P165 incorporates (is incorporated in) and digitazation

Detailed question: 

This is a guideline about the conditions it can be said that a digitization of a physical object incorporates an information object that the physical object that was digitized carries.

An important class of E90 Symbolic Objects consists of arrangements of instances of a finite set of symbols, such as the character types of an alphabet, following rules of arrangement that make the relative order of the symbols unambiguous, such as writing symbols regularly spaced, in regularly spaced lines, aggregated into paragraphs etc. Most texts, but also diagrams such as metro maps fall under this category, because they represent stations and their connections in a way only loosely related to their actual geometry. The rules for the arrangements of symbols quantify relative positions so that they can unambiguously be interpreted as logical structures or grammars. For instance, inter-word spaces are sufficiently larger than inter-character spaces not to confuse them. We denote these objects as “formal symbol structures”. Common to them is the property that there is a minimal resolution under which they are still “readable”, i.e. under which the used kinds of symbols can be distinguished and the logical role of their relative positions unambiguously be interpreted. This even holds for melodies expressed in some musical key. If the digitization of a physical carrier of such a formal symbol structure is carried out in the necessary resolution and coverage, the complete symbolic content of the physical carrier will also be readable in a representation of the reproducing digital object, as well known from operating paper scanners. Then, the digital object will incorporate (P165 incorporates) the symbolic object on the physical carrier.
Ambiguity about this property may, for instance, arise if some characters are badly readable on the original. For practical reasons, we recommend not to regard such minor shortcomings of the original as a reason to question the P165 incorporates relation of the digital representation, as long as the overall sense (or score) is recognizable, in particular, if the intended meaning can be guessed equally well from the original as from the digital representation. The same holds for minor flaws in the digital representation itself.
In contrast, for symbolic objects in a non-discrete form, such as paintings, there is no clear minimal resolution and the actual color reflection behavior cannot be reproduced digitally with current means. As long as this is the case, the digitized image cannot be said to incorporate the original, it only “P138 represents” it. (For audio recordings, there is no equivalent to  P138 represents, and the more general P67 refers to should be employed). Actually, the symbolic object a physical object carries is not uniquely defined by the physical carrier but depends on the type of the symbolic object defined in a model, which in turn serves a purpose of representation. If, for instance, the original is a manuscript, a digitized image may incorporate its text, which is instantiated and defined as a symbolic object of type “character sequence” in an information system. However other research-relevant optical features, which belong to richer symbolic properties of the manuscript surface, such as colors, may not be resolved by the image. This richer definition of a symbolic object carried by the physical object would not be incorporated in the digitized image. In other words, the type of the symbolic object that is described to be carried by the physical object determines the features under consideration and hence allows for deciding if the digitized image has sufficient qualities to incorporate it. At the time of writing there is still no good typology of symbolic objects with respect to the relevant representational feature types.

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Martin Doerr
Øyvind Eide