The Square Root of Two, or the Generative Power, in Nature

Duality and the Growth of Human Consciousness

Now let us turn our attention to what the square root of two means to the human consciousness - not as a geometric figure, but as a fundamental part of human perception and understanding.

The most direct interpretation of the line that measures the square root of two is that it is that which divides unity into two perfect, apparently opposite halves. With the spanning of the square's diagonal, we have created two triangles - exactly similar in every measure, yet opposite and separate from one another.

The ramifications of the simple act of dividing unity into duality is so vast as to be barely comprehensible. At the most basic level humans perceive and understand their environment by comparing and contrasting opposites. In the human consciousness, with the exception of a few states of being - specifically understood as spiritual or religious states - every time a quality is perceived, there is an immediate juxtaposition against the opposite quality which is automatically effected long before conscious perception occurs. Thus we derive our understanding of everything by observing how much of one quality, as opposed to it's opposing quality, a thing possesses.

Everything that we take in from our environment comes through this filter of duality, and it is the basic creation of dualistic perception which leads to the eventual growth of individual intelligence and personality as it is known to exist in humans today. In this way it becomes very clear why the square root of two is known as the "Generative function" - the square root of two generates the universe as it is perceived in the human realm.

The number of pairs of dualities that the human mind employs in its search for understanding the phenomena which manifest around and within it are literally infinite - no list could ever begin to scratch the surface of possibilities. But certain pairs are more archetypal than others - dualistic motifs that come up over and over in every human experience. All of these pairs appear very simple on the surface, but it would seem that it is these simplicities which can effect our experiences the most. Examples include day and night, light and dark, life and death, summer and winter, male and female, good and evil, love and hate, earth and sky, passivity and aggression, creation and destruction, spirituality and materialism, and inner self versus outer world. The list could continue without end.