Abstract expressionism offers both freedom and an enormous challenge to the artist. On the one hand he is unbound from conventional symbols and their rules of use, and can truly speak with a voice that is his alone. On the other, now cut off from the norms of expression, he must invent his own syntax, grammar, even vocabulary, and further, he must convey them to his audience along with whatever it is he is trying to express. This is more than most can handle, and the world is full of the attempts of those who had the ambition but not the talent. "Bad abstract art" is practically a redundancy, but for those who succeed....they are the people about whom it can be said that they reinvented their chosen form.
Jean-Luc Godard is one such artist, and watching First Name: Carmen it dawned on me that he is one of a very small number of successful abstract expressionists in film. There is nothing in any Godard picture I have seen that can be called conventional in moviemaking terms. Even when he borrows a bit of vocabulary from others, it is referential and never reverential.
"Abstract" doesn't necessarily mean non-representational. It can mean using conventional symbols in an unconventional way. Let it be said that Godard almost never uses conventional symbols in a conventional way. We may think we recognize concepts like "boy meets girl" and "class warfare" in Godard's work, but they never mean quite what they mean in the next guy's movie. In a Godard picture they are deconstructed, hooks to hang some other sort of idea on, or perhaps simply foils for a joke. You have to marvel at the man's audacity to work the way he does in what is, after all, a popular medium. But that is Godard's game, to upset our expectations, and it is our pleasure to play along.