In computational intelligence, the term 'memetic algorithm' has come to be associated with the algorithmic pairing of a global search method with a local search method. In a sociological context, a 'meme' has been loosely defined as a unit of cultural information, the social analog of genes for individuals. Both of these definitions are inadequate, as 'memetic algorithm' is too specific, and ultimately a misnomer, as much as a 'meme' is defined too generally to be of scientific use. In this paper, we extend the notion of memes from a computational viewpoint and explore the purpose, definitions, design guidelines and architecture for effective memetic computing. Utilizing two conceptual case studies, we illustrate the power of high-order meme-based learning. With applications ranging from cognitive science to machine learning, memetic computing has the potential to provide much-needed stimulation to the field of computational intelligence by providing a framework for higher order learning.