## 2 Resolution, Scale, Scope and Other Properties of Descriptions
### Scale  
All of us have an intuitive notion of scale. Commonly, the term scale is associated with the distance from which the system is observed. Thus, the term'scale' is typically used to mean that the system is being interpreted from a closer point of view--higher scale with finer detail, or from a further point of view--lower scale with less detail. This works fine if the scale is exclusively established by the distance between the observer and the object but this not always the case. In fact, the size of an element within the perception of a system, does not necessarily represent the relevance of that element as part of the system's description. Thus, the observation distance cannot reflect in a sole parameter the property defined as'scale'. Additionally, the frequent exchange of the terms 'detail of degree', 'level', 'observation distance' and'scale', promotes the confusion between the concepts of scale and resolution. I think this confusion of terms has hindered a clear conception of what a scale actually is and as a result, we are still lacking a unified definition of scale of a description that can work in an information space with non-regular shaped symbols. During the last decade, several studies reflected the relevance of the concept of scale in our interpretation of descriptions. In 2004, [PERSON] [2; 3] presented complexity as a property intimately related to the scale. His treatment of scale as a parameter capable of varying continuously rather than discrerely, led him to present the so called'scale profiles'; a sort of'structure' relating entropy to scale, where entropy decreases monotonically as the observation scale shows less detail. Even though these profiles are a good representation of the envelope of the complexity, they would only be constructible by representing scale as the result of the increase, or decrease, of the resolution with which the system is observed. Thus, these profiles illustrate the relationship between complexity and resolution, while the actual scale parameter is left out of the analysis. [PERSON] and [PERSON] [10] presented entropy as a function of scale length. They defined scale as the size of the group of pixels used to represent each object in a pattern of regularly distributed grayscale pixels. Their graphs show local minimal values of entropy when the scale length is a multiple of the characteristic size of the pattern measured in pixels. Again, [PERSON] and [PERSON] [10] actually work with resolution changes but their experiment shows how, when the size of the objects described fits with an integer number of pixels, the entropy drops, implying that the arbitrary choice of the number of pixels used to describe an object modifies the entropy, thus the system's observed complexity. This confirms that the observation scale is not either exclusively dominated by the system properties nor the resolution. Scale seems to be a result of our process of interpretation. When we consider a description, our brain probably scans several interpretations of the observed description. At each interpretation, we combine raw information by joining adjacent information elements and forming with them larger hypothetical symbols. Simultaneously, we look for patterns which we can associate with previous experiences and learned notions, or even with our personal conceptions of beauty, thus giving certain meaning to a message that was initially abstract. Therefore, the scale is a property of the way the observer looks at the system's description. Once the observed system's conception is 'organized' in our brain, a clear account of the symbols resulting from our interpretation, along with their frequency of appearance and their relative position, constitute our model of the description. This lets me introduce statements about the scale that do not contradict our previous intuitive notions: the scale of a description, as it is observed, is directly related to the set of symbols used to create the description's model.