The Beauty of the Matrix
In 2003, Scientrix pioneered the use of a Matrix architecture for complex problem solving. Complex problems have more than one dimension, a dimension being a concept that can be broken down into variables. Matrix architecture enables us to integrate multiple dimensions within a problem statement, to subdivide the problem into parts and to master one part at a time within the context of the whole.
Why a matrix?
Since the beginning of time, the structure of the Matrix has appealed to the human mind. A Matrix is simple, powerful and accessible to everyone. It enables us to filter out noise and construct brilliant solutions through collaboration.
Normally our minds can only deal with 3 to 5 concepts at once, but in a Matrix we can deal with multiple concepts and the interrelationship between these concepts simultaneously. We can also construct solution architectures that enable broader participation while maintaining the cohesion of the different parts. These architectures require a combination of engineering, architecture and practical solution construct. But let’s start at the beginning:
The First Matrices
Fig1.1 Early matrices
The ancestor of modern chess was another early Matrix. Said to have originated in India in the 6th Century, this game of strategy was called Chatarunga, which means ‘the game of four armies’. Played on an 8 x 8 uncheckered board, its pieces were similar to those of modern chess.
The ancient Egyptians constructed their pyramids on a perfect square, representing the four corners of the earth, and mirroring the architecture of heaven supporting the four winds. The Great Pyramid is the most accurately aligned structure in existence and faces true north, deviating by only 3/60th of a degree.
Leonardo Da Vinci used the ‘grid method’ in his works and teaching. Gridding makes use of a frame with squares, enabling the artist to transfer the outline of the observed subject in each square to a drawing’s corresponding squares, creating more accurate proportions and perspective.
The Matrix or grid also contains the Fibonacci sequence and its golden spiral, also known as the mathematics of nature.
Fig1.2 Fibonacci golden spiral
The 8 Attributes of a Matrix
The Matrix has 8 key attributes that are very powerful for complex problem solving, strategy design and execution.
To imagine the application of the Matrix in strategy, just replace the word landscape with strategy in the section below.
1. Dilenates Scope, Outlines a Landscape and Facilitates Overview
A Matrix delineates scope along two dimensions. It outlines a landscape, a playfield, a portfolio, a canvas or a game, and facilitates the overview of all the elements within a landscape.
Fig1.3 The matrix landscape
2. Enables Coordination, Clear Positioning and Alignment
It enables coordination, alignment and clear positioning of elements within a landscape through the coordinates on the two axes.
Fig1.4 Matrix alignment
3. Contains cells in a Landscape where Creativity Sparks
Each intersect in the Matrix is a cell that holds a rich repository of variables. It can be seen as a nexus point – a place where many variables meet. The Matrix orchestrates and aligns the contents of these ‘rich’ cells. Imagine one dimension is output and the other is input. The resulting nexus point will be a value-creating opportunity. At Scientrix we believe that art is borne out of art. A creative spark is ignited where one dimension meets another.
Fig1.5 Matrix connections
4. Facilitates Seamless Cascading of Landscapes
The Matrix ensures seamless cascading of concepts, level by level, while sustaining the linkage between the elements on the way down. It ensures that everything in a hierarchy is connected in a continuous flow of value.
Fig1.6 Matrix cascading
5. Enables Interconnectivity within a Landscape
The Matrix establishes relations that reinforce the variables within each dimension, by combining the variables of the same dimension. A kind of ‘internet of things’ in an ecosystem of thinking.
6. Enables Deep Granularity of a Landscape
A Matrix-in-a-Matrix represents a system-within-a-system. This Matrix enables deep diving while sustaining cause-effect relationships, both linear and non-linear. It spirals to link everything together in an ever more granular universe.
Fig1.7 Matrix deep-dive
7. Enables Multiple Perspectives of a Landscape
When a solution has too many dimensions, the complexity becomes overwhelming. At that point, the most effective dimension needs to be identified and the other dimensions analysed in relation to one another, as if looking at a landscape from multiple viewpoints.
8. Enables Constellation of Landscapes
In a creative, highly agile world, rigid architectures or structures can limit change and prevent organizations from moving forward faster. A constellation of landscapes is created where all parts pull together.
Fig1.8 Matrix connections
Fig1.9 Matrix tree constructs