We do have assumptions to chop up the world, but they only to help give us a place to start exploring (as we know, we find better assumptions that make old assu

We do have assumptions to chop up the world, but they only to help give us a place to start exploring (as we know, we find better assumptions that make old assumptions obsolete). I think the chopping up problem is one people run up into a lot with discrete spaces vs continuous spaces. Exploring the permutation space of 302 elements is one thing (302!), but exploring the permutation space of 20 billion+ elements is another[0]. Though there are some interesting approaches I have seen with exploring such spaces like projecting discrete spaces onto higher dimensional spaces and then using mathematics more suited to continuous spaces for exploring regions of interest [1]. [0] http://www.neurology.org/content/64/12/2004 http://www.neurology.org/content/64/12/2004 [1] http://jmlr.csail.mit.edu/proceedings/papers/v15/plis11a/plis11a.pdf http://jmlr.csail.mit.edu/proceedings/papers/v15/plis11a/pli...