An Introduction to Cybernetics

The following material is extracted from An Introduction to Cybernetics by W. Ross Ashby. This book offers a foundation upon which to examine the complexity of modern business. The numbers [in brackets] refer to sections in Ashby's book.

Dealing with Complexity

Simple Science

"Science stands today on something of a divide. For two centuries it has been exploring systems that are either intrinsically simple or that are capable of being analysed into simple components. The fact that such a dogma as 'vary the factors one at a time' could be accepted for a century, shows that scientists were largely concerned in investigating such systems as allowed this method; for this method is often fundamentally impossible in complex systems. Not until Sir Ronald Fisher's work in the '20s ... did it become clearly recognised that there are complex systems that just do not allow the varying of only one factor at a time -- they are so dynamic and interconnected that the alteration of one factor immediately acts as cause to evoke alterations to others, perhaps in a great many others." [Ashby, 1/7]


"So today we see psychoses untreated, societies declining, and economic systems faltering, the scientist being able to do little more than to appreciate the full complexity of the subject he is studying. But science today is also taking the first steps towards studying 'complexity' in its own right." [Ashby, 1/7]

The Hope of Cybernetics

"Cybernetics offers the hope of providing effective methods for the study, and control, of systems that are intrinsically extremely complex.... It offers the hope of providing the essential methods by which to attack the ills -- psychological, social, economic -- which at present are defeating us by their intrinsic complexity." [Ashby, 1/7]

Some Definitions


"The change that occurs [to that which is acted on] is the transition. A set of transitions is a transformation." [Ashby, 2/2, 2/3]


"When the transformation becomes more complex an important feature begins to show.... [It] always moves either to some state at which it stops or to some cycle around which it circulates indefinitely ... like a map of a country's water drainage, showing, if a drop of water starts at any place, to what region it will come eventually. These separate regions are basins. These matters obviously have some relation to what is meant by 'stability'...." [Ashby, 2/17]

Very Large Systems

"I shall use the words 'very large' to imply that some definite observer is given, with definite resources and techniques, and that the system is, in some practical way, too large for him; so that he cannot observe it completely, or control it completely, or carry out the calculations for prediction completely. In other words, he says the system is very large if in some way it beats him by its richness and complexity.

"Such systems are common enough. A classic case occurred when the theoretical physicist of the nineteenth century tried to use Newtonian mechanics to calculate how a gas would behave. The number of particles in an ordinary volume of gas is so vast that no practical observation could record the system's state, and no practical calculation could predict its future." [Ashby, 4/17]

"It is now coming to be recognized, however, that this complexity is something that can be ignored no longer.... Von Neumann: 'The number of neurons in the central nervous system is somewhere of the order of 10^10. We have absolutely no past experience with systems of this degree of complexity." [Ashby, 4/17]

How to Deal with Large Systems

"Suppose now that the observer faces a system that, for him, is very large. How is he to proceed?...

"By definition, the observer can specify it only incompletely. This is synonymous with saying that he must specify it 'statistically'.... If it has too many parts for their specification individually, they must be specified by a manageable number of rules, each which applies to many parts....

"The same method must be used for specification of the coupling... between the parts. Thus the coupling must contain a 'random' element....

"This 'statistical' method of specifying a system... should not be thought of as essentially different from other methods.... What is new about the statistical system is that the specification allows a number of machines, not identical, to qualify for inclusion....

"... It is, in a sense, possible for an observer to specify a system that is too large for him to specify! The method is simple in principle: he must specify broadly, and must specify a general method by which the details shall be specified by some source other than himself." [Ashby,4/19]

"The whole is at a state of equilibrium if and only if each part is at a state of equilibrium in the conditions provided by the other part(s)." [Ashby, 5/12]

"No state (of the whole) can be in a state of equilibrium unless it is acceptable to every one of the component parts, each acting in the conditions given by the others." [Ashby, 5/13]

"Given ... a set of states [of a system] and some particular disturbance we can ask whether, after a disturbance, the system will return to its initial region. And if the system is continuous, we can ask whether it is stable against all disturbances within a certain range of values.

The advantage of the concept of stability "is that, in the suitable case, it can sum up various more or less intricate possibilities briefly.... The question 'what will this system do?', applied to, say, an economic system, may require a full description of every detail,... but it may be adequately answered by the much simpler statement 'It will return to its usual state'. [Ashby, 5/15]

The Black Box


"In our daily lives we are confronted at every turn with systems whose internal mechanisms are not fully open to inspection, and which must be treated by the methods appropriate to the Black Box.... The child who tries to open a door has to manipulate the handle so as to produce the desired movement at the latch; and he has to learn how to control the one by the other without being able to see the internal mechanism that links them." [Ashby, 6/1]


"The Problem of the Black Box arose in electrical engineering. The engineer is given a sealed box that has terminals for input, to which he may bring any voltages, shocks, or other disturbances he pleases, and terminals for output, from which he may observe what he can. He is to deduce what he can of its contents.

"Sometimes the problem arose literally... sometimes... practically, as when a telephone engineer considered a complicated set of relations between tests applied and results observed, in the middle of a mass of functioning machinery that was not to be dismantled for insufficient reason." [Ashby, 6/1]

"We now see the experimenter much like the engineer in a ship, who sits before a set of levers and telegraphs by which he may act on the engines, and who can observe the results on a row of dials.... The representation... is... capable of representing the great majority of natural systems, even if biological or economic." [Ashby, 6/2]

The Large Black Box

"There comes a stage, however, as the system becomes larger and larger, when the reception of all the information is impossible by reason of its sheer bulk. Either the recording channels cannot carry all the information, or the observer, presented with it all, is overwhelmed. When this occurs, what is he to do? The answer is clear: he must give up any ambition to know the whole system. His aim must be to achieve a partial knowledge that, though partial over the whole, is none the less complete within itself, and is sufficient for his ultimate practical purpose....

"It follows that there can be no such thing as the (unique) behaviour of a very large system, apart from a given observer....

"The point of view taken here is that science (as represented by the observer's discoveries) is not immediately concerned with discovering what the system 'really' is, but with co-ordinating the various observers' discoveries, each of which is only a portion, or an aspect, of the whole truth.

"Were the engineer to treat bridgebuilding by a consideration of every atom he would find the task impossible by its very size. He therefore ignores the fact that his girders and blocks are really composite, made of atoms, and treats them as his units. As it happens, the nature of girders permits this simplificaton, and the engineer's work becomes a practical possibility." [Ashby, 6/14]

The Folly of Oversimplification

"Between... extremes lie the various simplifications, in their natural and exact order. Near the top lie those that differ from the full truth only in some trifling matter. Those that lie near the bottom are the simplifications of the grossest type. Near the bottom lies such a simplification as would reduce a whole economic system with a vast number of interacting parts, going through a trade cycle, to the simple form of two states:

Boom ----> Slump." [Ashby, 6/15]


A Definition of Variety (Freedom)

"... Variety, in relation to a set of distinguishable elements, will be used to mean either (i) the number of distinct elements, or (ii) the logarithm to the base 2 of the number.... When variety is measured in the logarithmic form its unit is the 'bit'.... The chief advantage of this way of reckoning is that multiplicative combinations now combine by simple addition." [Ashby, 7/7]

"Constraint... is a relation between two sets, and occurs when the variety that exists under one condition is less than the variety that exists under another." [Ashby, 7/8]

"A constraint may be slight or severe. Suppose, for instance, that a squad of soldiers is to be drawn up in a single rank, and that 'independence' means that they may stand in any order they please. Various constraints might be placed on the order of standing, and these constraints may differ in their degree of restriction. Thus, if the order were given that no man may stand next a man whose birthday falls on the same day, the constraint would be slight, for of all the possible arrangements few would be excluded. If, however, the order were given that no man was to stand at the left of a man who was taller than himself, the constraint would be severe; for it would, in fact, allow only one order of standing (unless two men were exactly of the same height). The intensity of the constraint is thus shown by the reduction it causes in the number of possible arrangements." [Ashby, 7/9]

Importance of Constraint

"When a constraint exists advantage can usually be taken of it." [Ashby, 7/14]

"As every law of nature implies the existence of an invariant, it follows that every law of nature is a constraint....

"Science looks for laws; it is therefore much concerned with looking for constraints. (Here the larger set is composed of what might happen if the behaviour were free and chaotic, and the smaller set is composed of what does actually happen.) [Ashby, 7/15]

"Constraints are exceedingly common in the world around us.... Consider as example the basic concept of a 'thing' or 'object'.... A chair is a thing because it has coherence.... The chair is also a collection of parts.

"Now any free object in our three dimensional world has six degrees of freedom for movement. Were the parts of the chair unconnected each would have its own six degrees of freedom; and this is in fact the amount of mobility available to the parts in the workshop before they are assembled. Thus, the four legs, when separate, have 24 degrees of freedom. After they are joined, however, they have only the six degrees of freedom of the single object....

"Thus the essense of the chair's being a 'thing', a unity, rather than a collection of independent parts corresponds to the presence of the constraint." [Ashby, 7/16]

"Seen from this point of view, the world around us is extremely rich in constraints. We are so familiar with them that we take most of them for granted, and are often not even aware that they exist....

"A world without constraints would be totally chaotic.... It will be suggested that the organism can adapt just so far as the real world is constrained, and no further." [Ashby, 7/17]

Now we consider a Disturbance, a Regulator, and an Outcome. Then:

"The first estimate of Disturbance's variety puts it too high, and we are in danger of deducing (if the regulator's capacity is given) that regulation of Outcome to a certain degree is not possible. Further examination of Disturbance may, however, show that the components are not independent, that constraint exists, and that the real variety in Disturbance is much lower than the first estimate. It may be found that, with Regulator's capacity given, this smaller variety can be regulated against, and full regulation or control achieved at Outcome. Thus the discovery of a constraint may convert 'regulation impossible' to 'regulation possible'. If Regulator's capacity is fixed, it is the only way....

If Regulator's capacity is not easily increased and the other methods are not possible, then the Law of Requisite Variety says that the discovery of a constraint is the would-be regulator's only hope." [Ashby, 13/5]

Erroneous Assumptions

"Cybernetic methods may be decisive in the treatment of certain difficult problems not by a direct winning of the solution but by a demonstration that the problem is wrongly conceived, or based on an erroneous assumption.

"Some of today's outstanding problems about the brain and behaviour come to us from mediaeval and earlier times, when the basic assumptions were very different and often, by today's standards, ludicrously false. Some of the problems are probably wrongly put, and are on a par with the problem, classic in mediaeval medicine: what are the relations between the four elements and the four humours? This problem, be it noticed, was never solved -- what happened was that when chemists and pathologists got to know more about the body they realised that they must ignore it....

"It seems likely that the new insight given by cybernetics may enable us to advance to a better discrimination; if this happens, it will dispose of some questions by a clear demonstration that they should not be asked." [Ashby, 9/22]

[In like fashion, we might advance to a better discrimination, enabling us to dispose of businesses that should never have been formed.]


Reflecting upon the discussion of stability above, we now can define survival:

"Suppose a mouse is trying to escape from a cat, so that the survival of the mouse is in question. As a dynamic system, the mouse can be in a variety of states; thus it can be in various postures, its head can be turned this way or that, it may have two ears or one. These different states may occur during its attempt to escape and it may still be said to have survived. On the other hand if the mouse changes its state in which it ... has lost its head, or has become a solution of amino-acids circulating in the cat's blood then we do not consider its arrival at one of these states as corresponding to "survival".... We shall restrict the words "living mouse" to mean the mouse in one of the states in some subset of these possibilities....

"This representation of survival is identical with that of the "stability" of a set.... The states ... that correspond to the living organism are then those states in which certain essential variables are kept within assigned ("physiological") limits." [Ashby, 10/4]

The Law of Requisite Variety

"Only variety in R [regulator] can force down the variety due to D [disturbance]; only variety can destroy variety." [Ashby, 11/7]


While this presentation of the work of Dr. Ashby is incomplete, it offers useful terminology for nurture capital. For example, by using these definitions of freedom (variety) and constraint, we remove some of the emotional baggage and political overtones which confuse effective management of complexity. The interested reader is encouraged to obtain this profound text, still in print as of this writing, to explore the subject in greater depth.