Saturday, January 28, 2017

Thoughts in the shower

Narwhal is pushing me in more mathematical direction with the idea of a segmented text supplanting the idea of tokenized text. Instead of tokens, a 'segment' replaces words of text with keyword id's called VARs. The VAR also stores the indices of tokens where they are found.

In the shower I was thinking about segmented text and the analogy to a spatial curve. We fit a narrative frame to the segment analogously with fitting a Frenet frame to the curve. So in the shower I ask "what do the Truisms have to do with this?". And that reminds me that things like Truism 4 are specifying the "parallel transport" for some of the dimensions of the moving frame, and that reminds me that the concept of Narrative Continuity introduced in Elements, which refers to a kind of connectivity property of coherent narratives. This needs to be seen as a kind of topological property of the segmented text.
In turn, I am reminded that the definition of Narrative Continuity is made awkward by the possibility of a sub narrative structure where a local variable introduced in one place doesn't occur in the next sub narrative but does occur in a later one. A key mathematical trick is to define away the problem. This leads to the idea of a coherent segment as one that can be divided into sub segments s1,s2,...., sN so that if a local VAR appears in si then either it also appears in si-1 or in si+1. All other VARs are assumed global.
Lemma: The alternating sum of the local VARs in a coherent segment cancel.
Proof: definition of coherent segment.
Coming back to the relation of Truisms to segment text, a Truism is an insert-able segment. So I guess the Truisms represent transformations or dimensions in the total space that permit narrative coherence to be implicit in the segmented text. It is like a Truism allows continuity violations...have to think about that.

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