Saturday, December 22, 2007

Uncertainty and Continuous Hierarchy

Uncertainty may be thought of as a form of continuous hierarchy. You aren't certain of the levels within the hierarchy, the nodes within the hierarchy, and where the arcs are connected within the hierarchy.

For elements, you aren't certain exactly what the element's value is.
For sets, you aren't exactly certain what the elements are.
For both, you aren't sure whether it's an element or a set, or both.
For order, you aren't certain of the order of the elements.

Thus uncertainty is a form of continuous hierarchy.

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