There is certainly a kind of personal, affective, and somatic experience of having an idea. As the brilliant commenters have noted — we fidget, we are disoriented, we feel taken up, overwhelmed, the idea running through our blood and bones.
But I still wonder: What is the experience of having an idea? Not as much what happens to me when I think — although that, too — but what is happening when I have this idea?
One way to think about this thinking is to think about the experience of things making sense. I love this phrase, "making sense," because we use it to mean we understand a given idea when the phrase suggests we just created the idea: we made the sense rather than recognized it.
Anyway, what is this experience? I can't escape the architectural component: things — visible and invisible, historical and immediate, personal and societal, specific and general — seem to fit together in some scheme.
I want to say they fit like a puzzle but that's not right. There are hierarchies and contingencies that a puzzle does not have; this is not a flat database of pieces but a grammatical database with all sorts of rules. When I have an idea that makes sense, I have organized bodies with a series of logics — the logics of cause and effect and of hierarchy, of course, but there are other logics, too: the logics of sensation, of the varying flows of liquids, gasses, the materiality of things, the structures of other ideas such as Leibniz's monadology or Deleuze and Guattari's planes of immanence. All these things order, organize, distribute bodies — including my own body.
All of this shows me that the logics that I find immanent are, in fact, cultural and historical. But my next thought is that these things are not opposed: immanence and history are one and the same (sometimes).
And then there is that affective, personal experience — the exhilaration, the disorientation, delirium, waves, a feeling of being at once in control and out of control: the idea is driving now!
Having an idea, then, (which is different than an idea) is an experience that takes place between me and the world, between me and history, between me and ghosts past and present and future (surely an idea extends into possible future worlds, if not into actual future worlds; in some sense, the idea makes the future as it makes sense).
So I come back to my question: What is the experience of having an idea? It is a participating in the world, lending my body to the flow of different logics, logics that are material and conceptual and historical — all of it working within architectures and speeds, within moving shapes and how they might go together.
And then — boom — the idea. We are overtaken. We are gloriously delirious. But what's happened? Do I know understand the world? Does having an idea — does making sense of things — tame the chaos? Sure, to some degree. Having an idea is like being a very strange version of Moses — making laws of the land. But very private laws that nonetheless legislate everything. Yes, an idea is akin to a law.
But as we know the best ideas forge a certain vertigo, a delirium. A legislation, then, but one that wreaks a very special kind of havoc.
Is there a kind of achievement? Yes, there are great architectural feats of ideas — Kant's three critiques, for instance, or Leibniz's monadology, or D&G's thousand plateaus.
After having had the idea — after creating this moving monument, writing this weird law — do I approach the world differently? Yes, I imagine so. And this is what makes ideas so strange: they change the way we see and they change the way we act. As we said, an idea is a kind of law.
Maybe an idea is akin to a design — the shadow of an event, the ghost that moves between visible and invisible worlds.
Or perhaps I was right at the beginning and an idea is an image, a refraction of a sort. It takes up the world and gives is not just something seen: an idea, like any great image, gives us a seeing.