A map is a symbiotic composite of information and entropy where the information is suspended in the configuration of matter. The substrate protects the information from instantaneous dispersion until the material itself decays or the key to the map is lost. A map is a representation of relationships that contains information configured into an entropic substrate. It is a composite of information and entropy that makes the information physically accessible. A book is a map, with or without picture.
In information space, entropy is uncertainty. In material space, entropy is position. A map blends the two spaces so that the entropy of a map is uncertainty about position and the position of uncertainty. Much of the confusion about entropy comes from this blending. The only information we can have about the position of real things is probability because there is no actual information about their location, so a map stabilises the information we have about the probability of finding any given thing in a particular location in relation to another thing. On the other hand, the physical structure of the map, whether a picture or a vector field or set of numbers or a book, has a position of its own. In this way a map is a nesting doll of information and position or a conformal field of informations compressed into position.
The central nervous system may have no other job than making maps. First, the nerves mapped the body to coordinate movement. Next they began mapping their environment to add value to their movements. Finally, they mapped the relationships between their own body and other moving bodies. And even now, the mind insists on making maps of things that are not really mappable, and places where the map serves no purpose. Consider the map of living organisms, the tree of life, which turns out to have been neither terribly helpful nor terribly accurate, but was poured over by generations of naturalists for reasons known only to them. In hindsight, the notion that animals live in one kingdom, plants in another and fungi in a third is as absurd as it is unhelpful. Lichens, corals and the bacteria in the human gut illustrate the codependence of all types of living organisms. Where would viruses slot into the map, let alone prions? A map of the abstract forms of life reduces their relationships to something less mysterious and more familiar, in the way that the map of social hierarchies serves no purpose other than to satisfy the mind’s compulsion to map every physical thing in terms of accessible information.
It is no coincidence that the foremost mnemonic technique is to imagine placing information in particular locations in the map of a familiar place. Because the conscious mind is almost entirely concerned with mapping, and because information and configuration are interleaved in a map, even in the way thoughts come into existence, it is almost impossible to tease information and configuration apart intelligibly. Indeed, you cannot imagine entropy without creating a map of it, which immediately violates the separation of information and material position. But the problem is not in the map; it is in the primacy of the information that goes into the map, the assumption that information comes first, and finally that the map solves entropy by defining it. Creating a grid to force the city into an information-friendly configuration is rational, just incredibly stupid if you want the city to function as a city because energy can’t flow in and waste can’t escape. The grid ensures minimal flow and maximum entropy. Trying to conform physical configuration to the priorities of an information system is ass-backwards, like shoving food up your rectum in the hope that it will work its way up into your stomach to be digested. Information, after all, is indifferent to position and direction.
It is important to remember that quantum information is real. Quantum bits are not observations made by the measuring instruments; they are real communications from the measured particle to the measuring instrument. The descriptions of the information – momentum, spin, charge and number – may be metaphorical, but the information itself is not a heuristic. The information is an actual thing in the universe. Note, then, that the information does not include position. Position relative to the instrument depends upon additional information not found in the instrument or the particle. It depends on mapping, starting with a map of the instrument itself, and then a map of the observatory space, and finally a map of the possible locations of the particle and the instrument in that space. Then you can see why information about position (which must be manufactured) and information about momentum (which is directly communicated) are mutually exclusive. Only by taking momentum information from the particle can you begin to map its location, and more detail requires more information.
“In connection with this issue of where the division between the subjectively described “self” and the physically described objectively conceived world lies Bohr writes:
One need only remember here the sensation, often cited by psychologists, which everyone has experienced when attempting to orient himself in a dark room by feeling with a stick. When the stick is held loosely, it appears to the sense of touch to be an object. When, however, it is held firmly, we lose the sensation that it is a foreign body, and the impression of touch becomes immediately localized at the point where the stick is touching the body under investigation. (Bohr, 1934, p. 99)
This illustration clarifies a point made repeatedly in Bohr’s writings that “even words like ‘to be’ and ‘to know’ lose their unambiguous meaning.” (Bohr. 1934, p. 19)”