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) Izenzo zeenkampani ngokunxulumene nabasebenzi kwinyanga ephelileyo (ewe / hayi)

2) Izenzo zeenkampani ngokunxulumene nabasebenzi kwinyanga ephelileyo (inyani kwi%)

3) Uloyiko

4) Iingxaki ezinkulu ezijongene nelizwe lam

5) Zeziphi iimpawu kunye nobuchule obasebenzisa kakuhle xa wakha amaqela aphumeleleyo?

6) Google. Izinto ezinokuthi zenziwe ngeqela

7) Izinto eziphambili ngokubaluleka kwabafuna umsebenzi

8) Yintoni eyenza umphathi omkhulu?

9) Yintoni eyenza abantu baphumelele emsebenzini?

10) Ngaba ukulungele ukufumana umvuzo omncinci ukusebenza kude?

11) Ngaba Ubuncinci bukhona?

12) Ubudala bomsebenzi

13) Ubudala ebomini

14) Unobangela wobubi

15) Izizathu zokuba kutheni abantu benikezela (ngo-Anna kubalulekile)

16) Ukuthembana (#WVS)

17) Uvavanyo lwe-Oxford

18) Impilo yengqondo

19) Ingaba liphi ixesha lakho elinomdla?

20) Yintoni oza kuyenza kule veki ukhathalela impilo yakho yengqondo?

21) Ndihlala ndicinga ngexesha lam elidlulileyo, elikhoyo okanye elizayo

22) I-Meiritocy

23) Ubukrelekrele bokwenzela kunye nokuphela kwempucuko

24) Kutheni le nto abantu behlazela?

25) Umahluko wesini ekwakheni ukuzithemba (i-Allensbach)

26) Uvavanyo lwenkcubeko ye Xing.com

27) I-Patrick Lentance Lencn's

28) Uvelwano yi ...

29) Yintoni ebalulekileyo kuba ziingcali ze-IT ekukhetheni umsebenzi?

30) Isizathu sokuba abantu baxhathise utshintsho (nguSiobhán Mchale)

31) Uzilawula njani iimvakalelo zakho? (nge-nawal manafa m.a.)

32) 21 Izakhono ezikuhlawula ngonaphakade (nguYeremiya Teo / 赵汉昇)

33) Inkululeko yokwenyani ...

34) Iindlela ezili-12 zokwakha ukuthembana nabanye (nguJustin Wright)

35) Iimpawu zomsebenzi onetalente (ngeTelenter Institute)

36) Iindlela ezili-10 zokukhuthaza iqela lakho

37) IAlgebra yesazela (nguVladimir Lefebvre)

38) Amathuba amathathu Ahlukeneyo ekamva (nguGqr. 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.

Uloyiko

iitshati Ukuhlanganisa

VUCA

Ixabiso elibalulekileyo lomlinganiso wolungelelwaniso

Ukuhanjiswa okuqhelekileyo, nge-william gosset (umfundi) r = 0.033

Ukusasazwa okuqhelekileyo, nge-spearman r = 0.0013

Bonisa iziphumo kuphela > r = 0.033

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

Rhweba ngaphandle ku MS Excel

Lo msebenzi uza kufumaneka kwi-vuca yakho yeVUCA

Kulungile

You can not only just create your poll in the weRhafu «V.U.C.A vo mqambi» (with a unique link and your logo) but also you can earn money by selling its results in the weRhafu «Ivenkile yePoll», 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 weRhafu «My SDT»

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

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

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

2023.10.13

I-Valerii Kosenko

Imveliso ye-Saas ye-SDTEst®

UValerii wakufanelekela njenge-Pedagogue-Psychologitha ngo-1993 kwaye ukusebenzise ulwazi lwakhe kulawulo lweprojekthi.
I-Valerii ifumene isidanga se-Master kunye neProjekthi yeProjekthi kunye neNkqubo yeNkqubo yeNkqubo ngo-2013. Ngexesha lenkqubo yenkosi yakhe, waqhelana neProtsep yeProjek ye-E. V.
UValerii wathatha iimvavanyo ezahlukeneyo ze-spimics kwaye wasebenzisa ulwazi kunye namava akhe ukuhlengahlengisa uhlobo lwangoku lwe-SDTEst.
UValerii ngumbhali wokuphonononga ukungaqiniseki kweV.U.C.C.C.C.C.A. Umxholo usebenzisa i-spirals synamics nakwiinkcukacha-manani zemathematics kwi-Psychologlogy, ngaphezulu kwe-20 yamazwe aphesheya.

Esi sithuba sinayo 0 Izimvo

Phendula kwi

Cima impendulo

Shiya uluvo lwakho