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 = 0.0335

Spearman tarafından normal olmayan dağılım r = 0.0014

Sadece sonuçları göster > r = 0.0335

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 0.0521	Zayıf pozitif 0.0294	Zayıf negatif -0.0147	Zayıf pozitif 0.0885	Zayıf pozitif 0.0316	Zayıf negatif -0.0110	Zayıf negatif -0.1513
Answer 2	-	Zayıf pozitif 0.0213	Zayıf pozitif 0.0013	Zayıf negatif -0.0432	Zayıf pozitif 0.0618	Zayıf pozitif 0.0453	Zayıf pozitif 0.0103	Zayıf negatif -0.0918
Answer 3	-	Zayıf negatif -0.0042	Zayıf negatif -0.0116	Zayıf negatif -0.0406	Zayıf negatif -0.0477	Zayıf pozitif 0.0487	Zayıf pozitif 0.0767	Zayıf negatif -0.0191
Answer 4	-	Zayıf pozitif 0.0421	Zayıf pozitif 0.0350	Zayıf negatif -0.0115	Zayıf pozitif 0.0112	Zayıf pozitif 0.0307	Zayıf pozitif 0.0175	Zayıf negatif -0.0980
Answer 5	-	Zayıf pozitif 0.0288	Zayıf pozitif 0.1272	Zayıf pozitif 0.0146	Zayıf pozitif 0.0697	Zayıf pozitif 0.0037	Zayıf negatif -0.0215	Zayıf negatif -0.1746
Answer 6	-	Zayıf negatif -0.0001	Zayıf pozitif 0.0042	Zayıf negatif -0.0607	Zayıf negatif -0.0115	Zayıf pozitif 0.0231	Zayıf pozitif 0.0826	Zayıf negatif -0.0309
Answer 7	-	Zayıf pozitif 0.0117	Zayıf pozitif 0.0372	Zayıf negatif -0.0653	Zayıf negatif -0.0283	Zayıf pozitif 0.0495	Zayıf pozitif 0.0626	Zayıf negatif -0.0505
Answer 8	-	Zayıf pozitif 0.0658	Zayıf pozitif 0.0830	Zayıf negatif -0.0310	Zayıf pozitif 0.0139	Zayıf pozitif 0.0334	Zayıf pozitif 0.0134	Zayıf negatif -0.1322
Answer 9	-	Zayıf pozitif 0.0660	Zayıf pozitif 0.1658	Zayıf pozitif 0.0051	Zayıf pozitif 0.0691	Zayıf negatif -0.0093	Zayıf negatif -0.0498	Zayıf negatif -0.1820
Answer 10	-	Zayıf pozitif 0.0758	Zayıf pozitif 0.0724	Zayıf negatif -0.0173	Zayıf pozitif 0.0236	Zayıf pozitif 0.0312	Zayıf negatif -0.0115	Zayıf negatif -0.1263
Answer 11	-	Zayıf pozitif 0.0577	Zayıf pozitif 0.0544	Zayıf negatif -0.0075	Zayıf pozitif 0.0082	Zayıf pozitif 0.0185	Zayıf pozitif 0.0293	Zayıf negatif -0.1190
Answer 12	-	Zayıf pozitif 0.0376	Zayıf pozitif 0.1007	Zayıf negatif -0.0342	Zayıf pozitif 0.0296	Zayıf pozitif 0.0273	Zayıf pozitif 0.0341	Zayıf negatif -0.1500
Answer 13	-	Zayıf pozitif 0.0627	Zayıf pozitif 0.1017	Zayıf negatif -0.0443	Zayıf pozitif 0.0248	Zayıf pozitif 0.0434	Zayıf pozitif 0.0189	Zayıf negatif -0.1576
Answer 14	-	Zayıf pozitif 0.0732	Zayıf pozitif 0.1036	Zayıf pozitif 0.0048	Zayıf negatif -0.0105	Zayıf negatif -0.0039	Zayıf pozitif 0.0041	Zayıf negatif -0.1157
Answer 15	-	Zayıf pozitif 0.0539	Zayıf pozitif 0.1381	Zayıf negatif -0.0424	Zayıf pozitif 0.0163	Zayıf negatif -0.0147	Zayıf pozitif 0.0216	Zayıf negatif -0.1173
Answer 16	-	Zayıf pozitif 0.0590	Zayıf pozitif 0.0274	Zayıf negatif -0.0375	Zayıf negatif -0.0429	Zayıf pozitif 0.0687	Zayıf pozitif 0.0253	Zayıf negatif -0.0698

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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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