I. Prologue

I am greatly honoured to have been given this wonderful theme, "Strange Attractors and the Origin of Chaos" for my presentation today. First I would like to take this opportunity to offer a special thanks to each one of the people who planned and made this symposium possible.

At present, people say that the data I was collecting with my analog computer on 27 November 1961 are the oldest example of chaos discovered in a second-order non-autonomous periodic system. Around the same time, it was Lorenz who made the discovery of chaos in a third-order autonomous system.

At that time I was simply frustrated with this seemingly mysterious phenomenon which I accidentally came upon during my experiments. For my part, it was nothing as glorious as an act of discovery - all I did for a long period of time was to keep on pursuing my stubborn desire to understand this unsettling phenomenon. "What are the possible steady states of a nonlinear system?" - this has always been my question. And my paradigm has always been the phenomena themselves, not papers with their abstractions, but something we can actually observe or quantify.

In this report, I would like to reflect upon the circumstances of my research and the general conditions of Japanese science around 1978 before the study of chaos began. As I prepared this talk, I kept asking myself what propelled me to pursue my question so relentlessly, but I must confess that I don't know the answer. I have not, in my wildest dreams, imagined that I would be given an opportunity to speak on this very subject. It was so unexpected, my mind was reduced to total chaos!

As an academic term, I do not find the word "chaos" very appropriate. But what shall we call it then? My proposal has been "randomly transitional phenomena"; I will explain this below.

The characteristics of chaos in a physical system can be summarized as follows:

- Random phenomena that occur in deterministic systems.
- Random phenomena whose short-term behaviour is predictable.
- Random phenomena whose long-term behaviour is unpredictable.
- Although the phenomena are irregular and unpredictable, chaos does have a definite structure.

The original meaning of chaos, I feel, is "total disorder and ultimate unpredictability." But as scientific terminology, the word "chaos" seems to overemphasize the unpredictability alone. This symposium provides an opportunity to clear this misunderstanding and to inform the non-specialist of the correct meaning of the word.

Even so I have to use the word "chaos" here, instead of "randomly transitional phenomena." It is a concise expression which has already filtered into people's minds, and therefore I have decided it is rather pointless to resist it.