**Message-ID:** <Pine.NEB.4.63.0605211615550.1322@panix3.panix.com>

**From:** Alan Sondheim <sondheim@panix.com>

**To:** Cyb <cybermind@listserv.aol.com>,
"WRYTING-L : Writing and Theory across Disciplines" <WRYTING-L@LISTSERV.UTORONTO.CA>

**Subject:** Automata - please comment; I'm over my head here - thanks, Alan

**Date:** Sun, 21 May 2006 16:16:23 -0400 (EDT)

(please comment if you can unpack the below - thanks, Alan) Automata I'm reading a book describing automata in practical terms - Automata Theory: An Engineering Approach, Igor Aleksander and F. Keith Hanna, Crane Russak, 1975. This is prior to Wolfram's main work of course on cellular automata; it's classical theory. In any case, as far as I can tell, given states and transitions, there is no indication _how long_ any particular transition will take; i.e. this isn't queuing theory. So one might consider the transitions occurring in present - as if digital-in-present, collapsed across what might otherwise be temporal, analogic. Given Wolfram's reformulation in A New Kind of Science, I wonder about the ontology (mathematical, even within an engineering approach) and epistem- ology (perhaps fundamentally discrete mathematics). Automata may at times be partitioned into independent automata; the substitution property is important here and seems to have implications for labeling. Again I'm thinking in terms of temporal collapse, flattening. In any case: "Formally, a partition of the set of states of an automaton has the substitution property if and only if each of its boxes maps into a single block under all possible inputs." And: "The crucial significance of an automaton and an SP partition is that as far as next-state mappings are concerned [...], the states within a block could be considered as a _single state_ and an automaton could be found which behaves in the same way as the original automaton, but with only one state per block. This property is used directly in state minimization, as will be seen later." Further: "Given an SP partition of the states of an automaton, each block of which is completely output consistent, every such block may be replaced by a single state, providing a state-minimal automa- ton." At this point, I'm well over my head (I've not reproduced the mathematical apparatus of course). The two points I want to make are: the possibility of state-minimal automatons as a rough model for language (think of the emblematic), and the collapse of temporality in relation to presencing present. To push this analogy etc. into the realm of absurdity - consider a state- minimal automaton network or sememe (holarchy); if we average across the transitions as infinitesimals, can anything be located in relation to the appearance of time (as well as subjective time); second, consider one of the chaotic cellular automata described by Wolfram; if we average across the 'landscape' as it develops, can we consider this the origin of the analogic? I realize neither my mathematics nor my grasp of automata concepts is particularly strong, but I wanted to throw this out (not literally) for comment - Alan