Objects in the world can be described by data. Such descriptions can come in different forms: picture and sound files, data base tables representing addresses or measurements, maps or databases representing them (think of navigation devices), descriptive texts and so on. If the structure of an object is complex, this will be mirrored in the complexity of descriptions of it.
One way to define the complexity of an object is to look at the amount of information needed to store a description of it. If the object has some inherent regularity, the amount of information is small. Take the following example, taken from Wikipedia, comparing two strings:
The first one can be described in English language as “ab, 16 times”. For the second, such a short description is not possible. It does not contain any obvious regularity. Probably that string itself is the shortest description of itself…
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