Re: abstraction = compression
if it's sufficient to identify any one of 7 billion numbers you would need a minimum resolution of 10 digits. this is a minimum. if the specs of fingerprints would be randomly spread over the fingertip surface you would need more resolution to make an ID than if the specs would be somehow within a limited region of the total of location possibilites, that could be interpreted as non-random, like in 7 billion unique numbers starting from 1 to 7 billion instead of, for instance, freely variegating within the total possibility space. both the measure of the ID entropy and the proportion of total ID space to ID total could provide indications to rule out coincidence. to assess the total ID space the resolution of fingerprint spec images that the police uses would be a usefull datum. if it would cover the entire finger tip, it would represent the total ID space, that is, of course, limited by the number of possible actual fingeprints within the matrix. if it would cover just part of the fingertip, it could be indicative of a lack of entropy, that is of coincidence, and as such of some form of sequential numbering.
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