A Tribute to Binary Notation - And the Old Shall Become New

...there are many algorithms which might be used for combining contingencies, the simplest of these is known as the algebra of logic par excellence, or the Boolean algebra. This algorithm, like the binary arithmetic, is based on the dichotomy, the choice between yes and no, the choice between being in a class and outside it. The reason for its superiority to other systems are of the same nature as the reasons for the superiority of the binary arithmetic over other arithmetics.

-Norbert Wiener, Cybernetics, p.140

I was first introduced to the aesthetic beauty of binary numbering systems in a course in Digital Techniques at Technical College in the mid-1960s. I had not heard of binary arithmetic at school. Most school children today are taught the now familiar base two numbering system that uses only two symbols, 0 and 1, and carry a galaxy of pulsating flip-flops in their Blackberries and iPads around with them in their satchels.

As someone has observed, "For many years, mathematicians saw base two as a primitive system and overlooked the potential of the binary system as a tool for developing computer science and many electrical devices." http://www.bookrags.com/research/binary-number-system-wom/

And yet it has a fascinating history. Many ancient civilisations used a form of binary system but credit must surely go to the Chinese for their sophisticated use of binary notation as illustrated, for instance, in the trigrams of the  I Ching,  which interestingly might also describe the Genetic Code of Life if not also the Essence of Creation itself.

The West was a relatively late starter but took binary notation to new heights. Francis Bacon (1561-1626)  invented his "bilateral code" but used the symbols "A" and "B" to represent the letters of the alphabet much as dots and dashes are used in Morse Code or the 0's and 1's in the ASCII Code  today.

Gottfried Wilhelm Leibniz (1646-1716), mathematician, philosopher, theologian, learned of the binary system from Jesuit missionaries who had lived in China. He wrote, "Two Letters on the Binary Number System and Chinese Philosophy" (Norbert Wiener). He also attempted to apply binary thinking to theology. He speculated that the creation of the universe may have been based on a binary system, where "God, represented by the number 1, created the Universe out of nothing, represented by 0."

"The rest is history," as they say. Most electronic devices now are digital and we appreciate the purity, beauty, authenticity, and convenience, from digital music to digital cameras, digital television and even awesome digitized images from Mars and beyond to the very fringes of time.

What was once dismissed as crude and primitive has become the corner stone, the musical yin-yang of our technological age. Therein lies a parable. Today, few would dispute the elegance inherent in binary systems from ancient Chinese bi-cosmologists to yellow polka dot bikinis! Symmetry weaves her thread mysteriously into the fabric of the universe. Unless we appreciate that historically, mathematical systems such as the binary system were regarded as reflections, symbols, and algorithms of spiritual truth, much of the significance and alchemy of number systems will remain incomprehensible and obscure to us. (Davis and Hersh, The Mathematical Experience, p.96f) Binary notation and Boolean Algebra is indeed "the algebra of logic par excellence", the Alpha and Omega of the manifest World!

Photo Credit: NASA Hubble Galaxy Pair

©Colin G Garvie HomePage: http://www.garvies.co.za