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

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 = 0.0353

Ukusasazwa okuqhelekileyo, nge-spearman r = 0.0014

Bonisa iziphumo kuphela > r = 0.0353

Ukuhanjiswa	Ayiqhelekanga	Eqhelekileyo	Ayiqhelekanga	Eqhelekileyo	Eqhelekileyo	Eqhelekileyo	Eqhelekileyo	Eqhelekileyo
Yonke imibuzo Yonke imibuzo Olona loyiko lwam lukhulu
Olona loyiko lwam lukhulu
Answer 1	-	HIV amandla 0.0297	HIV amandla 0.0298	Emibi amandla -0.0106	HIV amandla 0.0970	HIV amandla 0.0325	Emibi amandla -0.0019	Emibi amandla -0.1558
Answer 2	-	HIV amandla 0.0188	HIV amandla 0.0076	Emibi amandla -0.0360	HIV amandla 0.0711	HIV amandla 0.0387	HIV amandla 0.0082	Emibi amandla -0.1011
Answer 3	-	HIV amandla 0.0026	Emibi amandla -0.0170	Emibi amandla -0.0443	Emibi amandla -0.0458	HIV amandla 0.0547	HIV amandla 0.0808	Emibi amandla -0.0270
Answer 4	-	HIV amandla 0.0332	HIV amandla 0.0285	Emibi amandla -0.0006	HIV amandla 0.0155	HIV amandla 0.0276	HIV amandla 0.0105	Emibi amandla -0.0917
Answer 5	-	HIV amandla 0.0122	HIV amandla 0.1193	HIV amandla 0.0095	HIV amandla 0.0721	HIV amandla 0.0057	Emibi amandla -0.0083	Emibi amandla -0.1687
Answer 6	-	HIV amandla 0.0044	HIV amandla 0.0005	Emibi amandla -0.0582	Emibi amandla -0.0004	HIV amandla 0.0210	HIV amandla 0.0830	Emibi amandla -0.0418
Answer 7	-	HIV amandla 0.0242	HIV amandla 0.0368	Emibi amandla -0.0521	Emibi amandla -0.0234	HIV amandla 0.0403	HIV amandla 0.0568	Emibi amandla -0.0597
Answer 8	-	HIV amandla 0.0707	HIV amandla 0.0781	Emibi amandla -0.0244	HIV amandla 0.0140	HIV amandla 0.0303	HIV amandla 0.0137	Emibi amandla -0.1334
Answer 9	-	HIV amandla 0.0564	HIV amandla 0.1531	HIV amandla 0.0127	HIV amandla 0.0769	Emibi amandla -0.0136	Emibi amandla -0.0495	Emibi amandla -0.1752
Answer 10	-	HIV amandla 0.0711	HIV amandla 0.0700	Emibi amandla -0.0127	HIV amandla 0.0246	HIV amandla 0.0363	Emibi amandla -0.0156	Emibi amandla -0.1273
Answer 11	-	HIV amandla 0.0542	HIV amandla 0.0488	HIV amandla 0.0086	HIV amandla 0.0078	HIV amandla 0.0162	HIV amandla 0.0315	Emibi amandla -0.1248
Answer 12	-	HIV amandla 0.0281	HIV amandla 0.0929	Emibi amandla -0.0325	HIV amandla 0.0361	HIV amandla 0.0276	HIV amandla 0.0365	Emibi amandla -0.1482
Answer 13	-	HIV amandla 0.0643	HIV amandla 0.0916	Emibi amandla -0.0418	HIV amandla 0.0237	HIV amandla 0.0425	HIV amandla 0.0239	Emibi amandla -0.1558
Answer 14	-	HIV amandla 0.0697	HIV amandla 0.1017	HIV amandla 0.0149	Emibi amandla -0.0062	Emibi amandla -0.0087	Emibi amandla -0.0002	Emibi amandla -0.1161
Answer 15	-	HIV amandla 0.0603	HIV amandla 0.1299	Emibi amandla -0.0379	HIV amandla 0.0163	Emibi amandla -0.0091	HIV amandla 0.0164	Emibi amandla -0.1204
Answer 16	-	HIV amandla 0.0691	HIV amandla 0.0221	Emibi amandla -0.0305	Emibi amandla -0.0515	HIV amandla 0.0750	HIV amandla 0.0187	Emibi amandla -0.0696

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