Shape as Memory Storage - Ambient Intelligence for Scientific Discovery - page 82

Fig. 1. Shape as history.
2 The Process-Grammar
The purpose of the present chapter is to give an example of the theory without
going deeply into the extensive technicalities. The example we shall choose is
the extraction of memory stored in curvature extrema . I show that curvature
extrema contain an extremely high amount of memory storage, and furthermore
that this storage is organized in a hierarchy I called a Process-Grammar .AfterI
published this grammar in the 1980's it was applied by scientists in over 20 dis-
ciplines: radiology, meteorology, computer vision, chemical engineering, geology,
computer-aided design, anatomy, botany, forensic science, robotics, software en-
gineering, architecture, linguistics, mechanical engineering, computer graphics,
art, semiotics, archaeology, anthropology, etc.
Let us begin by understanding the purpose for which the grammar was de-
veloped: inferring history from shape; e.g., from the shapes of tumors, embryos,
clouds, etc. For example, the shape shown in Fig 1 can be understood as the
result of various processes such as protrusion, indentation, squashing, resistance.
My topic Symmetry, Causality, Mind (MIT Press), was essentially a 630-page
rule-system for deducing the past history that formed any shape. The Process-
Grammar is part of that rule-system - the part related to the use of curvature
extrema.
3 The PISA Symmetry Analysis
It is first necessary to understand how symmetry can be defined in complex
shape. Clearly, in a simple shape, such as an equilateral triangle, a symmetry
axis is easy to define. One simply places a straight mirror across the shape such
that one half is reflected onto the other. The straight line of the mirror is then
defined to be a symmetry axis of the shape. However, in a complex shape, it is
often impossible to place a mirror that will reflect one half of the figure onto the