The Square Kilometre Array is conceived as a telescope which will both test fundamental physical laws and transform our current picture of the Universe. However, the scientific challenges outlined in this book are today's problems--will they still be the outstanding problems that will confront astronomers in the period 2020 to 2050 and beyond, when the SKA will be in its most productive years? If history is any example, the excitement of the SKA will not be in the old questions which are answered, but the new questions that will be raised by the new types of observations it will permit. The SKA is a tool for as-yet-unborn users and there is an onus on its designers to allow for the exploration of the unknown. We outline a philosophy for the design and operation of the SKA that can lead the radio astronomers in the 21st century to add to the many discoveries of new phenomena made by radio astronomers in the 20th century.