But once you assign randomness so that it can have some range of values then it 
becomes more problematic. And, if you can just assign the randomness to some 
characteristics of the data, then there is even more room for non-intuitive 
uses. For instance, we might say that randomness is the normalized inverse of 
the probability of an event occurrence. This complicates the abstract 
boundary-discovery process since it might turn out that our experiences with 
similar events have been limited and part of what we are calling randomness is 
merely that which we have not yet understood - relative to the statistical 
definition of the event in this case. 
But I appreciate your explanation of Algorithmic Randomness relative to AIT and 
Kolmogorov Complexity.
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