Forma, Vol. 13 (No. 2), pp. 47-50, 1998

Preface: Why Spheres?

This is a special issue of a research meeting entitled Pattern Formation and Information Processing on the Sphere organized as one of the Cooperative Research Projects of the Institute of Statistical Mathematics in Tokyo. The first meeting was held there from 17th to 18th January, 1991 and the second meeting on 24th January, 1992. The titles of all the lectures and comments are listed below. The proceedings in Japanese language (159 pages, which covers two meetings in one volume) were published as The Institute of Statistical Mathematics Cooperative Research Report 37 in March 1992. In this issue, only seven papers are contained from the total 23 lectures of the two meetings.
The Gulf War happened to start just at the opening day of the first meeting. This coincidence brought the feeling to the organizers and the participants that the problems of spherically closed systems were getting more and more serious and important.
Nowadays, the situation of the civilization requires us to consider the problems globally. When the scale of human activity was not so large and it used to be enough to consider the problems on a local scale, a global or holistic consideration has not necessarily been required. It was considered natural and reasonable that there exists an exterior of the local system where everything useless can be treated. However, it is not allowed now to do so, since the scale of the activity is comparative or, rather, exceeds that of the earth.
While an Euclidean space is uniform, infinite, and open, a spherical surface is uniform but finite and closed. The preparation of some framework of science or some logic which is applicable for such a kind of closed system. It is noted that environmental, allocational, configurational and ethical problems are all connected. It is not easy to find the answer to these problems. But we should keep them in mind.
There were two main themes of the meeting: geometry of spherical surface and topics of global size. For example, what is the best network to perform a simulation of some system on a spherical surface, for example. As is well known, it is generally impossible to introduce a uniform network, though there are a few exceptional cases for comparatively small number of net-points.

Tohru Ogawa
Masaharu Tanemura
Takayuki Hirata
(Editors of the issue)