The Philosophy of Vacuum Part 28. Physicists will find it extremely interesting, covering, as it does, technical subjects in an accessible way. For those with the necessary expertise, this book will provide an illuminating and authoritative exposition of a many-sided subject." -John D. Barrow, Times Literary Supplement. | Theory of Vacuum 263 An equation of the form 1 giving the N successors az E 1 . . . N of an event a is called an N-ary node or A-ode. A binary node for example is represented by a graph such as Any collection of nodes defines a classical causal network. The classical network is invariant under exchange of the inputs to any event and each N-ary node has the group SN the symmetric group on its N final events. Mathematical topology today still describes timeless undirected spatial connections. Its module is a simplex a set of points with all possible two-way connections. This is because Euler could cross the bridges of Konigsburg in both directions. But our paths in space-time are one-way streets. It would be atavistic to think of the world topology as simplicial physical topology needs to be built on asymmetric physical connections with nodes replacing simplices. Classical Sets I express this prequantum network theory in a set algebra Set adapted to subsequent quantization. The sets of Set are ancestrally finite this is the only kind of set we admit. Let 1 be the null set 0 the undefined set v the disjoint union of classical sets giving 0 when the sets are not disjoint i the monad operator i ah- ja a forming the monad unit set of a. When we read the symbol a as a set ux. is the unit set or monad of a ua is the monad of the monad of a and so forth. When we read a as a class or predicate as we are entitled to do by the principle of intensionality ta is an identity predicate the predicate of being a and ua is the predicate of being the predicate of being a and so forth. We omit an intersection operation because it gives us no new sets we omit complementation because the complement of a set in Set is not finite hence not in Set. This language is rich enough to write our sets but not to say much about them we enlarge our vocabulary for dynamics in Section . The concepts of 0 and v are C. S. PeirCe s Peirce 1931-5 but the symbols are Grassmann s Pierce uses oo and 0
