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)

39) Gnìomhan gus fèin-earbsa do-chreidsinneach a thogail (le Suren Samarchyan)

40)

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 = 0.0317

Sgaoileadh neo-àbhaisteach, le spearman r = 0.0013

Seall a-mhàin toraidhean a-mhàin > r = 0.0317

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 0.0537	Lag deimhinneach 0.0288	Lag àicheil -0.0175	Lag deimhinneach 0.0948	Lag deimhinneach 0.0381	Lag àicheil -0.0178	Lag àicheil -0.1563
Answer 2	-	Lag deimhinneach 0.0194	Lag àicheil -0.0048	Lag àicheil -0.0385	Lag deimhinneach 0.0655	Lag deimhinneach 0.0495	Lag deimhinneach 0.0106	Lag àicheil -0.0982
Answer 3	-	Lag àicheil -0.0001	Lag àicheil -0.0084	Lag àicheil -0.0449	Lag àicheil -0.0445	Lag deimhinneach 0.0485	Lag deimhinneach 0.0742	Lag àicheil -0.0207
Answer 4	-	Lag deimhinneach 0.0433	Lag deimhinneach 0.0291	Lag àicheil -0.0232	Lag deimhinneach 0.0163	Lag deimhinneach 0.0367	Lag deimhinneach 0.0226	Lag àicheil -0.0996
Answer 5	-	Lag deimhinneach 0.0277	Lag deimhinneach 0.1291	Lag deimhinneach 0.0108	Lag deimhinneach 0.0745	Lag deimhinneach 0.0012	Lag àicheil -0.0177	Lag àicheil -0.1783
Answer 6	-	Lag àicheil -0.0015	Lag deimhinneach 0.0058	Lag àicheil -0.0607	Lag àicheil -0.0094	Lag deimhinneach 0.0255	Lag deimhinneach 0.0844	Lag àicheil -0.0363
Answer 7	-	Lag deimhinneach 0.0113	Lag deimhinneach 0.0348	Lag àicheil -0.0657	Lag àicheil -0.0305	Lag deimhinneach 0.0521	Lag deimhinneach 0.0686	Lag àicheil -0.0532
Answer 8	-	Lag deimhinneach 0.0657	Lag deimhinneach 0.0728	Lag àicheil -0.0255	Lag deimhinneach 0.0124	Lag deimhinneach 0.0386	Lag deimhinneach 0.0153	Lag àicheil -0.1345
Answer 9	-	Lag deimhinneach 0.0757	Lag deimhinneach 0.1605	Lag deimhinneach 0.0066	Lag deimhinneach 0.0612	Lag àicheil -0.0063	Lag àicheil -0.0492	Lag àicheil -0.1822
Answer 10	-	Lag deimhinneach 0.0764	Lag deimhinneach 0.0669	Lag àicheil -0.0124	Lag deimhinneach 0.0271	Lag deimhinneach 0.0365	Lag àicheil -0.0130	Lag àicheil -0.1348
Answer 11	-	Lag deimhinneach 0.0634	Lag deimhinneach 0.0526	Lag àicheil -0.0075	Lag deimhinneach 0.0096	Lag deimhinneach 0.0264	Lag deimhinneach 0.0242	Lag àicheil -0.1270
Answer 12	-	Lag deimhinneach 0.0450	Lag deimhinneach 0.0944	Lag àicheil -0.0323	Lag deimhinneach 0.0307	Lag deimhinneach 0.0343	Lag deimhinneach 0.0260	Lag àicheil -0.1530
Answer 13	-	Lag deimhinneach 0.0725	Lag deimhinneach 0.0947	Lag àicheil -0.0389	Lag deimhinneach 0.0265	Lag deimhinneach 0.0443	Lag deimhinneach 0.0144	Lag àicheil -0.1631
Answer 14	-	Lag deimhinneach 0.0820	Lag deimhinneach 0.0897	Lag àicheil -0.0030	Lag àicheil -0.0122	Lag deimhinneach 0.0060	Lag deimhinneach 0.0135	Lag àicheil -0.1213
Answer 15	-	Lag deimhinneach 0.0549	Lag deimhinneach 0.1265	Lag àicheil -0.0334	Lag deimhinneach 0.0119	Lag àicheil -0.0153	Lag deimhinneach 0.0242	Lag àicheil -0.1157
Answer 16	-	Lag deimhinneach 0.0732	Lag deimhinneach 0.0242	Lag àicheil -0.0373	Lag àicheil -0.0398	Lag deimhinneach 0.0729	Lag deimhinneach 0.0169	Lag àicheil -0.0774

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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

Sealbhadair Bathar SaaS SDTEST®

Fhuair Valerii teisteanas mar pedagogue-psychologist sòisealta ann an 1993 agus bhon uair sin tha e air a chuid eòlais a chleachdadh ann an stiùireadh pròiseict.
Fhuair Valerii ceum Maighstireachd agus an teisteanas manaidsear pròiseict agus prògram ann an 2013. Rè a phrògram Maighstireachd, dh'fhàs e eòlach air Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) agus Spiral Dynamics.
Tha Valerii na ùghdar air sgrùdadh a dhèanamh air mì-chinnt an V.U.C.A. bun-bheachd a’ cleachdadh Spiral Dynamics agus staitistig matamataigeach ann an eòlas-inntinn, agus 38 cunntasan-bheachd eadar-nàiseanta.

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