## THE MATHIAS COMPANIES TM | ABOUT TRIADS

The logic of The Mathias Way is based on elements arranged in sets of threes and fours called

In geometry, tetrahedrons (better known as pyramids) are triangular shapes that have four sides. As such, they are among the most stable structures in nature. No wonder that sociologist Max Weber and others symbolized the organizational form known as the bureaucracy as a pyramid.

But as anyone familiar with the Great Pyramids in Egypt knows, their stability is also their greatest weakness. They stand immovable, eroded by desert winds. Similarly, many of today’s organizations are also being buffeted by the winds of change.

But strangely, in fractal geometry there is a pyramidal pattern that emerges out of chaos. The triad logic in The Way is based on the

The Sierpinski triangle is one form of geometric progression that is both stable and dynamic. It is order generated out of randomness, and thus constitutes a balance between chaos and order. Former Visa Chairman Dee Hock called this quality “chaordic”. It has the effect of taking one solid pyramid and dividing it into a number of smaller triangles that are all connected. This is an important property, considering the need in today’s business environment for organizations to be flexible and scalable, while retaining a fundamental sense of coherence and identity.

Triads within The Way are illustrated using a topological diagram of a triangle, and they are interpreted as follows:

The remainder of this overview will follow this triadic convention.

*. Throughout time, the number three has symbolized generativity and creativity, while the number four has stood for stability and completion. The first one is active, implying movement. The second is passive and at rest.***triads**In geometry, tetrahedrons (better known as pyramids) are triangular shapes that have four sides. As such, they are among the most stable structures in nature. No wonder that sociologist Max Weber and others symbolized the organizational form known as the bureaucracy as a pyramid.

But as anyone familiar with the Great Pyramids in Egypt knows, their stability is also their greatest weakness. They stand immovable, eroded by desert winds. Similarly, many of today’s organizations are also being buffeted by the winds of change.

But strangely, in fractal geometry there is a pyramidal pattern that emerges out of chaos. The triad logic in The Way is based on the

*, a type of fractal. The Sierpinski triangle is one of the basic examples of self-similar sets, or a mathematically generated pattern that is reproducible at any magnification or reduction of scale. In other words, a Sierpinski triangle, like all self-similar fractals, will look almost, or even exactly, the same no matter what size at which it is viewed.***Sierpinski triangle**The Sierpinski triangle is one form of geometric progression that is both stable and dynamic. It is order generated out of randomness, and thus constitutes a balance between chaos and order. Former Visa Chairman Dee Hock called this quality “chaordic”. It has the effect of taking one solid pyramid and dividing it into a number of smaller triangles that are all connected. This is an important property, considering the need in today’s business environment for organizations to be flexible and scalable, while retaining a fundamental sense of coherence and identity.

Triads within The Way are illustrated using a topological diagram of a triangle, and they are interpreted as follows:

- The point in the center is the core. This is considered a fundamental starting point or defining essence.
- The bottom right and left points are aspects which propel the whole triad forward. As an analogy, think of the booster engines on a rocket.
- The topmost point, or apex, is the aspect that “leads the way.” It is considered a driver of the triad's future, the achievement of some visionary state.

The remainder of this overview will follow this triadic convention.