These notes describe how the "SP theory of intelligence", and its embodiment in the "SP machine", may help to realise cognitive computing, as described in the book "Smart Machines". In the SP system, information compression and a concept of "multiple alignment" are centre stage. The system is designed to integrate such things as unsupervised learning, pattern recognition, probabilistic reasoning, and more. It may help to overcome the problem of variety in big data, it may serve in pattern recognition and in the unsupervised learning of structure in data, and it may facilitate the management and transmission of big data. There is potential, via information compression, for substantial gains in computational efficiency, especially in the use of energy. The SP system may help to realise data-centric computing, perhaps via a development of Hebb's concept of a "cell assembly", or via the use of light or DNA for the processing of information. It has potential in the management of errors and uncertainty in data, in medical diagnosis, in processing streams of data, and in promoting adaptability in robots.