Toward Another Possible Visualization of Massaging: The First Short Step from Klee to Scientific Visualization

Part of the Mathematics for Industry book series (MFI, volume 9)


Recently, researchers have created what is called a ‘tactile score,’ through which they have clarified that there are three basic constituents to massaging: the area of touching (S), the pressure of massaging (P), and the velocity of hand movement (V), and that their relation is constant [8]. This tactile score borrows its style from the five-line musical score. However, this five-line score is not the only way to present a visual interpretation of a musical score. If we can find another way of visualizing music, we can apply its style to the visualization of massaging. In this paper, we take the first tentative step toward doing so. We pay attention to the pedagogical posthumous notes of the Swiss painter Paul Klee (1879–1940) because he is famous for his unique visualization of music. We treat these notes as follows. First, we select the three basic constituents of Klee’s paintings: measure, weight, and quality. By using these three constituents, Klee makes music visible in his paintings. Second, we confirm the three media that realize these constituents—lines, chiaroscuro, and colors—and interpret their generative procedures from the point of algorithm. Then we suggest that we can recapture one of these generative algorithms, that is, a grid line, as a kind of visualization of massaging. Finally, we show affinities between Klee’s generative algorithm and some contemporary scientific thoughts and conclude this paper.


Massaging Visualization Paul klee Bildnerische gestaltungslehre Algorithm 



This work was supported by JSPS KAKENHI No. 24520106.


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Copyright information

© Springer Japan 2015

Authors and Affiliations

  1. 1.Graduate School of Information ScienceNagoya UniversityNagoyaJapan

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