Our modern-day nomenclature owes a lot to the 'arrays' and 'threads' that made up these weaving machines (see Howard Rheinhold's Tools for Thought)[0].
Evidently, the punch cards that stored Jacquard's weaving patterns were a direct inspiration for Babbage's analytical engine.
From a computer-science theoretic view, any any recursively enumerable transform is computing. It's pretty easy to see the translation between a Jaquard loom and an abstract Turing machine. Just because it smells of machine oil and lanolin instead of ozone and magic smoke doesn't mean an automated loom and a modern computer are not essentially the same device, mathematically speaking.
What I remember from school (late 90s) is that Babbage was inspired by Jacquard’s punched cards to use then in his Engine, and either this, or Jacquard directly, inspired the same in Hollerith. I don’t recall it as there being a direct line in terms of “modified loom is general purpose computer) but it was certainly an important influence.
In hindsight it seems easy for some of us to make the connection, but, at the time, it must have been quite the breakthrough.
I'm not disputing the influence of jacquard machines in general, but there is big difference between "having influence on computing" and "is a computer".
It's an interesting question, where the boundaries of an innovation lie. If we take Jacquard's loom as an 'ordinateur' or information ordering machine, its 'computing' properties become more recognisable -- composite outputs and patterns derived from stringing together smaller bits (and strings) of information.
When I was younger I worked with a lot of prototype devices. The lab always had the smell of rosin core and ozone and, from time to time, something worse that resulted in the requirement for a new board. And once, a new desk.
