As a general point , we have to assume that the configurations of matter is limited by some function of mass and available space. For any given space and matter, that matter can only be configured in some finite set of ways.
In that regard, the number of inventions (as subset of all sets of configured matter)- is similarly bound. We might argue that such a bounding is infinitely expanding along with the universe, as space is a important variable in the equation. Even so, my assumption is that space becomes irrelevant after a certain point of expansions. (If I have 2 atoms in a field of a billion of square miles, the number of configurations is only trivially changed by adding a few more square miles.
Once more, even if an infinitely expanding universe equates to an infinitely expanding art of inventions (configurations) - the fact remains that the set is fixed for any given time point.
In that regard, the number of inventions (as subset of all sets of configured matter)- is similarly bound. We might argue that such a bounding is infinitely expanding along with the universe, as space is a important variable in the equation. Even so, my assumption is that space becomes irrelevant after a certain point of expansions. (If I have 2 atoms in a field of a billion of square miles, the number of configurations is only trivially changed by adding a few more square miles.
Once more, even if an infinitely expanding universe equates to an infinitely expanding art of inventions (configurations) - the fact remains that the set is fixed for any given time point.