ON SPONTANEOUS EMERGENCE OF OPINIONS
                       Mike Keane

One of the distinguishing properties of the present scientific method
is reproducibility.

In one of its guises, probability theory is based on statistical 
reproduction, near certainty being obtained of truth of statements 
by averaging over long term to remove randomness occurring in 
individual experiments.

When one assumes, as is often the case, that events farther and
farther in the past have less and less influence on the present, 
the probabilistic paradigm is currently well understood and is 
successful in many scientific and technological applications.

Recently, however, we have come to realize that precisely in these 
applications important stocahstic processes occur whose present 
outcomes are significantly influenced by events in the remote past.

This behaviour is not at all well understood and some of the simplest 
questions remain today irritatingly beyond reach.

A salient example occurs in the theory of random walks, where there 
is a dichotomy between recurrent and transient behaviour.

After explaining this classical dichotomy, we present a very simple 
example with infinite memory which is neither known to be transient 
nor recurrent.

Then, using a reinforcement mechanism due to POLYA, we explain the 
nature of a particular infinite memory process in terms of spontaneous 
emergence of opinions.

Finally we would like to discuss briefly some of our recent results 
towards understanding the recurrence-transience dichotomy for 
reinforced random walks, and indicate an application to universal 
coding used in optical CD technology.