Leibniz’s Theory of Time

I have developed an informational interpretation of Leibniz’s metaphysics and dynamics, but in this paper I will concentrate on his theory of time. According to my interpretation, each monad is an incorporeal automaton programed by God, and likewise each organized group of monads is a cellular automaton (in von Neumann’s sense) governed by a single dominant monad (entelechy). The activities of these produce phenomena, which must be “coded appearances” of these activities; God determines this coding. A crucially important point here is that we have to distinguish the phenomena for a monad from its states (perceptions). Both are a kind of representation: a state represents the whole world of monads, and phenomena for a monad “result” from the activities of monads. But the coding for each must be different; R(W) for the first, Ph(W) for the second, where W is a state of the monadic world. The reason for this is that no monadic state is in space and time, but phenomena occur in space and time. Now, the basis of the phenomenal time must be in the timeless realm of monads. This basis is the order of state-transition of each monads. All the changes of these states are given at once by God, and these do not presuppose time. The coded appearances (which may well be different for different creatures) of this order occur in time (for any finite creatures), and its metric must depend on God’s coding for phenomena. For humans, in particular, this metric time is derived from spatial distance (metric space) via the laws of dynamics. Thus there may well be an interrelation between spatial and temporal metric. This means that the Leibnizian frame allows relativistic metric of space-time. I will show this after outlining Leibniz’s scenario. 1. Informational Interpretation of Monadology When I first read Leibniz’s Monadology (1714) and related papers, I was struck by his characterization of monads as “incorporeal or spiritual automata.” A monad is, according to Leibniz, a simple substance with the primitive force, and this force governs its state-transition. What we usually regard as the “world” is phenomena produced by the activities of the monads. Many people may think that this whole idea is crazy, but as John Archibald Wheeler said, “crazy ideas are worth pursuing.” First, I should give a rough idea of what Monadology is all about. It is Leibniz’s almost final formulation of metaphysics. He forcefully argued that there must be simple substances (in reality) which support everything we see and feel in this world, the world of phenomena. The spheres of phenomena and of reality must be strictly separated. Physics or dynamics studies motions which are supposed to underlie phenomena, but the laws of dynamics must be grounded on metaphysical principles. In particular, space and time, which are usually assumed as a framework of dynamics must be explained from the metaphysical basis. In short, everything must be explained, ultimately, in terms of the activities of the monads. This is Leibniz’s grand vision. And this vision was described in more detail in Monadology. S. Uchii, Leibniz’s Theory of Time, page 1 Each monad is a simple substance, a metaphysical point with no shape, no parts, no magnitude. But each monad must be different from each other, and this difference comes form its internal state, or more precisely, the whole series of states. But, as Leibniz repeats many times, each monad is a “living mirror” of the whole world, and each of its states is a “representation” of an instantaneous state of the whole world. Here, it is clear that representation needs coding, since something can be represented by another thing, only by coding. For example, the color red is represented by the word “red” in English, but by the word “rouge” in French. Obviously, these two representations depend on two different codings. Likewise, when the reality (the world of monad) is somehow represented in phenomena, this representation needs another coding, since the two spheres, reality and phenomena, are completely different and their ontological status is radically different. See Figure 1 for a rough image. These representations are, mathematically speaking, a mapping from one domain to another domain, by means of a function. Thus, we can express the representation in a monad by R(W), the representation in phenomena by Ph(W), where W is either the whole world or its relevant portion.This is my shorthand symbolism; if we are to distinguish different monads we need different subscripts for R and Ph. And what is unique in Leibniz is that W itself can be regarded as the totality of representations, R’s of all monads. In other words, this totality is nothing but the information of the world. In our modern terms, Leibniz’s metaphysics is not only informational, but full of recursion of this sort. Figure 1. Reality and Phenomena S. Uchii, Leibniz’s Theory of Time, page 2 Each monad with a sequence of states REALITY programmed by God (No space, No time)