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) Åtgärder från företag i relation till personal under den senaste månaden (ja / nej)

2) Aktiviteter för företag i förhållande till personal under den senaste månaden (fakta i%)

3) Rädsla

4) Största problem som mitt land står inför

5) Vilka egenskaper och förmågor använder bra ledare när de bygger framgångsrika team?

6) Google. Faktorer som påverkar teameffektiviteten

7) De viktigaste prioriteringarna för arbetssökande

8) Vad gör en chef till en stor ledare?

9) Vad gör människor framgångsrika på jobbet?

10) Är du redo att få mindre lön för att arbeta på distans?

11) Finns ageism?

12) Ageism i karriären

13) Ageism i livet

14) Causes of Ageism

15) Anledningar till att människor ger upp (av Anna Vital)

16) FÖRTROENDE (#WVS)

17) Oxford Happiness Survey

18) Psykologiskt välmående

19) Var skulle vara din nästa mest spännande möjlighet?

20) Vad ska du göra den här veckan för att ta hand om din mentala hälsa?

21) Jag lever och tänker på mitt förflutna, nutid eller framtid

22) Meritokrati

23) Konstgjord intelligens och slutet på civilisationen

24) Varför skjuter människor?

25) Könsskillnad i att bygga självförtroende (IFD Allensbach)

26) Xing.com kulturbedömning

27) Patrick Lencionis "The Five Dysfunctions of a Team"

28) Empati är ...

29) Vad är viktigt för IT -specialisterna för att välja ett jobberbjudande?

30) Varför människor motstår förändring (av Siobhán McHale)

31) Hur reglerar du dina känslor? (av Nawal Mustafa M.A.)

32) 21 färdigheter som betalar dig för alltid (av Jeremiah Teo / 赵汉昇)

33) Verklig frihet är ...

34) 12 sätt att bygga förtroende med andra (av Justin Wright)

35) Egenskaper hos en begåvad anställd (av Talent Management Institute)

36) 10 nycklar för att motivera ditt team

37) Samvetets algebra (av Vladimir Lefebvre)

38) Framtidens tre distinkta möjligheter (av Dr. Clare W. Graves)

39) Åtgärder för att bygga orubbligt självförtroende (av 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.

Rädsla

diagram Korrelation

VUCA

Kritiska värdet av korrelationskoefficienten

Normal Distribution, av William Sealy Gosset (Student) r = 0.0318

Icke normal distribution, av Spearman r = 0.0013

Visa endast resultat > r = 0.0318

Distribution	Icke normal	Icke normal	Icke normal	Vanligt	Vanligt	Vanligt	Vanligt	Vanligt
Alla frågor Alla frågor Min största rädsla är
Min största rädsla är
Answer 1	-	Svagt positivt 0.0524	Svagt positivt 0.0258	Svagt negativt -0.0180	Svagt positivt 0.0949	Svagt positivt 0.0355	Svagt negativt -0.0146	Svagt negativt -0.1537
Answer 2	-	Svagt positivt 0.0175	Svagt negativt -0.0058	Svagt negativt -0.0387	Svagt positivt 0.0669	Svagt positivt 0.0494	Svagt positivt 0.0116	Svagt negativt -0.0969
Answer 3	-	Svagt negativt -0.0035	Svagt negativt -0.0091	Svagt negativt -0.0441	Svagt negativt -0.0435	Svagt positivt 0.0477	Svagt positivt 0.0747	Svagt negativt -0.0199
Answer 4	-	Svagt positivt 0.0412	Svagt positivt 0.0255	Svagt negativt -0.0229	Svagt positivt 0.0192	Svagt positivt 0.0353	Svagt positivt 0.0246	Svagt negativt -0.0990
Answer 5	-	Svagt positivt 0.0227	Svagt positivt 0.1271	Svagt positivt 0.0109	Svagt positivt 0.0770	Svagt negativt -0.0005	Svagt negativt -0.0175	Svagt negativt -0.1774
Answer 6	-	Svagt negativt -0.0055	Svagt positivt 0.0042	Svagt negativt -0.0622	Svagt negativt -0.0080	Svagt positivt 0.0249	Svagt positivt 0.0863	Svagt negativt -0.0354
Answer 7	-	Svagt positivt 0.0084	Svagt positivt 0.0331	Svagt negativt -0.0656	Svagt negativt -0.0297	Svagt positivt 0.0523	Svagt positivt 0.0696	Svagt negativt -0.0522
Answer 8	-	Svagt positivt 0.0629	Svagt positivt 0.0710	Svagt negativt -0.0267	Svagt positivt 0.0130	Svagt positivt 0.0379	Svagt positivt 0.0184	Svagt negativt -0.1339
Answer 9	-	Svagt positivt 0.0711	Svagt positivt 0.1602	Svagt positivt 0.0072	Svagt positivt 0.0643	Svagt negativt -0.0106	Svagt negativt -0.0484	Svagt negativt -0.1819
Answer 10	-	Svagt positivt 0.0740	Svagt positivt 0.0656	Svagt negativt -0.0150	Svagt positivt 0.0292	Svagt positivt 0.0321	Svagt negativt -0.0123	Svagt negativt -0.1359
Answer 11	-	Svagt positivt 0.0629	Svagt positivt 0.0524	Svagt negativt -0.0098	Svagt positivt 0.0104	Svagt positivt 0.0253	Svagt positivt 0.0247	Svagt negativt -0.1270
Answer 12	-	Svagt positivt 0.0433	Svagt positivt 0.0921	Svagt negativt -0.0338	Svagt positivt 0.0335	Svagt positivt 0.0331	Svagt positivt 0.0257	Svagt negativt -0.1540
Answer 13	-	Svagt positivt 0.0687	Svagt positivt 0.0957	Svagt negativt -0.0396	Svagt positivt 0.0304	Svagt positivt 0.0408	Svagt positivt 0.0151	Svagt negativt -0.1630
Answer 14	-	Svagt positivt 0.0781	Svagt positivt 0.0884	Svagt negativt -0.0003	Svagt negativt -0.0096	Svagt positivt 0.0050	Svagt positivt 0.0138	Svagt negativt -0.1228
Answer 15	-	Svagt positivt 0.0539	Svagt positivt 0.1269	Svagt negativt -0.0339	Svagt positivt 0.0148	Svagt negativt -0.0172	Svagt positivt 0.0237	Svagt negativt -0.1160
Answer 16	-	Svagt positivt 0.0690	Svagt positivt 0.0248	Svagt negativt -0.0372	Svagt negativt -0.0385	Svagt positivt 0.0703	Svagt positivt 0.0205	Svagt negativt -0.0792

Export till MS Excel

Denna funktionalitet kommer att finnas tillgänglig i dina egna VUCA-undersökningar

You can not only just create your poll in the Taxa «V.U.C.A enkät designer» (with a unique link and your logo) but also you can earn money by selling its results in the Taxa «Omröstningsbutik», 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 Taxa «Min SDT»

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

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

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

2023.10.13

Valerii Kosenko

Produktägare SaaS SDTEST®

Valerii utbildades till socialpedagog-psykolog 1993 och har sedan dess tillämpat sina kunskaper inom projektledning.
Valerii tog en magisterexamen och projekt- och programledarexamen 2013. Under masterprogrammet blev han bekant med Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) och Spiral Dynamics.
Valerii är författaren till att utforska osäkerheten i V.U.C.A. koncept med Spiral Dynamics och matematisk statistik i psykologi, och 38 internationella undersökningar.

Det här inlägget har 0 Kommentarer

Svara till

Avbryt ett svar

Lämna din kommentar