“The goal of this lecture is to explain mathematical dreams”. It shows how to create new mathematical results, objects, theories, by treating complexification, symplectification, contactization as independent entities rather than as subcases of higher-dimensional real entities with an extra structure. As well there is an emphasis on order, pattern, method: many ideas occur in natural threes, such as the real, complex and quaternionic numbers: extending sequences of spaces, geometries, etc. from one triple to another when we are given two (real and complex say).
For the entire collection see [Zbl 0929.00102].