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Tury Virtual Reality System forum Short Papers Leibniz's Palace of the Fates: A Seventeenth-Cen- tury Virtual Reality System Abstract with the problems of information flow and coordination in massively parallel systems, and devised notions of per- In the late 1600s the mathematician and philosopher Leibniz spective and harmony to solve them. VR theorists (and produced the first description of a virtual reality system. He computer scientists generally) have much to learn from described an organized system of virtual worlds available for his thought, which, though often speculative, is always human perceptual exploration, along with an interface for clearheaded and rich. The most accessible collection of exploring them. Leibniz's work on the logic of possible worlds his work is Rescher (1991);2 MacDonald-Ross (1984) has direct relevance to the conceptual foundations of virtual offers a good survey of both his life and work. reality work today. Leibniz believed there were many possible worlds and that God selected "the best of all possible worlds" for actualization. All of these possible worlds exist conceptu- The philosopher Leibniz is well known as a discoverer as ideas in God's mind. The totality of possible (along with Newton) of the calculus. It is less well ally, worlds is a system (much like the to- known that he provides what is likely the earliest descrip- logically organized tality of mathematical theorems) and constitutes a con- tion of a virtual reality system. His description is neither ceptual structure available for human exploration. For a technical specification nor a fiction, but a precise and those of us in the real world, these possible worlds are conceptually correct description of an organized system virtual realities. At the end of his ofvirtual worlds available for human perceptual explora- Theodicy (1710/1996; sees. 414-17), Leibniz allegorically describes how an tion. Here we a brief overview of the VR system provide actual human this ofvirtual Leibniz describes. being might explore system realities. In his allegory, the Greek goddess Pallas Athena Although Leibniz never built anything like the VR (the goddess ofwisdom) leads the ancient mathemati- system he describes, he did build one of the first calculat- cian Theodorus into the "palace of the fates," a kind of ing machines (which he presented to the Royal Society library containing compressed representations of all pos- in 1673). Leibniz was among the first to use the binary sible worlds. Athena says to Theodorus: number system, and the central thesis of his thought is that the world is a kind of massively parallel computing "Here are representations not only ofthat which hap- system (Leibniz, 1720/1991). Viewing the world as a pens but also of all possibilities. Jupiter, having sur- totality of synchronized but independent computing he called Leibniz was concerned agents monads,1 deeply 2. Despite the conceptual coherence of his thought, Leibniz's writ- ings are almost exclusively fragmentary. Leibniz published relatively Presence, Vol. 6. No. I. February 1997. I 33-135 little, and most of what he wrote is in the form of letters and fragmen- © / 997 by the Massachusetts Institute of Technology tary articles. His short article "Monadology" functions as a guide to the of his In Rescher's each section of the 1. Monads arc deterministic automata; in many respects the collec- entirity thought. book, is followed four to five of related material col- tion of monads is like a cellular automaton, except that each monad Monadology by pages lected from the remainder of Leibniz's The result is an ex- computes a unique function whereby it derives its present state from writings. clear and detailed of Leibniz's work that is not only its own its past states. According to Leibniz, each monad is like a tremely presentation available else. musician playing in an orchestra: the score of each musician (i.e., the anywhere function of each monad) is given to that musician prior to playing (i.e., prior to the beginning of the world) and does not change. There is no causal interaction between musicians, but their scores are so written that together they form a causally coherent whole, the symphony. This Eric Steinhart coherence is what Leibniz called preestablished harmony. A striking of Philosophy and of this is that virtual communication channels exist be- Department Religion consequence Hofstra tween all musicians (i.e., monads), such that each perceives the sym- University New York 10025 phony (i.e., collective computations) of all others from its own unique Hempstead, perspective. [email protected] Steinhart 133 Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/pres.1997.6.1.133 by guest on 02 October 2021 134 PRESENCE: VOLUME 6, NUMBER I veyed them before the beginning of the existing such path has been realized. This path is the possible world, classified all the possibilities into [possible] world realized by the program execution as determined worlds... I have only to speak, and we shall see a by the user's interactions. Exactly as in a VR system, the whole world that my father [Jupiter] might have pro- totality of possible worlds in the palace of fates is interac- duced, wherein will be represented anything that can tive, in the sense that one can actively construct any pos- be asked of him and in this way one may know also sible history by asking Jupiter to reveal successively re- what would happen if any particular possibilities fined equivalence classes of possible worlds. should attain unto existence. These worlds are all In the palace of fates, a human explorer navigates by . here, that is, in ideas. ." (Rescher, 1991, p. 305; posing "What if?" questions to Jupiter. For instance, . Leibniz, 1710/1996, sec. 414) What if JFK had not been assassinated? These questions constitute the human user's input to the Leibnizian VR As might be expected, the structure of the totality of system, and Jupiter's response constitutes the system's possible worlds is complex, since every alternative out- output. Each such question causes Jupiter to reveal an come of any event determines a distinct possible world. equivalence class of alternative possible worlds (e.g., the As an image of this complexity, Leibniz describes the set of all possible worlds in which JFK had not been as- palace of fates as an elaborate system of halls and rooms, The size of this class varies with all of which contain classes of possible worlds. Though sassinated). equivalence the of the a "What if?" daunting, this complexity is easily reduced to order by vagueness question (i.e., ques- tion about the color of socks on the of considering how worlds are formed from sequences of Kennedy's day the assassination determines a set of alternative events. Such sequences are possible histories, each of probably worlds one member, which is a successive refinement ofequivalence classes of possible containing only differing in but the color of his Successive interac- possible worlds. To see how this works, consider a trivial nothing socks). tions successive refinements of the to- series of alternatives: three coin tosses. If these are all the with Jupiter yield of worlds revealed, much as a user refines a possible events there are, then there are eight possible tality possible execution choices. worlds, corresponding to the eight different paths (i.e., program's paths by making input describes to user like histories) through the three tosses. Before the first coin Leibniz Jupiter's responses input this: toss, any of these eight possible worlds is open for actu- alization, so there is an equivalence class of eight worlds. "... whenever the conditions [specified by the user's After the first four of these are available for toss, only question] are not determinate enough, there will be as after the second after the actualization; toss, only two; many such worlds differing from one another as one first one world remains—the world that has in toss, only shall wish, which will answer differently the same fact been actualized by the three tosses. Every possible question, in as many ways as possible. But ifyou refines classes of history successively equivalence possible put a case [to Jupiter] that differs from the actual worlds, beginning with all possible worlds and ending world only in one single definite thing and in its re- with the single one that history in fact actualizes. sults, a certain one of those determinate worlds will In many respects, the totality of possible worlds is thus answer you." (Rescher, 1991, p. 305; Leibniz, 1710/ like a computer program, particularly a VR program, 1996, sec. 414) and each possible world is like an execution path. Any nontrivial program defines avast multiplicity of execu- As Athena and Theodorus explore the palace of the tion paths, a multiplicity that explodes as program com- fates, their investigations become focused on a person plexity increases. At program invocation, all possible ex- named Sextus, a character in ancient Rome. Leibniz con- ecution paths are open for realization. But each tends that Sextus has many possible lives (as we all do), a successive user interaction reduces the set of execution different one in each different possible world. These paths that remain open, until at termination exactly one lives will be explored by Theodorus and Athena: Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/pres.1997.6.1.133 by guest on 02 October 2021 Steinhart 135 "I will show you some [possible worlds], wherein your finger on any line you please, Pallas said to him, shall be found, not absolutely the same Sextus [as is in and you will see represented actually in all its detail the actual world] but several Sextuses resembling that which the line broadly indicates.
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