______________________ Tekiah (Initial)
_______ _______ _______ Shevarim
__ __ __ __ __ __ __ __ __ Teruah
If we continue to divide each segment recursively, each pulse becomes so brief that the series of them reconstitutes itself into a steady sound:
--------------------------- Tekiah (Closing)
This type of pattern is known in mathematics as a Cantor Set. Described by Georg Cantor in 1883, a Cantor set can be modeled by a line segment divided into two smaller segments, each of which is further divided into two smaller segments, and so on without end. Here is how the set is commonly portrayed:
Cantor realized the set contains an infinite number of line segments, each with an infinite number of points. While modern mathematicians recognize the Cantor set as a fractal, many of Cantor's contemporaries felt an "infinity of infinities" was a challenge to the uniqueness of the absolute infinity in the nature of God.
Cantor was not put off by this. He wrote:
I have never proceeded from any 'Genus supermum' [categorization of everything] of the actual infinite. Quite the contrary, I have rigorously proved that there is absolutely no "Genus supremum' of the actual infinite. What surpasses all that is finite and transfinite is no 'Genus'; it is the single, completely individual unity in which everything is included, which includes the Absolute, incomprehensible to the human understanding. This is the Actus Purissimus, [pure or perfect act] which by many is called God."
There appears to be a deeply mystical aspect to his work. His notation for cardinal numbers is (aleph) with a natural number subscript. His set theory diagrams look like the kabbalistic charts with permutations of God's names. John D. Barrow writes in The Infinite Book: A Short Guide to the Boundless, Timeless and Endless, Cantor "started to tell his friends that he had not been the inventor of the ideas about infinity that he had published. He was merely a mouthpiece, inspired by God to communicate parts of the mind of God to everyone else."
From this brief introduction to the Cantor set, we see that the "Shofar set" of blasts leads us to a new understanding of the Holy, a mathematical kavanah.
As an aside, I love the way the Cantor set is applied to "Cantor" below. Note how the individual line segments have become indistinct and a new solid line appears to emerge:
The design, from http://complex.upf.es/~josep/fractals.html, inspired me to create the following Hebrew script spelling of "shofar" with broken lines as a mnemonic for the blast sequence.
|If you develop this idea further, please send me a copy of your design.|