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

ChartsCo-dhàimh

VUCA

Seòrsa co-dhàimh	sreathach (Pearson) sreathach (Pearson) Neo-loidhneach (Spearman)
Critical luach na co-dhàimh coefficient	Sgaoileadh àbhaisteach, le Uilleam Sealy Howet (Oileanach) Sgaoileadh àbhaisteach, le Uilleam Sealy Howet (Oileanach) Sgaoileadh neo-àbhaisteach, le spearman	Seall a-mhàin toraidhean a-mhàin > r = 0.0308

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 0.0513	Lag deimhinneach 0.0254	Lag àicheil -0.0233	Lag deimhinneach 0.0989	Lag deimhinneach 0.0408	Lag àicheil -0.0127	Lag àicheil -0.1587
Answer 2	-	Lag deimhinneach 0.0181	Lag àicheil -0.0044	Lag àicheil -0.0427	Lag deimhinneach 0.0621	Lag deimhinneach 0.0508	Lag deimhinneach 0.0135	Lag àicheil -0.0948
Answer 3	-	Lag àicheil -0.0029	Lag àicheil -0.0024	Lag àicheil -0.0464	Lag àicheil -0.0400	Lag deimhinneach 0.0481	Lag deimhinneach 0.0743	Lag àicheil -0.0259
Answer 4	-	Lag deimhinneach 0.0451	Lag deimhinneach 0.0355	Lag àicheil -0.0270	Lag deimhinneach 0.0160	Lag deimhinneach 0.0403	Lag deimhinneach 0.0212	Lag àicheil -0.1042
Answer 5	-	Lag deimhinneach 0.0234	Lag deimhinneach 0.1266	Lag deimhinneach 0.0077	Lag deimhinneach 0.0782	Lag àicheil -0.0002	Lag àicheil -0.0152	Lag àicheil -0.1754
Answer 6	-	Lag deimhinneach 0.0024	Lag deimhinneach 0.0096	Lag àicheil -0.0623	Lag àicheil -0.0099	Lag deimhinneach 0.0203	Lag deimhinneach 0.0861	Lag àicheil -0.0367
Answer 7	-	Lag deimhinneach 0.0083	Lag deimhinneach 0.0357	Lag àicheil -0.0660	Lag àicheil -0.0302	Lag deimhinneach 0.0504	Lag deimhinneach 0.0703	Lag àicheil -0.0521
Answer 8	-	Lag deimhinneach 0.0649	Lag deimhinneach 0.0748	Lag àicheil -0.0281	Lag deimhinneach 0.0104	Lag deimhinneach 0.0417	Lag deimhinneach 0.0155	Lag àicheil -0.1351
Answer 9	-	Lag deimhinneach 0.0759	Lag deimhinneach 0.1617	Lag deimhinneach 0.0039	Lag deimhinneach 0.0618	Lag àicheil -0.0055	Lag àicheil -0.0517	Lag àicheil -0.1810
Answer 10	-	Lag deimhinneach 0.0785	Lag deimhinneach 0.0610	Lag àicheil -0.0173	Lag deimhinneach 0.0245	Lag deimhinneach 0.0381	Lag àicheil -0.0074	Lag àicheil -0.1321
Answer 11	-	Lag deimhinneach 0.0614	Lag deimhinneach 0.0542	Lag àicheil -0.0108	Lag deimhinneach 0.0117	Lag deimhinneach 0.0294	Lag deimhinneach 0.0214	Lag àicheil -0.1270
Answer 12	-	Lag deimhinneach 0.0396	Lag deimhinneach 0.0957	Lag àicheil -0.0333	Lag deimhinneach 0.0354	Lag deimhinneach 0.0300	Lag deimhinneach 0.0254	Lag àicheil -0.1503
Answer 13	-	Lag deimhinneach 0.0707	Lag deimhinneach 0.0958	Lag àicheil -0.0380	Lag deimhinneach 0.0277	Lag deimhinneach 0.0397	Lag deimhinneach 0.0129	Lag àicheil -0.1594
Answer 14	-	Lag deimhinneach 0.0869	Lag deimhinneach 0.0902	Lag àicheil -0.0039	Lag àicheil -0.0156	Lag deimhinneach 0.0053	Lag deimhinneach 0.0105	Lag àicheil -0.1177
Answer 15	-	Lag deimhinneach 0.0576	Lag deimhinneach 0.1222	Lag àicheil -0.0338	Lag deimhinneach 0.0127	Lag àicheil -0.0156	Lag deimhinneach 0.0267	Lag àicheil -0.1173
Answer 16	-	Lag deimhinneach 0.0710	Lag deimhinneach 0.0241	Lag àicheil -0.0386	Lag àicheil -0.0407	Lag deimhinneach 0.0724	Lag deimhinneach 0.0175	Lag àicheil -0.0739

Export gu MS Excel

Bidh an gnìomh seo ri fhaighinn anns na cunntasan-bheachd VUCA agad fhèin

Ceart gu leòr

You can not only just create your poll in the Cìs «V.U.C.A bhòtaidh dealbhaiche» (with a unique link and your logo) but also you can earn money by selling its results in the Cìs «Bùth Poll», as already the authors of polls.

If you participated in VUCA polls, you can see your results and compare them with the overall polls results, which are constantly growing, in your personal account after purchasing Cìs «My SDT»

[1] https://twitter.com/wileyprof

[2] https://colinallen.dnsalias.org

[3] https://philpeople.org/profiles/colin-allen

2023.10.13

FearpersonqualitiesprojectorganizationalstructureRACIresponsibilitymatrixCritical ChainProject Managementfocus factorJiraempathyleadersbossGermanyChinaPolicyUkraineRussiawarvolatilityuncertaintycomplexityambiguityVUCArelocatejobproblemcountryreasongive upobjectivekeyresultmathematicalpsychologyMBTIHR metricsstandardDEIcorrelationriskscoringmodelGame TheoryPrisoner's Dilemma

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.

Tha an dreuchd seo air 0 Beachdan

Freagairt gu

Cuir dheth freagairt

Fàg do bheachd