TRANSMISSION OF VARIETY 8/8 



The inverter will now emit the same sequence as was put into the 

 coder. Thus suppose Q was put in and caused the transition A^ D 

 in the coder. This imphes that the inverter will be receiving at this 

 step, D directly from the coder (for the coder is at D), and a from 

 the delayer (for the coder was at A the step before). With input 

 {a,D), the inverter goes to state Q, which is the state we supposed. 

 And similarly for the other possible states put in. 



Thus, given a transducer that does not lose distinctions, an 

 automatic inverter can always be built. The importance of the 

 demonstration is that it makes no reference to the transducer's actual 

 material — it does not matter whether it is mechanical, or electronic, 

 or neuronic, or hydraulic — the possibility of inversion exists. What 

 is necessary is the determinateness of the coder's actions, and its 

 maintenance of all distinctions. 



Ex. I : Why cannot the Coder of S.8/5 be used as example? 

 Ex. 2: Complete the specification of the inverter just given. 

 Ex. 3 : Specify a two-step delayer in tabular form. 



8/8. (This section may be omitted at first reading.) Now that the 

 construction of the inverter has been identified in the most general 

 form, we can examine its construction when the transducer is less 

 general and more Hke the machines of every-day life. The next 

 step is to examine the construction of the inverter when the trans- 

 formations, of transducer and inverter, are given, not in the abstract 

 form of a table but by some mathematical function. 



As a preliminary, consider building an inverter for the transducer 

 with input a, variable n, and transformation n' = n -{■ a. A suitable 

 device for delay would be the transducer with parameter «, variable 

 p, and transformation p' = n. It is now easily verified that, given 

 the input a as shown, n (if started at 3) and p (if started at 1) will 

 change as : 



It is now obvious that if the inverter, with a variable /;;, is to receive 

 n and p as input, as vector (n,p), and give back a as output, then M, 

 as transformation, must include such transitions as: 



M: \ 



