To Dream The Possible Dream

There are several seemingly reasonable problems that are exciting and challenging, and yet are currently unsolvable. Solutions to these problems will require major new insights and fundamental advances in computer science and artificial intelligence. Such problems include: World Champion Chess machine, Translating Telephone, Discovery of a major mathematical result by a computer, and so on. Here I will present two such grand challenges which if successful can be expected have major impact on society: Self-Organizing Systems that learn from examples and observations and Self-Replicating Systems that can make copies of themselves.