[ Pobierz całość w formacie PDF ]
.The thesis was stated in S.5/13 for the determi-Ex.2: Is the game Heads, I win; Tails, we toss again regulatory?nate machine, but it is just as true for the Markovian.Let the regulator R be built as follows.Let it have an input thatcan take two values, ² and ³.When its input is ² (for bad ) let no12/13.So far we have considered only the way in which a Marko-state be one of equilibrium, and when its input is ³ (for good ) letvian machine moves to its goal.In principle, its sole difference fromthem all be equilibrial.Now couple it to T so that all the states ina determinate machine is that its trajectory is not unique.Provided· are transformed, at R s input, to the value ³ , and all others to thewe bear this difference in mind, regulation by the Markovianvalue ².Let the whole follow some trajectory.The only states ofmachine can have applied to it all the concepts we have developedequilibrium the whole can go to are those that have R at a state ofin the earlier chapters of this Part.equilibrium (by S.5/13); but this implies that R s input must be at(The warning given in S.11/11 (pare.5) must be borne in mind.³ , and this implies that T s state must be at one of ·.Thus the con-The steps that take a Markovian machine along its trajectory arestruction of R makes it a vetoer of all states of equilibrium in Tof a smaller order of magnitude than the steps that separate one actsave those in ·.The whole is thus regulatory; and as T and R areof regulation (one move in the sense of S.11/3) from another.here Markovian, the whole will seem to be hunting for a desira-The latter steps correspond to change from one trajectory toble state, and will stick to it when found.R might be regarded asanother quite different to the change from one point to the next directing T s hunting.along one trajectory.)(The possibility that T and R may become trapped in a stableThus the basic formulation of S.11/4 is compatible with eitherregion that contains states not in · can be made as small as wedeterminate or Markovian machines in T and R to provide theplease by making R large, i.e.by giving it plenty of states, and byactual outcome.No difference in principle exists, though if weseeing that its ² - matrix is richly connected, so that from any statedescribe their behaviour in psychological or anthropomorphicit has some non- zero probability of moving to any other state.)terms the descriptions may seem very different.Thus if R isrequired (for given disturbance) to show its regulatory power by Ex.1: What, briefly, must characterise the matrix ³ , and what ² ?going to some state, then a determinate R will go to it directly, as *Ex.2: Show that the thesis of S.5/13 is equally true for the Markovian machine.if it knows what it wants, while a Markovian R will appear tosearch for it.12/15.The homeostat.In this form we can get another point of viewThe Markovian machine can be used, like the determinate, as aon the homeostat.In S.5/14 (which the reader should read again) wemeans to control; for the arguments of S.11/14 apply to both (theyconsidered it as a whole which moved to an equilibrium, but therewere concerned only with which outcomes were obtained, notwe considered the values on the stepping-switches to be solderedwith how they were obtained.) So used, it has the disadvantage ofon, given, and known.Thus B s behaviour was determinate.Webeing uncertain in its trajectory, but it has the advantage of beingcan, however, re- define the homeostat to include the process byeasily designed.232 233 AN INTRODUCTION TO CYBERNETICS THE ERROR-CONTROLLED REGULATORwhich the values in Fisher and Yates Table of Random Numbers generality freely, so that often we shall not need to make the distinc-acted as determinants (as they certainly did).If now we ignore (i.e.tion between determinate and Markovian.take for granted) the resistors on the switches, then we can regard Another example of regulation by a Markovian system is worthpart B (of S.5/14) as being composed of a relay and a channel only, considering as it is so well known.Children play a game calledto which comes values from the Table.We now regard B as having Hot or Cold? One player (call him Tom for T) is blindfolded.two inputs.The others then place some object in one of a variety of places,and thus initiate the disturbance D.Tom can use his hands to findthe object, and tries to find it, but the outcome is apt to be failure.The process is usually made regulatory by the partnership of RobB(for R), who sees where the object is (input from D) and who canRelaygive information to Tom.He does this with the convention thatAthe object is emitting heat, and he informs Tom of how this wouldbe felt by Tom: You re freezing; still freezing; getting a littleChannelTablewarmer; no, you re getting cold again; & .And the children (ifyoung) are delighted to find that this process is actually regula-tory, in that Tom is always brought finally to the goal.Here, of course, it is Tom who is Markovian, for he wanders, atB s state is still a vector of two components a value provided byeach next step, somewhat at random.Rob s behaviour is morethe Table and the state of the relay (whether energised or not).Todeterminate, for he aims at giving an accurate coding of the rela-an Observer who cannot observe the Table, B is Markovian (com-tive position.pare S.12/9).Its input from A has two states, ² and ³ ; and it has beenRegulation that uses Markovian machinery can therefore nowbuilt so that at ² no state is equilibrial, and at ³ every state is.Finallybe regarded as familiar and ordinary.it is coupled as in S.5/14.The whole is now Markovian (so long as the Table is notobserved).It goes to an equilibrium (as in S.5/14), but will nowDETERMINATE REGULATIONseem, to this Observer, to proceed to it by the process of hunt andstick, searching apparently at random for what it wants, and 12/17.Having treated the case in which T and R are embodied inretaining it when it gets it.machines, and considered that in which the machinery is Marko-It is worth noticing that while the relay s input is at ² , variety in vian, we can now take up again the thread dropped in S.12/7, andthe Table is transmitted to A, but when the input comes to y, the can specialise further and consider the case in which the probabili-transmission is stopped.The relay thus acts as a tap to the flow ties have all become 0 or 1 (S.12/8), so that the machinery is deter-of variety from the Table to A.The whole moves to a state of equi- minate.We continue with the regulator that is error-controlled.Inlibrium, which must be one in which the entry of variety from the order, as biologists, to explore thoroughly the more primitive formsTable is blocked.It has now gone to a state such that the entry of of regulation, let us consider the case in which the feedback has avariety from the Table (which would displace it from the state) is variety of only two states.prevented.Thus the whole is, as it were, self-locking in this con- An example of such a system occurs in the telephone exchangedition.(It thus exemplifies the thesis of S.4/22.) when a selector starts to hunt for a disengaged line.The selectortries each in turn, in a determinate order, gets from each in turn theinformation engaged or disengaged , and stops moving12/16
[ Pobierz całość w formacie PDF ]
