A typology of mathematical diagrams

Mikkel Willum Johansen*, Morten Misfeldt, Josefine Lomholt Pallavicini

*Kontaktforfatter

Publikation: Bidrag til bog/antologi/rapport/konference proceedingKonferenceartikel i proceedingForskningpeer review

2 Citationer (Scopus)

Resumé

In this paper, we develop and discuss a classification scheme that allows us to distinguish between the types of diagrams used in mathematical research based on the cognitive support offered by diagrams. By cognitive support, we refer to the gain that research mathematicians get from using diagrams. This support transcends the specific mathematical topic and diagram type involved and arises from the cognitive strategies mathematicians tend to use. The overall goal of this classification scheme is to facilitate a large-scale quantitative investigation of the norms and values governing the publication style of mathematical research, as well as trends in the kinds of cognitive support used in mathematics. This paper, however, focuses only on the development of the classification scheme.

The classification scheme takes its point of departure from case studies known from the literature, but in this paper, we validate the scheme using examples from a preliminary investigation of developments in the use of diagrams. Building on these results, we discuss the potential and pitfalls in using one generic classification scheme, as done in this analysis. This approach is contrasted with attempts that respect and build on individual diagram types, and as part of this discussion, we report the problems we experienced when using that strategy. The paper ends with a description of possible next steps in using text corpora as an empirical approach to understanding the nature of mathematical diagrams and their relation to mathematical culture.
OriginalsprogEngelsk
TitelDiagrammatic Representation and Inference : 10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings
RedaktørerPeter Chapman, Gem Stapleton, Amirouche Moktefi, Sarah Perez-Kriz, Francesco Bellucci
Antal sider15
ForlagSpringer
Publikationsdato1 jan. 2018
Sider105-119
ISBN (Trykt)978-3-319-91375-9, 978-3-319-91376-6
DOI
StatusUdgivet - 1 jan. 2018
Begivenhed10th International Conference on the Theory and Application of Diagrams, Diagrams 2018 - Edinburgh, Storbritannien
Varighed: 18 jun. 201822 jun. 2018

Konference

Konference10th International Conference on the Theory and Application of Diagrams, Diagrams 2018
LandStorbritannien
ByEdinburgh
Periode18/06/201822/06/2018
NavnLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Vol/bind10871 LNAI
ISSN0302-9743

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Johansen, M. W., Misfeldt, M., & Pallavicini, J. L. (2018). A typology of mathematical diagrams. I P. Chapman, G. Stapleton, A. Moktefi, S. Perez-Kriz, & F. Bellucci (red.), Diagrammatic Representation and Inference: 10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings (s. 105-119). Springer. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind. 10871 LNAI https://doi.org/10.1007/978-3-319-91376-6_13
Johansen, Mikkel Willum ; Misfeldt, Morten ; Pallavicini, Josefine Lomholt. / A typology of mathematical diagrams. Diagrammatic Representation and Inference: 10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings. red. / Peter Chapman ; Gem Stapleton ; Amirouche Moktefi ; Sarah Perez-Kriz ; Francesco Bellucci. Springer, 2018. s. 105-119 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind 10871 LNAI).
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title = "A typology of mathematical diagrams",
abstract = "In this paper, we develop and discuss a classification scheme that allows us to distinguish between the types of diagrams used in mathematical research based on the cognitive support offered by diagrams. By cognitive support, we refer to the gain that research mathematicians get from using diagrams. This support transcends the specific mathematical topic and diagram type involved and arises from the cognitive strategies mathematicians tend to use. The overall goal of this classification scheme is to facilitate a large-scale quantitative investigation of the norms and values governing the publication style of mathematical research, as well as trends in the kinds of cognitive support used in mathematics. This paper, however, focuses only on the development of the classification scheme.The classification scheme takes its point of departure from case studies known from the literature, but in this paper, we validate the scheme using examples from a preliminary investigation of developments in the use of diagrams. Building on these results, we discuss the potential and pitfalls in using one generic classification scheme, as done in this analysis. This approach is contrasted with attempts that respect and build on individual diagram types, and as part of this discussion, we report the problems we experienced when using that strategy. The paper ends with a description of possible next steps in using text corpora as an empirical approach to understanding the nature of mathematical diagrams and their relation to mathematical culture.",
keywords = "Classification of diagrams, Corpus analysis, Mathematical cognition",
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Johansen, MW, Misfeldt, M & Pallavicini, JL 2018, A typology of mathematical diagrams. i P Chapman, G Stapleton, A Moktefi, S Perez-Kriz & F Bellucci (red), Diagrammatic Representation and Inference: 10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings. Springer, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), bind 10871 LNAI, s. 105-119, Edinburgh, Storbritannien, 18/06/2018. https://doi.org/10.1007/978-3-319-91376-6_13

A typology of mathematical diagrams. / Johansen, Mikkel Willum; Misfeldt, Morten; Pallavicini, Josefine Lomholt.

Diagrammatic Representation and Inference: 10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings. red. / Peter Chapman; Gem Stapleton; Amirouche Moktefi; Sarah Perez-Kriz; Francesco Bellucci. Springer, 2018. s. 105-119 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind 10871 LNAI).

Publikation: Bidrag til bog/antologi/rapport/konference proceedingKonferenceartikel i proceedingForskningpeer review

TY - GEN

T1 - A typology of mathematical diagrams

AU - Johansen, Mikkel Willum

AU - Misfeldt, Morten

AU - Pallavicini, Josefine Lomholt

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this paper, we develop and discuss a classification scheme that allows us to distinguish between the types of diagrams used in mathematical research based on the cognitive support offered by diagrams. By cognitive support, we refer to the gain that research mathematicians get from using diagrams. This support transcends the specific mathematical topic and diagram type involved and arises from the cognitive strategies mathematicians tend to use. The overall goal of this classification scheme is to facilitate a large-scale quantitative investigation of the norms and values governing the publication style of mathematical research, as well as trends in the kinds of cognitive support used in mathematics. This paper, however, focuses only on the development of the classification scheme.The classification scheme takes its point of departure from case studies known from the literature, but in this paper, we validate the scheme using examples from a preliminary investigation of developments in the use of diagrams. Building on these results, we discuss the potential and pitfalls in using one generic classification scheme, as done in this analysis. This approach is contrasted with attempts that respect and build on individual diagram types, and as part of this discussion, we report the problems we experienced when using that strategy. The paper ends with a description of possible next steps in using text corpora as an empirical approach to understanding the nature of mathematical diagrams and their relation to mathematical culture.

AB - In this paper, we develop and discuss a classification scheme that allows us to distinguish between the types of diagrams used in mathematical research based on the cognitive support offered by diagrams. By cognitive support, we refer to the gain that research mathematicians get from using diagrams. This support transcends the specific mathematical topic and diagram type involved and arises from the cognitive strategies mathematicians tend to use. The overall goal of this classification scheme is to facilitate a large-scale quantitative investigation of the norms and values governing the publication style of mathematical research, as well as trends in the kinds of cognitive support used in mathematics. This paper, however, focuses only on the development of the classification scheme.The classification scheme takes its point of departure from case studies known from the literature, but in this paper, we validate the scheme using examples from a preliminary investigation of developments in the use of diagrams. Building on these results, we discuss the potential and pitfalls in using one generic classification scheme, as done in this analysis. This approach is contrasted with attempts that respect and build on individual diagram types, and as part of this discussion, we report the problems we experienced when using that strategy. The paper ends with a description of possible next steps in using text corpora as an empirical approach to understanding the nature of mathematical diagrams and their relation to mathematical culture.

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KW - Corpus analysis

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Johansen MW, Misfeldt M, Pallavicini JL. A typology of mathematical diagrams. I Chapman P, Stapleton G, Moktefi A, Perez-Kriz S, Bellucci F, red., Diagrammatic Representation and Inference: 10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings. Springer. 2018. s. 105-119. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bind 10871 LNAI). https://doi.org/10.1007/978-3-319-91376-6_13