Cantor then rigorously proved using his famous “diagonalization proof by contradiction” that whereas our numbering system on the left a1, a2, a3, ….. belongs to the set א0, the set of numbers on the right will always have more members and is a Higher set. This set is continuous and Cantor called it the “indenumerable infinite” which he named א1 (Aleph-one).
A corollary to this is also very interesting – Cantor proved that the set of fractions like 1/2, 1/3,1/4, 1/5 …… 2/3, 2/5, 2/7, ….. 3/4, 3/5, 3/7 ……. and so on, also belong to the “countable infinite” set א0 and even though this א0 is removed from א1 this “indenumerable infinite” set is not diminished. That is א1 – א0 = א1 however many times we perform this subtraction. Every continuous line segment whether big or small, irrespective of size will have א1 points.
No wonder on the title page of his Chapter “Who is the I?” Mishraji gives the Shānti Pāṭḥ :-
“Om poornan adah poornam idam, poornāt poornam udachyate, poornasya poornamādāya, poornam ewaawshishyate.”
That is whole; This is whole. That is Infinite; This is infinite. When the infinite is taken out of Infinity, What remains is Infinite.
Now, coming back to the Sibilants, the Vedās treat the idea of Shakti or energy very differently from the western scientific method. The Shakti unfolds as part of the individual consciousness. Its perception is always as a ‘movement’ a kriyā. The first Sibilant ‘sh’ is Shri Lakshmi. It is the countable infinite and belongs to the domain of א0. Here the energy transactions are conserved. It moves from one place to another without leaving anything behind. I give you money, it decreases with me but improves your balance. This energy is discrete.
The next letter is ‘shha’ and it signifies Ushā the Shakti that keeps getting replenished. ….the rays of the sun; the flowing rivers; the sprouting leaves are all examples of this form of Shakti. The reservoir of energy is so huge that we get a feeling of ‘continuity’ in using it. I go to the river and take a bucket of water, I get it but the river immediately fills up. This belongs to the domain of א1 and it is continuous.The third Sibilant ‘sa’ is Saraswati. It is the energy which increases by giving – the lighting of the lamps, the spread of knowledge and the abundant fruits and seeds of the plants and trees constitute this Shakti. It is this relentless increasing magnitude of Saraswati that leads one to the fourth sibilant ‘ha’. Saraswati is all those processes where the count increases exponentially. This increasing is the root √brih from which Brahmn is derived.
The trees are a good example of the balancing of all these three Shaktīs – the trunk belongs to Shri because they are countable. We could actually go about the task of numbering all the trees in the world. The leaves belong to the realm of Ushā. Their number keeps changing and replenishing, it is dynamic and continuous. But, if we were to ask how many fruits and seeds can grow on all these trees and how many more trees and seeds can subsequently grow? It is an endless task and this is Saraswati.
We are equipped now to truly appreciate the last passage from “Reflections” – Mishraji writes (quote) – “I sketch consciousness as an enthralling Goddess; a finite figure on the limitless canvas of infinity. A sculptor carves her in stone. A painter draws her on the walls of a cave. These are efforts to convey the incommunicable. Ecstasy captured in a poem. Infinity secured in finiteness. The limitless sky caged within the confines of my mind. Indescribable beauty imprisoned in an image”.
“What is there before the beginning? What is there after the end?” Mishraji asks in “Reflections”. And then he answers in the same breath (quote) –“There is a rhythm in the Universe. The planets move regularly. The stars ride their appointed paths. Everywhere, there is the Law of Rhythm. Everything conforms to that Law.”
The rhythms of the Universe are non-linear. They merge mysteriously into each other. That which is linear lends itself to straight ‘cause & effect’. I push the pencil and it moves – this is linear. All machines are based on this linear mathematics. But in a non-linear world – the cause does not immediately come up with an immediate ‘effect’.
A push here may not result in an immediate effect there, the effects may collect over ‘space and time’ zones to precipitate entelechies, sudden occurrences or epiphanies which seem totally disconnected or small effects can cause huge changes.
In reality, all processes are cyclical, in that, the effects are again fed back to the original causes through various loops of energy and this makes mathematical calculations by hand impossible. The global weather problem was the first non-linear equation to be widely studied and Edward Lorenz showed in 1963, how very small changes in weather patterns could precipitate huge changes thousands of miles away. He coined the phrase ‘the butterfly effect’ whereby he meant that a small butterfly flapping its wings in Peking could change the weather in New York. And this was prophetic indeed because the ‘El-Nino factor’ is now legendary. A small current in the Pacific has been empirically found to effect world weather.
The advent of super-computers in the 1980s actually brought about the detailed study of these ‘Non-linear’ equations and this gave birth to the fields of ‘Chaos and Order’ and ‘Fractals’. The western scientists and mathematicians saw that in real-world problems there was no absolute size. As you scaled the solutions, that is looked at bigger or smaller sizes the same forms and designs kept repeating themselves. There was symmetry within symmetry endlessly. Chaos Theory and Fractals are today being applied to just about every subject ranging from economics, share prices to study of heart beats. The list is endless.