abstract: In 1992 or so, Steve Smale and I proved that the average number of real roots of a square polynomial system is the square root of the Bezout number. Now Axel Kodat and I have proven a similar theorem for the number of intersection points of complimentary dimension sub manifolds of a given manifold. The average taken over a finite dimensional submanifold of Diff. The average is comparable to the product of the volumes.