The Relativity of Entropy

This research begins to forward John A. Wheeler's ``It from Bit'' research paradigm. We ask, ``can the concepts of dimensionality and causal (spacetime) geometry emerge from information theory in some semi-classical limit?'' We describe the beginnings of an information-theoretic structure for sweeping out spacetime based on an network and an information metric. Following Leibnizian point of view that we live in a world of relationships, not of machinery, and recognizing that every physical quantity (every ``it'') derives its ultimate significance from bits, binary yes-no indications, we forward this information-based information pregeometry. We have shown one thing:given three random variables a, b and c, with each of them having a very large number of possible values, it is possible to make b half way between a and b in the sense of information distance. That is we can satisfy the triangle inequality. This is possible only if the variables take a large number of values, a fact which suggests that a spacetime point should be thought of as a variable having many possible values. One model is this: a spacetime event is a conglomeration of many binary variables.