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Essay / Research Paper Abstract
An 11 page paper discussing qualities of true randomness. Albert Einstein consistently maintained that the mark of genius was and always would be that of simplicity. He held that anyone could make a concept difficult, but that it took true intelligence and a firm understanding of the subject to put it in its simplest terms. The analogy of the drunkard's path is fitting for a description of the next step of any process that has achieved true randomness-the location of his next step depends only on where he is, not how he arrived there. For that and other applications such as DNA sequencing and animal learning investigations the finite Markov chain is ever useful. With new-found interest in fuzzy logic, no doubt we will see in the future increasing numbers of investigation into the infinite state and integration into the principles of learning within the context of neural networks. Bibliography lists 9 sources.
Page Count:
11 pages (~225 words per page)
File: CC6_KSmarkov.rtf
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weight of the outgoing edges be positive. A random journey in a Markov chain begins at some node s and then performs steps according to the standard rule which dicates
that s is the initial node. If node v is the current node and that e_0, ..., e_d-1 are the edges out of v. If v has no outgoing edge
no further advance can be taken. Otherwise, the walk follows edge e_i with probability proportional to w[e_i] for all i, 0 <= i < d. And thus, the target node
of the chosen edge becomes the new current node. Hence, we have the function of a proper Markov Chain. In this light, it is interesting to
note that Albert Einstein consistently maintained that the mark of genius was and always would be that of simplicity. He held that anyone could make a concept difficult, but
that it took true intelligence and a firm understanding of the subject to put it in its simplest terms. Britains The Economist does just that with any topic that others
find perplexing. In the case of Markov chains, the publication urges the reader to "think of a drunkard staggering about. His next step depends only on where he
is now, not on where he came from" (Anonymous 87). The same holds true for card shuffling, another example of the simplest expression of the theory of Markov chains. "Card
shuffling, when imperfect, is a good example of something called a Markov chain. This is a random process in which the future depends only on the present, not on
the past. For instance, what a shuffle does to a pack of cards depends only on the order they are in before that shuffle, not on how they got to
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