	Lag deimhinneach 0.0728	Lag àicheil -0.0011	Lag àicheil -0.0195	Lag àicheil -0.1757
Answer 6	-	Lag àicheil -0.0001	Lag deimhinneach 0.0086	Lag àicheil -0.0623	Lag àicheil -0.0085	Lag deimhinneach 0.0193	Lag deimhinneach 0.0829	Lag àicheil -0.0319
Answer 7	-	Lag deimhinneach 0.0127	Lag deimhinneach 0.0385	Lag àicheil -0.0683	Lag àicheil -0.0246	Lag deimhinneach 0.0468	Lag deimhinneach 0.0640	Lag àicheil -0.0519
Answer 8	-	Lag deimhinneach 0.0700	Lag deimhinneach 0.0853	Lag àicheil -0.0322	Lag deimhinneach 0.0146	Lag deimhinneach 0.0344	Lag deimhinneach 0.0132	Lag àicheil -0.1370
Answer 9	-	Lag deimhinneach 0.0670	Lag deimhinneach 0.1680	Lag deimhinneach 0.0087	Lag deimhinneach 0.0692	Lag àicheil -0.0132	Lag àicheil -0.0518	Lag àicheil -0.1822
Answer 10	-	Lag deimhinneach 0.0784	Lag deimhinneach 0.0758	Lag àicheil -0.0199	Lag deimhinneach 0.0245	Lag deimhinneach 0.0342	Lag àicheil -0.0133	Lag àicheil -0.1308
Answer 11	-	Lag deimhinneach 0.0586	Lag deimhinneach 0.0528	Lag àicheil -0.0091	Lag deimhinneach 0.0074	Lag deimhinneach 0.0198	Lag deimhinneach 0.0318	Lag àicheil -0.1198
Answer 12	-	Lag deimhinneach 0.0392	Lag deimhinneach 0.1042	Lag àicheil -0.0353	Lag deimhinneach 0.0357	Lag deimhinneach 0.0249	Lag deimhinneach 0.0297	Lag àicheil -0.1526
Answer 13	-	Lag deimhinneach 0.0646	Lag deimhinneach 0.1052	Lag àicheil -0.0444	Lag deimhinneach 0.0266	Lag deimhinneach 0.0416	Lag deimhinneach 0.0176	Lag àicheil -0.1605
Answer 14	-	Lag deimhinneach 0.0714	Lag deimhinneach 0.1026	Lag àicheil -0.0002	Lag àicheil -0.0090	Lag àicheil -0.0012	Lag deimhinneach 0.0086	Lag àicheil -0.1174
Answer 15	-	Lag deimhinneach 0.0558	Lag deimhinneach 0.1369	Lag àicheil -0.0419	Lag deimhinneach 0.0176	Lag àicheil -0.0163	Lag deimhinneach 0.0222	Lag àicheil -0.1183
Answer 16	-	Lag deimhinneach 0.0592	Lag deimhinneach 0.0275	Lag àicheil -0.0384	Lag àicheil -0.0402	Lag deimhinneach 0.0652	Lag deimhinneach 0.0283	Lag àicheil -0.0710

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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

Pròiseact Pet WAS SAS SASTSTS®

Bha Valerii airidh air eòlaiche-inntinn oideachaidh oideachaidh sòisealta ann an 1993 agus tha e air an eòlas aige a chuir an gnìomh ann an riaghladh pròiseict.
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