A representation is the relationship existing between a set of characteristics' values in the output of one or more functions and the set of characteristics' values that were the function's input, with one or more of the characteristics' values in the input set being correlated with values in the output set. If there are no related values, we can say that no representation exists. Obviously, the nature of the set of characteristics present at a function's input and output is crucial to whether representation occurs or not. We can look at representation as the process through which information is transmitted to a neighboring level in the hierarchy or, if it is the bottom, physical layer, through the connecting media from one physical layer to another. The relationships between representations and names are examined in [Cof91,Cum91,Cum96,Gil92,Kri80,Moo93,Ros94].
Consider two layers in an information hierarchy: one containing a representation and the other what is being represented (a representandum). An apple might have a set of characteristics including edible, red, stemmed, and round. It might also have a worm hole on the backside, away from the viewer. A pictorial representation of the apple, let us say a black and white image, might show that it is round and has a stem. This representation isn't perfect; it does not contain all the characteristic values of the object, such as that there is a worm hole or that the apple is red.
Imagine that I am a very sophisticated biochemist and botanist and can make an apple representation in the laboratory that appears to be identical to the original; it crunches, oozes apple juice, tastes, and generally appears just like the original. If it is like the original in all characteristics being evaluated, then it is a perfect representation. The set of characteristics chosen obviously determines the degree of accuracy of a representation. A botanist might note after careful examination that the apple seeds in the representation are poor copies and consider the representation to be far from perfect, while a child with less sophistication and using a smaller set of characteristics, might consider the representation to be perfect. The choice of characteristics incorporated into the representation and observation has a great deal to do with its perceived quality.
A representation is usually thought of as being somehow less than the original. This loss (of information) often occurs as one moves from one process to another within the hierarchy. Each stage receiving information from a neighboring level has the potential to lose some of the information. If the representation does not encode all the characteristics of the neighboring level, information about the omitted characteristics is not present. This neighboring representation is imperfect and the process lossy when these characteristics of the neighboring layer are not present.
If a tree falls in a forest and nobody hears it, is information transmitted? The hierarchical approach to information suggests that the answer is ``yes." While no human hears the crash of the branches hitting the ground, there have been changes brought about, although not in a human's ear or mind. A series of functional relationships transmitted the sound through physical processes, each process providing output informative about the process and about its input. None of these processes eventually resulted in a process feeding the representation of the sound to a human's mind. Information was transmitted, but none was received by a human.
In our conceptual framework, information doesn't require the presence of a human, and information science should not be viewed as a discipline with humans as its only focus. The focus of information science is information, with the discipline containing individual scholars interested primarily in information used by humans, as well as, for example, those interested in information as measured and discussed by physicists. The author believes that a diversity of interests and views about information are necessary in information science, and rejects the notion that it is acceptable to define the discipline as limited to the study of information created, organized, retrieved, and used by humans alone, excluding other ideas about information. While studying humans is obviously useful, humans are not the information universe; information predates humans and long after there are no more humans there will continue to be information.