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Boethius and his followers used diagrammatic methods to estimate musical intervals with epimoric ratios, they determined geometric number sequences with triangular tables, and they treated the converse problem of dividing musical intervals equally. The collection of mathematical manuscripts Codex Basel F II 33 (ca. 1360) contains treatises by Nicolaus Oresme, Jordanus Nemorarius and others. Images in Nemorarius' treatise combine number triangles into complex spider webs and they display recursive algorithms. Oresme diagrams make use of irrational ratios. These little known images and their relationship to music theory are the focus of this paper., + ID: 590951 + PeerReviewed

As the use and diversity of diagrams across many disciplines grows, there is an increasing interest in the diagrams research community concerning how such diversity might be documented and explained. In this article, we argue that one way of achieving increased reliability, coverage, and utility for a general classification of diagrams is to draw on recently developed semiotic principles developed within the field of multimodality. To this end, we sketch out the internal details of what may tentatively be termed the diagrammatic semiotic mode. This provides a natural account of how diagrammatic representations may integrate natural language, various forms of graphics, diagrammatic elements such as arrows, lines and other expressive resources into coherent organisations, while still respecting the crucial diagrammatic contributions of visual organisation. We illustrate the proposed approach using two recent diagram corpora and show how a multimodal approach supports the empirical analysis of diagrammatic representations, especially in identifying diagrammatic constituents and describing their interrelations in a manner that may be generalised across diagram types and be used to characterise distinct kinds of functionality., Comment: 16 pages; accepted at Diagrams 2022

The way we choose to draw the networks on the plane (layout) is found to be important for the readability of networks by humans. In this study, we examine how different layouts affect our perception of specific properties of small networks of 16 nodes each. We compare a simple grid layout to the planar and force-directed layouts, which are some of the most well-established layout algorithms. We also introduce an alternative ‘improved’ grid layout, which optimizes the outcome layout in terms of specific aesthetics. When people had to decide whether a network is a tree given a node-link diagram, the layout significantly affected their performance. The same pattern appeared for the detection of the connectedness property. However, when people had to detect two properties at a time, the layout didn't affect their performance. The results show that the layout we choose for representing a network is crucial for our perception of some of the network's basic properties. However, when people had to detect more than one property at a time, the chosen layout didn't seem to significantly affect their performance.

In this paper we investigate the cognitive potential of Derivative Meaning—defined in terms of Abstraction Tracking (Shimojima 2015)—in order to characterise various families of Aristotelian diagrams. In a first part we consider the notion of subdiagrams—i.e. uniform triangles of contrariety relations and implication relations—inside Aristotelian hexagons and octagons. In a second part we look at different strategies for embedding complete Aristotelian diagrams—i.e. classical and degenerate squares—into Aristotelian hexagons and octagons.

The paper examines Schopenhauer’s complex diagrams from the Berlin Lectures of the 1820 s, which show certain partitions of classes. Drawing upon ideas and techniques from logical geometry, we show that Schopenhauer’s partition diagrams systematically give rise to a special type of Aristotelian diagrams, viz. (strong) \(\alpha \)-structures.