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) Aðgerðir fyrirtækja í tengslum við starfsfólk í síðasta mánuði (já / nei)

2) Aðgerðir fyrirtækja í tengslum við starfsfólk í síðasta mánuði (staðreynd í%)

3) Ótta.

4) Stærstu vandamálin standa frammi fyrir mínu landi

5) Hvaða eiginleikar og hæfileikar nota góðir leiðtogar þegar þeir byggja árangursrík teymi?

6) Google. Þættir sem hafa áhrif á teymisáhrif

7) Helstu forgangsröðun atvinnuleitenda

8) Hvað gerir yfirmann að frábærum leiðtoga?

9) Hvað gerir fólk farsælt í vinnunni?

10) Ertu tilbúinn að fá minni laun til að vinna lítillega?

11) Er aldurshyggja til?

12) Aldurshyggja á ferli

13) Aldurshyggja í lífinu

14) Orsakir aldurshyggju

15) Ástæður þess að fólk gefst upp (eftir Anna Vital)

16) Traust (#WVS)

17) Hamingjukönnun Oxford

18) Sálfræðileg vellíðan

19) Hvar væri næsta spennandi tækifæri þitt?

20) Hvað ætlar þú að gera þessa vikuna til að sjá um geðheilsu þína?

21) Ég lifi að hugsa um fortíð mína, nútíð eða framtíð

22) Meritocracy

23) Gervigreind og lok siðmenningarinnar

24) Af hverju frestast fólk?

25) Kynjamunur á að byggja upp sjálfstraust (IFD Allensbach)

26) Xing.com menningarmat

27) Patrick Lencioni „Fimm truflanir liðs“

28) Samkennd er ...

29) Hvað er mikilvægt fyrir það sérfræðinga í því að velja atvinnutilboð?

30) Af hverju fólk standast breytingar (eftir Siobhán McHale)

31) Hvernig stjórnarðu tilfinningum þínum? (eftir Nawal Mustafa M.A.)

32) 21 Færni sem borgar þér að eilífu (eftir Jeremiah Teo / 赵汉昇)

33) Raunverulegt frelsi er ...

34) 12 leiðir til að byggja upp traust með öðrum (eftir Justin Wright)

35) Einkenni hæfileikaríks starfsmanns (eftir hæfileikastjórnunarstofnun)

36) 10 lyklar til að hvetja liðið þitt

37) Algebra samviskunnar (eftir Vladimir Lefebvre)

38) Þrír aðskildir möguleikar framtíðarinnar (eftir Dr. 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.

Ótta.

Töflur Fylgni

VUCA

Critical gildi fylgnistuðull

Venjuleg dreifing, eftir William Sealy Gosset (námsmaður) r = 0.0329

Ekki venjuleg dreifing, eftir Spearman r = 0.0013

Sýna aðeins niðurstöður > r = 0.0329

Dreifing	Ekki eðlilegt	Ekki eðlilegt	Ekki eðlilegt	Venjulegt	Venjulegt	Venjulegt	Venjulegt	Venjulegt
Allar spurningar Allar spurningar Mesta ótta mín er
Mesta ótta mín er
Answer 1	-	Veikt jákvætt 0.0566	Veikt jákvætt 0.0332	Veikt neikvætt -0.0170	Veikt jákvætt 0.0912	Veikt jákvætt 0.0308	Veikt neikvætt -0.0153	Veikt neikvætt -0.1537
Answer 2	-	Veikt jákvætt 0.0223	Veikt jákvætt 0.0011	Veikt neikvætt -0.0442	Veikt jákvætt 0.0639	Veikt jákvætt 0.0464	Veikt jákvætt 0.0120	Veikt neikvætt -0.0960
Answer 3	-	Veikt neikvætt -0.0031	Veikt neikvætt -0.0104	Veikt neikvætt -0.0407	Veikt neikvætt -0.0463	Veikt jákvætt 0.0475	Veikt jákvætt 0.0779	Veikt neikvætt -0.0213
Answer 4	-	Veikt jákvætt 0.0437	Veikt jákvætt 0.0357	Veikt neikvætt -0.0197	Veikt jákvætt 0.0161	Veikt jákvætt 0.0311	Veikt jákvætt 0.0187	Veikt neikvætt -0.0987
Answer 5	-	Veikt jákvætt 0.0296	Veikt jákvætt 0.1300	Veikt jákvætt 0.0124	Veikt jákvætt 0.0749	Veikt jákvætt 0.0014	Veikt neikvætt -0.0231	Veikt neikvætt -0.1771
Answer 6	-	Veikt neikvætt -0.0008	Veikt jákvætt 0.0090	Veikt neikvætt -0.0613	Veikt neikvætt -0.0070	Veikt jákvætt 0.0196	Veikt jákvætt 0.0803	Veikt neikvætt -0.0321
Answer 7	-	Veikt jákvætt 0.0118	Veikt jákvætt 0.0401	Veikt neikvætt -0.0693	Veikt neikvætt -0.0246	Veikt jákvætt 0.0471	Veikt jákvætt 0.0623	Veikt neikvætt -0.0505
Answer 8	-	Veikt jákvætt 0.0697	Veikt jákvætt 0.0875	Veikt neikvætt -0.0316	Veikt jákvætt 0.0155	Veikt jákvætt 0.0346	Veikt jákvætt 0.0098	Veikt neikvætt -0.1373
Answer 9	-	Veikt jákvætt 0.0679	Veikt jákvætt 0.1707	Veikt jákvætt 0.0105	Veikt jákvætt 0.0676	Veikt neikvætt -0.0138	Veikt neikvætt -0.0545	Veikt neikvætt -0.1821
Answer 10	-	Veikt jákvætt 0.0793	Veikt jákvætt 0.0772	Veikt neikvætt -0.0208	Veikt jákvætt 0.0242	Veikt jákvætt 0.0343	Veikt neikvætt -0.0152	Veikt neikvætt -0.1300
Answer 11	-	Veikt jákvætt 0.0590	Veikt jákvætt 0.0559	Veikt neikvætt -0.0071	Veikt jákvætt 0.0082	Veikt jákvætt 0.0205	Veikt jákvætt 0.0266	Veikt neikvætt -0.1213
Answer 12	-	Veikt jákvætt 0.0405	Veikt jákvætt 0.1050	Veikt neikvætt -0.0363	Veikt jákvætt 0.0361	Veikt jákvætt 0.0253	Veikt jákvætt 0.0277	Veikt neikvætt -0.1522
Answer 13	-	Veikt jákvætt 0.0655	Veikt jákvætt 0.1056	Veikt neikvætt -0.0439	Veikt jákvætt 0.0270	Veikt jákvætt 0.0417	Veikt jákvætt 0.0152	Veikt neikvætt -0.1601
Answer 14	-	Veikt jákvætt 0.0728	Veikt jákvætt 0.1049	Veikt neikvætt -0.0002	Veikt neikvætt -0.0088	Veikt neikvætt -0.0007	Veikt jákvætt 0.0061	Veikt neikvætt -0.1187
Answer 15	-	Veikt jákvætt 0.0561	Veikt jákvætt 0.1378	Veikt neikvætt -0.0415	Veikt jákvætt 0.0178	Veikt neikvætt -0.0162	Veikt jákvætt 0.0194	Veikt neikvætt -0.1176
Answer 16	-	Veikt jákvætt 0.0606	Veikt jákvætt 0.0308	Veikt neikvætt -0.0348	Veikt neikvætt -0.0421	Veikt jákvætt 0.0642	Veikt jákvætt 0.0250	Veikt neikvætt -0.0717

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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

Vörueigandi SaaS SDTEST®

Valerii var menntaður félags- og sálfræðingur árið 1993 og hefur síðan beitt þekkingu sinni í verkefnastjórnun.
Valerii fékk meistaragráðu og verkefna- og námsstjóraréttindi árið 2013. Á meistaranáminu kynntist hann Project Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) og Spiral Dynamics.
Valerii er höfundur þess að kanna óvissu V.U.C.A. hugtak sem notar Spiral Dynamics og stærðfræðilega tölfræði í sálfræði, og 38 alþjóðlegar kannanir.

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