Decision Making / 7 / 7.2

7.2 MANAGING COMPLEXITY—BUILDING A MULTI-DIMENSIONAL JIGSAW PUZZLE

To help us build a useful mental picture of the challenges we face, the reader is asked to imagine a game where players build a multi-dimensional jigsaw puzzle. We are all familiar with the two-dimensional jigsaw puzzles we built as children. A simple jigsaw puzzle is a complete picture, normally on a cardboard backing, which has been cut into irregularly shaped pieces. These pieces are deceptively similar in shape. They fit together in a unique way. The colours, shades and textures of pieces and shapes at the interfaces where pieces might mate with adjoining pieces determine the way the pieces are joined together, thereby ensuring the puzzle’s uniqueness.

The familiar strategy for building a jigsaw puzzle is to collect the pieces, turn them face upwards so that the colours, shapes, textures and other detail essential to recognising the patterns are readily seen. Next, the pieces are clustered together with like pieces, such as those with straight edges or those having like colours, shades or textures or complementary edge shapes. Further indicators to a workable puzzle-assembly strategy include identifying pieces having two or more contrasting colours or repeating patterns, as might indicate the edge of an object in the picture.

Our metaphorical n-dimensional puzzle has the familiar characteristics of the conventional two-dimensional puzzle but has a number of dramatic differences. Because the human mind is unable to visualise more than three dimensions, the metaphor will be limited to visualisation of a three-dimensional puzzle. Our risk-management puzzle is very different to our conventional one in that it is dynamic: the picture we might attempt to capture is endlessly changing in its colours, textures, size and shape. Our puzzle is also different in that it is more complex. Both our conventional puzzle and our dynamic n -dimensional puzzle are complex in that they contain large amounts of detail. However, our n -dimensional puzzle is significantly different because of its dynamic systemic structure: certain pieces are strongly linked, or coupled, to other selected pieces according to business rules that are difficult for us to discover.

We must work continually at building the puzzle. Sometimes pieces we have already placed in their correct position disappear or change. We can never expect to have a completed puzzle. The game of building the puzzle never ends. What we have, what we know, what we do not have and what we do not know about this puzzle are described below.

What we do have:

• At any time, we have at least some of the many pieces of the n -dimensional, dynamic jigsaw puzzle—we may even have most of the pieces.
• The capacity to assemble larger numbers of pieces. This depends on how hard we are prepared to work, or fight, to win more and more pieces of the puzzle.
• Though we may not fully understand why or how, we have the skills needed to discover effective strategies for assembling the pieces so that we might recognise the picture and discover its meaning.

What we do know:

• The typical size, shape, colours and textures of the pieces of the jigsaw puzzle are known because they have been characterised by our previous exposure to the game. If we have not previously played the game we must take advice about its characteristics. We may be able to seek advice of a mentor with experience of the game.
• The detailed size, shape, colours and textures of all the pieces we have in our hands at any one time are clearly distinguishable, though the meaning of size, shape, colours, textures and linkages with possible adjoining pieces is not.
• Unlike other jigsaw puzzle games, the number, size, shape, colours, textures of the pieces can change with little or no warning.
• Pieces are sometimes obscured by other pieces that are closer to our viewing point.
• Not all the pieces are equally valuable. That is, some pieces carry greater amounts of intelligence, or information, than others. For example, we might have pieces we can identify as making up the vast expanse of a single coloured, large area. Having more of certain similarly coloured pieces adds little value. Edge pieces, or pieces defining the boundary or texture of the edge of an item in the picture, could be of great value. Pieces that might be coupled, that is, linked in a systemic way to other pieces, could be of greater value. Discovering the higher-value pieces will accelerate our puzzle building activities and bring forward the earliest time we might recognise the picture.

What we do not know:

• How the number, size, shape, colours and texture of the pieces will change.
• How big the jigsaw puzzle is.
• How long any piece will exist before it fades to the point where it is unrecognisable, or until it disintegrates. That is, there could be a point in time for each and every piece of the puzzle, when that piece no longer contains any intelligible information. A disintegrating piece may also allow us to discover what lies behind. A disintegrating piece may have an alias that can fit into its place, thereby still allowing us to complete that part of the puzzle.
• Exactly how many other players there are in our dynamic game of building (or dissembling) the puzzle. Other players are able to add or remove pieces without asking permission, or informing any of the other players that they have done so.
• The business rules that underlie the coupling of pieces are unknown initially. One business rule, for example, may produce the result that if we remove one critical piece a number of others are simultaneously and automatically removed. Conversely, if we add a critical piece, a number of others coupled to it are simultaneously and automatically added. However, it is only by playing the game over a period of time, or modelling and simulating¹ it as we discover more and more of the business rules, that we can progressively develop a relatively complete understanding of what the rules might be.

What we do not have:

• All the pieces of the jigsaw puzzle at any one time.
• We do not have visibility of the whole jigsaw puzzle at any one time, regardless of how much of it has been assembled. Our challenge of building the puzzle might be likened to viewing the world through a rolled-up newspaper. We are able to move in closer or move further away with our rolled-up newspaper, to zoom in or zoom out, to work at different levels of aggregation as we choose. Unfortunately, we can never have an all-encompassing view.