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| I must disagree with your first point. When you subdivide an hypergraph into a set of 2-node edges, there is indeed loss of information. Consider the hypergraph {{1,2,3}{3,4,5}} in the first picture. (Taken form [here][1]) ![hypergraph][2] It... |
| Hi David, do you mean that specific case ({{X,X,Y},{X,Z,V}} -> {{V,V,W},{W,V,Y},{Z,Y,W}}) or a rule in general? Have you taken a look at this book, where most of the subject is explained in details:... |
| In a word, yes, because [emergent properties][1] are, by definition, not derivable by any means other than direct observation (which some might even argue is entirely subjective). Put another way, the only way to detect any emergent mathematical... |
| This rule was actually illustrated in Stephen Wolfram's article, "[A Class of Models with the Potential to Represent Fundamental Physics][1]" at the beginning of Section 3.5: "[Rules Depending on a Single Binary Relation][2]". Stephen however,... |