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) Şirketlerin geçen ay personelle ilgili eylemleri (evet / hayır)

2) Şirketlerin geçen ay personel ile ilgili olarak eylemleri (gerçeği% olarak)

3) Korku

4) Ülkemin karşılaştığı en büyük sorunlar

5) Başarılı ekipler oluştururken iyi liderlerin kullandığı nitelikler ve yetenekler ne gibi?

6) Google. Takım etkinliğini etkileyen faktörler

7) İş arayanların ana öncelikleri

8) Bir patronu büyük bir lider yapan nedir?

9) İnsanları işte başarılı kılan nedir?

10) Uzaktan çalışmak için daha az ücret almaya hazır mısınız?

11) Yaşcılık var mı?

12) Kariyerde yaşlanma

13) Hayatta Yaşlılık

14) Yaşlılığın nedenleri

15) İnsanların Vazgeçme Nedenleri (Anna Vital)

16) GÜVEN (#WVS)

17) Oxford Mutluluk Araştırması

18) Psikolojik refah

19) Bir sonraki en heyecan verici fırsatınız nerede?

20) Zihinsel sağlığınıza bakmak için bu hafta ne yapacaksınız?

21) Geçmişim, şimdiki zamanımı veya geleceğimi düşünerek yaşıyorum

22) Meritokrasi

23) Yapay zeka ve medeniyetin sonu

24) İnsanlar neden erteliyor?

25) Kendine güven oluşturmada cinsiyet farkı (IFD Allensbach)

26) Xing.com Kültür Değerlendirmesi

27) Patrick Lencioni'nin "Bir Ekibin Beş İşlev Konstrüksiyonu"

28) Empati ...

29) Bir iş teklifi seçme konusunda BT uzmanları için gerekli olan nedir?

30) İnsanlar neden değişime direniyor (Siobhán McHale tarafından)

31) Duygularınızı nasıl düzenlersiniz? (Nawal Mustafa M.A. tarafından)

32) 21 Sonsuza Kadar Ödeme Becerileri (Jeremiah Teo / 赵汉昇 tarafından)

33) Gerçek özgürlük ...

34) Başkalarına Güven Yapmanın 12 Yolu (Justin Wright tarafından)

35) Yetenekli bir çalışanın özellikleri (Yetenek Yönetim Enstitüsü tarafından)

36) Ekibinizi motive etmek için 10 anahtar

37) Vicdan Cebiri (Vladimir Lefebvre tarafından)

38) Geleceğin Üç Farklı Olasılığı (Dr. Clare W. Graves tarafından)

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.

Korku

Grafikler Bağıntı

VUCA

Korelasyon katsayısının kritik değeri

Normal Dağıtım, William Sealy Gosset (Öğrenci) r = 0.0331

Spearman tarafından normal olmayan dağılım r = 0.0013

Sadece sonuçları göster > r = 0.0331

Dağıtım	Normal olmayan	Normal olmayan	Normal olmayan	Normal	Normal	Normal	Normal	Normal
Tüm Sorular Tüm Sorular En büyük korkum
En büyük korkum
Answer 1	-	Zayıf pozitif 0.0562	Zayıf pozitif 0.0311	Zayıf negatif -0.0164	Zayıf pozitif 0.0903	Zayıf pozitif 0.0301	Zayıf negatif -0.0120	Zayıf negatif -0.1534
Answer 2	-	Zayıf pozitif 0.0217	Zayıf pozitif 0.0011	Zayıf negatif -0.0455	Zayıf pozitif 0.0660	Zayıf pozitif 0.0440	Zayıf pozitif 0.0117	Zayıf negatif -0.0942
Answer 3	-	Zayıf negatif -0.0034	Zayıf negatif -0.0104	Zayıf negatif -0.0419	Zayıf negatif -0.0451	Zayıf pozitif 0.0462	Zayıf pozitif 0.0780	Zayıf negatif -0.0204
Answer 4	-	Zayıf pozitif 0.0436	Zayıf pozitif 0.0362	Zayıf negatif -0.0177	Zayıf pozitif 0.0150	Zayıf pozitif 0.0296	Zayıf pozitif 0.0189	Zayıf negatif -0.0984
Answer 5	-	Zayıf pozitif 0.0298	Zayıf pozitif 0.1270	Zayıf pozitif 0.0133	Zayıf pozitif 0.0724	Zayıf negatif -0.0002	Zayıf negatif -0.0199	Zayıf negatif -0.1742
Answer 6	-	Zayıf negatif -0.0003	Zayıf pozitif 0.0089	Zayıf negatif -0.0627	Zayıf negatif -0.0074	Zayıf pozitif 0.0190	Zayıf pozitif 0.0825	Zayıf negatif -0.0321
Answer 7	-	Zayıf pozitif 0.0123	Zayıf pozitif 0.0388	Zayıf negatif -0.0684	Zayıf negatif -0.0238	Zayıf pozitif 0.0468	Zayıf pozitif 0.0631	Zayıf negatif -0.0517
Answer 8	-	Zayıf pozitif 0.0699	Zayıf pozitif 0.0857	Zayıf negatif -0.0318	Zayıf pozitif 0.0150	Zayıf pozitif 0.0341	Zayıf pozitif 0.0125	Zayıf negatif -0.1372
Answer 9	-	Zayıf pozitif 0.0666	Zayıf pozitif 0.1681	Zayıf pozitif 0.0094	Zayıf pozitif 0.0694	Zayıf negatif -0.0131	Zayıf negatif -0.0533	Zayıf negatif -0.1815
Answer 10	-	Zayıf pozitif 0.0776	Zayıf pozitif 0.0744	Zayıf negatif -0.0185	Zayıf pozitif 0.0224	Zayıf pozitif 0.0352	Zayıf negatif -0.0135	Zayıf negatif -0.1293
Answer 11	-	Zayıf pozitif 0.0585	Zayıf pozitif 0.0531	Zayıf negatif -0.0094	Zayıf pozitif 0.0086	Zayıf pozitif 0.0195	Zayıf pozitif 0.0313	Zayıf negatif -0.1200
Answer 12	-	Zayıf pozitif 0.0378	Zayıf pozitif 0.1030	Zayıf negatif -0.0357	Zayıf pozitif 0.0350	Zayıf pozitif 0.0261	Zayıf pozitif 0.0297	Zayıf negatif -0.1510
Answer 13	-	Zayıf pozitif 0.0642	Zayıf pozitif 0.1044	Zayıf negatif -0.0454	Zayıf pozitif 0.0259	Zayıf pozitif 0.0424	Zayıf pozitif 0.0183	Zayıf negatif -0.1595
Answer 14	-	Zayıf pozitif 0.0718	Zayıf pozitif 0.1034	Zayıf negatif -0.0003	Zayıf negatif -0.0085	Zayıf negatif -0.0016	Zayıf pozitif 0.0074	Zayıf negatif -0.1172
Answer 15	-	Zayıf pozitif 0.0550	Zayıf pozitif 0.1382	Zayıf negatif -0.0418	Zayıf pozitif 0.0181	Zayıf negatif -0.0163	Zayıf pozitif 0.0211	Zayıf negatif -0.1183
Answer 16	-	Zayıf pozitif 0.0591	Zayıf pozitif 0.0276	Zayıf negatif -0.0384	Zayıf negatif -0.0397	Zayıf pozitif 0.0651	Zayıf pozitif 0.0280	Zayıf negatif -0.0710

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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

Ürün Sahibi SaaS Pet Projesi SDTEST®

Valerii, 1993 yılında sosyal pedagog-psikolog olarak nitelendirildi ve o zamandan beri proje yönetiminde bilgisini uyguladı.
Valerii, 2013 yılında bir yüksek lisans derecesi ve Proje ve Program Yöneticisi kalifikasyonu aldı. Yüksek lisans programı sırasında proje yol haritası (GPM Deutsche Geselschaft Für Projektmanagement E. V.) ve spiral dinamiklere aşina oldu.
Valerii çeşitli spiral dinamik testleri aldı ve bilgi ve deneyimini SDTest'in mevcut versiyonunu uyarlamak için kullandı.
Valerii, V.U.C.A.'nın belirsizliğini araştırmanın yazarıdır. Psikolojide spiral dinamikler ve matematiksel istatistikler kullanan kavram, 20'den fazla uluslararası anket.

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