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) Tindakan perusahaan sehubungan dengan personel dalam sebulan terakhir (ya / tidak)

2) Tindakan perusahaan sehubungan dengan personel pada bulan lalu (fakta dalam%)

3) Ketakutan

4) Masalah terbesar yang dihadapi negara saya

5) Kualitas dan kemampuan apa yang digunakan pemimpin yang baik saat membangun tim yang sukses?

6) Google. Faktor -faktor yang memengaruhi efektivitas tim

7) Prioritas utama pencari kerja

8) Apa yang membuat bos pemimpin yang hebat?

9) Apa yang membuat orang sukses di tempat kerja?

10) Apakah Anda siap menerima lebih sedikit gaji untuk bekerja dari jarak jauh?

11) Apakah Ageism ada?

12) Usia dalam karier

13) Usia dalam hidup

14) Penyebab Ageism

15) Alasan mengapa orang menyerah (oleh Anna Vital)

16) MEMERCAYAI (#WVS)

17) Survei Kebahagiaan Oxford

18) Kesejahteraan psikologis

19) Di mana peluang paling menarik Anda berikutnya?

20) Apa yang akan Anda lakukan minggu ini untuk menjaga kesehatan mental Anda?

21) Saya hidup berpikir tentang masa lalu, masa kini atau masa depan saya

22) Meritokrasi

23) Kecerdasan buatan dan akhir peradaban

24) Mengapa orang menunda -nunda?

25) Perbedaan gender dalam membangun kepercayaan diri (IFD Allensbach)

26) Xing.com Penilaian Budaya

27) Patrick Lencioni "The Five Disfunctions of a Team"

28) Empati adalah ...

29) Apa yang penting bagi spesialis TI dalam memilih tawaran pekerjaan?

30) Mengapa orang menolak perubahan (oleh Siobhán McHale)

31) Bagaimana Anda mengatur emosi Anda? (oleh Nawal Mustafa M.A.)

32) 21 Keterampilan yang Membayar Anda Selamanya (oleh Jeremiah Teo / 赵汉昇)

33) Kebebasan nyata adalah ...

34) 12 cara untuk membangun kepercayaan dengan orang lain (oleh Justin Wright)

35) Karakteristik karyawan yang berbakat (oleh Talent Management Institute)

36) 10 kunci untuk memotivasi tim Anda

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.

Ketakutan

grafik Korelasi

VUCA

Nilai kritis dari koefisien korelasi

Distribusi normal, oleh William Sealy Gosset (siswa) r = 0.0353

Distribusi non normal, oleh Spearman r = 0.0014

Hanya menunjukkan hasil > r = 0.0353

Distribusi	Tidak normal	Normal	Tidak normal	Normal	Normal	Normal	Normal	Normal
Semua pertanyaan Semua pertanyaan Ketakutan terbesar saya adalah
Ketakutan terbesar saya adalah
Answer 1	-	Positif lemah 0.0297	Positif lemah 0.0298	Negatif lemah -0.0106	Positif lemah 0.0970	Positif lemah 0.0325	Negatif lemah -0.0019	Negatif lemah -0.1558
Answer 2	-	Positif lemah 0.0188	Positif lemah 0.0076	Negatif lemah -0.0360	Positif lemah 0.0711	Positif lemah 0.0387	Positif lemah 0.0082	Negatif lemah -0.1011
Answer 3	-	Positif lemah 0.0026	Negatif lemah -0.0170	Negatif lemah -0.0443	Negatif lemah -0.0458	Positif lemah 0.0547	Positif lemah 0.0808	Negatif lemah -0.0270
Answer 4	-	Positif lemah 0.0332	Positif lemah 0.0285	Negatif lemah -0.0006	Positif lemah 0.0155	Positif lemah 0.0276	Positif lemah 0.0105	Negatif lemah -0.0917
Answer 5	-	Positif lemah 0.0122	Positif lemah 0.1193	Positif lemah 0.0095	Positif lemah 0.0721	Positif lemah 0.0057	Negatif lemah -0.0083	Negatif lemah -0.1687
Answer 6	-	Positif lemah 0.0044	Positif lemah 0.0005	Negatif lemah -0.0582	Negatif lemah -0.0004	Positif lemah 0.0210	Positif lemah 0.0830	Negatif lemah -0.0418
Answer 7	-	Positif lemah 0.0242	Positif lemah 0.0368	Negatif lemah -0.0521	Negatif lemah -0.0234	Positif lemah 0.0403	Positif lemah 0.0568	Negatif lemah -0.0597
Answer 8	-	Positif lemah 0.0707	Positif lemah 0.0781	Negatif lemah -0.0244	Positif lemah 0.0140	Positif lemah 0.0303	Positif lemah 0.0137	Negatif lemah -0.1334
Answer 9	-	Positif lemah 0.0564	Positif lemah 0.1531	Positif lemah 0.0127	Positif lemah 0.0769	Negatif lemah -0.0136	Negatif lemah -0.0495	Negatif lemah -0.1752
Answer 10	-	Positif lemah 0.0711	Positif lemah 0.0700	Negatif lemah -0.0127	Positif lemah 0.0246	Positif lemah 0.0363	Negatif lemah -0.0156	Negatif lemah -0.1273
Answer 11	-	Positif lemah 0.0542	Positif lemah 0.0488	Positif lemah 0.0086	Positif lemah 0.0078	Positif lemah 0.0162	Positif lemah 0.0315	Negatif lemah -0.1248
Answer 12	-	Positif lemah 0.0281	Positif lemah 0.0929	Negatif lemah -0.0325	Positif lemah 0.0361	Positif lemah 0.0276	Positif lemah 0.0365	Negatif lemah -0.1482
Answer 13	-	Positif lemah 0.0643	Positif lemah 0.0916	Negatif lemah -0.0418	Positif lemah 0.0237	Positif lemah 0.0425	Positif lemah 0.0239	Negatif lemah -0.1558
Answer 14	-	Positif lemah 0.0697	Positif lemah 0.1017	Positif lemah 0.0149	Negatif lemah -0.0062	Negatif lemah -0.0087	Negatif lemah -0.0002	Negatif lemah -0.1161
Answer 15	-	Positif lemah 0.0603	Positif lemah 0.1299	Negatif lemah -0.0379	Positif lemah 0.0163	Negatif lemah -0.0091	Positif lemah 0.0164	Negatif lemah -0.1204
Answer 16	-	Positif lemah 0.0691	Positif lemah 0.0221	Negatif lemah -0.0305	Negatif lemah -0.0515	Positif lemah 0.0750	Positif lemah 0.0187	Negatif lemah -0.0696

Ekspor ke MS Excel

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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

Pemilik Produk SaaS Pet Project SDTest®

Valerii memenuhi syarat sebagai ahli pedagog sosial pada tahun 1993 dan sejak itu menerapkan pengetahuannya dalam manajemen proyek.
Valerii memperoleh gelar master dan kualifikasi Proyek dan Program Manajer pada tahun 2013. Selama program masternya, ia menjadi terbiasa dengan Project Roadmap (GPM Deutsche Gesellschaft für ProJektanagement e. V.) dan dinamika spiral.
Valerii mengambil berbagai tes dinamika spiral dan menggunakan pengetahuan dan pengalamannya untuk mengadaptasi versi SDTest saat ini.
Valerii adalah penulis menjelajahi ketidakpastian V.U.C.A. Konsep menggunakan dinamika spiral dan statistik matematika dalam psikologi, lebih dari 20 jajak pendapat internasional.

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