We may say most aptly, that the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves…
It holds a position wholly its own; and the considerations it suggests are most interesting in their nature. In enabling mechanism to combine together general symbols in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental processes of the most abstract branch of mathematical science. A new, a vast, and a powerful language is developed for the future use of analysis, in which to wield its truths so that these may become of more speedy and accurate practical application for the purposes of mankind than the means hitherto in our possession have rendered possible. Thus not only the mental and the material, but the theoretical and the practical in the mathematical world, are brought into more intimate and effective connexion with each other.
(The Analytical Engine was an odd dead-end of Victorian genius: a sort of proto-computer that was never constructed and that was largely forgotten until the rise of computers a century later sent people scurrying back to the archives to claim a “first”. The rather daft arguments over whether Ada Lovelace was or wasn’t “the first computer programmer”are much less interesting than the consequences of the idea she expresses here: that mathematical reasoning needn’t be confined by the limits of the human brain. Very few working mathematicians today — not to mention engineers, physicists and their kin — could get anywhere without the “intimate and effective connexion” the outlines of which she saw…)