Wednesday, January 16, 2008

More on "Man is Nilpotent"

This was a response to a comment on my very first post on this blog, but on second thoughts, I felt that it must be posted in the main page, so here it is.

Here, I try to justify two issues that were raised (by one of my very good friends) with respect to the title of this blog and its suggested relevance to Man. The first is how Man can be represented as a square matrix and the second is how time (compared to the finite positive integer n of my definition) can be seen as discrete, while its best described as a continuous variable. Here are the answers:

a) Man can be approximated to be a directed graph as follows - the vertices of the digraph are the various states he can be in (for example, happy, sad, excited, etc.) Of course, the meanings of these emotions depends on the person who is being represented. There will exist an edge from node u to node v if there is some action (either his own action or an environmental change) that can cause that change. The weight of an edge would be the sum of the likelihoods of all such actions causing the state change. Now, the weighted adjacency matrix of this graph is a square matrix, is it not?

b) In reality, there is always a limit on the precision of time - how accurately we can measure it, in spite of the fact that it is continuous. Well, if one can measure time to an accuracy of, say for example, k seconds, then think of the discrete scale to be calibrated in units of k seconds. As technology advances, k would become smaller and smaller, and the scale would become finer and finer - remaining discrete.

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