INCESSANT TRANSMISSION 9/8 



These dependencies are characteristic in language, which contains 

 many of them. They range from the simple linkages of the type 

 just mentioned to the long range linkages that make the ending 

 ". . . of Kantian transcendentalism" more probable in a book that 

 starts "The university of the eighteenth century . . ." than in one that 

 starts "The modern racehorse . . .". 



Ex.: How are the four transitions C -^ C, C-^D, D->C, and D -> D, 



affected in frequency of occurrence by the state that immediately pre- 

 ceded each operand, in the protocol: 



DDCCDCCDDCCDCCDDCCDCCDDCCDDDDCC 

 DDDDCCDDDCCDCCDC? 



(Hint : Classify the observed transitions.) 



9/8. Re-coding to Markov form. When a system is found to pro- 

 duce trajectories in which the transition probabilities depend in a 

 constant way on what states preceded each operand, the system, 

 though not Markovian, can be made so by a method that is more 

 important than may at first seem — one re-defines the system. 



Thus suppose that the system is like that of Ex. 9/7/1 (the pre- 

 ceding), and suppose that the transitions are such that after the two- 

 state sequence . . . CC it always goes to D, regardless of what occurred 

 earlier, that after . . . DC it always goes to C, that after . . . CD it 

 goes equally frequently in the long run to C and D, and similarly 

 after . . . DD. We now simply define new states that are vectors, 

 having two components — the earlier state as first component and the 

 later one as second. Thus if the original system has just produced 

 a trajectory ending . . . DC, we say that the new system is at the 

 state (Z),C). If the original then moves on to state C, so that its 

 trajectory is now . . . DCC, we say that the new system has gone on 

 to the state {C,C). So the new system has undergone the transition 

 (D,C) -> {C,C). These new states do form a Markov chain, for their 

 probabilities (as assumed here) do not depend on earlier states : and 

 in fact the matrix is 



(Notice that the transition {C,D)—>{C,D) is impossible; for any 

 state that ends ( — ,D) can only go to one that starts (D, — ). Some 

 other transitions are similarly impossible in the new system.) 



171 



