Weaving is presented in this paper with relation to the four key categories of computational thinking: decomposition, pattern recognition, abstraction, and algorithms. The role of weaving for the development of theoretical concepts is underestimated, because we perceive weaving as a minor craft with little technological challenge and impact. Where technological progress is measured in terms of gaining time from dull and tedious repetitive tasks, weaving appears to be the archetype of such repetitive work and thus as the more technological the faster it goes. We address this framing of perception by presenting ancient weaving as the earliest binary and digital technology. The PENELOPE project (ERC CoGrant no. 682711) aims to develop a theory of weaving as part of a deep history and epistemology for digital technology. In explicating the mathematical and computing principles invoked in weaving, we furthermore explore weaving as a kind of education that has the potential to engage tacit knowledge that is necessary to make technical and aesthetic choices in coding. By this, we argue for an alternative history of digital art.