What does it mean for an artificial intelligence (AI) to think? Will AIs ever be sentient? How would we even know, when they have been trained to fake it so well? Large language models and other generative AI systems are usually described as predicting the next token in a sequence --- forecasting the most likely next word. However, they actually do a bit more than this. A combination of clever high-dimensional embedding of the tokens and simultaneous prediction at points throughout the token sequence gives an effective illusion of relevance and coherence. Such systems are still prone to fabrications and, as a consequence, are often claimed to be ``creative.'' Nonetheless, they fail to gra...