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) ການກະທໍາຂອງບໍລິສັດທີ່ກ່ຽວຂ້ອງກັບພະນັກງານໃນເດືອນທີ່ຜ່ານມາ (ແມ່ນ / ບໍ່ແມ່ນ)

2) ການກະທໍາຂອງບໍລິສັດທີ່ກ່ຽວຂ້ອງກັບບຸກຄະລາກອນໃນເດືອນທີ່ຜ່ານມາ (ຄວາມເປັນຈິງໃນ%)

3) ຄວາມຢ້ານກົວ

4) ບັນຫາໃຫຍ່ທີ່ສຸດທີ່ປະເຊີນຫນ້າກັບປະເທດຂອງຂ້ອຍ

5) ຄຸນລັກສະນະແລະຄວາມສາມາດໃດທີ່ຜູ້ນໍາທີ່ດີໃຊ້ໃນເວລາສ້າງທີມງານທີ່ປະສົບຜົນສໍາເລັດ?

6) Google ປັດໄຈທີ່ເຮັດໃຫ້ທີມງານມີຜົນກະທົບ

7) ບຸລິມະສິດຕົ້ນຕໍຂອງຜູ້ຊອກວຽກ

8) ສິ່ງທີ່ເຮັດໃຫ້ນາຍຈ້າງເປັນຜູ້ນໍາທີ່ຍິ່ງໃຫຍ່?

9) ສິ່ງທີ່ເຮັດໃຫ້ຄົນປະສົບຜົນສໍາເລັດຢູ່ບ່ອນເຮັດວຽກ?

10) ທ່ານພ້ອມແລ້ວບໍທີ່ຈະໄດ້ຮັບເງິນເດືອນຫນ້ອຍລົງທີ່ຈະເຮັດວຽກຫ່າງໄກສອກຫຼີກ?

11) ມີ Agelim ມີຢູ່ບໍ?

12) Ageism ໃນການເຮັດວຽກ

13) ການເປັນຣະວັງໃນຊີວິດ

14) ສາເຫດຂອງການມີຄວາມຫມາຍ

15) ເຫດຜົນທີ່ຄົນເຮົາຍອມແພ້ (ໂດຍ Anna ທີ່ສໍາຄັນ)

16) ໄວ້ວາງໃຈ (#WVS)

17) ການສໍາຫຼວດຄວາມສຸກ Oxford

18) ສະຫວັດດີການທາງຈິດວິທະຍາ

19) ບ່ອນທີ່ທ່ານຈະເປັນໂອກາດທີ່ຫນ້າຕື່ນເຕັ້ນທີ່ສຸດຕໍ່ໄປຂອງທ່ານ?

20) ທ່ານຈະເຮັດແນວໃດໃນອາທິດນີ້ເພື່ອເບິ່ງແຍງສຸຂະພາບຈິດຂອງທ່ານ?

21) ຂ້ອຍມີຊີວິດຢູ່ໃນການຄິດກ່ຽວກັບອະດີດຂອງຂ້ອຍ, ປະຈຸບັນຫຼືອະນາຄົດ

22) ຄວາມຮູ້ບຸນບຸນ

23) ປັນຍາປະດິດແລະໃນຕອນທ້າຍຂອງພົນລະເມືອງ

24) ເປັນຫຍັງຜູ້ຄົນຈຶ່ງຊັກຊ້າ?

25) ຄວາມແຕກຕ່າງລະຫວ່າງເພດໃນການສ້າງຄວາມຫມັ້ນໃຈໃນຕົນເອງ (IFD ASD ESTENSBACH)

26) ການປະເມີນວັດທະນະທໍາ Xing.com

27) Patrick Lencioni's "ຄວາມຜິດພາດຫ້າຂອງທີມງານ"

28) ຄວາມເຫັນອົກເຫັນໃຈແມ່ນ ...

29) ສິ່ງທີ່ຈໍາເປັນສໍາລັບຜູ້ຊ່ຽວຊານໃນການເລືອກຂໍ້ສະເຫນີວຽກ?

30) ເປັນຫຍັງຜູ້ຄົນຈຶ່ງຕ້ານທານກັບການປ່ຽນແປງ (ໂດຍsioobhán mchale)

31) ທ່ານກໍານົດອາລົມຂອງທ່ານແນວໃດ? (ໂດຍ Nawal Mustafa M.A. )

32) 21 ທັກສະທີ່ຈ່າຍໃຫ້ເຈົ້າຕະຫຼອດໄປ (ໂດຍ Jeremiah Teo / 赵汉昇)

33) ເສລີພາບທີ່ແທ້ຈິງແມ່ນ ...

34) 12 ວິທີການສ້າງຄວາມໄວ້ວາງໃຈກັບຄົນອື່ນ (ໂດຍ Wright Justin)

35) ຄຸນລັກສະນະຂອງພະນັກງານທີ່ມີພອນສະຫວັນ (ໂດຍສະຖາບັນຄຸ້ມຄອງພອນສະຫວັນ)

36) ຈໍານວນ 10 ທີ່ຈະກະຕຸ້ນໃຫ້ທີມງານຂອງທ່ານ

37) Algebra of Conscience (ໂດຍ Vladimir Lefebvre)

38) ສາມຄວາມເປັນໄປໄດ້ທີ່ແຕກຕ່າງກັນຂອງອະນາຄົດ (ໂດຍ 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.

ຄວາມຢ້ານກົວ

ຕາຕະລາງ ພັນ

VUCA

ມູນຄ່າທີ່ສໍາຄັນຂອງຄ່າສໍາປະສິດສໍາພັນ

ການແຈກຢາຍຕາມປົກກະຕິ, ໂດຍ William Sealy Gosset (ນັກຮຽນ) r = 0.0329

ການແຈກຢາຍແບບທໍາມະດາທີ່ບໍ່ແມ່ນປົກກະຕິ, ໂດຍ Spearman r = 0.0013

ສະແດງຜົນໄດ້ຮັບເທົ່ານັ້ນ > r = 0.0329

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

ເຈົ້າຂອງຜະລິດຕະພັນ SaaS SDTEST®

Valerii ມີຄຸນສົມບັດເປັນນັກວິຊາການດ້ານຈິດຕະວິທະຍາສັງຄົມໃນ 1993 ແລະໄດ້ນໍາໃຊ້ຄວາມຮູ້ຂອງລາວໃນການຄຸ້ມຄອງໂຄງການ.
Valerii ໄດ້ຮັບປະລິນຍາໂທແລະຄຸນສົມບັດຂອງຜູ້ຈັດການໂຄງການແລະໂຄງການໃນປີ 2013. ໃນລະຫວ່າງໂຄງການປະລິນຍາໂທຂອງລາວ, ລາວໄດ້ກາຍເປັນຄວາມຄຸ້ນເຄີຍກັບໂຄງການ Roadmap (GPM Deutsche Gesellschaft für Projektmanagement e. V.) ແລະ Spiral Dynamics.
Valerii ເປັນຜູ້ຂຽນຂອງການສໍາຫຼວດຄວາມບໍ່ແນ່ນອນຂອງ V.U.C.A. ແນວຄວາມຄິດໂດຍໃຊ້ Spiral Dynamics ແລະສະຖິຕິຄະນິດສາດໃນຈິດຕະວິທະຍາ, ແລະ 38 ການສໍາຫຼວດສາກົນ.

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