Negative space is a concept frequently taught in visual design courses. When looking through a viewfinder of a camera or composing a sketch or painting, the shape of spaces in between objects becomes a design element. It is odd however, that this idea is considered negative ‘space’, since it is generally realized in two-dimensional representations. I only remember one instance of an artist truly exhibiting negative space. I don’t remember the artist’s name, but her project was fascinating. Somehow, she was able to completely fill a full size room with concrete. Then she removed the walls to reveal a sculpture of the space inside the room, what we would call negative space when the room was an actual room. Usually a sculptor casting a metal sculpture would reverse the process. For example, in the ‘lost wax’ process, the artist forms the sculpture completely from wax, then coats it with ceramic material. If we could look at inside the completed ceramic form, ignoring the wax, we would see a negative space. After the artist pours molten metal into the form, the wax is vaporized and the metal occupies the negative space. The metal sculpture, a positive space, is revealed when the ceramic is removed.
Space of an organism
Everyone occupies space. Alva Noë, the author who has inspired my past few posts, has a very interesting take on the space of a living organism. He uses the sea snail as an example, defining it by the characteristic way it acts. Noë proposes that the boundary between the sea snail and the rest of the world is not at its body surface. “…[H]ow it acts is shaped by how it was acted on; the snail is a vector resulting from distinct forces of the body, the nervous system, the world. Its past history in environmental context and its ongoing dynamic exchanges with the environment makes the sea snail what it is.” [emphasis in original] 
More than spatial occupation
The negative space around a person is everywhere a person isn’t. The idea of absence of space makes sense when we think of three dimensions: a hole in a board is the absence of board; a hole in the ground is absence of ground. If we’re taking about a person who is, for example, writing a blog post, everywhere around him is space that his body does not occupy: negative space. If the person is walking down the street, the negative physical space created is a person-shaped tunnel, if we add the dimension of time.
But let us consider for a moment that the person is defined as a vector that interacts with the environment. How do we describe the components of that vector? Ambient heat, wind direction, temperature, electromagnetic radiation, reflected light, and many more qualities of the environment can influence the actions of the individual and can thus be considered vector components.
How do we define everywhere a person isn’t if a person is a vector?
Does it make sense?
Given the idea that an organism is a vector whose components interact with its environment, I don’t think the concept of negative space or ‘the place where the organism isn’t’ has much meaning. Negative space is best left for visual artists. What is intriguing however is the possibility that there could be a finite, exhaustive list of vector components describing a person in his or her environment, or context. If this were the case, I could study my brother  and understand what his particular ‘dance’ with his environment is.