In 1937, Jorge Luis Borges looked back some 650 years at Ramon Llull‘s machinic ars inveniendi.  This is one of five essays that looks at contemporary learning machines through the lens of Borges‘s characteristically engimatic historical note and literary reflection. It examines the epistemological tension between determinism and randomness in projects of formalising thought – from Ramon Llull's Ars Magna (1305) to contemporary generative transformers. Borges's 1937 critique of Llull revealed a fundamental impasse: closed combinatorial systems, lacking contextual sensitivity, produce syntactic noise rather than truth. Yet Borges proposed an alternative, namely, to use such machines as generators of random combinations subject to human selection. This shift finds unexpected validation in AI transformer models. By replacing discrete symbols with continuous semantic embeddings and dynamic attention mechanisms, transformers overcome Llull's linear blindness. However, in deterministic mode (low temperature), they merely reproduce linguistic clichés, exhibiting neural text degeneration. Genuine novelty emerges only through stochastic sampling–temperature-based deviation into the probability distribution's long tail, actualising latent semantic projections (as in the Borgesian “red tiger”). Drawing on recent empirical studies, the paper demonstrates a fundamental trade-off between alignment due to reinforcement learning (RLHF) and stochastic creativity. As an alternative, calibrated uncertainty is proposed, allowing models to acknowledge the limits of knowledge. The transformer that legitimises its stochastic nature thereby approaches Borges's ideal of a poetic machine – an instrument that does not prove but suggests, that does not close off truth but opens a space for play.