A crisis is a point or a region of unstable equilibrium where little is needed to tip the balance one way or another.

Fig 1

There is a crisis in an illness when the patient reaches a point when the odds are evens whether they will get better or swiftly decline; there is a crisis of confidence when confidence wavers; there is the financial crisis when it is a toss-up whether a value drops drastically or slowly recovers; there is a political crisis when a vote is as likely to be lost as won; and a crisis of law & order where the situation could just as easily degenerate into civil unrest or relapse back into peaceful behaviour.

These crises seldom, if ever, arise without warning: their occurrence is precipitated by the events preceding them. Each preceding event contributes to the ultimate crisis - a fact well known to exercise planners.

So how does each event contribute to the current situation? One important consideration is the significance of an event. If it is trivial, then it will not appear to contribute much, however, the significance of any event is dependent on the context: the nearer the crisis becomes, the more significant each event becomes. This relative significance will be called the FINAL IMPACT of the event. The following graph illustrates how the impact of an event varies as the crisis approaches.

Fig 2

The SIGNIFICANCE of an event can be considered to be made up of two parts: absolute significance which is the broad category of the event and relative significance within that category. Examples of these will be given later.

The memory of an event fades with time although the memory will not be lost entirely so its impact decreases with time, most rapidly at first and then ever more slowly. This sort of fall is where the rate of fall is proportional to the amount left to fall. An exponential curve in fact.

Fig 3

If antagonistic events are separated by large intervals of time then the cumulative effect is very small.

Fig 4

The initial rate of decay of the impact depends on the state of relations between the antagonists. If relations are good, then incidents are soon forgotten, but, if they are bad, then the memory will only slowly fade.

Fig 5

The level to which the decay of the impact tends depends on a residual resentment which can be fanned into life or maintained by commemorative rallies, propaganda or speeches. Under these circumstances, each incident will leave a residual resentment which accumulates unless positive steps are taken to counteract it.

Fig 6

The start of the fall of impact can be delayed by media coverage, drawn out legal proceedings, or propaganda - resulting in the nine-days wonder effect.

Fig 7

These effects are shown, together with their symbols in the diagram below.

Fig 8

There are other factors that affect the impact of an event. For example, there is the intention behind it; the INTENTION ranging from fortuitous to deliberate. Then there is the reliability of the report of an event to be considered. This can range from certain to impossible and can be termed LIKELIHOOD.

The total impact is thus of the form:

ABSOLUTE SERIOUSNESS X RELATIVE SERIOUSNESS X INTENTION modified by the LIKELIHOOD

The range of ABSOLUTE SERIOUSNESS is likely to be from 1 to 6

That of RELATIVE SERIOUSNESS between 1 and 3.

The LIKELIHOOD between 1 and 5

And the INTENTION between 1 and 3

The following tables will illustrate this:

ABSOLUTE SERIOUSNESS of an event

RELATIVE SERIOUSNESS of an event

INTENTION

Other factors are:

LIKELIHOOD

NEWSWORTHINESS

A final factor to be taken into account is the volatility of the environment in which the incidents take place. This will affect the relative scaling of a graph of tension. To keep the plot within bounds, this can be set initially at 1/2.718 (i.e. the reciprocal of the exponential e)

The likelihood of an occurrence having taken place has a linear effect on impact. The calculation of impact takes place in the following stages:

Power sum = seriousness absolute + seriousness relative + intention

Impact = 2 ^{power sum} X likelihood

This would give rise to a range of impacts from:

2⁰⁺¹⁺¹ X 1 = 4 to 2 ⁷⁺³⁺³ X 5 = 40960

The physical dimensions of the screen impose a restriction of this range by a process of impact compression. The compression is achieved by taking a fractional power of the impact. The fraction used is 1/2.718 multiplied by a compression factor set initially at 1.3:

Impact = impact ^{impact compression / 2.718}

This gives an impact range of 1.94 to 160.71. This will take the plot from a trivial matter to disaster. This range can be adjusted by a scaling factor.

The final adjustment made to the impact is to allow for the tension level on which it is imposed, i.e. the sensitivity of the situation.

Final Impact = impact X (1 + level X sensitivity)

Vertical scaling is also subject to local conditions. For example; if one is dealing with human interaction within an area then, perhaps, a deprivation factor can be derived from the inputs to the local conditions screen (such as those described in the Department of Environment Information Note 2 on the 1981 Census):

Basic Z Score = 2 X (log(unemployment=1)-2.2)/0.6 +

(log(overcrowding+1)-14)/0.7 +

(log(single parents+1)-1.6)/0.6 +

log (amenities+2) +

log(ethnic minorities+2) +

(log(pensioners-14.1))/8.1

This is then adjusted by the factor:

100/(100-public:private housing ratio) to become deprivation.

The final vertical scaling factor for the graph is made up of the departure from average ‘deprivation’ and from average ‘inter-group tension’. The latter coming from the inputs to the inter-group tension screen:

scaling = (((16.5-deprivation)/50) X ((50+inter-group tension)/100)) X a manually set

vertical scaling factor.

In order to judge the short and longer term trends, plots showing hours on the X axis or days on the X axis, (or even months on the X axis) will be required. This scaling is different for the day and for the hour plots because screen resolution will add 24 hour plots into one day plot. The calculations take care of this but the value used can be modified by a manual setting of the day/hour scaling.

As mentioned above, sensitivity controls how impact varies with the level on which it is imposed. Using the example of human interaction, the initial value used will be:

(16.5- deprivation)/1500

but this can be modified by manually adjusting a level sensitivity setting.

The time constant varies with inter-group tension:

(50+inter-group tension)/100

with manual adjustment override.

depends on national and local newsworthiness:

(local news-1) X 6.4 X national news/100

modified by a manually adjustable sustain factor.

Any new residual that is input with an incident is multiplied by a manually adjustable residual factor setting

before being added to the existing level of residual. These residuals decay slowly by 1/1000 in each plot.

The trend of the impact graph is plotted from continual recalculation of an average such that:

average at any position along the horizontal axis =

total X (1-weight)/distance along graph + new value X weight total =

average X distance along graph

This gives less weight to older values and is thus a form of exponential smoothing.

The prediction into the future is found by:

(average at present – average 1/weight units back) X weight X time in the future

The weighting factor is adjustable.

The impact graph is plotted in real time while inputting incidents.  The projection of this graph as described

 above will show when the crisis point is likely to be reached.  Not only incidents can be input but also

 countermeasures, allowing possible strategies to be tried out before implementation.

©  John Locke 2001