Abstract
The “Blind Men and an Elephant” is an old Indian story about a group of blind men who encounter an elephant and do not know what it is. This story describes the difficulties of understanding a large concept or global view based on only local information. Modern technologies enable us to easily obtain and retain local information. However, simply collecting local information does not give us a global view, as evident in this old story. This paper gives a concrete model of this story on the plane to theoretically and mathematically discuss it. It analyzes what information we can obtain from collected local information. For a convex target object modeling the elephant and a convex sensing area, it is proven that the size and perimeter length of the target object are the only parameters that can be observed by randomly deployed sensors modeling the blind men. To increase the number of observable parameters, this paper argues that non-convex sensing areas are important and introduces composite sensor nodes as an approach to implement non-convex sensing areas. The paper also derives a model on the discrete space and analyzes it. The analysis results on the discrete space are applicable to some network related issues such as link quality estimation in a part of a network based on end-to-end probing.
